Review ArticleElectrical Switching in Thin Film Structures Based onTransition Metal Oxides

A Pergament G Stefanovich V Malinenko and A Velichko

Faculty of Physical Engineering Petrozavodsk State University Petrozavodsk 185910 Russia

Correspondence should be addressed to A Pergament apergpsukareliaru and G Stefanovich gstefyandexru

Received 6 April 2015 Revised 19 July 2015 Accepted 18 August 2015

Academic Editor Ram N P Choudhary

Copyright copy 2015 A Pergament et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Electrical switching manifesting itself in the nonlinear current-voltage characteristics with S- and N-type NDR (negativedifferential resistance) is inherent in a variety of materials in particular transition metal oxides Although this phenomenonhas been known for a long time recent suggestions to use oxide-based switching elements as neuristor synapses and relaxation-oscillation circuit components have resumed the interest in this area In the present review we describe the experimental facts andtheoretical models mainly on the basis of the Mott transition in vanadium dioxide as a model object of the switching effect withspecial emphasis on the emerging applied potentialities for oxide electronics

1 Introduction

The phenomenon of electrical switching [1] is a rapid andreversible transition between a high-resistance (HR) state anda low-resistance (LR) state affected by an applied electric fieldTwo main types of the switching effect are described by anN-shaped or an S-shaped I-V characteristic and denoted asN-NDR and S-NDR [2] respectively where the abbreviationldquoNDRrdquomeans ldquonegative differential resistancerdquo (see Figure 1)The two stable states are also frequently referred to as an OFFstate (which is equivalent to HR for the case of S-NDR and toLR forN-NDR) and correspondingly anON state (Figure 2)

The switching effect with S-NDR was originally foundand investigated in chalcogenide-glass semiconductors(CGS) [1 3] Electronic switching in amorphous CGSthin films can be divided into two general types [4](a) monostable threshold switching in which continuouselectrical power is required tomaintain the highly conductingON state and (b) bistable memory switching in which bothON and OFF states can be maintained without electricalpower In other words for threshold switching the OFF-to-ON transition is absolutely reversible and repetitive whereasfor memory switching a large voltage pulse is usually appliedin the erase operation cycle to switch a device from the ONback to the OFF state

We note apropos that recently the studies of bistableswitching in CGS have been renewed in connexion with the

development of phase changememory (PCM) technology Atpresent PCM is considered to be a promising candidate fornext generation nonvolatile memory As compared with flashmemory PCMprovides larger endurance considerably fasterread and write speeds and lower power consumption [5]

Thus current-voltage characteristics of some CGS-basedthin film sandwich structures after electrical forming (theprocess of electroforming EF will be described below) areS-shaped Similar phenomena have also been then observedin oxides [6ndash8] (mainly those of transition metals) andoxide glasses amorphous and polycrystalline Si and othersemiconductors [2] halides nitrides sulphides of metalscarbon-containingmaterials particularly nanotubes organiccompounds such as conducting polymers and self-assembledmonolayers andmany othermaterials (see [4] and referencestherein)

Note that S-NDR andN-NDR switching devices in theirsoperation are the analogues of the conventional semiconduc-tor devices such as for example thyristors and tunnel diodesrespectively However in contrast to the latter the CGS-basedand oxide-based switching devices do not require formationof p-n junctions

Finally we remind the reader that memory switchingin oxide thin film structures is now considered on a parwith PCM as a promising approach to the design of newgeneration of computer memory oxide ReRAM (resistive

Hindawi Publishing CorporationAdvances in Condensed Matter PhysicsVolume 2015 Article ID 654840 26 pageshttpdxdoiorg1011552015654840

2 Advances in Condensed Matter Physics

Voltage

1

2 3 4

1Cu

rren

t

(a)

Voltage

1

23

1

1

1

1

Curr

ent

5

(b)

Figure 1 Schematic I-V curves for two types of NDR which corresponds to the regions in the curves where dVdI lt 0 Inserts show sketchesof a high-current filament (a) and a high-field domain (b) inherent to S- and N-NDR respectively [2] (where (1) is metal electrodes (2) isinsulating (eg initial oxide or amorphous CGS) film (3) is switching channel emerging after electrical forming (4) is current filament and(5) is high-field domain)

O

ON

NDR

A

C

OFF

B

I998400998400

Ith

I

Ih

I998400

V998400998400Vh V998400 Vth

A998400

C998400

V

Figure 2 S-type current-voltage characteristic (O-C1015840-A-A1015840-B-A1015840-C-C1015840-O) of a switching deviceThe O-C1015840-A branch represents the OFFstate C-A1015840-B the ON state and A-A1015840 and C-C1015840 the NDR region witha hysteresis 119881th and 119881

ℎ(119868th and 119868

ℎ) are the threshold and holding

voltages (currents) respectively

random access memory) [9] Conceptually unsophisticateddesign of a cross-point metaloxidemetal (MOM) memorycell allows easily scalable ReRAM architecture with nanome-tre cell dimensions This in turn provides the basis for3D integrated terabit memory with a multilayer stackablestructure [10]

Among transition metal oxides (TMOs) thresholdswitching (without any memory effects) with an S-type I-V characteristic has been observed in MOM structures withNb2O5[7 11] NbO

2[12ndash14] TiO

2[7 15] VO

2[16] Ta

2O5

[7] Fe oxide [17] and some other TMOs [8] As-fabricateddevices rarely show threshold or memory switching effectswithout an initial modification of their structure a processwhich is usually called EF or just ldquoformingrdquo [18] There is astriking similarity in the EF behaviour observed in a widerange of oxide halide sulphide polymer and CGS films [18ndash21] and further we will follow the discussion of this problemin review [18]

Electroforming is achieved by the application of suitablevoltage pulses which are always higher in magnitude thanthe subsequent operating pulses This invariably produces anirreversible change in the characteristics of a device oftenwith a substantial decrease in the overall terminal resistanceThe processes involved in electroforming depend on thenature and quality of the thin film the geometrical structureof the device and in some cases the electrode material Thechanges can be either structural involving a movement ofmaterial from one part of the device to another or theycan be electronic wherein a quasipermanent change in theoccupancy of some electronic states takes place The changescan occur throughout the bulk of the film or in a localizedregion The most common localized effect is the formationof a fibre of highly conducting material a switching channelSuch permanent channel formation is a consequence oftemporary filamentary breakdown often observed in metal-insulator-metal and metal-semiconductor-metal sandwichstructures However electroforming differs from dielectricbreakdown in the sense that it is a nondestructive processthat is it rather resembles a self-healing type of breakdown[20]

The EF characteristics of different materials are generallyill defined and exhibit large variations even for devicesfabricated under the same conditions Nevertheless since thisprocess is observed in a wide variety of insulating films itis unlikely to result from a peculiarity of any one system In

Advances in Condensed Matter Physics 3

the case of amorphous thin film structures switching channelformation can occur via crystallization of an amorphous filmstoichiometric changes diffusion of the electrode materialinto the film or ionization of deep traps All of these changesusually refer to a localized modification of the structurein the area of the channel The modification of the initialstructure during the forming process is the most importantfactor determining the subsequent switching operation Thisis because in most cases forming creates a ldquonew devicerdquo(within the original structure) whose characteristics deter-mine the ensuing threshold or memory switching [18 22]

In TMOs a set of valence states associated with theexistence of unfilled 119889-shells in the atoms of transitionmetals leads to formation of several oxide phases withdifferent properties ranging from metallic to insulating Onthe other hand it is specifically the behaviour of 119889-electronsin the compounds of transition metals that is responsiblefor the unique properties of these materials causing strongelectron-electron correlations which play an important rolein the mechanisms of such phenomena as for examplemetal-insulator transitions (MITs) high-119879

119888superconductiv-

ity colossal magnetoresistance and multiferroicity whichare inherent to many TMOs [23ndash26] That is TMOs exhibitan astonishing array of functionalities that result from acombination of the strongly polarizable metal-oxygen bondand strong electron correlations [25]

In our works [4 22 27ndash29] it has been shown thatswitching in a number of TMOs with the S-NDR exhibitsseveral common features Particularly in most cases theswitching effect is associated with the insulator-to-metaltransition in an electric field The channels consisting oflower oxides exhibiting MITs are formed in an initial oxidefilm during the process of EF

In many TMOs the switching mechanism has beenshown to be associated with an electronically induced MottMIT occurring in conditions of the nonequilibrium carrierdensity excess under the applied electric field The requiredincrease in electron density under the action of electric fieldmight be caused by the Poole-Frenkel effect [30] or someother high-field-assisted charge carrier generation effectssuch as avalanche ionization and Zener breakdown as wellas Schottky tunnel or avalanche injection from contacts andso forth

This review focuses on earlier obtained results currentresearch the state of the art and recent progress in the field ofscience and applications of the phenomenon of monostablethreshold switching in oxides of transition metals We startby discussing the switching effects inMOM structures on thebasis of anodic oxide films (Sections 21 and 22) and then turnto recent results concerning electrical switching in Mn andMo oxides obtained by deposition in vacuum (Section 23)Effects of doping to stabilize the switching parameters andunify the electroforming process are described in Section 24and Section 3 is devoted to various physical mechanisms atplay which could be responsible for the NDR behaviouremphasizing the particular relationship between the switch-ing effect and MIT electronically induced Mott transitionfirst of all Further in Section 4 we discuss applied poten-tialities of the TMO-based thin film devices exhibiting the

NDR phenomena and finally in Section 5 we will try to for-mulate some conclusions and outlook concerning the topicdiscussed It should be stressed that the scope of the review isnot to describe comprehensively all the results reported in theliterature but rather to sketch out the main pertinent worksand discuss the physical mechanisms involved in the phe-nomenon of electrical switching in transition metal oxides

2 Overview of Experimental Results

21 Switching in Anodic Oxide Films In this section wepresent our results [4 22 27ndash31] on electroforming andswitching in thin film MOM structures with oxides oftransition metals (V Ti Fe Nb Mo W Hf Zr Mn Y andTa) obtained by electrochemical anodic oxidation Anodicoxidation permits the synthesis of high quality homogeneousdielectric oxide films [32] and as a rule anodic oxide films(AOFs) are amorphous

The sandwich devices under study were fabricated by oxi-dation of themetal substrates both polished foils and vacuumdeposited layers Au electrodes were vacuum-evaporatedonto the surfaces of oxide films to complete the MOM struc-ture (Figure 3(a)) The spring-loaded point contacts made ofgildedwire 05mm in diameter were also usedThe oxidationwas carried out electrochemically under anodic polarizationin an electrolyte Ta Nb W Zr and Hf were anodized in01 N aqueous solutions of phosphoric and sulphuric acids[32] while for oxidation of vanadium and molybdenum theacetone-based electrolyte was used [33] Fe Ti Mn andseveral of Nb and Ta samples were anodized in a KNO

3+

NaNO3eutectic melt [34] at 570ndash620K Anodic oxidation of

yttrium was carried out as described in [31] The oxide filmthicknesses were typically from 50 to 200 nm

The current-voltage characteristics of the initial struc-tures are nonlinear and slightly asymmetric The resistanceat zero bias measured with the point contact is in the range107ndash108Ω for the vanadium anodic oxide which is the mosthighly conductive among all the materials studied Whenthe amplitude of the applied voltage reaches the formingvoltage 119881

119891 a sharp and irreversible increase in conductivity

is observed and the 119868(119881) curve becomes S-shaped Withincreasing current the I-V characteristicmay change until theparameters of the switching structure are finally stabilizedThe process outlined above is qualitatively similar to EF ofthe switching devices based on amorphous semiconductors[18] The forming voltage depends on the temperature (119881

119891

increases upon cooling) and film thickness The thicker thefilm the higher the required 119881

119891 The value of 119881

119891correlates

with the anodizing voltage 119881119886(because 119889 is proportional to

119881119886) A similar correlation is characteristic of the AOF break-

down the breakdown voltage is also of the order of 119881119886[32]

Thus the first stage of the forming does not differfrom the conventional electrical breakdown of oxide filmsHowever if the postbreakdown current is limited this resultsin formation of a switching channel rather than a breakdownchannel The latter would be expected to have metallic-like conductivity and no negative resistance in the I-Vcharacteristic It is quite evident that the phase compositionof this switching channel must differ from the material of the

4 Advances in Condensed Matter Physics

1

2

3 4

(a)

00 05 10 15 20 250

20

40

60

80

100

Voltage (V)Cu

rren

t (120583

A)

Vth

(b)

Figure 3 (a) The sandwich switching structure (schematic) (1) vanadium metal substrate (2) anodic oxide film (3) Au electrical contactand (4) switching channel (VO

2 as will be shown below in Section 22) (b) the I-V characteristic after EF for one of the samples at room

temperature

initial oxide film because the channel conductivity exceedsthat of an unformed structure by several orders ofmagnitude

Forming does not always result in an S-type characteris-tic In some instances a transition of the structure to a highconductivity state (119877 sim 100Ω) with ohmic behaviour takesplace that is in this case breakdown rather than formingoccurs Breakdown is more probable in Ta

2O5 WO3 HfO

2

and MoO3films while in the V- and Nb-based structures

it is the electroforming that results in the S-shaped I-Vcurves in most cases The anodic films on Ti and Fe holdan intermediate position S-type switching has not beenobserved in Zr Y and Mn oxide films EF of W- Fe- andHf-based structures was carried out at 77 K because at roomtemperature breakdown took place and no switching effectswere observed The characteristic feature of switching in TaMo Hf and to a lesser extent W oxide films is the instabilityof parameters and the gradual disappearance of the S-typeNDRunder the influence of current flow and thermal cycling

The voltage-current characteristic for electroformedvanadium-AOF-metal structure is shown in Figure 3(b) Theparameters of the structures (threshold voltage 119881th andcurrent 119868th resistances of OFF and ON states) may varyby up to an order of magnitude from point to point forthe same specimen Such a wide range of variation of the119881th and 119877off values as well as the absence of correlationbetween these switching parameters and the parameters ofthe sandwich structures (the electrode material and area andthe film thickness) leads to the conclusion that resistanceand threshold parameters are mainly determined by theforming process Conditions of the forming process cannotbe unified in principle because the first stage of forming

is linked to breakdown which is statistical in nature As aresult the diameter and phase composition of the channel(and consequently its effective specific conductivity) varywith position in the sample This accounts for the scatterin the parameters and for the seeming absence of theirthickness dependence The I-V curves for Ti- Nb- and W-based structures are also shown in Figure 4

Similar behaviour has been observed for the other mate-rials On average for 119889 sim 100 nm a typical value of 119881this 1 to 10V that is the threshold field is 105ndash106 Vcm atroom temperature The greatest differences between theseoxides are observed when the temperature dependence oftheir threshold parameters such as119881th is measured Figure 5shows 119881th(119879) curves for the sandwich structures based oniron tungsten vanadium titanium and niobium For Ta

2O5

HfO2 and MoO

3 no reproducible results were obtained

because of instabilities of their voltage-current character-istics with temperature As the temperature increased 119881thdecreased tending to zero at some finite temperature 119879

119900

This is best exhibited by the vanadium and titanium oxidestructures The values of 119879

119900vary considerably for different

oxides but they are nearly identical for different structuresof the same oxide [28] For the Nb-Nb

2O5-metal structures

it was impossible to measure the 119881th(119879) relationship overthe whole temperature range because heating above 300∘Cinduced processes related to diffusion and change in thechannel phase composition leading to degradation of theswitching structure Nevertheless it is evident from Figure 5that for the niobium oxide 119879

119900exceeds 600K

As was mentioned above S-type switching has not beenobserved inZr Y andMnoxide films Instead thesematerialshave sometimes demonstrated N-NDR at 119879 = 293K (Zr and

Advances in Condensed Matter Physics 5

000102030405

Curr

ent (

mA

)

minus01

minus02

minus03

minus04

minus05

minus10minus20 minus05minus15 05 10 15 2000Voltage (V)

(a)

minus7minus6minus5minus4minus3minus2minus1

01234567

Curr

ent (

mA

)

minus15 minus10 minus5 5 10 150Voltage (V)

(b)

minus4

minus2

0

2

4

Curr

ent (

mA

)

minus10 minus6 minus4minus8 minus2 2 4 6 8 100Voltage (V)

(c)

Figure 4 Current-voltage characteristics of MOM structures with AOFs on (a) Ti (b) Nb and (c) W [29]

Y see Figure 6) or at 119879 = 77K (Mn oxide) The process ofelectroforming for these materials was hindered like that forTa Hf and Mo Switching in Mo and Mn oxides will also beadditionally discussed in Section 23 below

22 Switching as an Electrically DrivenMetal-Insulator Transi-tion Next we discuss the process of electroforming in moredetail The initial AOF represents as a rule a highest oxideof the metal (eg Nb

2O5in the case of niobium) However

lower oxides always exist near the AOF-metal interface inthe form of transition layers or as separate inclusions Thiscan be explained in terms of thermodynamics Consider thefollowing reaction

Nb + 2Nb2O5997888rarr 5NbO

2(1)

The change of the Gibbs (isobaric) potential for thisreaction is

Δ119866119903= ]2Δ1198662minus ]1Δ1198661 (2)

where Δ1198661and Δ119866

2are the standard isobaric potentials

of formation and ]1and ]

2are the numbers of moles of

oxides which take part in the reaction For Reaction (1) the

subscripts 1 and 2 in (2) are related to Nb2O5and NbO

2

respectively and Δ119866119903

= minus163 kJmol [28] Since Δ119866119903

lt 0Reaction (1) proceeds spontaneously and hence NbO

2is

always present at the Nb-Nb2O5interface

Transition metals exhibit multiple oxidation states andform a number of oxides Therefore it is obvious that thelower oxide to be formed is mainly that with the mini-mum Δ119866

119903 Figure 7 demonstrates the variation of Δ119866

119903(119909)

for Fe2O3 Nb2O5 V2O5 TiO2 and some other oxides in

reactions similar to (1) where 119909 is the stoichiometric indexof oxygen Δ119866

119903values were calculated using (2) the data

on Δ119866119900 for the calculations were taken from [35] The

minima in these curves correspond to Fe3O4 NbO

2 VO2

and Ti2O3 therefore these oxides form as intermediate

layers between the metal substrate and the correspondingoxide of highest valence Real systems are far from beinga plane parallel structure with two oxide layers hence thesuggested approach is rather oversimplifiedNevertheless theabove considerations show that formation of those oxidesis thermodynamically reasonable whether it is kineticallypossible can only be judged from experiment For exampleas was shown in [33] in AOF on vanadium the vanadiumdioxide layer may be rather thick and only a very thin film

6 Advances in Condensed Matter Physics

00

05

10

15

20

25

30

V (a

u)

1 2

3 4

5

200 300 400 500 600100T (K)

Figure 5 Threshold voltage in arbitrary units 119881 = 119881th(119879)119881th(1198791015840)

for theMOM structures on the basis of different oxides as a functionof ambient temperature (1) Fe (2)W (3)V (4)Ti and (5)Nb anodicoxideData for different samples have been averaged andnormalizedto a certain temperature 119879

1015840 which is different for different oxides[22 27 28]

0

5

10

15

20

25

30

35

Curr

ent (120583

A)

05 10 15 20 2500Voltage (V)

Figure 6 I-V curve with N-NDR of the structure metalY anodicoxidemetal [31]

near the outer boundary is close to the V2O5stoichiometry

The similar ordering of layers evidently exists in iron oxideparticularly it is known that in a thermal oxide of iron theFe3O4phase usually predominates [28] On the other hand

the AOFs on Nb and Ti mainly consist of Nb2O5and TiO

2

and NbO2or Ti2O3layers seem to be relatively thin [27 28]

For the W-WO3system a wide minimum of Δ119866

119903(119909) lies

in the range 119909 = 27ndash30 (Figure 7) the same behaviour seemsto be characteristic of the Mo-MoO

3system The calculation

for manganese oxides yields the minimum at 119909 = 15 that isfor Mn

2O3 The curve Δ119866

119903(119909) for uranium is also presented

just as an example note however that MITs have beenreported for lower uranium oxide U

4O9[36] For Zr Hf Ta

and Y such calculations have not been made because thereexist no clear data on the thermodynamic properties of thelower oxides of those metals

F1

F2F3

T1

T2

T11N1

N2

N3

W1W2

W3

W4

W5U5

V1

V2

V9

V10

V11

U1U2

U3 U4

M4

M1

M2 M3

900

800

700

600

500

400

300

200

100

0

minusΔGr

(kJm

ol)

15 20 25 3010X

V9998400

V3ndashV8

T2998400

Figure 7 Gibbs potential change Δ119866119903(per 1 g atom of metal) for

the reaction of the highest oxide with the metal substrate versus119909 the oxygen stoichiometric index of the lower oxide which isformed in this reaction Symbol indications are as follows (i) IronF1ndashFeO F2ndashFe

3O4 F3ndashFe

2O3 (ii) Niobium N1ndashNbO N2ndashNbO

2

N3ndashNb2O5 (iii) Titanium T1ndashTiO T2ndashTi

2O3 T3ndashT10ndashTi

119899O2119899minus1

(119899 = 3ndash10) T11ndashTiO2 (iv) Vanadium V1ndashVO V2ndashV

2O3 V3ndashV8ndash

V119899O2119899minus1

(119899 = 3ndash8) V9ndashVO2 V10ndashV

6O13 V11ndashV

2O5 (v) Tungsten

W1ndashWO2W2ndashW

18O49W3ndashW

10O29W4ndashW

50O148

W5ndashWO3 (vi)

Manganese M1ndashMnO M2ndashMn3O4 M3ndashMn

2O3 M4ndashMnO

2 (vii)

Uranium U1ndashUO2 U2ndashU

4O9 U3ndashU

3O7 U4ndashU

3O8 U5ndashUO

3 The

points T21015840 and V91015840 characterize a scatter due to the Δ1198660 data

difference [22 28]

During electroforming current-induced heating of thefilm under the electrode leads to a diffusion of both metalfrom the substrate into the film and oxygen from the outerlayer to the inner one Also the transport of metal andoxygen ions due to the applied electric field is possible Sinceduring electroforming (unlike thermal or electrochemicaloxidation) no external oxygen is present no reaction cantake place except the reduction of the highest oxide of AOFThe reduction results in growth of the channel consisting oflower oxide through the film from one electrode to anotherEvidently substances with the minimum Δ119866

119903value (see

Figure 7)will be predominant in the phase composition of thechannelThe current increase after formingmay cause furtherreduction of the channel material leading to a predominanceof the phases such as VO NbO and TiO Many of the lowestoxides of transition metals (mono- and suboxides) exhibitmetallic properties [23] the accumulation of these phases inthe channel will therefore lead to an irreversible increase inconductivity that is to breakdown

The above compounds (VO2 Fe3O4 Ti2O3 and NbO

2)

have one feature in common namely a metal-insulator phasetransition [24] The MIT phenomenon is characterized bythe sharp and reversible change in the conductivity at acertain temperature 119879

119905 for instance vanadium dioxide at

Advances in Condensed Matter Physics 7

1 2

3

0

1

2

3

4

5

6

240 260 280 300 320 340220T (K)

V2 th

(V2)

(a)

1

2

3

(V2th times 04)

420 440 460 480 500 520 540400T (K)

0

1

2

3

4

5

6

7

V2 th

(V2)

(b)

Figure 8 Squared threshold voltage as a function of temperature for (a) vanadium oxide-based switch and (b) titanium oxide (1) (2) and(3) three different samples

119879 lt 340K is a semiconductor at 119879 = 119879119905

= 340K theconductivity abruptly increases by 4-5 orders of magnitudeand above the transition temperature VO

2exhibits metallic

properties ForNbO2119879119905= 1070K Ti

2O3undergoes a gradual

transition in the range 400ndash600K and magnetite (Fe3O4)

is a semiconductor both above and below the Verwey tran-sition temperature (120K) though its resistivity decreaseson heating by two orders of magnitude at 119879 = 119879

119905 For the

switching devices based on these metals the temperatures 119879119900

coincide with the corresponding values of 119879119905(see Figure 5)

This suggests that the switching mechanism is caused by themetal-insulator transition

Electrical switching due to MIT has been first revealedfor vanadium dioxide [16 27 37ndash45] Switching in VO

2

is explained by the current-induced Joule heating of thesample up to 119879 = 119879

119905 which has been confirmed by the

direct IR-radiation measurements of the switching channeltemperature [38 45] In these early works switching hasbeen observed in single crystals [39] and planar thin filmdevices [37 38 45] as well as in vanadate glasses [40 41]VO2-containing ceramics [44] and V

2O5-gel films [42 43]

When as-prepared samples do not consist of pure vanadiumdioxide preliminary electroforming is required resulting inthe formation of the VO

2-containing channel [40 42] The

latter examples as well as the discussed AOFs here supportthe assumption that the formation of vanadium dioxide isthermodynamically preferable at a V

2O5-V interface [22

27] For such samples the threshold voltage decreases withtemperature and reaches zero at 119879 = 119879

119905sim 340K

In this case the switchingmechanismmight be describedin terms of the ldquocritical temperaturerdquo model [29 37] (if theambient temperature is not much lower than 119879

119905)

119881th sim (119879 minus 119879119905)12

(3)

that is the squared threshold voltage linearly tends to zero at119879 rarr 119879

119905 see Figure 8 Switching elements for other transition

metal (FeW Ti and Nb) oxides exhibitingMIT are expected

to show similar behaviour but for different 119879119905rsquos which is

demonstrated by Figure 8(b) for Ti oxideThe switching effect in the WO

3-based sandwich struc-

tures can also be explained in terms of ametal-insulator tran-sition which occurs in nonstoichiometric WO

3minus119910(within a

very narrow interval of variable 119910) at 119879119905ranging from 160 to

280K [46] Because of the narrow interval of ldquoappropriaterdquostoichiometric compositions the S-type I-V characteristicis not likely to appear in tungsten trioxide and in mostcases breakdown occurs instead For switching structureson anodic films on W 119879

119900was found to lie around sim200K

(Figure 5) Therefore 119879119900may turn out to be equal to 119879

119905

Almost no data on MIT in molybdenum oxides are avail-able in the literature except for the transition in Mo

8O23

(MoO2875

) and the switching effect in molybdenum oxidewill be discussed in more detail in the next section Asto Ta and Hf oxides the formation of metastable loweroxides during electroforming should also be possible Theproperties of these oxides are practically unknown but somemetastable oxides of this type have been referred to forexample for the Ta-O system [47] Recently formation ofHfO119909[48] and TaO

119909[49] suboxides has been reported As

to Mn oxides it is known [23] that MnO and Mn3O4are

Mott insulators Mn2O3is a semiconductor and MnO

2is

also a semiconductor but it shows a change in electricalconductivity at 119879 = 119879

119873sim 90K (the Neel temperature) This

might account for the N-NDR effect in Mn oxide this issuewill also be more thoroughly investigated in the next section

Thus the experimental data on the switching effect in119889-metal oxide thin films can be explained in terms of theswitching mechanism driven by the MIT We can state thatin all cases the electrothermal and electrochemical processesduring electroforming are responsible for the switching chan-nel formation The channel consists of a material which canundergo a transition from semiconducting state to metallicstate at a certain temperature 119879

119905 For the V- Ti- Nb- and Fe-

based structures the possibility of formation of the channelsconsisting completely or partly of VO

2 Ti2O3 NbO

2 and

8 Advances in Condensed Matter Physics

Fe3O4 respectively is also confirmed by the thermodynamic

calculations In oxides of W and Mo switching may beassociated with MIT in the channels consisting of WO

3minus119909

and Mo8O23 The S-shaped voltage-current characteristic

is conditioned by the development of an electrothermalinstability in the channel When a voltage is applied thechannel is heated up to 119879 = 119879

119905(at 119881 = 119881th) by the current

and the structure undergoes a transition fromhigh-resistance(OFF) insulating state to low-resistance (ON) metallic state

In high electric fields (105ndash106 Vcm) the possible influ-ence of electronic effects on the MIT should be taken intoaccount A field-induced increase in charge carrier densitywill act to screen Coulomb interactions [12] leading to theelimination of the Mott-Hubbard energy gap at 119879 lt 119879

119905

Moreover a transition of this type may be important in thosematerials where the usual temperature-induced MIT with awell-defined 119879

119905does not take place for example in oxides

of Ta or Hf (and in CGS-based switching structures as well[50]) In the case of vanadium dioxide such a possibilityof the electronically induced MIT was suggested from theinjection experiments [22] and will be discussed also belowin connection with the transition mechanism in VO

2

To summarize the results presented above as well asthe other data on the switching in transition metal oxides[11ndash17 27ndash31] indicate that current instabilities with the S-type NDR exhibit several common features In particularfor each of the investigated materials there is a certain fixedtemperature 119879

119900 above which switching disappears At 119879 lt

119879119900 the threshold voltage decreases as the temperature rises

tending to zero at 119879 = 119879119900 Comparison of these temperatures

with the temperatures of MIT for some compounds (119879119905

=

120K for Fe3O4 sim200K for WO

3minus119909 340K for VO

2 sim500K

for Ti2O3 and 1070K for NbO

2) shows that the switching

effect is associated with the insulator-metal transition in anelectric field The channels consisting of these lower oxidesare formed in initial anodic films during the process ofpreliminary EF

And finally in conclusion of this section we would like todiscuss onemore vanadium oxide where the switching effectsare caused by MITs namely vanadium sesquioxide The I-Vcharacteristics of chromium-doped V

2O3shown in Figure 9

are distinctive in that they exhibit in a certain temperaturerange two regions of negative differential resistance both N-NDR and S-NDR The experimental data on the switchingeffect ofMOM structures based onV

2O3Cr can be explained

in terms of the switching mechanism driven by the variableMIT The S-shaped I-V characteristic is conditioned by thedevelopment of an electrothermal instability in the sampleWhen a voltage is applied the sample is heated by the currentup to 119879 = 119879

1199051(at the threshold voltage 119881 = 119881th119878) and

the structure undergoes a transition from a high-resistance(OFF-1) AFI state to a low-resistance (ON) PM state Asthe current in the ON state increases the sample is furtherheated and at 119879 = 119879

1199052(119868 = 119868th119873) the second transition

to the OFF-2 (or PI) state occurs [51] In the OFF-1 statethe plot of current versus the square root of the appliedvoltage is indicative of a Poole-Frenkel type of conductivityenhancement [52] (Figure 10)

12

34

0

20

40

60

80

100

120

140

160

180

Curr

ent (

mA

)

05 10 15 20 25 3000Voltage (V)

Figure 9 Current-voltage characteristics for V2O3doped with 12

at of Cr at different temperatures 1705 K (1) 1733 K (2) 2210 K(3) and 2655 K (4) [51]

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

Curr

ent (

A)

05 10 15 20 2500Square root of voltage (V05)

150K140K130K120K110K

100K90K80K70K60K

50K40K30K20K10K

Figure 10 Current versus voltage in Poole-Frenkel coordinates fora V2O3-based switching device [52]

23 Switching Effects and Metal-Insulator Transitions in MnandMoOxides In this section we consider electrical switch-ing in oxides of Mn and Mo obtained by vacuum depositionin comparison with those obtained by anodic oxidation [5354] It should be emphasized here that AOFs are (as a ruleexcept for some rare cases) amorphous [32 33] Therefore inMOM structures with anodic films the process of EF similarto that in CGSs usually takes place However in some cases(Mo Mn) as was described in previous sections we havefailed to obtain stable switching with anodic films and herewe present an alternative approach to this problem

Advances in Condensed Matter Physics 9

231 Electrical Switching in Thin Film Structures Based onMolybdenumOxide As inmost TMOs in the molybdenum-oxygen system there exist a number of oxides with variablevalence which are characterized by a wide diversity ofstructures and physical properties [53 55 56] MolybdenumtrioxideMoO

3has a structure based on layers of edge-sharing

distorted MoO6octahedra [23] Similar layered structures

are inherent in lower molybdenum oxides including MoO2

Mo18O52 Mo9O26 Mo8O23 Mo5O14 and Mo

17O47 as well

as 120578- and 120574-Mo4O11[55ndash57]

Stoichiometric MoO3 in its most thermodynamically

stable form 120572-MoO3 is an insulator with a band gap of sim3 eV

[23] During reduction by means of either oxygen deficiencyformation or introducing donor impurity atoms additionaldonor levels near the conduction band bottom appear andthe reduced oxide behaves therefore as a semiconductorPolycrystalline MoO

3 as well as a single crystal has a grey-

yellow colour and the minimum value of the absorption edgeis 440 nm which corresponds to the smallest value of theband gap of 28 eV [58] thus the band gap depends upon thestoichiometry and the crystalline state [53] The conductivityvalues of molybdenum oxides range from dielectric MoO

3

to semiconductor Mo18O52

(resistivity 120588 = 781Ωsdotcm)and down to metal 120578-V]

411

(120588 = 166 times 10minus4Ωsdotcm) [58]Molybdenum dioxide also exhibits metallic properties [2358] and at room temperature 120588 = 88 times 10minus5Ωsdotcm for bulkMoO2samples [55]

Because of their special physical and chemical propertiesmolybdenum oxides are used in various electronic devicessuch as electrochromic displays and indicators reversiblecathodes of lithium batteries gas sensors and memoryelements [55ndash61] Metal-insulator transitions have also beenobserved in some oxides of molybdenum and related com-pounds [62ndash70] In particular Mo

8O23

exhibits a two-stagestructural MIT with formation of a charge-density wave at1198791199051= 315 K and 119879

1199052= 285K [62] However as far as we know

no data are available in the literature concerning thresholdswitching associated with these transitions except for ourwork [53] In this work we have particularly noted thatmemory switching is observed inmany TMOs molybdenumoxides included [4 9 59 60]

The most discussed models in the literature for theReRAMmechanism in oxide structures are those based eitheron the growth and rupture of a metal filament inside theoxide matrix under the action of electric current or onthe redox processes responsible for the formation of somehigh-conductivity or low-conductivity local inclusions cor-responding to particular oxygen stoichiometry [4] The MITideology is also sometimes involved to explain the propertiesof the structures and the memory switching mechanismtherein [71] In any case thememory switching phenomenonseems to be associated with the ion transport [4 9] It isalso appropriate to mention here the works discussing thememory effects in a material with MIT (vanadium dioxide)associated with the presence of hysteresis in the temperaturedependence of conductivity [72]

On the other hand as was shown in the previous sectionmonostable threshold switching (with no memory effects)

associated with the MIT is also characteristic of a numberof TMOs That is why the study of threshold switchingin molybdenum oxide and its possible connection withthe phenomenon of MIT is of considerable scientific andpractical interest

Thinfilm samples ofmolybdenumoxidewere obtained bytwo ways anodic oxidation and thermal vacuum evaporation[53] Anodization of molybdenum was carried out in anacetone-based electrolyte (22 g of benzoic acid plus 40mLof saturated borax aqueous solution per litre of acetone[33 73]) AOFs on Mo might include lower molybdenumoxides for example Mo

4O11andMoO

2with a relatively high

electronic conductivity [53] The fact that the anodic oxideon molybdenum contained lower oxides was confirmed byexperimental data in the work [74] where it was shown thatthe degree of oxidation (valence state) of molybdenum in anAOF is less than six Also this was confirmed theoretically interms of the thermodynamics of the process the formation ofunsaturated oxide MoO

2had been shown to be energetically

more favourable than MoO3[75]

Vacuum deposited film samples were fabricated by ther-mal evaporation of MoO

3powder at residual pressure of

10minus4 Torr onto polished tantalum plates or glass substratesfor electrical and optical studies respectivelyThe thicknessesof the films were determined from the transmission andreflection interference spectra measurements [76] and theywere found to lie in the range from 300 to 800 nm

The XRD pattern of a vacuum-deposited molybdenumoxide sample is presented in Figure 11(a) It is shown thatthe samples represent amorphousMoO

3with a slight oxygen

nonstoichiometry [53] Anodic oxide films on Mo are alsoamorphous (or amorphous-microcrystalline according tothe literature data [73]) but their composition correspondsas described above to ratherMoO

2or other lower oxides and

not to the highest oxide MoO3

Figure 11(b) shows the reflection and transmission spec-tra for one of the samples obtained by vacuum depositionThe experimental data processing using the envelope of theinterference extrema [76] yields the film thickness of (620 plusmn

50) nm and the absorption edge around 120582 asymp 400 nm indi-cates the fact that the oxide phase composition correspondsto MoO

3with a band gap of sim3 eV

Before electroforming initial structures demonstrate thenonlinear and slightly asymmetric current-voltage charac-teristics with no NDR regions When the amplitude of theapplied voltage reaches the forming voltage a sharp andirreversible increase in conductivity is observed and theI(V) curve becomes S-shaped (Figure 12) With increas-ing current the I-V characteristic may change until theparameters of the switching structure are finally stabilizedThe process outlined above is qualitatively similar to theelectroforming of the switching devices based on other TMOs(see Section 22 above) We emphasize once again that thephase composition of the ensuing switching channel mustdiffer from the material of the pristine oxide film becausethe channel conductivity is higher than that of the unformedstructure by several orders of magnitude

The current-voltage characteristics of vacuum-depositedfilms and those of anodic films are qualitatively similar but

10 Advances in Condensed Matter Physics

1

2

20 40 60 8002120579∘

0100200300400500600700800900

I (co

unts

s)

(a)

1

2

3

0

20

40

60

80

100

T (

)

300 400 500 600 700 800 900 1000 1100200Wavelength (nm)

(b)

Figure 11 (a) XRD pattern of the molybdenum oxide film (1) andV]3powder (2) (b) Optical spectra of the sample obtained by vacuum

deposition (1) transmission coefficient of substrate (glass) (2) transmittance and (3) reflectance of Mo oxide film on glass [53]

0 5 10minus5minus10

Voltage (V)

minus016

minus012

minus008

minus004

000

004

008

012

016

Curr

ent (

mA

)

(a)

minus072 072 216 360minus216minus360

Voltage (V)

minus064

minus048

minus032

minus016

000

016

032

048

064

Curr

ent (

mA

)

(b)

Figure 12 Current-voltage characteristics ofMOMstructures with vacuum-deposited (a) and anodic (b)Mo oxide films after electroforming

there is a significant quantitative difference in their thresholdparameters For instance the switching voltage 119881th for theAOF based structures is sim2V (Figure 12(b)) whereas forthe structures on the basis of the films prepared by thermalevaporation119881th is sim10V (Figure 12(a))This difference can beexplained by the difference in thickness of the films

For anodic oxide the thickness can be estimated fromFaradayrsquos law [53]

119889 =

120583119868119886119905

4119890120588119878119873119860

(4)

where 120583 = 128 gmol and 120588 = 65 gcm3 are respectivelythe molar mass and density of V]

2and 119890 and 119873

119860are the

unit charge and Avogadro constant For 119868119886= 70m0 and 119905 =

10min (4) yields 119889 sim 20 nm which is significantly less thanthe typical thickness of the vacuum deposited films and as aresult the threshold voltage for AOFs is also lower than thatfor the films obtained by thermal evaporation

As is discussed in [53] switching is not observed inthinner films obtained by vacuum evaporation (119889 lt 100 nm)

in contrast to ultrathin AOFs A plausible reason for thismight be the fact that relatively thin vacuum depositedfilms contain through-the-thickness conducting defects dueto local stoichiometry variations whereas such defects areimpossible in anodic films because they are grown in highelectric field during anodic oxidation and an appearanceof such defects would interrupt the film growth processThis is similar to what is observed in vanadium oxide inpolycrystalline vanadium dioxide films such pin-hole defectsare usually associated with the grain boundaries which couldundergo local metallization due to strain or nonstoichiom-etry That is why it had been difficult to observe switchingin sandwich MOM structures with sputtered or thermallyoxidized polycrystalline VO

2films and most studies had

been conducted with planar thin-film structures whilst foranodically oxidized VO

2the switching effect has then been

observed in a sandwich structure for the first time in [16]Next we note that unlike the most other TMOs the

process of electroforming in Mo-based structures was hin-dered as was mentioned above in Section 21 that is theconventional electrical breakdown often occurred not the

Advances in Condensed Matter Physics 11

020406080

100120

30 40 50 60 7020Temperature (∘C)

30 40 50 60 7020Temperature (∘C)

0

2

4

6

8

10

12

Thre

shol

d vo

ltage

(V)

5 15minus5minus15

Voltage (V)

minus010

minus005

000005010

Curr

ent (

mA

)

V2 th

(V2)

Figure 13 Threshold voltage as a function of temperature for theTa-MoOx-Au switching structure and the temperature dependenceof (119881th)

2 (lower inset) in compliancewith (3) I-V curve at RT (upperinset)

formation of a switching channel However for the Mooxide films prepared by vacuum deposition the processesof electroforming and switching were more stable whichallowed in this case observation of the transformation of I-V curves at a temperature change It was found that as thetemperature increased the threshold voltage was reducedAt 119879 = 119879

119900sim 55ndash65∘C the NDR region degeneration

commenced at 119879 asymp 60ndash70∘C 119881th rarr 0 and at still highertemperatures the switching effect no longer occurred Inthis case the switching mechanism might be described interms of the ldquocritical temperaturerdquo model (Figure 13) It issupposed [53] that in the case of Mo like in other TMO-based structures formation of a channel also takes placeand this channel should consist of a material exhibiting MITwhich is the reason for switching with an S-shaped current-voltage characteristic (Figure 12)

A brief review of the materials with MIT in the familyof molybdenum compounds presented in [53] shows that themost suitable candidate for the role of such a channel-formingcompound is Mo

8O23

because in this case the value of 1198791199051

almost coincides with the above reported experimentallymeasured 119879

0 It should be noted that formation of other

compounds of molybdenum (eg pyrochlores bronzes sul-fides or chalcogenide glasses) exhibiting MITs with similarorder of magnitude transition temperatures [64ndash68 70] isimpossible because of the lack of the necessary chemicalelements (ie rare earths alkali metals or hydrogen sulfurand tellurium) in the phase composition of both the oxidefilm and the metal electrodes (Au Ta and Mo)

In conclusion the results presented in this subsection onswitching from the HR state to the LR state with an S-NDRin molybdenum oxides obtained by both thermal vacuumdeposition and electrochemical anodic oxidation show thatthe switching effect is due to apparently an insulator-to-metal phase transition in the switching channel consistingcompletely or partly of the lower oxide Mo

8O23 formed in

the initial film during the process of electroforming Thecurrent flowing through the channel heats it up to the MIT

temperature 1198791199051= 315K [62] and the structure switches into

the metallic low-resistance stateThus the channels consisting of this lower oxide are

formed in initial Mo oxide films during preliminary elec-troforming Electrical forming results in the changes inoxygen stoichiometry conditioned by the ionic processes inan electric field close to the MOM structure breakdown fieldThis picture is quite similar to what is observed inmany otherTMOs exhibiting the insulator-to-metal transitions

232 Metal-Insulator Transition and Switching in ManganeseDioxide Manganese dioxide is one of the most interestinginorganic materials because of its wide range of applica-tions In particular nanostructured MnO

2has received great

attention due to its high specific surface area functionalproperties and potential applications as molecular and ionselective membranes in capacitors Li-ion batteries andcatalysts [77] Originally MnO

2has been widely used as a

cathode material for oxide-semiconductor capacitors basedon tantalum niobium and aluminium oxides and the mostimportant properties of the material for this application areits high conductivity and ability to undergo a thermal phasetransition into the lower valence states accompanied by evo-lution of atomic oxygen while the resistance increases by 3-4orders of magnitude (see eg [54] and references therein)Much attention is currently paid to various other propertiesof MnO

2 such as for example the electrochromic effect

[78] thermopower wave phenomenon [79] supercapacitivebehaviour [80] andmemory and threshold switching [54 8182] Also there are a number of papers [83ndash85] describing ananomaly in theMnO

2conductivity near theNeel temperature

which is shown to be associated with the metal-insulatortransition [52] That is why the electrical properties of MnO

2

are of special scientific interest and applied importanceThe most common methods for manganese oxide prepa-

ration are the pyrolytic decomposition of manganese nitrateelectrochemical method hydrothermal synthesis in a mag-netic field and chemical deposition [54 86ndash89] Due to awide range of possible valence states of cations the structureand phase composition of manganese oxides are determinedby the synthesis conditions and process temperature Man-ganese dioxide has many crystallographic forms (120572- 120573- 120574-120575- 120576- and 120582-MnO

2) that connect MnO

6octahedron units to

each other in different ways and have different characters ofspatial alternation of the octahedra filled by Mn atoms andempty octahedra [54 77 90ndash94]

The crystal structure of the 120573-MnO2phase (Figure 14) is a

tetragonal modification of the rutile structural type P4mnmsymmetry group which represents a slightly distorted close-packed hexagonal lattice of oxygen ions [93] Filled octahedraare bound by two common edges in columns oriented alongthe 119888 axis and octahedra of adjacent columns are bound bytheir vertices (Figure 14(c)) Manganese atoms are arrangedin positions 2(a) (000) and oxygen atoms in positions 4(f )(xx0) Because there are vacancies in the oxygen packingthe formula unit can be written as MnO

2minus119910where the

nonstoichiometry index is in the range 119910 = 001ndash010depending on the synthesis method [93]

12 Advances in Condensed Matter Physics

Mn

O

(a)

a

b

c

(b)

O2O4

O1O3

Mn2

Mn1

Mn1998400

O3998400

O4998400

(c)

Figure 14 Crystal structure of manganese dioxide (a) MnO6

octahedron connection in 120573-MnO2(b) [90ndash94] and projection of

octahedron binding onto the ab plane [93]

As to the lower manganese oxides MnO and Mn3O4are

known to be theMott insulatorswith relatively high resistivity[90] and Mn

2O3shows p-type semiconducting properties

MnO2is an n-type semiconductor and antiferromagnetic

with the Neel temperature 119879119873= 925 K [91] Conductivity of

manganese dioxide is higher than that of MnO and Mn2O3

by several orders of magnitude At temperatures above 723Kmanganese dioxide loses oxygen and transforms intoMn

2O3

which is accompanied by the transformation of the crystallinestructure from the tetragonal crystal system of the rutile typeinto the complex large-period cubic lattice (119886 = 94gt) and alarge number of formula units per unit cell [54 92 93]

In this subsection we present the results on electricalproperties of manganese dioxide particularly the natureof the 120573-MnO

2conductivity at low temperatures in its

interrelation with characteristic features of the material crys-talline structure and the metal-insulator phase transitionin this compound as well The effect of electrical switchingwith current-voltage characteristics of both N- and S-typehas been found in thin-film MOM structures on the basisof manganese oxides Possible mechanisms of switching interms of the MIT and thermistor effects are discussed

Mn oxide samples under study have been obtained bythree methods anodic oxidation and vacuum evaporation(thin films) as well as by pyrolysis [54] Thin films ofmanganese dioxide were deposited by means of thermalevaporation onto glass substrates covered by a SnO

2layer

using a VUP-5 vacuum setup the film thickness was 119889 =

250 nmAlso thin films ofmanganese oxidewere obtained byelectrochemical oxidation of metal Mn in the KNO

3-NaNO

3

eutectic melt (see Section 21) at 119879 = 600K at a constantvoltage of about 2V for 3min the current density diminishedfrom 200 to 100mAcm2 during the oxidation process Foranodic oxide films on Mn the value of 119889 was sim100 nm Bulksamples of manganese dioxide were obtained by multipledecomposition (pyrolysis) of manganese nitrate at 119879 = 670Kon a glass-ceramic substrate or on a tantalum sheetmetal withthe subsequent separation from the substrate [92 93] Thetotal coating thickness was about 1mm

The manganese oxide samples were characterized by X-ray diffraction (XRD) using a DRON-6 diffractometer inCuK120572and FeK

120572radiation The characteristics of the atomic

structure of pyrolytic manganese dioxide were refined by thefull-profile analysis of the XRD patterns of polycrystallinesamples [93]The resistivity of pyrolyticMnO

2wasmeasured

in the temperature range 15 to 300K bymeans of a four-probetechnique both DC and AC (in a frequency range from 50 to104Hz) in a Gifford-McMahon cycle cryorefrigerator [54]We also measured electrical conductivity in the range T =293ndash423K the Hall effect in the magnetic field of 23 T andthe Seebeck coefficient (thermoelectromotive force thermo-emf ) The dynamic current-voltage (I-V) characteristics ofthe thin-film MOM structures were measured by oscillo-graphic method using an AC sinusoidal signal

The XRD patterns of the manganese oxide samples arepresented in Figures 15 and 16 The vacuum-deposited filmsare amorphous and represent a mixture of 120573- and 120574-MnO

2

(Figure 16) The results of the full-profile analysis show thatthe pyrolytic MnO

2samples (Figure 15) are composed of

the finely dispersed 120573-MnO2phase with the traces of 120574-

MnO2 120576-MnO

2 and Mn

2O3phases The periods of the

tetragonal unit cell of 120573-MnO2are 119886 = 119887 = 4401 A and

119888 = 2872 A The oxygen coordinates in 4119891 positions (seediscussion of the crystal structure above and Figure 14) arefound to be119909 = 0302 Calculations of the oxygen-manganeseinteratomic distances show [93] that the oxygen octahedron

Advances in Condensed Matter Physics 13

330222

040231

212202

112

130002

220

121

120

111

110

101

020

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 80 100 12002120579∘

Figure 15 XRD (Cu K120572radiation) pattern of pyrolytic MnO

2

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 8002120579∘ Fe

120573-MnO2

120574-MnO2

Experiment

Figure 16 XRD (Fe K120572radiation) pattern of Mn oxide film and

reference spectra of crystalline MnO2samples

is compressed along the (100) direction which connects theoctahedron vertices This deformation results in an increaseof the overlap of electron119901 orbitals of oxygen and119889 orbitals ofmanganese and can form the additional splitting of electronlevels in the crystal field leading to the appearance of unpairedelectrons [94]

The measurements of the conductivity temperaturedependence Hall effect and thermo-emf show that man-ganese dioxide is the electron semiconductor with conductiv-ity of about 1Ωminus1cmminus1 and mobility of sim10 cm2Vsdots The Hallmeasurements give the carrier density ofsim1018 cmminus3 which isclose to the density values in degenerate semiconductorsTheactivation energy of conductivity is sim01 eV and the band gapwidth is equal to 2 eV [90] The estimated value of the Fermienergy from the thermo-emf temperature dependence is inthe range of 002 to 005 eV which also indicates the degener-ate character of the electron gasThe nonstoichiometry indexdetermined by the XRD peaks which are not contributed

by the manganese atoms that is by those with the oddsum of indexes is 119910 = 006 Such nonstoichiometry providesthe concentration of trap states of about 1017-1018 cmminus3which correlates with the above mentioned Hall-effect-basedmeasurements of electron density

Such high vacancy concentration allows us to considerthe nonstoichiometric 120573-MnO

2as a heavily doped semicon-

ductor with a subband of impurity levels which provides afeasibility of the out-of-band electron transfer at low tem-peratures The structural distortions high nonstoichiometryand as a consequence sufficiently high concentration ofimpurity states cause the density state tails near the bandedges similarly to those in heavily doped semiconductorsHowever at room and higher temperatures the conduction isdetermined by the activation mechanism Thus the electronstructure and a low mobility of charge carriers promotethe manifestation of different charge transfer mechanismsin different temperature ranges namely both the hoppingmechanism and the activation one

The electron capturing oxygen vacancies create mixedvalence states of manganese cations (Mn3+ndashMn4+) Interest-ingly the mixed valence of Mn ions is also characteristic ofmanganites Ln

1minus119910Sr119910MnO3[95] where Ln is La or another

rare-earth element possessing the effect of colossal magne-toresistance (CMR) In these compounds the mixed valenceof manganese is attained via doping It had been deemed thatholes introduced by strontium are localized at manganeseions that is the Mn4+ ions with concentration 119910 are formedHowever recent X-ray emission studies have shown that boththe chemical shift and the exchange splitting of the emissionX-ray Mn K

1205731line are almost the same in the range 119910 lt 04ndash

05 as is the case in Mn2O3 and then they decrease quickly

to the values characteristic of MnO2[96] which suggests that

the introduced holes are localized at oxygen atoms in the holedoping region (at relatively low 119910) and atmanganese atoms inthe electron doping region that is at higher 119910 values

The temperature dependence of conductivity is presentedin Figure 17 The resistance peak observed in the figure ina temperature range of 80ndash90K is the result of the phasetransition of 120573-MnO

2from a semiconducting state to a metal

state upon decreasing the temperature to 15 K [54] The tem-perature region of the transition is close to the known Neeltransition from the paramagnetic state into the ferromagneticone for manganese dioxide The temperature dependenceof resistance indicates thus the MIT to occur in MnO

2 In

the temperature range from 300 to 80K (Figure 17) thisdependence does not correspond to the exponential one yetit fits well with the linear dependence in theMott coordinatesln(119877) sim 119879

14 which indicates the hopping conductivitymechanism over the polyvalent states ofmanganese ions witha distance between the centres of 25ndash35gt [92] However inthe temperature range from 90 to 15 K the dependence ofln119877 on ln119879 is almost linear with the slope of about unity(ie 120597 ln119877120597 ln119879 asymp 1) which is characteristic of the metallicconductionThus the character of conductivity ofmanganesedioxide indicates the presence of the MIT at 119879

119888sim 80K (on

cooling)

14 Advances in Condensed Matter Physics

CoolingHeating

40 80 120 160 2000T (K)

0

2

4

6

8

10

Resis

tivity

(Ohm

timescm

)

Figure 17 Temperature dependence of AC (70Hz) resistivity ofpyrolytic MnO

2

In the low temperature region manganese dioxide is anantiferromagnetwith the helical spin ordering [97]The inter-action between the magnetic ions of manganese which leadsto the antiferromagnetic state occurs through the intermedi-ate interaction with diamagnetic oxygen ions which weakensthe exchange interaction The conductivity increases proba-bly due to exceeding the energy of the exchange interactionby the thermal energy as the temperature increases whichleads to an increase in the number of unpaired electrons inthe paramagnetic state As the temperature further increasesthe conductivity continues to rise and the Mott hoppingmechanism of charge transfer becomes predominant Similarcharacter of the temperature dependence in ferromagneticdegenerate semiconductors has previously been described[85 98] for substoichiometric (oxygen-deficient) europiummonoxide The transition from the highly conductive stateinto the insulating state occurs in such semiconductors uponvarying the type of magnetic ordering or its destruction

For EuO1minus119910

lowering the peak magnitude in the 119877(119879)

dependence is associatedwith a decrease in the concentrationof impurities (oxygen vacancies) In magnetic semicon-ductors the phase transition is associated both with themagnetoelectric effects and with the variation in the electricpolarization under the action of the magnetic field at theantiferromagnetic transition [98] The dielectric constant formanganese dioxide is equal to sim10 but the effective dielectricconstant can decrease near 119879

119888by a factor of several times

thereby affecting the mobility of carriers located in the tailsof the density of states near the band edge and promotingtheir delocalization at the phase transition temperatureManganese dioxide also belongs to this group of substanceshowever the phase transition in MnO

2reported here can be

also described in terms of the Mott transition [24]According to the Mott criterion electrons delocalize if

the distance between the atoms 119899minus13 becomes comparable

with their atomic radius 119886119860 where 119886

119860is associated with the

Bohr radius 119886119861= ℏ2120576me2The static permittivity 120576 is replaced

by the effective permittivity which takes into account theexchange interaction of the spins of conduction electronswith orbitalmagneticmoments of atoms At the temperature-induced Mott MIT the orbital radius 119886

119861decreases near 119879 =

119879119888thereby providing the fulfillment of the Mott criterion at a

given level of impurity centres [24 98] The transition fromthe metallic state into the semiconductor state is possible insuch semiconductors as the temperature increases Thus theMIT in manganese dioxide is brought about by temperaturevariation

In conclusion we note that the phase transition describedabove is inverse (reentrant) MIT that is the metallic phaseis low-temperature while the high-temperature state is insu-lating This is rather rare yet not unique and unusualphenomenon In most cases (eg in vanadium dioxide) thelow-temperature phase is insulating and on heating abovea certain temperature 119879

119888 the material becomes metallic for

VO2 this transition temperature is 119879

119888= 340K The inverse

transitions are observed in such compounds as the abovementioned EuO

1minus119910 NiS2Se Y2O3minus119910

and LaMnO3films [24

31 52 85 98 99] Also the high-temperature Mott transi-tion from paramagnetic metal to paramagnetic insulator inV2O3Cr is an inverse transition with the resistivity peak at

119879119888sim 350K for a chromium concentration of around 1 at

[24 51] and in mixed valence CMR-manganites the sharpresistivity peak has been shown to be caused by the AndersonMIT [95]

It is known that many TMOs exhibit electrical switchingassociated with MITs [28] For the anodic oxide films onMn the study of the effect of electrical switching in thin-film Mn-MnO

2-Au sandwich structures showed that the S-

type switching was not observed in contrast to for examplethe similar structures based on oxides of vanadium andsome other transition metals [28] Instead switching withthe N-shaped I-V characteristic occurred after EF at 119879 lt

80K (Figure 18(a)) In addition the EF process in the Mn-based structures was hindered likewise for example for thestructures based on yttrium oxide [31] that is the breakdowntook place more often It should be noted that EF at roomtemperature always led to breakdown and the switchingeffect had never been observed in this case As was arguedin [54] this switching effect was associated with the MIT inMnO2

On the other hand in the films obtained by vacuumsputtering we have observed S-type switching at roomtemperature (Figure 18(b)) The threshold voltage is of theorder of 1 V and almost independent of temperature up to 119879

= 375KThis situation resembles that with yttrium oxide where

both S-type and N-type switching has been observed too[31] One can assume that switching with the S-shapedI-V curves is due to the so-called ldquothermistor effectrdquo Itis well known that the current flowing through a solidgenerates Joule heat resulting in an increased temperatureIn materials with a negative TCR a rising temperatureinduces a current enhancement and an increased powerdissipation resulting in a farther temperature increase Thispositive electrothermal feedback causes the appearance of anNDR and accordingly an S-shaped I-V characteristic [2]

Advances in Condensed Matter Physics 15

minus15

minus10

minus5

0

5

10

15Cu

rren

t (m

A)

0500 10 15minus10 minus05minus15

Voltage (V)

(a)

minus2

minus1

0

1

2

Curr

ent (

mA

)

10 2minus2 minus1

Voltage (V)

(b)

Figure 18 (a) I-V characteristic of anodic oxide film on manganese at T = 77K (b) I-V characteristic of vacuum-deposited MnO2at 119879 =

293K

In some cases this process might by modified by high-fieldeffects such as Schottky injection impact ionization Poole-Frenkel effect and Zener or avalanche breakdown Notethat unlike a conventional thermistor with an Arrhenius-like conductivity law manganese oxide exhibits a weaker119877(119879) dependence characteristic of the hopping conductivitymechanism which seems to account for the observed weaktemperature dependence of the threshold voltage

An alternative mechanism for the S-type switching effectmay be connected with a possible high-temperature usual(ie not inverse)MIT in somemanganese oxide As is knownEF (see Section 22) leads to the formation of a filament ofhighly conducting material a switching channel Similarlyto what is observed for Mo oxide (Section 231) and otherTMOs (Sections 21 and 22) we suppose that the compositionof this channel differs from the material of the initial oxidefilm since its conductivity noticeably exceeds that of anunformed structure In view of such a plentiful set of phasesand crystal structures in the Mn-O system one can supposethat the channelmight consist of nonstoichiometric120573-MnO

2

some other polymorphic modifications of manganese diox-ide or lower Mn oxides which might undergo a MIT underthe action of either temperature or electric field Howeverthis question obviously requires additional investigation inparticularmeasurements of119877(119879)dependences and switchingproperties at higher temperatures If this assumed high-temperature MIT would occur in for example nonstoichio-metric 120573-MnO

2 one could expect observation of double-

NDR I-V characteristics in such samples at low temperaturesanalogously to those in V

2O3Cr (Figure 9) where this effect

is due to the MITs [29] with the only difference being thatin the case of MnO

2this curve should be N-S-shaped (unlike

the S-N-shaped one in Figure 9) since in chromium-dopedvanadium sesquioxide the inverse MIT is high-temperatureas opposed to MnO

2which as we discussed above (see

Figure 17) exhibits the inverse MIT at low temperaturesNote however that the discussed high-temperature MIT

in 120573-MnO2minus119910

may be unobservable under the temperature

change in equilibrium conditions but displays itself onlyunder the applied electric field as the S-type electricalswitching effect because the transition temperature is closeto or higher than the temperature of MnO

2decomposition

(723K) Such a nonequilibrium transition occurs at switchingin those materials where the usual temperature-inducedMITwith a well-defined 119879

119905does not take place for example in

CGSs for which the equilibrium transition temperature 1198791199050

is higher than 119879119892 while in a high electric field 119879

119905(119864) lt 119879

1199050

might be lower than 119879119892 where 119879

119892is the temperature of the

glass-crystal transition and119864 is the electric field strength [30]Summarizing we have studied the electrical properties

(conductivity temperature dependence and Hall and Seebeckeffects) of the 120573 phase of manganese dioxide obtained bypyrolysis thermal vacuum evaporation and anodic oxida-tion The change of conductivity mechanisms dependingon temperature in a range of 450ndash25K has been shownand the metal-insulator phase transition at low (lt90K)temperatures has been revealed The specific feature of thistransition described in terms of the Mott mechanism isthat the metal phase exists at low temperatures while athigher temperatures the material is a semiconductor withthe hopping conductivity over the mixed valence states ofmanganese ions

The low-temperature switching effect with an NDR andN-shaped current-voltage characteristic associated with thephase transition in manganese dioxide has been found in theMOM two-terminal devices based on anodicMn oxide filmsOn the contrary the devices based on vacuum-depositedfilms have been found to exhibit an S-NDR at room andhigher temperatures which is suggested to be caused byeither the thermistor effect or a high-temperature MIT innonstoichiometric 120573-MnO

2

It should be emphasized that the low-temperature MITin 120573-MnO

2with 119879

119905= 70ndash80K is the inverse Mott transition

which is akin for instance to the transition in V2O3Cr

at 119879119905= 190ndash385K (for chromium dopant concentration in

the range of 05ndash18 at) [51] We thus assume that farther

16 Advances in Condensed Matter Physics

5 10 150Voltage (V)

0

1

2

3

4

5

6

7

8Cu

rren

t (m

A)

(a)ΔV

th(V

)

0

1

2

3

1 2 3 4 5 6 7 80W (at )

(b)

Figure 19 I-V curve (a) of Au-V2minus119910

W119910O5times 119899H2O-Au sandwich structure with119910= 003 and119881th scattering as a function of tungsten admixture

percentage 119910 (b) [104 105]

investigations of the phase transition in manganese dioxidedescribed in this paper are a rather interesting and topicalscientific problem since manganese dioxide can serve as amodel object for studying such inverse metal-insulator phasetransitions

Finally we note that the results presented in this sectionindicate the possibility of application of manganese oxide asa material for thin film sandwich switching devices Deviceswith NDR (N- and S-shaped I-V characteristics) have poten-tial applications in microelectronics as switches memoryelements and microsensors (these issues will be discussedin more detail below in Section 4) Particularly manganeseoxide microswitches [82] can be utilized for implementationof neuristors built with Mott-transition-based memristors[100]

24 Effect of Doping It is only natural that the systemsexhibiting the NDR effects possess a high applied potential inelectronics [2 4 8 18 100 101] yet the stage of EF is a weaklink of chain in the technology process Note that the formingprocess may be brought about by laser irradiation [102] notby applying of electric field In the case of laser treatment(or ldquolaser formingrdquo unlike the above described electricalforming) the parameters of the structures are characterizedby the absence of the scatter that is the I-V characteristics ofall structures are almost identical [103] One more demerit tobe avoided is the scatter in switching parameters (the value of119881th first of all) and their instability during operation In thissubsection we discuss the issues concerning the switchingparameter stabilization by means of doping

In the work [104] we have studied the switching effectin the MOM structures on the basis of W-doped V

2O5-gel

filmsThese structures require preliminary EF similar to thatin anodic oxide films resulting in formation of a conducting

channel within the initial dielectric xerogel filmThe channelconsists of vanadiumdioxide and switching is associatedwiththe insulator-to-metal transition in VO

2 As was shown in

[104 105] for the pure (undoped) V2O5-gel the switching

parameters vary in a wide range because the phenomenonof EF is statistical in nature (like electrical breakdown) andits statistical character shows itself as a spread in the observedthreshold voltages of the ensuing structures that is actuallyat multiple measurements 119881th = ⟨119881th⟩ plusmn Δ119881th

It has been shown [104] that the statistical spread in valuesof the threshold parameters can be minimized by means ofdoping (Figure 19) Unsophisticated reasoning could accountfor this result for pure V

2O5-gel electroforming leads to

formation of VO2with 119879

119905= 340K and each switching

event requires heating up and cooling down from roomtemperature to 119879

119905 this thermal cycling can modify the

peripheral regions of the channel which leads to the changeof the switching threshold voltage On the other hand forthe samples with a high concentration of W the MIT issuppressed [104] and switching is degenerated Betweenthese two outermost points an optimum should exist Asone can see from Figure 19 this optimal value correspondsto 3 at of W that is for V

097W003

O2the switching

parameters are the most stableThe transition temperature ofV097

W003

O2is lower than that for pure vanadium dioxide

and hence the magnitude of the aforesaid thermal cyclingis decreased which results in an increase of stability of theswitching parameters

Next we have studied the effect of doping on switchingin AOFs on Ti [29] These films were obtained in 5 watersolution of citric acid (C

6H8O7) in volt-static regime at 119881

119886

= 20V The samples were doped with aluminium by meansof adding soluble Al-containing substances to the electrolyte

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

Films vol 97 no 2 pp 129ndash143 1982[46] R Collongues La Non-Stoechiometrie Masson Paris France

1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

9 no 5 pp 391ndash396 2014[67] B Sun W Zhao Y Liu and P Chen ldquoResistive switching effect

of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

1990[70] S Mukherjee S Karmakar H Sakata and B K Chaudhuri

ldquoLow-temperature metallic behavior of amorphous MoO3-

TeO2thin filmsrdquo Journal of Applied Physics vol 97 no 12 Article

ID 123707 2005[71] AMottaghizadeh Q Yu P L Lang A Zimmers andH Aubin

ldquoMetal oxide resistive switching evolution of the density ofstates across the metal-insulator transitionrdquo Physical ReviewLetters vol 112 no 6 Article ID 066803 2014

[72] R Xie C T Bui B Varghese et al ldquoAn electrically tunedsolid-state thermalmemory based onmetal-insulator transitionof single-crystalline VO

2nanobeamsrdquo Advanced Functional

Materials vol 21 no 9 pp 1602ndash1607 2011

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

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AstrophysicsJournal of

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Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

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PhotonicsJournal of

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Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

2 Advances in Condensed Matter Physics

Voltage

1

2 3 4

1Cu

rren

t

(a)

Voltage

1

23

1

1

1

1

Curr

ent

5

(b)

Figure 1 Schematic I-V curves for two types of NDR which corresponds to the regions in the curves where dVdI lt 0 Inserts show sketchesof a high-current filament (a) and a high-field domain (b) inherent to S- and N-NDR respectively [2] (where (1) is metal electrodes (2) isinsulating (eg initial oxide or amorphous CGS) film (3) is switching channel emerging after electrical forming (4) is current filament and(5) is high-field domain)

O

ON

NDR

A

C

OFF

B

I998400998400

Ith

I

Ih

I998400

V998400998400Vh V998400 Vth

A998400

C998400

V

Figure 2 S-type current-voltage characteristic (O-C1015840-A-A1015840-B-A1015840-C-C1015840-O) of a switching deviceThe O-C1015840-A branch represents the OFFstate C-A1015840-B the ON state and A-A1015840 and C-C1015840 the NDR region witha hysteresis 119881th and 119881

ℎ(119868th and 119868

ℎ) are the threshold and holding

voltages (currents) respectively

random access memory) [9] Conceptually unsophisticateddesign of a cross-point metaloxidemetal (MOM) memorycell allows easily scalable ReRAM architecture with nanome-tre cell dimensions This in turn provides the basis for3D integrated terabit memory with a multilayer stackablestructure [10]

Among transition metal oxides (TMOs) thresholdswitching (without any memory effects) with an S-type I-V characteristic has been observed in MOM structures withNb2O5[7 11] NbO

2[12ndash14] TiO

2[7 15] VO

2[16] Ta

2O5

[7] Fe oxide [17] and some other TMOs [8] As-fabricateddevices rarely show threshold or memory switching effectswithout an initial modification of their structure a processwhich is usually called EF or just ldquoformingrdquo [18] There is astriking similarity in the EF behaviour observed in a widerange of oxide halide sulphide polymer and CGS films [18ndash21] and further we will follow the discussion of this problemin review [18]

Electroforming is achieved by the application of suitablevoltage pulses which are always higher in magnitude thanthe subsequent operating pulses This invariably produces anirreversible change in the characteristics of a device oftenwith a substantial decrease in the overall terminal resistanceThe processes involved in electroforming depend on thenature and quality of the thin film the geometrical structureof the device and in some cases the electrode material Thechanges can be either structural involving a movement ofmaterial from one part of the device to another or theycan be electronic wherein a quasipermanent change in theoccupancy of some electronic states takes place The changescan occur throughout the bulk of the film or in a localizedregion The most common localized effect is the formationof a fibre of highly conducting material a switching channelSuch permanent channel formation is a consequence oftemporary filamentary breakdown often observed in metal-insulator-metal and metal-semiconductor-metal sandwichstructures However electroforming differs from dielectricbreakdown in the sense that it is a nondestructive processthat is it rather resembles a self-healing type of breakdown[20]

The EF characteristics of different materials are generallyill defined and exhibit large variations even for devicesfabricated under the same conditions Nevertheless since thisprocess is observed in a wide variety of insulating films itis unlikely to result from a peculiarity of any one system In

Advances in Condensed Matter Physics 3

the case of amorphous thin film structures switching channelformation can occur via crystallization of an amorphous filmstoichiometric changes diffusion of the electrode materialinto the film or ionization of deep traps All of these changesusually refer to a localized modification of the structurein the area of the channel The modification of the initialstructure during the forming process is the most importantfactor determining the subsequent switching operation Thisis because in most cases forming creates a ldquonew devicerdquo(within the original structure) whose characteristics deter-mine the ensuing threshold or memory switching [18 22]

In TMOs a set of valence states associated with theexistence of unfilled 119889-shells in the atoms of transitionmetals leads to formation of several oxide phases withdifferent properties ranging from metallic to insulating Onthe other hand it is specifically the behaviour of 119889-electronsin the compounds of transition metals that is responsiblefor the unique properties of these materials causing strongelectron-electron correlations which play an important rolein the mechanisms of such phenomena as for examplemetal-insulator transitions (MITs) high-119879

119888superconductiv-

ity colossal magnetoresistance and multiferroicity whichare inherent to many TMOs [23ndash26] That is TMOs exhibitan astonishing array of functionalities that result from acombination of the strongly polarizable metal-oxygen bondand strong electron correlations [25]

In our works [4 22 27ndash29] it has been shown thatswitching in a number of TMOs with the S-NDR exhibitsseveral common features Particularly in most cases theswitching effect is associated with the insulator-to-metaltransition in an electric field The channels consisting oflower oxides exhibiting MITs are formed in an initial oxidefilm during the process of EF

In many TMOs the switching mechanism has beenshown to be associated with an electronically induced MottMIT occurring in conditions of the nonequilibrium carrierdensity excess under the applied electric field The requiredincrease in electron density under the action of electric fieldmight be caused by the Poole-Frenkel effect [30] or someother high-field-assisted charge carrier generation effectssuch as avalanche ionization and Zener breakdown as wellas Schottky tunnel or avalanche injection from contacts andso forth

This review focuses on earlier obtained results currentresearch the state of the art and recent progress in the field ofscience and applications of the phenomenon of monostablethreshold switching in oxides of transition metals We startby discussing the switching effects inMOM structures on thebasis of anodic oxide films (Sections 21 and 22) and then turnto recent results concerning electrical switching in Mn andMo oxides obtained by deposition in vacuum (Section 23)Effects of doping to stabilize the switching parameters andunify the electroforming process are described in Section 24and Section 3 is devoted to various physical mechanisms atplay which could be responsible for the NDR behaviouremphasizing the particular relationship between the switch-ing effect and MIT electronically induced Mott transitionfirst of all Further in Section 4 we discuss applied poten-tialities of the TMO-based thin film devices exhibiting the

NDR phenomena and finally in Section 5 we will try to for-mulate some conclusions and outlook concerning the topicdiscussed It should be stressed that the scope of the review isnot to describe comprehensively all the results reported in theliterature but rather to sketch out the main pertinent worksand discuss the physical mechanisms involved in the phe-nomenon of electrical switching in transition metal oxides

2 Overview of Experimental Results

21 Switching in Anodic Oxide Films In this section wepresent our results [4 22 27ndash31] on electroforming andswitching in thin film MOM structures with oxides oftransition metals (V Ti Fe Nb Mo W Hf Zr Mn Y andTa) obtained by electrochemical anodic oxidation Anodicoxidation permits the synthesis of high quality homogeneousdielectric oxide films [32] and as a rule anodic oxide films(AOFs) are amorphous

The sandwich devices under study were fabricated by oxi-dation of themetal substrates both polished foils and vacuumdeposited layers Au electrodes were vacuum-evaporatedonto the surfaces of oxide films to complete the MOM struc-ture (Figure 3(a)) The spring-loaded point contacts made ofgildedwire 05mm in diameter were also usedThe oxidationwas carried out electrochemically under anodic polarizationin an electrolyte Ta Nb W Zr and Hf were anodized in01 N aqueous solutions of phosphoric and sulphuric acids[32] while for oxidation of vanadium and molybdenum theacetone-based electrolyte was used [33] Fe Ti Mn andseveral of Nb and Ta samples were anodized in a KNO

3+

NaNO3eutectic melt [34] at 570ndash620K Anodic oxidation of

yttrium was carried out as described in [31] The oxide filmthicknesses were typically from 50 to 200 nm

The current-voltage characteristics of the initial struc-tures are nonlinear and slightly asymmetric The resistanceat zero bias measured with the point contact is in the range107ndash108Ω for the vanadium anodic oxide which is the mosthighly conductive among all the materials studied Whenthe amplitude of the applied voltage reaches the formingvoltage 119881

119891 a sharp and irreversible increase in conductivity

is observed and the 119868(119881) curve becomes S-shaped Withincreasing current the I-V characteristicmay change until theparameters of the switching structure are finally stabilizedThe process outlined above is qualitatively similar to EF ofthe switching devices based on amorphous semiconductors[18] The forming voltage depends on the temperature (119881

119891

increases upon cooling) and film thickness The thicker thefilm the higher the required 119881

119891 The value of 119881

119891correlates

with the anodizing voltage 119881119886(because 119889 is proportional to

119881119886) A similar correlation is characteristic of the AOF break-

down the breakdown voltage is also of the order of 119881119886[32]

Thus the first stage of the forming does not differfrom the conventional electrical breakdown of oxide filmsHowever if the postbreakdown current is limited this resultsin formation of a switching channel rather than a breakdownchannel The latter would be expected to have metallic-like conductivity and no negative resistance in the I-Vcharacteristic It is quite evident that the phase compositionof this switching channel must differ from the material of the

4 Advances in Condensed Matter Physics

1

2

3 4

(a)

00 05 10 15 20 250

20

40

60

80

100

Voltage (V)Cu

rren

t (120583

A)

Vth

(b)

Figure 3 (a) The sandwich switching structure (schematic) (1) vanadium metal substrate (2) anodic oxide film (3) Au electrical contactand (4) switching channel (VO

2 as will be shown below in Section 22) (b) the I-V characteristic after EF for one of the samples at room

temperature

initial oxide film because the channel conductivity exceedsthat of an unformed structure by several orders ofmagnitude

Forming does not always result in an S-type characteris-tic In some instances a transition of the structure to a highconductivity state (119877 sim 100Ω) with ohmic behaviour takesplace that is in this case breakdown rather than formingoccurs Breakdown is more probable in Ta

2O5 WO3 HfO

2

and MoO3films while in the V- and Nb-based structures

it is the electroforming that results in the S-shaped I-Vcurves in most cases The anodic films on Ti and Fe holdan intermediate position S-type switching has not beenobserved in Zr Y and Mn oxide films EF of W- Fe- andHf-based structures was carried out at 77 K because at roomtemperature breakdown took place and no switching effectswere observed The characteristic feature of switching in TaMo Hf and to a lesser extent W oxide films is the instabilityof parameters and the gradual disappearance of the S-typeNDRunder the influence of current flow and thermal cycling

The voltage-current characteristic for electroformedvanadium-AOF-metal structure is shown in Figure 3(b) Theparameters of the structures (threshold voltage 119881th andcurrent 119868th resistances of OFF and ON states) may varyby up to an order of magnitude from point to point forthe same specimen Such a wide range of variation of the119881th and 119877off values as well as the absence of correlationbetween these switching parameters and the parameters ofthe sandwich structures (the electrode material and area andthe film thickness) leads to the conclusion that resistanceand threshold parameters are mainly determined by theforming process Conditions of the forming process cannotbe unified in principle because the first stage of forming

is linked to breakdown which is statistical in nature As aresult the diameter and phase composition of the channel(and consequently its effective specific conductivity) varywith position in the sample This accounts for the scatterin the parameters and for the seeming absence of theirthickness dependence The I-V curves for Ti- Nb- and W-based structures are also shown in Figure 4

Similar behaviour has been observed for the other mate-rials On average for 119889 sim 100 nm a typical value of 119881this 1 to 10V that is the threshold field is 105ndash106 Vcm atroom temperature The greatest differences between theseoxides are observed when the temperature dependence oftheir threshold parameters such as119881th is measured Figure 5shows 119881th(119879) curves for the sandwich structures based oniron tungsten vanadium titanium and niobium For Ta

2O5

HfO2 and MoO

3 no reproducible results were obtained

because of instabilities of their voltage-current character-istics with temperature As the temperature increased 119881thdecreased tending to zero at some finite temperature 119879

119900

This is best exhibited by the vanadium and titanium oxidestructures The values of 119879

119900vary considerably for different

oxides but they are nearly identical for different structuresof the same oxide [28] For the Nb-Nb

2O5-metal structures

it was impossible to measure the 119881th(119879) relationship overthe whole temperature range because heating above 300∘Cinduced processes related to diffusion and change in thechannel phase composition leading to degradation of theswitching structure Nevertheless it is evident from Figure 5that for the niobium oxide 119879

119900exceeds 600K

As was mentioned above S-type switching has not beenobserved inZr Y andMnoxide films Instead thesematerialshave sometimes demonstrated N-NDR at 119879 = 293K (Zr and

Advances in Condensed Matter Physics 5

000102030405

Curr

ent (

mA

)

minus01

minus02

minus03

minus04

minus05

minus10minus20 minus05minus15 05 10 15 2000Voltage (V)

(a)

minus7minus6minus5minus4minus3minus2minus1

01234567

Curr

ent (

mA

)

minus15 minus10 minus5 5 10 150Voltage (V)

(b)

minus4

minus2

0

2

4

Curr

ent (

mA

)

minus10 minus6 minus4minus8 minus2 2 4 6 8 100Voltage (V)

(c)

Figure 4 Current-voltage characteristics of MOM structures with AOFs on (a) Ti (b) Nb and (c) W [29]

Y see Figure 6) or at 119879 = 77K (Mn oxide) The process ofelectroforming for these materials was hindered like that forTa Hf and Mo Switching in Mo and Mn oxides will also beadditionally discussed in Section 23 below

22 Switching as an Electrically DrivenMetal-Insulator Transi-tion Next we discuss the process of electroforming in moredetail The initial AOF represents as a rule a highest oxideof the metal (eg Nb

2O5in the case of niobium) However

lower oxides always exist near the AOF-metal interface inthe form of transition layers or as separate inclusions Thiscan be explained in terms of thermodynamics Consider thefollowing reaction

Nb + 2Nb2O5997888rarr 5NbO

2(1)

The change of the Gibbs (isobaric) potential for thisreaction is

Δ119866119903= ]2Δ1198662minus ]1Δ1198661 (2)

where Δ1198661and Δ119866

2are the standard isobaric potentials

of formation and ]1and ]

2are the numbers of moles of

oxides which take part in the reaction For Reaction (1) the

subscripts 1 and 2 in (2) are related to Nb2O5and NbO

2

respectively and Δ119866119903

= minus163 kJmol [28] Since Δ119866119903

lt 0Reaction (1) proceeds spontaneously and hence NbO

2is

always present at the Nb-Nb2O5interface

Transition metals exhibit multiple oxidation states andform a number of oxides Therefore it is obvious that thelower oxide to be formed is mainly that with the mini-mum Δ119866

119903 Figure 7 demonstrates the variation of Δ119866

119903(119909)

for Fe2O3 Nb2O5 V2O5 TiO2 and some other oxides in

reactions similar to (1) where 119909 is the stoichiometric indexof oxygen Δ119866

119903values were calculated using (2) the data

on Δ119866119900 for the calculations were taken from [35] The

minima in these curves correspond to Fe3O4 NbO

2 VO2

and Ti2O3 therefore these oxides form as intermediate

layers between the metal substrate and the correspondingoxide of highest valence Real systems are far from beinga plane parallel structure with two oxide layers hence thesuggested approach is rather oversimplifiedNevertheless theabove considerations show that formation of those oxidesis thermodynamically reasonable whether it is kineticallypossible can only be judged from experiment For exampleas was shown in [33] in AOF on vanadium the vanadiumdioxide layer may be rather thick and only a very thin film

6 Advances in Condensed Matter Physics

00

05

10

15

20

25

30

V (a

u)

1 2

3 4

5

200 300 400 500 600100T (K)

Figure 5 Threshold voltage in arbitrary units 119881 = 119881th(119879)119881th(1198791015840)

for theMOM structures on the basis of different oxides as a functionof ambient temperature (1) Fe (2)W (3)V (4)Ti and (5)Nb anodicoxideData for different samples have been averaged andnormalizedto a certain temperature 119879

1015840 which is different for different oxides[22 27 28]

0

5

10

15

20

25

30

35

Curr

ent (120583

A)

05 10 15 20 2500Voltage (V)

Figure 6 I-V curve with N-NDR of the structure metalY anodicoxidemetal [31]

near the outer boundary is close to the V2O5stoichiometry

The similar ordering of layers evidently exists in iron oxideparticularly it is known that in a thermal oxide of iron theFe3O4phase usually predominates [28] On the other hand

the AOFs on Nb and Ti mainly consist of Nb2O5and TiO

2

and NbO2or Ti2O3layers seem to be relatively thin [27 28]

For the W-WO3system a wide minimum of Δ119866

119903(119909) lies

in the range 119909 = 27ndash30 (Figure 7) the same behaviour seemsto be characteristic of the Mo-MoO

3system The calculation

for manganese oxides yields the minimum at 119909 = 15 that isfor Mn

2O3 The curve Δ119866

119903(119909) for uranium is also presented

just as an example note however that MITs have beenreported for lower uranium oxide U

4O9[36] For Zr Hf Ta

and Y such calculations have not been made because thereexist no clear data on the thermodynamic properties of thelower oxides of those metals

F1

F2F3

T1

T2

T11N1

N2

N3

W1W2

W3

W4

W5U5

V1

V2

V9

V10

V11

U1U2

U3 U4

M4

M1

M2 M3

900

800

700

600

500

400

300

200

100

0

minusΔGr

(kJm

ol)

15 20 25 3010X

V9998400

V3ndashV8

T2998400

Figure 7 Gibbs potential change Δ119866119903(per 1 g atom of metal) for

the reaction of the highest oxide with the metal substrate versus119909 the oxygen stoichiometric index of the lower oxide which isformed in this reaction Symbol indications are as follows (i) IronF1ndashFeO F2ndashFe

3O4 F3ndashFe

2O3 (ii) Niobium N1ndashNbO N2ndashNbO

2

N3ndashNb2O5 (iii) Titanium T1ndashTiO T2ndashTi

2O3 T3ndashT10ndashTi

119899O2119899minus1

(119899 = 3ndash10) T11ndashTiO2 (iv) Vanadium V1ndashVO V2ndashV

2O3 V3ndashV8ndash

V119899O2119899minus1

(119899 = 3ndash8) V9ndashVO2 V10ndashV

6O13 V11ndashV

2O5 (v) Tungsten

W1ndashWO2W2ndashW

18O49W3ndashW

10O29W4ndashW

50O148

W5ndashWO3 (vi)

Manganese M1ndashMnO M2ndashMn3O4 M3ndashMn

2O3 M4ndashMnO

2 (vii)

Uranium U1ndashUO2 U2ndashU

4O9 U3ndashU

3O7 U4ndashU

3O8 U5ndashUO

3 The

points T21015840 and V91015840 characterize a scatter due to the Δ1198660 data

difference [22 28]

During electroforming current-induced heating of thefilm under the electrode leads to a diffusion of both metalfrom the substrate into the film and oxygen from the outerlayer to the inner one Also the transport of metal andoxygen ions due to the applied electric field is possible Sinceduring electroforming (unlike thermal or electrochemicaloxidation) no external oxygen is present no reaction cantake place except the reduction of the highest oxide of AOFThe reduction results in growth of the channel consisting oflower oxide through the film from one electrode to anotherEvidently substances with the minimum Δ119866

119903value (see

Figure 7)will be predominant in the phase composition of thechannelThe current increase after formingmay cause furtherreduction of the channel material leading to a predominanceof the phases such as VO NbO and TiO Many of the lowestoxides of transition metals (mono- and suboxides) exhibitmetallic properties [23] the accumulation of these phases inthe channel will therefore lead to an irreversible increase inconductivity that is to breakdown

The above compounds (VO2 Fe3O4 Ti2O3 and NbO

2)

have one feature in common namely a metal-insulator phasetransition [24] The MIT phenomenon is characterized bythe sharp and reversible change in the conductivity at acertain temperature 119879

119905 for instance vanadium dioxide at

Advances in Condensed Matter Physics 7

1 2

3

0

1

2

3

4

5

6

240 260 280 300 320 340220T (K)

V2 th

(V2)

(a)

1

2

3

(V2th times 04)

420 440 460 480 500 520 540400T (K)

0

1

2

3

4

5

6

7

V2 th

(V2)

(b)

Figure 8 Squared threshold voltage as a function of temperature for (a) vanadium oxide-based switch and (b) titanium oxide (1) (2) and(3) three different samples

119879 lt 340K is a semiconductor at 119879 = 119879119905

= 340K theconductivity abruptly increases by 4-5 orders of magnitudeand above the transition temperature VO

2exhibits metallic

properties ForNbO2119879119905= 1070K Ti

2O3undergoes a gradual

transition in the range 400ndash600K and magnetite (Fe3O4)

is a semiconductor both above and below the Verwey tran-sition temperature (120K) though its resistivity decreaseson heating by two orders of magnitude at 119879 = 119879

119905 For the

switching devices based on these metals the temperatures 119879119900

coincide with the corresponding values of 119879119905(see Figure 5)

This suggests that the switching mechanism is caused by themetal-insulator transition

Electrical switching due to MIT has been first revealedfor vanadium dioxide [16 27 37ndash45] Switching in VO

2

is explained by the current-induced Joule heating of thesample up to 119879 = 119879

119905 which has been confirmed by the

direct IR-radiation measurements of the switching channeltemperature [38 45] In these early works switching hasbeen observed in single crystals [39] and planar thin filmdevices [37 38 45] as well as in vanadate glasses [40 41]VO2-containing ceramics [44] and V

2O5-gel films [42 43]

When as-prepared samples do not consist of pure vanadiumdioxide preliminary electroforming is required resulting inthe formation of the VO

2-containing channel [40 42] The

latter examples as well as the discussed AOFs here supportthe assumption that the formation of vanadium dioxide isthermodynamically preferable at a V

2O5-V interface [22

27] For such samples the threshold voltage decreases withtemperature and reaches zero at 119879 = 119879

119905sim 340K

In this case the switchingmechanismmight be describedin terms of the ldquocritical temperaturerdquo model [29 37] (if theambient temperature is not much lower than 119879

119905)

119881th sim (119879 minus 119879119905)12

(3)

that is the squared threshold voltage linearly tends to zero at119879 rarr 119879

119905 see Figure 8 Switching elements for other transition

metal (FeW Ti and Nb) oxides exhibitingMIT are expected

to show similar behaviour but for different 119879119905rsquos which is

demonstrated by Figure 8(b) for Ti oxideThe switching effect in the WO

3-based sandwich struc-

tures can also be explained in terms of ametal-insulator tran-sition which occurs in nonstoichiometric WO

3minus119910(within a

very narrow interval of variable 119910) at 119879119905ranging from 160 to

280K [46] Because of the narrow interval of ldquoappropriaterdquostoichiometric compositions the S-type I-V characteristicis not likely to appear in tungsten trioxide and in mostcases breakdown occurs instead For switching structureson anodic films on W 119879

119900was found to lie around sim200K

(Figure 5) Therefore 119879119900may turn out to be equal to 119879

119905

Almost no data on MIT in molybdenum oxides are avail-able in the literature except for the transition in Mo

8O23

(MoO2875

) and the switching effect in molybdenum oxidewill be discussed in more detail in the next section Asto Ta and Hf oxides the formation of metastable loweroxides during electroforming should also be possible Theproperties of these oxides are practically unknown but somemetastable oxides of this type have been referred to forexample for the Ta-O system [47] Recently formation ofHfO119909[48] and TaO

119909[49] suboxides has been reported As

to Mn oxides it is known [23] that MnO and Mn3O4are

Mott insulators Mn2O3is a semiconductor and MnO

2is

also a semiconductor but it shows a change in electricalconductivity at 119879 = 119879

119873sim 90K (the Neel temperature) This

might account for the N-NDR effect in Mn oxide this issuewill also be more thoroughly investigated in the next section

Thus the experimental data on the switching effect in119889-metal oxide thin films can be explained in terms of theswitching mechanism driven by the MIT We can state thatin all cases the electrothermal and electrochemical processesduring electroforming are responsible for the switching chan-nel formation The channel consists of a material which canundergo a transition from semiconducting state to metallicstate at a certain temperature 119879

119905 For the V- Ti- Nb- and Fe-

based structures the possibility of formation of the channelsconsisting completely or partly of VO

2 Ti2O3 NbO

2 and

8 Advances in Condensed Matter Physics

Fe3O4 respectively is also confirmed by the thermodynamic

calculations In oxides of W and Mo switching may beassociated with MIT in the channels consisting of WO

3minus119909

and Mo8O23 The S-shaped voltage-current characteristic

is conditioned by the development of an electrothermalinstability in the channel When a voltage is applied thechannel is heated up to 119879 = 119879

119905(at 119881 = 119881th) by the current

and the structure undergoes a transition fromhigh-resistance(OFF) insulating state to low-resistance (ON) metallic state

In high electric fields (105ndash106 Vcm) the possible influ-ence of electronic effects on the MIT should be taken intoaccount A field-induced increase in charge carrier densitywill act to screen Coulomb interactions [12] leading to theelimination of the Mott-Hubbard energy gap at 119879 lt 119879

119905

Moreover a transition of this type may be important in thosematerials where the usual temperature-induced MIT with awell-defined 119879

119905does not take place for example in oxides

of Ta or Hf (and in CGS-based switching structures as well[50]) In the case of vanadium dioxide such a possibilityof the electronically induced MIT was suggested from theinjection experiments [22] and will be discussed also belowin connection with the transition mechanism in VO

2

To summarize the results presented above as well asthe other data on the switching in transition metal oxides[11ndash17 27ndash31] indicate that current instabilities with the S-type NDR exhibit several common features In particularfor each of the investigated materials there is a certain fixedtemperature 119879

119900 above which switching disappears At 119879 lt

119879119900 the threshold voltage decreases as the temperature rises

tending to zero at 119879 = 119879119900 Comparison of these temperatures

with the temperatures of MIT for some compounds (119879119905

=

120K for Fe3O4 sim200K for WO

3minus119909 340K for VO

2 sim500K

for Ti2O3 and 1070K for NbO

2) shows that the switching

effect is associated with the insulator-metal transition in anelectric field The channels consisting of these lower oxidesare formed in initial anodic films during the process ofpreliminary EF

And finally in conclusion of this section we would like todiscuss onemore vanadium oxide where the switching effectsare caused by MITs namely vanadium sesquioxide The I-Vcharacteristics of chromium-doped V

2O3shown in Figure 9

are distinctive in that they exhibit in a certain temperaturerange two regions of negative differential resistance both N-NDR and S-NDR The experimental data on the switchingeffect ofMOM structures based onV

2O3Cr can be explained

in terms of the switching mechanism driven by the variableMIT The S-shaped I-V characteristic is conditioned by thedevelopment of an electrothermal instability in the sampleWhen a voltage is applied the sample is heated by the currentup to 119879 = 119879

1199051(at the threshold voltage 119881 = 119881th119878) and

the structure undergoes a transition from a high-resistance(OFF-1) AFI state to a low-resistance (ON) PM state Asthe current in the ON state increases the sample is furtherheated and at 119879 = 119879

1199052(119868 = 119868th119873) the second transition

to the OFF-2 (or PI) state occurs [51] In the OFF-1 statethe plot of current versus the square root of the appliedvoltage is indicative of a Poole-Frenkel type of conductivityenhancement [52] (Figure 10)

12

34

0

20

40

60

80

100

120

140

160

180

Curr

ent (

mA

)

05 10 15 20 25 3000Voltage (V)

Figure 9 Current-voltage characteristics for V2O3doped with 12

at of Cr at different temperatures 1705 K (1) 1733 K (2) 2210 K(3) and 2655 K (4) [51]

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

Curr

ent (

A)

05 10 15 20 2500Square root of voltage (V05)

150K140K130K120K110K

100K90K80K70K60K

50K40K30K20K10K

Figure 10 Current versus voltage in Poole-Frenkel coordinates fora V2O3-based switching device [52]

23 Switching Effects and Metal-Insulator Transitions in MnandMoOxides In this section we consider electrical switch-ing in oxides of Mn and Mo obtained by vacuum depositionin comparison with those obtained by anodic oxidation [5354] It should be emphasized here that AOFs are (as a ruleexcept for some rare cases) amorphous [32 33] Therefore inMOM structures with anodic films the process of EF similarto that in CGSs usually takes place However in some cases(Mo Mn) as was described in previous sections we havefailed to obtain stable switching with anodic films and herewe present an alternative approach to this problem

Advances in Condensed Matter Physics 9

231 Electrical Switching in Thin Film Structures Based onMolybdenumOxide As inmost TMOs in the molybdenum-oxygen system there exist a number of oxides with variablevalence which are characterized by a wide diversity ofstructures and physical properties [53 55 56] MolybdenumtrioxideMoO

3has a structure based on layers of edge-sharing

distorted MoO6octahedra [23] Similar layered structures

are inherent in lower molybdenum oxides including MoO2

Mo18O52 Mo9O26 Mo8O23 Mo5O14 and Mo

17O47 as well

as 120578- and 120574-Mo4O11[55ndash57]

Stoichiometric MoO3 in its most thermodynamically

stable form 120572-MoO3 is an insulator with a band gap of sim3 eV

[23] During reduction by means of either oxygen deficiencyformation or introducing donor impurity atoms additionaldonor levels near the conduction band bottom appear andthe reduced oxide behaves therefore as a semiconductorPolycrystalline MoO

3 as well as a single crystal has a grey-

yellow colour and the minimum value of the absorption edgeis 440 nm which corresponds to the smallest value of theband gap of 28 eV [58] thus the band gap depends upon thestoichiometry and the crystalline state [53] The conductivityvalues of molybdenum oxides range from dielectric MoO

3

to semiconductor Mo18O52

(resistivity 120588 = 781Ωsdotcm)and down to metal 120578-V]

411

(120588 = 166 times 10minus4Ωsdotcm) [58]Molybdenum dioxide also exhibits metallic properties [2358] and at room temperature 120588 = 88 times 10minus5Ωsdotcm for bulkMoO2samples [55]

Because of their special physical and chemical propertiesmolybdenum oxides are used in various electronic devicessuch as electrochromic displays and indicators reversiblecathodes of lithium batteries gas sensors and memoryelements [55ndash61] Metal-insulator transitions have also beenobserved in some oxides of molybdenum and related com-pounds [62ndash70] In particular Mo

8O23

exhibits a two-stagestructural MIT with formation of a charge-density wave at1198791199051= 315 K and 119879

1199052= 285K [62] However as far as we know

no data are available in the literature concerning thresholdswitching associated with these transitions except for ourwork [53] In this work we have particularly noted thatmemory switching is observed inmany TMOs molybdenumoxides included [4 9 59 60]

The most discussed models in the literature for theReRAMmechanism in oxide structures are those based eitheron the growth and rupture of a metal filament inside theoxide matrix under the action of electric current or onthe redox processes responsible for the formation of somehigh-conductivity or low-conductivity local inclusions cor-responding to particular oxygen stoichiometry [4] The MITideology is also sometimes involved to explain the propertiesof the structures and the memory switching mechanismtherein [71] In any case thememory switching phenomenonseems to be associated with the ion transport [4 9] It isalso appropriate to mention here the works discussing thememory effects in a material with MIT (vanadium dioxide)associated with the presence of hysteresis in the temperaturedependence of conductivity [72]

On the other hand as was shown in the previous sectionmonostable threshold switching (with no memory effects)

associated with the MIT is also characteristic of a numberof TMOs That is why the study of threshold switchingin molybdenum oxide and its possible connection withthe phenomenon of MIT is of considerable scientific andpractical interest

Thinfilm samples ofmolybdenumoxidewere obtained bytwo ways anodic oxidation and thermal vacuum evaporation[53] Anodization of molybdenum was carried out in anacetone-based electrolyte (22 g of benzoic acid plus 40mLof saturated borax aqueous solution per litre of acetone[33 73]) AOFs on Mo might include lower molybdenumoxides for example Mo

4O11andMoO

2with a relatively high

electronic conductivity [53] The fact that the anodic oxideon molybdenum contained lower oxides was confirmed byexperimental data in the work [74] where it was shown thatthe degree of oxidation (valence state) of molybdenum in anAOF is less than six Also this was confirmed theoretically interms of the thermodynamics of the process the formation ofunsaturated oxide MoO

2had been shown to be energetically

more favourable than MoO3[75]

Vacuum deposited film samples were fabricated by ther-mal evaporation of MoO

3powder at residual pressure of

10minus4 Torr onto polished tantalum plates or glass substratesfor electrical and optical studies respectivelyThe thicknessesof the films were determined from the transmission andreflection interference spectra measurements [76] and theywere found to lie in the range from 300 to 800 nm

The XRD pattern of a vacuum-deposited molybdenumoxide sample is presented in Figure 11(a) It is shown thatthe samples represent amorphousMoO

3with a slight oxygen

nonstoichiometry [53] Anodic oxide films on Mo are alsoamorphous (or amorphous-microcrystalline according tothe literature data [73]) but their composition correspondsas described above to ratherMoO

2or other lower oxides and

not to the highest oxide MoO3

Figure 11(b) shows the reflection and transmission spec-tra for one of the samples obtained by vacuum depositionThe experimental data processing using the envelope of theinterference extrema [76] yields the film thickness of (620 plusmn

50) nm and the absorption edge around 120582 asymp 400 nm indi-cates the fact that the oxide phase composition correspondsto MoO

3with a band gap of sim3 eV

Before electroforming initial structures demonstrate thenonlinear and slightly asymmetric current-voltage charac-teristics with no NDR regions When the amplitude of theapplied voltage reaches the forming voltage a sharp andirreversible increase in conductivity is observed and theI(V) curve becomes S-shaped (Figure 12) With increas-ing current the I-V characteristic may change until theparameters of the switching structure are finally stabilizedThe process outlined above is qualitatively similar to theelectroforming of the switching devices based on other TMOs(see Section 22 above) We emphasize once again that thephase composition of the ensuing switching channel mustdiffer from the material of the pristine oxide film becausethe channel conductivity is higher than that of the unformedstructure by several orders of magnitude

The current-voltage characteristics of vacuum-depositedfilms and those of anodic films are qualitatively similar but

10 Advances in Condensed Matter Physics

1

2

20 40 60 8002120579∘

0100200300400500600700800900

I (co

unts

s)

(a)

1

2

3

0

20

40

60

80

100

T (

)

300 400 500 600 700 800 900 1000 1100200Wavelength (nm)

(b)

Figure 11 (a) XRD pattern of the molybdenum oxide film (1) andV]3powder (2) (b) Optical spectra of the sample obtained by vacuum

deposition (1) transmission coefficient of substrate (glass) (2) transmittance and (3) reflectance of Mo oxide film on glass [53]

0 5 10minus5minus10

Voltage (V)

minus016

minus012

minus008

minus004

000

004

008

012

016

Curr

ent (

mA

)

(a)

minus072 072 216 360minus216minus360

Voltage (V)

minus064

minus048

minus032

minus016

000

016

032

048

064

Curr

ent (

mA

)

(b)

Figure 12 Current-voltage characteristics ofMOMstructures with vacuum-deposited (a) and anodic (b)Mo oxide films after electroforming

there is a significant quantitative difference in their thresholdparameters For instance the switching voltage 119881th for theAOF based structures is sim2V (Figure 12(b)) whereas forthe structures on the basis of the films prepared by thermalevaporation119881th is sim10V (Figure 12(a))This difference can beexplained by the difference in thickness of the films

For anodic oxide the thickness can be estimated fromFaradayrsquos law [53]

119889 =

120583119868119886119905

4119890120588119878119873119860

(4)

where 120583 = 128 gmol and 120588 = 65 gcm3 are respectivelythe molar mass and density of V]

2and 119890 and 119873

119860are the

unit charge and Avogadro constant For 119868119886= 70m0 and 119905 =

10min (4) yields 119889 sim 20 nm which is significantly less thanthe typical thickness of the vacuum deposited films and as aresult the threshold voltage for AOFs is also lower than thatfor the films obtained by thermal evaporation

As is discussed in [53] switching is not observed inthinner films obtained by vacuum evaporation (119889 lt 100 nm)

in contrast to ultrathin AOFs A plausible reason for thismight be the fact that relatively thin vacuum depositedfilms contain through-the-thickness conducting defects dueto local stoichiometry variations whereas such defects areimpossible in anodic films because they are grown in highelectric field during anodic oxidation and an appearanceof such defects would interrupt the film growth processThis is similar to what is observed in vanadium oxide inpolycrystalline vanadium dioxide films such pin-hole defectsare usually associated with the grain boundaries which couldundergo local metallization due to strain or nonstoichiom-etry That is why it had been difficult to observe switchingin sandwich MOM structures with sputtered or thermallyoxidized polycrystalline VO

2films and most studies had

been conducted with planar thin-film structures whilst foranodically oxidized VO

2the switching effect has then been

observed in a sandwich structure for the first time in [16]Next we note that unlike the most other TMOs the

process of electroforming in Mo-based structures was hin-dered as was mentioned above in Section 21 that is theconventional electrical breakdown often occurred not the

Advances in Condensed Matter Physics 11

020406080

100120

30 40 50 60 7020Temperature (∘C)

30 40 50 60 7020Temperature (∘C)

0

2

4

6

8

10

12

Thre

shol

d vo

ltage

(V)

5 15minus5minus15

Voltage (V)

minus010

minus005

000005010

Curr

ent (

mA

)

V2 th

(V2)

Figure 13 Threshold voltage as a function of temperature for theTa-MoOx-Au switching structure and the temperature dependenceof (119881th)

2 (lower inset) in compliancewith (3) I-V curve at RT (upperinset)

formation of a switching channel However for the Mooxide films prepared by vacuum deposition the processesof electroforming and switching were more stable whichallowed in this case observation of the transformation of I-V curves at a temperature change It was found that as thetemperature increased the threshold voltage was reducedAt 119879 = 119879

119900sim 55ndash65∘C the NDR region degeneration

commenced at 119879 asymp 60ndash70∘C 119881th rarr 0 and at still highertemperatures the switching effect no longer occurred Inthis case the switching mechanism might be described interms of the ldquocritical temperaturerdquo model (Figure 13) It issupposed [53] that in the case of Mo like in other TMO-based structures formation of a channel also takes placeand this channel should consist of a material exhibiting MITwhich is the reason for switching with an S-shaped current-voltage characteristic (Figure 12)

A brief review of the materials with MIT in the familyof molybdenum compounds presented in [53] shows that themost suitable candidate for the role of such a channel-formingcompound is Mo

8O23

because in this case the value of 1198791199051

almost coincides with the above reported experimentallymeasured 119879

0 It should be noted that formation of other

compounds of molybdenum (eg pyrochlores bronzes sul-fides or chalcogenide glasses) exhibiting MITs with similarorder of magnitude transition temperatures [64ndash68 70] isimpossible because of the lack of the necessary chemicalelements (ie rare earths alkali metals or hydrogen sulfurand tellurium) in the phase composition of both the oxidefilm and the metal electrodes (Au Ta and Mo)

In conclusion the results presented in this subsection onswitching from the HR state to the LR state with an S-NDRin molybdenum oxides obtained by both thermal vacuumdeposition and electrochemical anodic oxidation show thatthe switching effect is due to apparently an insulator-to-metal phase transition in the switching channel consistingcompletely or partly of the lower oxide Mo

8O23 formed in

the initial film during the process of electroforming Thecurrent flowing through the channel heats it up to the MIT

temperature 1198791199051= 315K [62] and the structure switches into

the metallic low-resistance stateThus the channels consisting of this lower oxide are

formed in initial Mo oxide films during preliminary elec-troforming Electrical forming results in the changes inoxygen stoichiometry conditioned by the ionic processes inan electric field close to the MOM structure breakdown fieldThis picture is quite similar to what is observed inmany otherTMOs exhibiting the insulator-to-metal transitions

232 Metal-Insulator Transition and Switching in ManganeseDioxide Manganese dioxide is one of the most interestinginorganic materials because of its wide range of applica-tions In particular nanostructured MnO

2has received great

attention due to its high specific surface area functionalproperties and potential applications as molecular and ionselective membranes in capacitors Li-ion batteries andcatalysts [77] Originally MnO

2has been widely used as a

cathode material for oxide-semiconductor capacitors basedon tantalum niobium and aluminium oxides and the mostimportant properties of the material for this application areits high conductivity and ability to undergo a thermal phasetransition into the lower valence states accompanied by evo-lution of atomic oxygen while the resistance increases by 3-4orders of magnitude (see eg [54] and references therein)Much attention is currently paid to various other propertiesof MnO

2 such as for example the electrochromic effect

[78] thermopower wave phenomenon [79] supercapacitivebehaviour [80] andmemory and threshold switching [54 8182] Also there are a number of papers [83ndash85] describing ananomaly in theMnO

2conductivity near theNeel temperature

which is shown to be associated with the metal-insulatortransition [52] That is why the electrical properties of MnO

2

are of special scientific interest and applied importanceThe most common methods for manganese oxide prepa-

ration are the pyrolytic decomposition of manganese nitrateelectrochemical method hydrothermal synthesis in a mag-netic field and chemical deposition [54 86ndash89] Due to awide range of possible valence states of cations the structureand phase composition of manganese oxides are determinedby the synthesis conditions and process temperature Man-ganese dioxide has many crystallographic forms (120572- 120573- 120574-120575- 120576- and 120582-MnO

2) that connect MnO

6octahedron units to

each other in different ways and have different characters ofspatial alternation of the octahedra filled by Mn atoms andempty octahedra [54 77 90ndash94]

The crystal structure of the 120573-MnO2phase (Figure 14) is a

tetragonal modification of the rutile structural type P4mnmsymmetry group which represents a slightly distorted close-packed hexagonal lattice of oxygen ions [93] Filled octahedraare bound by two common edges in columns oriented alongthe 119888 axis and octahedra of adjacent columns are bound bytheir vertices (Figure 14(c)) Manganese atoms are arrangedin positions 2(a) (000) and oxygen atoms in positions 4(f )(xx0) Because there are vacancies in the oxygen packingthe formula unit can be written as MnO

2minus119910where the

nonstoichiometry index is in the range 119910 = 001ndash010depending on the synthesis method [93]

12 Advances in Condensed Matter Physics

Mn

O

(a)

a

b

c

(b)

O2O4

O1O3

Mn2

Mn1

Mn1998400

O3998400

O4998400

(c)

Figure 14 Crystal structure of manganese dioxide (a) MnO6

octahedron connection in 120573-MnO2(b) [90ndash94] and projection of

octahedron binding onto the ab plane [93]

As to the lower manganese oxides MnO and Mn3O4are

known to be theMott insulatorswith relatively high resistivity[90] and Mn

2O3shows p-type semiconducting properties

MnO2is an n-type semiconductor and antiferromagnetic

with the Neel temperature 119879119873= 925 K [91] Conductivity of

manganese dioxide is higher than that of MnO and Mn2O3

by several orders of magnitude At temperatures above 723Kmanganese dioxide loses oxygen and transforms intoMn

2O3

which is accompanied by the transformation of the crystallinestructure from the tetragonal crystal system of the rutile typeinto the complex large-period cubic lattice (119886 = 94gt) and alarge number of formula units per unit cell [54 92 93]

In this subsection we present the results on electricalproperties of manganese dioxide particularly the natureof the 120573-MnO

2conductivity at low temperatures in its

interrelation with characteristic features of the material crys-talline structure and the metal-insulator phase transitionin this compound as well The effect of electrical switchingwith current-voltage characteristics of both N- and S-typehas been found in thin-film MOM structures on the basisof manganese oxides Possible mechanisms of switching interms of the MIT and thermistor effects are discussed

Mn oxide samples under study have been obtained bythree methods anodic oxidation and vacuum evaporation(thin films) as well as by pyrolysis [54] Thin films ofmanganese dioxide were deposited by means of thermalevaporation onto glass substrates covered by a SnO

2layer

using a VUP-5 vacuum setup the film thickness was 119889 =

250 nmAlso thin films ofmanganese oxidewere obtained byelectrochemical oxidation of metal Mn in the KNO

3-NaNO

3

eutectic melt (see Section 21) at 119879 = 600K at a constantvoltage of about 2V for 3min the current density diminishedfrom 200 to 100mAcm2 during the oxidation process Foranodic oxide films on Mn the value of 119889 was sim100 nm Bulksamples of manganese dioxide were obtained by multipledecomposition (pyrolysis) of manganese nitrate at 119879 = 670Kon a glass-ceramic substrate or on a tantalum sheetmetal withthe subsequent separation from the substrate [92 93] Thetotal coating thickness was about 1mm

The manganese oxide samples were characterized by X-ray diffraction (XRD) using a DRON-6 diffractometer inCuK120572and FeK

120572radiation The characteristics of the atomic

structure of pyrolytic manganese dioxide were refined by thefull-profile analysis of the XRD patterns of polycrystallinesamples [93]The resistivity of pyrolyticMnO

2wasmeasured

in the temperature range 15 to 300K bymeans of a four-probetechnique both DC and AC (in a frequency range from 50 to104Hz) in a Gifford-McMahon cycle cryorefrigerator [54]We also measured electrical conductivity in the range T =293ndash423K the Hall effect in the magnetic field of 23 T andthe Seebeck coefficient (thermoelectromotive force thermo-emf ) The dynamic current-voltage (I-V) characteristics ofthe thin-film MOM structures were measured by oscillo-graphic method using an AC sinusoidal signal

The XRD patterns of the manganese oxide samples arepresented in Figures 15 and 16 The vacuum-deposited filmsare amorphous and represent a mixture of 120573- and 120574-MnO

2

(Figure 16) The results of the full-profile analysis show thatthe pyrolytic MnO

2samples (Figure 15) are composed of

the finely dispersed 120573-MnO2phase with the traces of 120574-

MnO2 120576-MnO

2 and Mn

2O3phases The periods of the

tetragonal unit cell of 120573-MnO2are 119886 = 119887 = 4401 A and

119888 = 2872 A The oxygen coordinates in 4119891 positions (seediscussion of the crystal structure above and Figure 14) arefound to be119909 = 0302 Calculations of the oxygen-manganeseinteratomic distances show [93] that the oxygen octahedron

Advances in Condensed Matter Physics 13

330222

040231

212202

112

130002

220

121

120

111

110

101

020

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 80 100 12002120579∘

Figure 15 XRD (Cu K120572radiation) pattern of pyrolytic MnO

2

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 8002120579∘ Fe

120573-MnO2

120574-MnO2

Experiment

Figure 16 XRD (Fe K120572radiation) pattern of Mn oxide film and

reference spectra of crystalline MnO2samples

is compressed along the (100) direction which connects theoctahedron vertices This deformation results in an increaseof the overlap of electron119901 orbitals of oxygen and119889 orbitals ofmanganese and can form the additional splitting of electronlevels in the crystal field leading to the appearance of unpairedelectrons [94]

The measurements of the conductivity temperaturedependence Hall effect and thermo-emf show that man-ganese dioxide is the electron semiconductor with conductiv-ity of about 1Ωminus1cmminus1 and mobility of sim10 cm2Vsdots The Hallmeasurements give the carrier density ofsim1018 cmminus3 which isclose to the density values in degenerate semiconductorsTheactivation energy of conductivity is sim01 eV and the band gapwidth is equal to 2 eV [90] The estimated value of the Fermienergy from the thermo-emf temperature dependence is inthe range of 002 to 005 eV which also indicates the degener-ate character of the electron gasThe nonstoichiometry indexdetermined by the XRD peaks which are not contributed

by the manganese atoms that is by those with the oddsum of indexes is 119910 = 006 Such nonstoichiometry providesthe concentration of trap states of about 1017-1018 cmminus3which correlates with the above mentioned Hall-effect-basedmeasurements of electron density

Such high vacancy concentration allows us to considerthe nonstoichiometric 120573-MnO

2as a heavily doped semicon-

ductor with a subband of impurity levels which provides afeasibility of the out-of-band electron transfer at low tem-peratures The structural distortions high nonstoichiometryand as a consequence sufficiently high concentration ofimpurity states cause the density state tails near the bandedges similarly to those in heavily doped semiconductorsHowever at room and higher temperatures the conduction isdetermined by the activation mechanism Thus the electronstructure and a low mobility of charge carriers promotethe manifestation of different charge transfer mechanismsin different temperature ranges namely both the hoppingmechanism and the activation one

The electron capturing oxygen vacancies create mixedvalence states of manganese cations (Mn3+ndashMn4+) Interest-ingly the mixed valence of Mn ions is also characteristic ofmanganites Ln

1minus119910Sr119910MnO3[95] where Ln is La or another

rare-earth element possessing the effect of colossal magne-toresistance (CMR) In these compounds the mixed valenceof manganese is attained via doping It had been deemed thatholes introduced by strontium are localized at manganeseions that is the Mn4+ ions with concentration 119910 are formedHowever recent X-ray emission studies have shown that boththe chemical shift and the exchange splitting of the emissionX-ray Mn K

1205731line are almost the same in the range 119910 lt 04ndash

05 as is the case in Mn2O3 and then they decrease quickly

to the values characteristic of MnO2[96] which suggests that

the introduced holes are localized at oxygen atoms in the holedoping region (at relatively low 119910) and atmanganese atoms inthe electron doping region that is at higher 119910 values

The temperature dependence of conductivity is presentedin Figure 17 The resistance peak observed in the figure ina temperature range of 80ndash90K is the result of the phasetransition of 120573-MnO

2from a semiconducting state to a metal

state upon decreasing the temperature to 15 K [54] The tem-perature region of the transition is close to the known Neeltransition from the paramagnetic state into the ferromagneticone for manganese dioxide The temperature dependenceof resistance indicates thus the MIT to occur in MnO

2 In

the temperature range from 300 to 80K (Figure 17) thisdependence does not correspond to the exponential one yetit fits well with the linear dependence in theMott coordinatesln(119877) sim 119879

14 which indicates the hopping conductivitymechanism over the polyvalent states ofmanganese ions witha distance between the centres of 25ndash35gt [92] However inthe temperature range from 90 to 15 K the dependence ofln119877 on ln119879 is almost linear with the slope of about unity(ie 120597 ln119877120597 ln119879 asymp 1) which is characteristic of the metallicconductionThus the character of conductivity ofmanganesedioxide indicates the presence of the MIT at 119879

119888sim 80K (on

cooling)

14 Advances in Condensed Matter Physics

CoolingHeating

40 80 120 160 2000T (K)

0

2

4

6

8

10

Resis

tivity

(Ohm

timescm

)

Figure 17 Temperature dependence of AC (70Hz) resistivity ofpyrolytic MnO

2

In the low temperature region manganese dioxide is anantiferromagnetwith the helical spin ordering [97]The inter-action between the magnetic ions of manganese which leadsto the antiferromagnetic state occurs through the intermedi-ate interaction with diamagnetic oxygen ions which weakensthe exchange interaction The conductivity increases proba-bly due to exceeding the energy of the exchange interactionby the thermal energy as the temperature increases whichleads to an increase in the number of unpaired electrons inthe paramagnetic state As the temperature further increasesthe conductivity continues to rise and the Mott hoppingmechanism of charge transfer becomes predominant Similarcharacter of the temperature dependence in ferromagneticdegenerate semiconductors has previously been described[85 98] for substoichiometric (oxygen-deficient) europiummonoxide The transition from the highly conductive stateinto the insulating state occurs in such semiconductors uponvarying the type of magnetic ordering or its destruction

For EuO1minus119910

lowering the peak magnitude in the 119877(119879)

dependence is associatedwith a decrease in the concentrationof impurities (oxygen vacancies) In magnetic semicon-ductors the phase transition is associated both with themagnetoelectric effects and with the variation in the electricpolarization under the action of the magnetic field at theantiferromagnetic transition [98] The dielectric constant formanganese dioxide is equal to sim10 but the effective dielectricconstant can decrease near 119879

119888by a factor of several times

thereby affecting the mobility of carriers located in the tailsof the density of states near the band edge and promotingtheir delocalization at the phase transition temperatureManganese dioxide also belongs to this group of substanceshowever the phase transition in MnO

2reported here can be

also described in terms of the Mott transition [24]According to the Mott criterion electrons delocalize if

the distance between the atoms 119899minus13 becomes comparable

with their atomic radius 119886119860 where 119886

119860is associated with the

Bohr radius 119886119861= ℏ2120576me2The static permittivity 120576 is replaced

by the effective permittivity which takes into account theexchange interaction of the spins of conduction electronswith orbitalmagneticmoments of atoms At the temperature-induced Mott MIT the orbital radius 119886

119861decreases near 119879 =

119879119888thereby providing the fulfillment of the Mott criterion at a

given level of impurity centres [24 98] The transition fromthe metallic state into the semiconductor state is possible insuch semiconductors as the temperature increases Thus theMIT in manganese dioxide is brought about by temperaturevariation

In conclusion we note that the phase transition describedabove is inverse (reentrant) MIT that is the metallic phaseis low-temperature while the high-temperature state is insu-lating This is rather rare yet not unique and unusualphenomenon In most cases (eg in vanadium dioxide) thelow-temperature phase is insulating and on heating abovea certain temperature 119879

119888 the material becomes metallic for

VO2 this transition temperature is 119879

119888= 340K The inverse

transitions are observed in such compounds as the abovementioned EuO

1minus119910 NiS2Se Y2O3minus119910

and LaMnO3films [24

31 52 85 98 99] Also the high-temperature Mott transi-tion from paramagnetic metal to paramagnetic insulator inV2O3Cr is an inverse transition with the resistivity peak at

119879119888sim 350K for a chromium concentration of around 1 at

[24 51] and in mixed valence CMR-manganites the sharpresistivity peak has been shown to be caused by the AndersonMIT [95]

It is known that many TMOs exhibit electrical switchingassociated with MITs [28] For the anodic oxide films onMn the study of the effect of electrical switching in thin-film Mn-MnO

2-Au sandwich structures showed that the S-

type switching was not observed in contrast to for examplethe similar structures based on oxides of vanadium andsome other transition metals [28] Instead switching withthe N-shaped I-V characteristic occurred after EF at 119879 lt

80K (Figure 18(a)) In addition the EF process in the Mn-based structures was hindered likewise for example for thestructures based on yttrium oxide [31] that is the breakdowntook place more often It should be noted that EF at roomtemperature always led to breakdown and the switchingeffect had never been observed in this case As was arguedin [54] this switching effect was associated with the MIT inMnO2

On the other hand in the films obtained by vacuumsputtering we have observed S-type switching at roomtemperature (Figure 18(b)) The threshold voltage is of theorder of 1 V and almost independent of temperature up to 119879

= 375KThis situation resembles that with yttrium oxide where

both S-type and N-type switching has been observed too[31] One can assume that switching with the S-shapedI-V curves is due to the so-called ldquothermistor effectrdquo Itis well known that the current flowing through a solidgenerates Joule heat resulting in an increased temperatureIn materials with a negative TCR a rising temperatureinduces a current enhancement and an increased powerdissipation resulting in a farther temperature increase Thispositive electrothermal feedback causes the appearance of anNDR and accordingly an S-shaped I-V characteristic [2]

Advances in Condensed Matter Physics 15

minus15

minus10

minus5

0

5

10

15Cu

rren

t (m

A)

0500 10 15minus10 minus05minus15

Voltage (V)

(a)

minus2

minus1

0

1

2

Curr

ent (

mA

)

10 2minus2 minus1

Voltage (V)

(b)

Figure 18 (a) I-V characteristic of anodic oxide film on manganese at T = 77K (b) I-V characteristic of vacuum-deposited MnO2at 119879 =

293K

In some cases this process might by modified by high-fieldeffects such as Schottky injection impact ionization Poole-Frenkel effect and Zener or avalanche breakdown Notethat unlike a conventional thermistor with an Arrhenius-like conductivity law manganese oxide exhibits a weaker119877(119879) dependence characteristic of the hopping conductivitymechanism which seems to account for the observed weaktemperature dependence of the threshold voltage

An alternative mechanism for the S-type switching effectmay be connected with a possible high-temperature usual(ie not inverse)MIT in somemanganese oxide As is knownEF (see Section 22) leads to the formation of a filament ofhighly conducting material a switching channel Similarlyto what is observed for Mo oxide (Section 231) and otherTMOs (Sections 21 and 22) we suppose that the compositionof this channel differs from the material of the initial oxidefilm since its conductivity noticeably exceeds that of anunformed structure In view of such a plentiful set of phasesand crystal structures in the Mn-O system one can supposethat the channelmight consist of nonstoichiometric120573-MnO

2

some other polymorphic modifications of manganese diox-ide or lower Mn oxides which might undergo a MIT underthe action of either temperature or electric field Howeverthis question obviously requires additional investigation inparticularmeasurements of119877(119879)dependences and switchingproperties at higher temperatures If this assumed high-temperature MIT would occur in for example nonstoichio-metric 120573-MnO

2 one could expect observation of double-

NDR I-V characteristics in such samples at low temperaturesanalogously to those in V

2O3Cr (Figure 9) where this effect

is due to the MITs [29] with the only difference being thatin the case of MnO

2this curve should be N-S-shaped (unlike

the S-N-shaped one in Figure 9) since in chromium-dopedvanadium sesquioxide the inverse MIT is high-temperatureas opposed to MnO

2which as we discussed above (see

Figure 17) exhibits the inverse MIT at low temperaturesNote however that the discussed high-temperature MIT

in 120573-MnO2minus119910

may be unobservable under the temperature

change in equilibrium conditions but displays itself onlyunder the applied electric field as the S-type electricalswitching effect because the transition temperature is closeto or higher than the temperature of MnO

2decomposition

(723K) Such a nonequilibrium transition occurs at switchingin those materials where the usual temperature-inducedMITwith a well-defined 119879

119905does not take place for example in

CGSs for which the equilibrium transition temperature 1198791199050

is higher than 119879119892 while in a high electric field 119879

119905(119864) lt 119879

1199050

might be lower than 119879119892 where 119879

119892is the temperature of the

glass-crystal transition and119864 is the electric field strength [30]Summarizing we have studied the electrical properties

(conductivity temperature dependence and Hall and Seebeckeffects) of the 120573 phase of manganese dioxide obtained bypyrolysis thermal vacuum evaporation and anodic oxida-tion The change of conductivity mechanisms dependingon temperature in a range of 450ndash25K has been shownand the metal-insulator phase transition at low (lt90K)temperatures has been revealed The specific feature of thistransition described in terms of the Mott mechanism isthat the metal phase exists at low temperatures while athigher temperatures the material is a semiconductor withthe hopping conductivity over the mixed valence states ofmanganese ions

The low-temperature switching effect with an NDR andN-shaped current-voltage characteristic associated with thephase transition in manganese dioxide has been found in theMOM two-terminal devices based on anodicMn oxide filmsOn the contrary the devices based on vacuum-depositedfilms have been found to exhibit an S-NDR at room andhigher temperatures which is suggested to be caused byeither the thermistor effect or a high-temperature MIT innonstoichiometric 120573-MnO

2

It should be emphasized that the low-temperature MITin 120573-MnO

2with 119879

119905= 70ndash80K is the inverse Mott transition

which is akin for instance to the transition in V2O3Cr

at 119879119905= 190ndash385K (for chromium dopant concentration in

the range of 05ndash18 at) [51] We thus assume that farther

16 Advances in Condensed Matter Physics

5 10 150Voltage (V)

0

1

2

3

4

5

6

7

8Cu

rren

t (m

A)

(a)ΔV

th(V

)

0

1

2

3

1 2 3 4 5 6 7 80W (at )

(b)

Figure 19 I-V curve (a) of Au-V2minus119910

W119910O5times 119899H2O-Au sandwich structure with119910= 003 and119881th scattering as a function of tungsten admixture

percentage 119910 (b) [104 105]

investigations of the phase transition in manganese dioxidedescribed in this paper are a rather interesting and topicalscientific problem since manganese dioxide can serve as amodel object for studying such inverse metal-insulator phasetransitions

Finally we note that the results presented in this sectionindicate the possibility of application of manganese oxide asa material for thin film sandwich switching devices Deviceswith NDR (N- and S-shaped I-V characteristics) have poten-tial applications in microelectronics as switches memoryelements and microsensors (these issues will be discussedin more detail below in Section 4) Particularly manganeseoxide microswitches [82] can be utilized for implementationof neuristors built with Mott-transition-based memristors[100]

24 Effect of Doping It is only natural that the systemsexhibiting the NDR effects possess a high applied potential inelectronics [2 4 8 18 100 101] yet the stage of EF is a weaklink of chain in the technology process Note that the formingprocess may be brought about by laser irradiation [102] notby applying of electric field In the case of laser treatment(or ldquolaser formingrdquo unlike the above described electricalforming) the parameters of the structures are characterizedby the absence of the scatter that is the I-V characteristics ofall structures are almost identical [103] One more demerit tobe avoided is the scatter in switching parameters (the value of119881th first of all) and their instability during operation In thissubsection we discuss the issues concerning the switchingparameter stabilization by means of doping

In the work [104] we have studied the switching effectin the MOM structures on the basis of W-doped V

2O5-gel

filmsThese structures require preliminary EF similar to thatin anodic oxide films resulting in formation of a conducting

channel within the initial dielectric xerogel filmThe channelconsists of vanadiumdioxide and switching is associatedwiththe insulator-to-metal transition in VO

2 As was shown in

[104 105] for the pure (undoped) V2O5-gel the switching

parameters vary in a wide range because the phenomenonof EF is statistical in nature (like electrical breakdown) andits statistical character shows itself as a spread in the observedthreshold voltages of the ensuing structures that is actuallyat multiple measurements 119881th = ⟨119881th⟩ plusmn Δ119881th

It has been shown [104] that the statistical spread in valuesof the threshold parameters can be minimized by means ofdoping (Figure 19) Unsophisticated reasoning could accountfor this result for pure V

2O5-gel electroforming leads to

formation of VO2with 119879

119905= 340K and each switching

event requires heating up and cooling down from roomtemperature to 119879

119905 this thermal cycling can modify the

peripheral regions of the channel which leads to the changeof the switching threshold voltage On the other hand forthe samples with a high concentration of W the MIT issuppressed [104] and switching is degenerated Betweenthese two outermost points an optimum should exist Asone can see from Figure 19 this optimal value correspondsto 3 at of W that is for V

097W003

O2the switching

parameters are the most stableThe transition temperature ofV097

W003

O2is lower than that for pure vanadium dioxide

and hence the magnitude of the aforesaid thermal cyclingis decreased which results in an increase of stability of theswitching parameters

Next we have studied the effect of doping on switchingin AOFs on Ti [29] These films were obtained in 5 watersolution of citric acid (C

6H8O7) in volt-static regime at 119881

119886

= 20V The samples were doped with aluminium by meansof adding soluble Al-containing substances to the electrolyte

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

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talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

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Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

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[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

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[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

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[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

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[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

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Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

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[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

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[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

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3thin

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3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

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Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

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2rdquo Journal of

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switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

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4)2I

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4O11

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Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

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perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

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1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

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semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

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3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

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[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

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[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

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2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

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24 Advances in Condensed Matter Physics

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2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

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2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

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[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

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2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

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2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

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AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

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AstrophysicsJournal of

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Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

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Soft MatterJournal of

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ThermodynamicsJournal of

Advances in Condensed Matter Physics 3

the case of amorphous thin film structures switching channelformation can occur via crystallization of an amorphous filmstoichiometric changes diffusion of the electrode materialinto the film or ionization of deep traps All of these changesusually refer to a localized modification of the structurein the area of the channel The modification of the initialstructure during the forming process is the most importantfactor determining the subsequent switching operation Thisis because in most cases forming creates a ldquonew devicerdquo(within the original structure) whose characteristics deter-mine the ensuing threshold or memory switching [18 22]

In TMOs a set of valence states associated with theexistence of unfilled 119889-shells in the atoms of transitionmetals leads to formation of several oxide phases withdifferent properties ranging from metallic to insulating Onthe other hand it is specifically the behaviour of 119889-electronsin the compounds of transition metals that is responsiblefor the unique properties of these materials causing strongelectron-electron correlations which play an important rolein the mechanisms of such phenomena as for examplemetal-insulator transitions (MITs) high-119879

119888superconductiv-

ity colossal magnetoresistance and multiferroicity whichare inherent to many TMOs [23ndash26] That is TMOs exhibitan astonishing array of functionalities that result from acombination of the strongly polarizable metal-oxygen bondand strong electron correlations [25]

In our works [4 22 27ndash29] it has been shown thatswitching in a number of TMOs with the S-NDR exhibitsseveral common features Particularly in most cases theswitching effect is associated with the insulator-to-metaltransition in an electric field The channels consisting oflower oxides exhibiting MITs are formed in an initial oxidefilm during the process of EF

In many TMOs the switching mechanism has beenshown to be associated with an electronically induced MottMIT occurring in conditions of the nonequilibrium carrierdensity excess under the applied electric field The requiredincrease in electron density under the action of electric fieldmight be caused by the Poole-Frenkel effect [30] or someother high-field-assisted charge carrier generation effectssuch as avalanche ionization and Zener breakdown as wellas Schottky tunnel or avalanche injection from contacts andso forth

This review focuses on earlier obtained results currentresearch the state of the art and recent progress in the field ofscience and applications of the phenomenon of monostablethreshold switching in oxides of transition metals We startby discussing the switching effects inMOM structures on thebasis of anodic oxide films (Sections 21 and 22) and then turnto recent results concerning electrical switching in Mn andMo oxides obtained by deposition in vacuum (Section 23)Effects of doping to stabilize the switching parameters andunify the electroforming process are described in Section 24and Section 3 is devoted to various physical mechanisms atplay which could be responsible for the NDR behaviouremphasizing the particular relationship between the switch-ing effect and MIT electronically induced Mott transitionfirst of all Further in Section 4 we discuss applied poten-tialities of the TMO-based thin film devices exhibiting the

NDR phenomena and finally in Section 5 we will try to for-mulate some conclusions and outlook concerning the topicdiscussed It should be stressed that the scope of the review isnot to describe comprehensively all the results reported in theliterature but rather to sketch out the main pertinent worksand discuss the physical mechanisms involved in the phe-nomenon of electrical switching in transition metal oxides

2 Overview of Experimental Results

21 Switching in Anodic Oxide Films In this section wepresent our results [4 22 27ndash31] on electroforming andswitching in thin film MOM structures with oxides oftransition metals (V Ti Fe Nb Mo W Hf Zr Mn Y andTa) obtained by electrochemical anodic oxidation Anodicoxidation permits the synthesis of high quality homogeneousdielectric oxide films [32] and as a rule anodic oxide films(AOFs) are amorphous

The sandwich devices under study were fabricated by oxi-dation of themetal substrates both polished foils and vacuumdeposited layers Au electrodes were vacuum-evaporatedonto the surfaces of oxide films to complete the MOM struc-ture (Figure 3(a)) The spring-loaded point contacts made ofgildedwire 05mm in diameter were also usedThe oxidationwas carried out electrochemically under anodic polarizationin an electrolyte Ta Nb W Zr and Hf were anodized in01 N aqueous solutions of phosphoric and sulphuric acids[32] while for oxidation of vanadium and molybdenum theacetone-based electrolyte was used [33] Fe Ti Mn andseveral of Nb and Ta samples were anodized in a KNO

3+

NaNO3eutectic melt [34] at 570ndash620K Anodic oxidation of

yttrium was carried out as described in [31] The oxide filmthicknesses were typically from 50 to 200 nm

The current-voltage characteristics of the initial struc-tures are nonlinear and slightly asymmetric The resistanceat zero bias measured with the point contact is in the range107ndash108Ω for the vanadium anodic oxide which is the mosthighly conductive among all the materials studied Whenthe amplitude of the applied voltage reaches the formingvoltage 119881

119891 a sharp and irreversible increase in conductivity

is observed and the 119868(119881) curve becomes S-shaped Withincreasing current the I-V characteristicmay change until theparameters of the switching structure are finally stabilizedThe process outlined above is qualitatively similar to EF ofthe switching devices based on amorphous semiconductors[18] The forming voltage depends on the temperature (119881

119891

increases upon cooling) and film thickness The thicker thefilm the higher the required 119881

119891 The value of 119881

119891correlates

with the anodizing voltage 119881119886(because 119889 is proportional to

119881119886) A similar correlation is characteristic of the AOF break-

down the breakdown voltage is also of the order of 119881119886[32]

Thus the first stage of the forming does not differfrom the conventional electrical breakdown of oxide filmsHowever if the postbreakdown current is limited this resultsin formation of a switching channel rather than a breakdownchannel The latter would be expected to have metallic-like conductivity and no negative resistance in the I-Vcharacteristic It is quite evident that the phase compositionof this switching channel must differ from the material of the

4 Advances in Condensed Matter Physics

1

2

3 4

(a)

00 05 10 15 20 250

20

40

60

80

100

Voltage (V)Cu

rren

t (120583

A)

Vth

(b)

Figure 3 (a) The sandwich switching structure (schematic) (1) vanadium metal substrate (2) anodic oxide film (3) Au electrical contactand (4) switching channel (VO

2 as will be shown below in Section 22) (b) the I-V characteristic after EF for one of the samples at room

temperature

initial oxide film because the channel conductivity exceedsthat of an unformed structure by several orders ofmagnitude

Forming does not always result in an S-type characteris-tic In some instances a transition of the structure to a highconductivity state (119877 sim 100Ω) with ohmic behaviour takesplace that is in this case breakdown rather than formingoccurs Breakdown is more probable in Ta

2O5 WO3 HfO

2

and MoO3films while in the V- and Nb-based structures

it is the electroforming that results in the S-shaped I-Vcurves in most cases The anodic films on Ti and Fe holdan intermediate position S-type switching has not beenobserved in Zr Y and Mn oxide films EF of W- Fe- andHf-based structures was carried out at 77 K because at roomtemperature breakdown took place and no switching effectswere observed The characteristic feature of switching in TaMo Hf and to a lesser extent W oxide films is the instabilityof parameters and the gradual disappearance of the S-typeNDRunder the influence of current flow and thermal cycling

The voltage-current characteristic for electroformedvanadium-AOF-metal structure is shown in Figure 3(b) Theparameters of the structures (threshold voltage 119881th andcurrent 119868th resistances of OFF and ON states) may varyby up to an order of magnitude from point to point forthe same specimen Such a wide range of variation of the119881th and 119877off values as well as the absence of correlationbetween these switching parameters and the parameters ofthe sandwich structures (the electrode material and area andthe film thickness) leads to the conclusion that resistanceand threshold parameters are mainly determined by theforming process Conditions of the forming process cannotbe unified in principle because the first stage of forming

is linked to breakdown which is statistical in nature As aresult the diameter and phase composition of the channel(and consequently its effective specific conductivity) varywith position in the sample This accounts for the scatterin the parameters and for the seeming absence of theirthickness dependence The I-V curves for Ti- Nb- and W-based structures are also shown in Figure 4

Similar behaviour has been observed for the other mate-rials On average for 119889 sim 100 nm a typical value of 119881this 1 to 10V that is the threshold field is 105ndash106 Vcm atroom temperature The greatest differences between theseoxides are observed when the temperature dependence oftheir threshold parameters such as119881th is measured Figure 5shows 119881th(119879) curves for the sandwich structures based oniron tungsten vanadium titanium and niobium For Ta

2O5

HfO2 and MoO

3 no reproducible results were obtained

because of instabilities of their voltage-current character-istics with temperature As the temperature increased 119881thdecreased tending to zero at some finite temperature 119879

119900

This is best exhibited by the vanadium and titanium oxidestructures The values of 119879

119900vary considerably for different

oxides but they are nearly identical for different structuresof the same oxide [28] For the Nb-Nb

2O5-metal structures

it was impossible to measure the 119881th(119879) relationship overthe whole temperature range because heating above 300∘Cinduced processes related to diffusion and change in thechannel phase composition leading to degradation of theswitching structure Nevertheless it is evident from Figure 5that for the niobium oxide 119879

119900exceeds 600K

As was mentioned above S-type switching has not beenobserved inZr Y andMnoxide films Instead thesematerialshave sometimes demonstrated N-NDR at 119879 = 293K (Zr and

Advances in Condensed Matter Physics 5

000102030405

Curr

ent (

mA

)

minus01

minus02

minus03

minus04

minus05

minus10minus20 minus05minus15 05 10 15 2000Voltage (V)

(a)

minus7minus6minus5minus4minus3minus2minus1

01234567

Curr

ent (

mA

)

minus15 minus10 minus5 5 10 150Voltage (V)

(b)

minus4

minus2

0

2

4

Curr

ent (

mA

)

minus10 minus6 minus4minus8 minus2 2 4 6 8 100Voltage (V)

(c)

Figure 4 Current-voltage characteristics of MOM structures with AOFs on (a) Ti (b) Nb and (c) W [29]

Y see Figure 6) or at 119879 = 77K (Mn oxide) The process ofelectroforming for these materials was hindered like that forTa Hf and Mo Switching in Mo and Mn oxides will also beadditionally discussed in Section 23 below

22 Switching as an Electrically DrivenMetal-Insulator Transi-tion Next we discuss the process of electroforming in moredetail The initial AOF represents as a rule a highest oxideof the metal (eg Nb

2O5in the case of niobium) However

lower oxides always exist near the AOF-metal interface inthe form of transition layers or as separate inclusions Thiscan be explained in terms of thermodynamics Consider thefollowing reaction

Nb + 2Nb2O5997888rarr 5NbO

2(1)

The change of the Gibbs (isobaric) potential for thisreaction is

Δ119866119903= ]2Δ1198662minus ]1Δ1198661 (2)

where Δ1198661and Δ119866

2are the standard isobaric potentials

of formation and ]1and ]

2are the numbers of moles of

oxides which take part in the reaction For Reaction (1) the

subscripts 1 and 2 in (2) are related to Nb2O5and NbO

2

respectively and Δ119866119903

= minus163 kJmol [28] Since Δ119866119903

lt 0Reaction (1) proceeds spontaneously and hence NbO

2is

always present at the Nb-Nb2O5interface

Transition metals exhibit multiple oxidation states andform a number of oxides Therefore it is obvious that thelower oxide to be formed is mainly that with the mini-mum Δ119866

119903 Figure 7 demonstrates the variation of Δ119866

119903(119909)

for Fe2O3 Nb2O5 V2O5 TiO2 and some other oxides in

reactions similar to (1) where 119909 is the stoichiometric indexof oxygen Δ119866

119903values were calculated using (2) the data

on Δ119866119900 for the calculations were taken from [35] The

minima in these curves correspond to Fe3O4 NbO

2 VO2

and Ti2O3 therefore these oxides form as intermediate

layers between the metal substrate and the correspondingoxide of highest valence Real systems are far from beinga plane parallel structure with two oxide layers hence thesuggested approach is rather oversimplifiedNevertheless theabove considerations show that formation of those oxidesis thermodynamically reasonable whether it is kineticallypossible can only be judged from experiment For exampleas was shown in [33] in AOF on vanadium the vanadiumdioxide layer may be rather thick and only a very thin film

6 Advances in Condensed Matter Physics

00

05

10

15

20

25

30

V (a

u)

1 2

3 4

5

200 300 400 500 600100T (K)

Figure 5 Threshold voltage in arbitrary units 119881 = 119881th(119879)119881th(1198791015840)

for theMOM structures on the basis of different oxides as a functionof ambient temperature (1) Fe (2)W (3)V (4)Ti and (5)Nb anodicoxideData for different samples have been averaged andnormalizedto a certain temperature 119879

1015840 which is different for different oxides[22 27 28]

0

5

10

15

20

25

30

35

Curr

ent (120583

A)

05 10 15 20 2500Voltage (V)

Figure 6 I-V curve with N-NDR of the structure metalY anodicoxidemetal [31]

near the outer boundary is close to the V2O5stoichiometry

The similar ordering of layers evidently exists in iron oxideparticularly it is known that in a thermal oxide of iron theFe3O4phase usually predominates [28] On the other hand

the AOFs on Nb and Ti mainly consist of Nb2O5and TiO

2

and NbO2or Ti2O3layers seem to be relatively thin [27 28]

For the W-WO3system a wide minimum of Δ119866

119903(119909) lies

in the range 119909 = 27ndash30 (Figure 7) the same behaviour seemsto be characteristic of the Mo-MoO

3system The calculation

for manganese oxides yields the minimum at 119909 = 15 that isfor Mn

2O3 The curve Δ119866

119903(119909) for uranium is also presented

just as an example note however that MITs have beenreported for lower uranium oxide U

4O9[36] For Zr Hf Ta

and Y such calculations have not been made because thereexist no clear data on the thermodynamic properties of thelower oxides of those metals

F1

F2F3

T1

T2

T11N1

N2

N3

W1W2

W3

W4

W5U5

V1

V2

V9

V10

V11

U1U2

U3 U4

M4

M1

M2 M3

900

800

700

600

500

400

300

200

100

0

minusΔGr

(kJm

ol)

15 20 25 3010X

V9998400

V3ndashV8

T2998400

Figure 7 Gibbs potential change Δ119866119903(per 1 g atom of metal) for

the reaction of the highest oxide with the metal substrate versus119909 the oxygen stoichiometric index of the lower oxide which isformed in this reaction Symbol indications are as follows (i) IronF1ndashFeO F2ndashFe

3O4 F3ndashFe

2O3 (ii) Niobium N1ndashNbO N2ndashNbO

2

N3ndashNb2O5 (iii) Titanium T1ndashTiO T2ndashTi

2O3 T3ndashT10ndashTi

119899O2119899minus1

(119899 = 3ndash10) T11ndashTiO2 (iv) Vanadium V1ndashVO V2ndashV

2O3 V3ndashV8ndash

V119899O2119899minus1

(119899 = 3ndash8) V9ndashVO2 V10ndashV

6O13 V11ndashV

2O5 (v) Tungsten

W1ndashWO2W2ndashW

18O49W3ndashW

10O29W4ndashW

50O148

W5ndashWO3 (vi)

Manganese M1ndashMnO M2ndashMn3O4 M3ndashMn

2O3 M4ndashMnO

2 (vii)

Uranium U1ndashUO2 U2ndashU

4O9 U3ndashU

3O7 U4ndashU

3O8 U5ndashUO

3 The

points T21015840 and V91015840 characterize a scatter due to the Δ1198660 data

difference [22 28]

During electroforming current-induced heating of thefilm under the electrode leads to a diffusion of both metalfrom the substrate into the film and oxygen from the outerlayer to the inner one Also the transport of metal andoxygen ions due to the applied electric field is possible Sinceduring electroforming (unlike thermal or electrochemicaloxidation) no external oxygen is present no reaction cantake place except the reduction of the highest oxide of AOFThe reduction results in growth of the channel consisting oflower oxide through the film from one electrode to anotherEvidently substances with the minimum Δ119866

119903value (see

Figure 7)will be predominant in the phase composition of thechannelThe current increase after formingmay cause furtherreduction of the channel material leading to a predominanceof the phases such as VO NbO and TiO Many of the lowestoxides of transition metals (mono- and suboxides) exhibitmetallic properties [23] the accumulation of these phases inthe channel will therefore lead to an irreversible increase inconductivity that is to breakdown

The above compounds (VO2 Fe3O4 Ti2O3 and NbO

2)

have one feature in common namely a metal-insulator phasetransition [24] The MIT phenomenon is characterized bythe sharp and reversible change in the conductivity at acertain temperature 119879

119905 for instance vanadium dioxide at

Advances in Condensed Matter Physics 7

1 2

3

0

1

2

3

4

5

6

240 260 280 300 320 340220T (K)

V2 th

(V2)

(a)

1

2

3

(V2th times 04)

420 440 460 480 500 520 540400T (K)

0

1

2

3

4

5

6

7

V2 th

(V2)

(b)

Figure 8 Squared threshold voltage as a function of temperature for (a) vanadium oxide-based switch and (b) titanium oxide (1) (2) and(3) three different samples

119879 lt 340K is a semiconductor at 119879 = 119879119905

= 340K theconductivity abruptly increases by 4-5 orders of magnitudeand above the transition temperature VO

2exhibits metallic

properties ForNbO2119879119905= 1070K Ti

2O3undergoes a gradual

transition in the range 400ndash600K and magnetite (Fe3O4)

is a semiconductor both above and below the Verwey tran-sition temperature (120K) though its resistivity decreaseson heating by two orders of magnitude at 119879 = 119879

119905 For the

switching devices based on these metals the temperatures 119879119900

coincide with the corresponding values of 119879119905(see Figure 5)

This suggests that the switching mechanism is caused by themetal-insulator transition

Electrical switching due to MIT has been first revealedfor vanadium dioxide [16 27 37ndash45] Switching in VO

2

is explained by the current-induced Joule heating of thesample up to 119879 = 119879

119905 which has been confirmed by the

direct IR-radiation measurements of the switching channeltemperature [38 45] In these early works switching hasbeen observed in single crystals [39] and planar thin filmdevices [37 38 45] as well as in vanadate glasses [40 41]VO2-containing ceramics [44] and V

2O5-gel films [42 43]

When as-prepared samples do not consist of pure vanadiumdioxide preliminary electroforming is required resulting inthe formation of the VO

2-containing channel [40 42] The

latter examples as well as the discussed AOFs here supportthe assumption that the formation of vanadium dioxide isthermodynamically preferable at a V

2O5-V interface [22

27] For such samples the threshold voltage decreases withtemperature and reaches zero at 119879 = 119879

119905sim 340K

In this case the switchingmechanismmight be describedin terms of the ldquocritical temperaturerdquo model [29 37] (if theambient temperature is not much lower than 119879

119905)

119881th sim (119879 minus 119879119905)12

(3)

that is the squared threshold voltage linearly tends to zero at119879 rarr 119879

119905 see Figure 8 Switching elements for other transition

metal (FeW Ti and Nb) oxides exhibitingMIT are expected

to show similar behaviour but for different 119879119905rsquos which is

demonstrated by Figure 8(b) for Ti oxideThe switching effect in the WO

3-based sandwich struc-

tures can also be explained in terms of ametal-insulator tran-sition which occurs in nonstoichiometric WO

3minus119910(within a

very narrow interval of variable 119910) at 119879119905ranging from 160 to

280K [46] Because of the narrow interval of ldquoappropriaterdquostoichiometric compositions the S-type I-V characteristicis not likely to appear in tungsten trioxide and in mostcases breakdown occurs instead For switching structureson anodic films on W 119879

119900was found to lie around sim200K

(Figure 5) Therefore 119879119900may turn out to be equal to 119879

119905

Almost no data on MIT in molybdenum oxides are avail-able in the literature except for the transition in Mo

8O23

(MoO2875

) and the switching effect in molybdenum oxidewill be discussed in more detail in the next section Asto Ta and Hf oxides the formation of metastable loweroxides during electroforming should also be possible Theproperties of these oxides are practically unknown but somemetastable oxides of this type have been referred to forexample for the Ta-O system [47] Recently formation ofHfO119909[48] and TaO

119909[49] suboxides has been reported As

to Mn oxides it is known [23] that MnO and Mn3O4are

Mott insulators Mn2O3is a semiconductor and MnO

2is

also a semiconductor but it shows a change in electricalconductivity at 119879 = 119879

119873sim 90K (the Neel temperature) This

might account for the N-NDR effect in Mn oxide this issuewill also be more thoroughly investigated in the next section

Thus the experimental data on the switching effect in119889-metal oxide thin films can be explained in terms of theswitching mechanism driven by the MIT We can state thatin all cases the electrothermal and electrochemical processesduring electroforming are responsible for the switching chan-nel formation The channel consists of a material which canundergo a transition from semiconducting state to metallicstate at a certain temperature 119879

119905 For the V- Ti- Nb- and Fe-

based structures the possibility of formation of the channelsconsisting completely or partly of VO

2 Ti2O3 NbO

2 and

8 Advances in Condensed Matter Physics

Fe3O4 respectively is also confirmed by the thermodynamic

calculations In oxides of W and Mo switching may beassociated with MIT in the channels consisting of WO

3minus119909

and Mo8O23 The S-shaped voltage-current characteristic

is conditioned by the development of an electrothermalinstability in the channel When a voltage is applied thechannel is heated up to 119879 = 119879

119905(at 119881 = 119881th) by the current

and the structure undergoes a transition fromhigh-resistance(OFF) insulating state to low-resistance (ON) metallic state

In high electric fields (105ndash106 Vcm) the possible influ-ence of electronic effects on the MIT should be taken intoaccount A field-induced increase in charge carrier densitywill act to screen Coulomb interactions [12] leading to theelimination of the Mott-Hubbard energy gap at 119879 lt 119879

119905

Moreover a transition of this type may be important in thosematerials where the usual temperature-induced MIT with awell-defined 119879

119905does not take place for example in oxides

of Ta or Hf (and in CGS-based switching structures as well[50]) In the case of vanadium dioxide such a possibilityof the electronically induced MIT was suggested from theinjection experiments [22] and will be discussed also belowin connection with the transition mechanism in VO

2

To summarize the results presented above as well asthe other data on the switching in transition metal oxides[11ndash17 27ndash31] indicate that current instabilities with the S-type NDR exhibit several common features In particularfor each of the investigated materials there is a certain fixedtemperature 119879

119900 above which switching disappears At 119879 lt

119879119900 the threshold voltage decreases as the temperature rises

tending to zero at 119879 = 119879119900 Comparison of these temperatures

with the temperatures of MIT for some compounds (119879119905

=

120K for Fe3O4 sim200K for WO

3minus119909 340K for VO

2 sim500K

for Ti2O3 and 1070K for NbO

2) shows that the switching

effect is associated with the insulator-metal transition in anelectric field The channels consisting of these lower oxidesare formed in initial anodic films during the process ofpreliminary EF

And finally in conclusion of this section we would like todiscuss onemore vanadium oxide where the switching effectsare caused by MITs namely vanadium sesquioxide The I-Vcharacteristics of chromium-doped V

2O3shown in Figure 9

are distinctive in that they exhibit in a certain temperaturerange two regions of negative differential resistance both N-NDR and S-NDR The experimental data on the switchingeffect ofMOM structures based onV

2O3Cr can be explained

in terms of the switching mechanism driven by the variableMIT The S-shaped I-V characteristic is conditioned by thedevelopment of an electrothermal instability in the sampleWhen a voltage is applied the sample is heated by the currentup to 119879 = 119879

1199051(at the threshold voltage 119881 = 119881th119878) and

the structure undergoes a transition from a high-resistance(OFF-1) AFI state to a low-resistance (ON) PM state Asthe current in the ON state increases the sample is furtherheated and at 119879 = 119879

1199052(119868 = 119868th119873) the second transition

to the OFF-2 (or PI) state occurs [51] In the OFF-1 statethe plot of current versus the square root of the appliedvoltage is indicative of a Poole-Frenkel type of conductivityenhancement [52] (Figure 10)

12

34

0

20

40

60

80

100

120

140

160

180

Curr

ent (

mA

)

05 10 15 20 25 3000Voltage (V)

Figure 9 Current-voltage characteristics for V2O3doped with 12

at of Cr at different temperatures 1705 K (1) 1733 K (2) 2210 K(3) and 2655 K (4) [51]

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

Curr

ent (

A)

05 10 15 20 2500Square root of voltage (V05)

150K140K130K120K110K

100K90K80K70K60K

50K40K30K20K10K

Figure 10 Current versus voltage in Poole-Frenkel coordinates fora V2O3-based switching device [52]

23 Switching Effects and Metal-Insulator Transitions in MnandMoOxides In this section we consider electrical switch-ing in oxides of Mn and Mo obtained by vacuum depositionin comparison with those obtained by anodic oxidation [5354] It should be emphasized here that AOFs are (as a ruleexcept for some rare cases) amorphous [32 33] Therefore inMOM structures with anodic films the process of EF similarto that in CGSs usually takes place However in some cases(Mo Mn) as was described in previous sections we havefailed to obtain stable switching with anodic films and herewe present an alternative approach to this problem

Advances in Condensed Matter Physics 9

231 Electrical Switching in Thin Film Structures Based onMolybdenumOxide As inmost TMOs in the molybdenum-oxygen system there exist a number of oxides with variablevalence which are characterized by a wide diversity ofstructures and physical properties [53 55 56] MolybdenumtrioxideMoO

3has a structure based on layers of edge-sharing

distorted MoO6octahedra [23] Similar layered structures

are inherent in lower molybdenum oxides including MoO2

Mo18O52 Mo9O26 Mo8O23 Mo5O14 and Mo

17O47 as well

as 120578- and 120574-Mo4O11[55ndash57]

Stoichiometric MoO3 in its most thermodynamically

stable form 120572-MoO3 is an insulator with a band gap of sim3 eV

[23] During reduction by means of either oxygen deficiencyformation or introducing donor impurity atoms additionaldonor levels near the conduction band bottom appear andthe reduced oxide behaves therefore as a semiconductorPolycrystalline MoO

3 as well as a single crystal has a grey-

yellow colour and the minimum value of the absorption edgeis 440 nm which corresponds to the smallest value of theband gap of 28 eV [58] thus the band gap depends upon thestoichiometry and the crystalline state [53] The conductivityvalues of molybdenum oxides range from dielectric MoO

3

to semiconductor Mo18O52

(resistivity 120588 = 781Ωsdotcm)and down to metal 120578-V]

411

(120588 = 166 times 10minus4Ωsdotcm) [58]Molybdenum dioxide also exhibits metallic properties [2358] and at room temperature 120588 = 88 times 10minus5Ωsdotcm for bulkMoO2samples [55]

Because of their special physical and chemical propertiesmolybdenum oxides are used in various electronic devicessuch as electrochromic displays and indicators reversiblecathodes of lithium batteries gas sensors and memoryelements [55ndash61] Metal-insulator transitions have also beenobserved in some oxides of molybdenum and related com-pounds [62ndash70] In particular Mo

8O23

exhibits a two-stagestructural MIT with formation of a charge-density wave at1198791199051= 315 K and 119879

1199052= 285K [62] However as far as we know

no data are available in the literature concerning thresholdswitching associated with these transitions except for ourwork [53] In this work we have particularly noted thatmemory switching is observed inmany TMOs molybdenumoxides included [4 9 59 60]

The most discussed models in the literature for theReRAMmechanism in oxide structures are those based eitheron the growth and rupture of a metal filament inside theoxide matrix under the action of electric current or onthe redox processes responsible for the formation of somehigh-conductivity or low-conductivity local inclusions cor-responding to particular oxygen stoichiometry [4] The MITideology is also sometimes involved to explain the propertiesof the structures and the memory switching mechanismtherein [71] In any case thememory switching phenomenonseems to be associated with the ion transport [4 9] It isalso appropriate to mention here the works discussing thememory effects in a material with MIT (vanadium dioxide)associated with the presence of hysteresis in the temperaturedependence of conductivity [72]

On the other hand as was shown in the previous sectionmonostable threshold switching (with no memory effects)

associated with the MIT is also characteristic of a numberof TMOs That is why the study of threshold switchingin molybdenum oxide and its possible connection withthe phenomenon of MIT is of considerable scientific andpractical interest

Thinfilm samples ofmolybdenumoxidewere obtained bytwo ways anodic oxidation and thermal vacuum evaporation[53] Anodization of molybdenum was carried out in anacetone-based electrolyte (22 g of benzoic acid plus 40mLof saturated borax aqueous solution per litre of acetone[33 73]) AOFs on Mo might include lower molybdenumoxides for example Mo

4O11andMoO

2with a relatively high

electronic conductivity [53] The fact that the anodic oxideon molybdenum contained lower oxides was confirmed byexperimental data in the work [74] where it was shown thatthe degree of oxidation (valence state) of molybdenum in anAOF is less than six Also this was confirmed theoretically interms of the thermodynamics of the process the formation ofunsaturated oxide MoO

2had been shown to be energetically

more favourable than MoO3[75]

Vacuum deposited film samples were fabricated by ther-mal evaporation of MoO

3powder at residual pressure of

10minus4 Torr onto polished tantalum plates or glass substratesfor electrical and optical studies respectivelyThe thicknessesof the films were determined from the transmission andreflection interference spectra measurements [76] and theywere found to lie in the range from 300 to 800 nm

The XRD pattern of a vacuum-deposited molybdenumoxide sample is presented in Figure 11(a) It is shown thatthe samples represent amorphousMoO

3with a slight oxygen

nonstoichiometry [53] Anodic oxide films on Mo are alsoamorphous (or amorphous-microcrystalline according tothe literature data [73]) but their composition correspondsas described above to ratherMoO

2or other lower oxides and

not to the highest oxide MoO3

Figure 11(b) shows the reflection and transmission spec-tra for one of the samples obtained by vacuum depositionThe experimental data processing using the envelope of theinterference extrema [76] yields the film thickness of (620 plusmn

50) nm and the absorption edge around 120582 asymp 400 nm indi-cates the fact that the oxide phase composition correspondsto MoO

3with a band gap of sim3 eV

Before electroforming initial structures demonstrate thenonlinear and slightly asymmetric current-voltage charac-teristics with no NDR regions When the amplitude of theapplied voltage reaches the forming voltage a sharp andirreversible increase in conductivity is observed and theI(V) curve becomes S-shaped (Figure 12) With increas-ing current the I-V characteristic may change until theparameters of the switching structure are finally stabilizedThe process outlined above is qualitatively similar to theelectroforming of the switching devices based on other TMOs(see Section 22 above) We emphasize once again that thephase composition of the ensuing switching channel mustdiffer from the material of the pristine oxide film becausethe channel conductivity is higher than that of the unformedstructure by several orders of magnitude

The current-voltage characteristics of vacuum-depositedfilms and those of anodic films are qualitatively similar but

10 Advances in Condensed Matter Physics

1

2

20 40 60 8002120579∘

0100200300400500600700800900

I (co

unts

s)

(a)

1

2

3

0

20

40

60

80

100

T (

)

300 400 500 600 700 800 900 1000 1100200Wavelength (nm)

(b)

Figure 11 (a) XRD pattern of the molybdenum oxide film (1) andV]3powder (2) (b) Optical spectra of the sample obtained by vacuum

deposition (1) transmission coefficient of substrate (glass) (2) transmittance and (3) reflectance of Mo oxide film on glass [53]

0 5 10minus5minus10

Voltage (V)

minus016

minus012

minus008

minus004

000

004

008

012

016

Curr

ent (

mA

)

(a)

minus072 072 216 360minus216minus360

Voltage (V)

minus064

minus048

minus032

minus016

000

016

032

048

064

Curr

ent (

mA

)

(b)

Figure 12 Current-voltage characteristics ofMOMstructures with vacuum-deposited (a) and anodic (b)Mo oxide films after electroforming

there is a significant quantitative difference in their thresholdparameters For instance the switching voltage 119881th for theAOF based structures is sim2V (Figure 12(b)) whereas forthe structures on the basis of the films prepared by thermalevaporation119881th is sim10V (Figure 12(a))This difference can beexplained by the difference in thickness of the films

For anodic oxide the thickness can be estimated fromFaradayrsquos law [53]

119889 =

120583119868119886119905

4119890120588119878119873119860

(4)

where 120583 = 128 gmol and 120588 = 65 gcm3 are respectivelythe molar mass and density of V]

2and 119890 and 119873

119860are the

unit charge and Avogadro constant For 119868119886= 70m0 and 119905 =

10min (4) yields 119889 sim 20 nm which is significantly less thanthe typical thickness of the vacuum deposited films and as aresult the threshold voltage for AOFs is also lower than thatfor the films obtained by thermal evaporation

As is discussed in [53] switching is not observed inthinner films obtained by vacuum evaporation (119889 lt 100 nm)

in contrast to ultrathin AOFs A plausible reason for thismight be the fact that relatively thin vacuum depositedfilms contain through-the-thickness conducting defects dueto local stoichiometry variations whereas such defects areimpossible in anodic films because they are grown in highelectric field during anodic oxidation and an appearanceof such defects would interrupt the film growth processThis is similar to what is observed in vanadium oxide inpolycrystalline vanadium dioxide films such pin-hole defectsare usually associated with the grain boundaries which couldundergo local metallization due to strain or nonstoichiom-etry That is why it had been difficult to observe switchingin sandwich MOM structures with sputtered or thermallyoxidized polycrystalline VO

2films and most studies had

been conducted with planar thin-film structures whilst foranodically oxidized VO

2the switching effect has then been

observed in a sandwich structure for the first time in [16]Next we note that unlike the most other TMOs the

process of electroforming in Mo-based structures was hin-dered as was mentioned above in Section 21 that is theconventional electrical breakdown often occurred not the

Advances in Condensed Matter Physics 11

020406080

100120

30 40 50 60 7020Temperature (∘C)

30 40 50 60 7020Temperature (∘C)

0

2

4

6

8

10

12

Thre

shol

d vo

ltage

(V)

5 15minus5minus15

Voltage (V)

minus010

minus005

000005010

Curr

ent (

mA

)

V2 th

(V2)

Figure 13 Threshold voltage as a function of temperature for theTa-MoOx-Au switching structure and the temperature dependenceof (119881th)

2 (lower inset) in compliancewith (3) I-V curve at RT (upperinset)

formation of a switching channel However for the Mooxide films prepared by vacuum deposition the processesof electroforming and switching were more stable whichallowed in this case observation of the transformation of I-V curves at a temperature change It was found that as thetemperature increased the threshold voltage was reducedAt 119879 = 119879

119900sim 55ndash65∘C the NDR region degeneration

commenced at 119879 asymp 60ndash70∘C 119881th rarr 0 and at still highertemperatures the switching effect no longer occurred Inthis case the switching mechanism might be described interms of the ldquocritical temperaturerdquo model (Figure 13) It issupposed [53] that in the case of Mo like in other TMO-based structures formation of a channel also takes placeand this channel should consist of a material exhibiting MITwhich is the reason for switching with an S-shaped current-voltage characteristic (Figure 12)

A brief review of the materials with MIT in the familyof molybdenum compounds presented in [53] shows that themost suitable candidate for the role of such a channel-formingcompound is Mo

8O23

because in this case the value of 1198791199051

almost coincides with the above reported experimentallymeasured 119879

0 It should be noted that formation of other

compounds of molybdenum (eg pyrochlores bronzes sul-fides or chalcogenide glasses) exhibiting MITs with similarorder of magnitude transition temperatures [64ndash68 70] isimpossible because of the lack of the necessary chemicalelements (ie rare earths alkali metals or hydrogen sulfurand tellurium) in the phase composition of both the oxidefilm and the metal electrodes (Au Ta and Mo)

In conclusion the results presented in this subsection onswitching from the HR state to the LR state with an S-NDRin molybdenum oxides obtained by both thermal vacuumdeposition and electrochemical anodic oxidation show thatthe switching effect is due to apparently an insulator-to-metal phase transition in the switching channel consistingcompletely or partly of the lower oxide Mo

8O23 formed in

the initial film during the process of electroforming Thecurrent flowing through the channel heats it up to the MIT

temperature 1198791199051= 315K [62] and the structure switches into

the metallic low-resistance stateThus the channels consisting of this lower oxide are

formed in initial Mo oxide films during preliminary elec-troforming Electrical forming results in the changes inoxygen stoichiometry conditioned by the ionic processes inan electric field close to the MOM structure breakdown fieldThis picture is quite similar to what is observed inmany otherTMOs exhibiting the insulator-to-metal transitions

232 Metal-Insulator Transition and Switching in ManganeseDioxide Manganese dioxide is one of the most interestinginorganic materials because of its wide range of applica-tions In particular nanostructured MnO

2has received great

attention due to its high specific surface area functionalproperties and potential applications as molecular and ionselective membranes in capacitors Li-ion batteries andcatalysts [77] Originally MnO

2has been widely used as a

cathode material for oxide-semiconductor capacitors basedon tantalum niobium and aluminium oxides and the mostimportant properties of the material for this application areits high conductivity and ability to undergo a thermal phasetransition into the lower valence states accompanied by evo-lution of atomic oxygen while the resistance increases by 3-4orders of magnitude (see eg [54] and references therein)Much attention is currently paid to various other propertiesof MnO

2 such as for example the electrochromic effect

[78] thermopower wave phenomenon [79] supercapacitivebehaviour [80] andmemory and threshold switching [54 8182] Also there are a number of papers [83ndash85] describing ananomaly in theMnO

2conductivity near theNeel temperature

which is shown to be associated with the metal-insulatortransition [52] That is why the electrical properties of MnO

2

are of special scientific interest and applied importanceThe most common methods for manganese oxide prepa-

ration are the pyrolytic decomposition of manganese nitrateelectrochemical method hydrothermal synthesis in a mag-netic field and chemical deposition [54 86ndash89] Due to awide range of possible valence states of cations the structureand phase composition of manganese oxides are determinedby the synthesis conditions and process temperature Man-ganese dioxide has many crystallographic forms (120572- 120573- 120574-120575- 120576- and 120582-MnO

2) that connect MnO

6octahedron units to

each other in different ways and have different characters ofspatial alternation of the octahedra filled by Mn atoms andempty octahedra [54 77 90ndash94]

The crystal structure of the 120573-MnO2phase (Figure 14) is a

tetragonal modification of the rutile structural type P4mnmsymmetry group which represents a slightly distorted close-packed hexagonal lattice of oxygen ions [93] Filled octahedraare bound by two common edges in columns oriented alongthe 119888 axis and octahedra of adjacent columns are bound bytheir vertices (Figure 14(c)) Manganese atoms are arrangedin positions 2(a) (000) and oxygen atoms in positions 4(f )(xx0) Because there are vacancies in the oxygen packingthe formula unit can be written as MnO

2minus119910where the

nonstoichiometry index is in the range 119910 = 001ndash010depending on the synthesis method [93]

12 Advances in Condensed Matter Physics

Mn

O

(a)

a

b

c

(b)

O2O4

O1O3

Mn2

Mn1

Mn1998400

O3998400

O4998400

(c)

Figure 14 Crystal structure of manganese dioxide (a) MnO6

octahedron connection in 120573-MnO2(b) [90ndash94] and projection of

octahedron binding onto the ab plane [93]

As to the lower manganese oxides MnO and Mn3O4are

known to be theMott insulatorswith relatively high resistivity[90] and Mn

2O3shows p-type semiconducting properties

MnO2is an n-type semiconductor and antiferromagnetic

with the Neel temperature 119879119873= 925 K [91] Conductivity of

manganese dioxide is higher than that of MnO and Mn2O3

by several orders of magnitude At temperatures above 723Kmanganese dioxide loses oxygen and transforms intoMn

2O3

which is accompanied by the transformation of the crystallinestructure from the tetragonal crystal system of the rutile typeinto the complex large-period cubic lattice (119886 = 94gt) and alarge number of formula units per unit cell [54 92 93]

In this subsection we present the results on electricalproperties of manganese dioxide particularly the natureof the 120573-MnO

2conductivity at low temperatures in its

interrelation with characteristic features of the material crys-talline structure and the metal-insulator phase transitionin this compound as well The effect of electrical switchingwith current-voltage characteristics of both N- and S-typehas been found in thin-film MOM structures on the basisof manganese oxides Possible mechanisms of switching interms of the MIT and thermistor effects are discussed

Mn oxide samples under study have been obtained bythree methods anodic oxidation and vacuum evaporation(thin films) as well as by pyrolysis [54] Thin films ofmanganese dioxide were deposited by means of thermalevaporation onto glass substrates covered by a SnO

2layer

using a VUP-5 vacuum setup the film thickness was 119889 =

250 nmAlso thin films ofmanganese oxidewere obtained byelectrochemical oxidation of metal Mn in the KNO

3-NaNO

3

eutectic melt (see Section 21) at 119879 = 600K at a constantvoltage of about 2V for 3min the current density diminishedfrom 200 to 100mAcm2 during the oxidation process Foranodic oxide films on Mn the value of 119889 was sim100 nm Bulksamples of manganese dioxide were obtained by multipledecomposition (pyrolysis) of manganese nitrate at 119879 = 670Kon a glass-ceramic substrate or on a tantalum sheetmetal withthe subsequent separation from the substrate [92 93] Thetotal coating thickness was about 1mm

The manganese oxide samples were characterized by X-ray diffraction (XRD) using a DRON-6 diffractometer inCuK120572and FeK

120572radiation The characteristics of the atomic

structure of pyrolytic manganese dioxide were refined by thefull-profile analysis of the XRD patterns of polycrystallinesamples [93]The resistivity of pyrolyticMnO

2wasmeasured

in the temperature range 15 to 300K bymeans of a four-probetechnique both DC and AC (in a frequency range from 50 to104Hz) in a Gifford-McMahon cycle cryorefrigerator [54]We also measured electrical conductivity in the range T =293ndash423K the Hall effect in the magnetic field of 23 T andthe Seebeck coefficient (thermoelectromotive force thermo-emf ) The dynamic current-voltage (I-V) characteristics ofthe thin-film MOM structures were measured by oscillo-graphic method using an AC sinusoidal signal

The XRD patterns of the manganese oxide samples arepresented in Figures 15 and 16 The vacuum-deposited filmsare amorphous and represent a mixture of 120573- and 120574-MnO

2

(Figure 16) The results of the full-profile analysis show thatthe pyrolytic MnO

2samples (Figure 15) are composed of

the finely dispersed 120573-MnO2phase with the traces of 120574-

MnO2 120576-MnO

2 and Mn

2O3phases The periods of the

tetragonal unit cell of 120573-MnO2are 119886 = 119887 = 4401 A and

119888 = 2872 A The oxygen coordinates in 4119891 positions (seediscussion of the crystal structure above and Figure 14) arefound to be119909 = 0302 Calculations of the oxygen-manganeseinteratomic distances show [93] that the oxygen octahedron

Advances in Condensed Matter Physics 13

330222

040231

212202

112

130002

220

121

120

111

110

101

020

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 80 100 12002120579∘

Figure 15 XRD (Cu K120572radiation) pattern of pyrolytic MnO

2

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 8002120579∘ Fe

120573-MnO2

120574-MnO2

Experiment

Figure 16 XRD (Fe K120572radiation) pattern of Mn oxide film and

reference spectra of crystalline MnO2samples

is compressed along the (100) direction which connects theoctahedron vertices This deformation results in an increaseof the overlap of electron119901 orbitals of oxygen and119889 orbitals ofmanganese and can form the additional splitting of electronlevels in the crystal field leading to the appearance of unpairedelectrons [94]

The measurements of the conductivity temperaturedependence Hall effect and thermo-emf show that man-ganese dioxide is the electron semiconductor with conductiv-ity of about 1Ωminus1cmminus1 and mobility of sim10 cm2Vsdots The Hallmeasurements give the carrier density ofsim1018 cmminus3 which isclose to the density values in degenerate semiconductorsTheactivation energy of conductivity is sim01 eV and the band gapwidth is equal to 2 eV [90] The estimated value of the Fermienergy from the thermo-emf temperature dependence is inthe range of 002 to 005 eV which also indicates the degener-ate character of the electron gasThe nonstoichiometry indexdetermined by the XRD peaks which are not contributed

by the manganese atoms that is by those with the oddsum of indexes is 119910 = 006 Such nonstoichiometry providesthe concentration of trap states of about 1017-1018 cmminus3which correlates with the above mentioned Hall-effect-basedmeasurements of electron density

Such high vacancy concentration allows us to considerthe nonstoichiometric 120573-MnO

2as a heavily doped semicon-

ductor with a subband of impurity levels which provides afeasibility of the out-of-band electron transfer at low tem-peratures The structural distortions high nonstoichiometryand as a consequence sufficiently high concentration ofimpurity states cause the density state tails near the bandedges similarly to those in heavily doped semiconductorsHowever at room and higher temperatures the conduction isdetermined by the activation mechanism Thus the electronstructure and a low mobility of charge carriers promotethe manifestation of different charge transfer mechanismsin different temperature ranges namely both the hoppingmechanism and the activation one

The electron capturing oxygen vacancies create mixedvalence states of manganese cations (Mn3+ndashMn4+) Interest-ingly the mixed valence of Mn ions is also characteristic ofmanganites Ln

1minus119910Sr119910MnO3[95] where Ln is La or another

rare-earth element possessing the effect of colossal magne-toresistance (CMR) In these compounds the mixed valenceof manganese is attained via doping It had been deemed thatholes introduced by strontium are localized at manganeseions that is the Mn4+ ions with concentration 119910 are formedHowever recent X-ray emission studies have shown that boththe chemical shift and the exchange splitting of the emissionX-ray Mn K

1205731line are almost the same in the range 119910 lt 04ndash

05 as is the case in Mn2O3 and then they decrease quickly

to the values characteristic of MnO2[96] which suggests that

the introduced holes are localized at oxygen atoms in the holedoping region (at relatively low 119910) and atmanganese atoms inthe electron doping region that is at higher 119910 values

The temperature dependence of conductivity is presentedin Figure 17 The resistance peak observed in the figure ina temperature range of 80ndash90K is the result of the phasetransition of 120573-MnO

2from a semiconducting state to a metal

state upon decreasing the temperature to 15 K [54] The tem-perature region of the transition is close to the known Neeltransition from the paramagnetic state into the ferromagneticone for manganese dioxide The temperature dependenceof resistance indicates thus the MIT to occur in MnO

2 In

the temperature range from 300 to 80K (Figure 17) thisdependence does not correspond to the exponential one yetit fits well with the linear dependence in theMott coordinatesln(119877) sim 119879

14 which indicates the hopping conductivitymechanism over the polyvalent states ofmanganese ions witha distance between the centres of 25ndash35gt [92] However inthe temperature range from 90 to 15 K the dependence ofln119877 on ln119879 is almost linear with the slope of about unity(ie 120597 ln119877120597 ln119879 asymp 1) which is characteristic of the metallicconductionThus the character of conductivity ofmanganesedioxide indicates the presence of the MIT at 119879

119888sim 80K (on

cooling)

14 Advances in Condensed Matter Physics

CoolingHeating

40 80 120 160 2000T (K)

0

2

4

6

8

10

Resis

tivity

(Ohm

timescm

)

Figure 17 Temperature dependence of AC (70Hz) resistivity ofpyrolytic MnO

2

In the low temperature region manganese dioxide is anantiferromagnetwith the helical spin ordering [97]The inter-action between the magnetic ions of manganese which leadsto the antiferromagnetic state occurs through the intermedi-ate interaction with diamagnetic oxygen ions which weakensthe exchange interaction The conductivity increases proba-bly due to exceeding the energy of the exchange interactionby the thermal energy as the temperature increases whichleads to an increase in the number of unpaired electrons inthe paramagnetic state As the temperature further increasesthe conductivity continues to rise and the Mott hoppingmechanism of charge transfer becomes predominant Similarcharacter of the temperature dependence in ferromagneticdegenerate semiconductors has previously been described[85 98] for substoichiometric (oxygen-deficient) europiummonoxide The transition from the highly conductive stateinto the insulating state occurs in such semiconductors uponvarying the type of magnetic ordering or its destruction

For EuO1minus119910

lowering the peak magnitude in the 119877(119879)

dependence is associatedwith a decrease in the concentrationof impurities (oxygen vacancies) In magnetic semicon-ductors the phase transition is associated both with themagnetoelectric effects and with the variation in the electricpolarization under the action of the magnetic field at theantiferromagnetic transition [98] The dielectric constant formanganese dioxide is equal to sim10 but the effective dielectricconstant can decrease near 119879

119888by a factor of several times

thereby affecting the mobility of carriers located in the tailsof the density of states near the band edge and promotingtheir delocalization at the phase transition temperatureManganese dioxide also belongs to this group of substanceshowever the phase transition in MnO

2reported here can be

also described in terms of the Mott transition [24]According to the Mott criterion electrons delocalize if

the distance between the atoms 119899minus13 becomes comparable

with their atomic radius 119886119860 where 119886

119860is associated with the

Bohr radius 119886119861= ℏ2120576me2The static permittivity 120576 is replaced

by the effective permittivity which takes into account theexchange interaction of the spins of conduction electronswith orbitalmagneticmoments of atoms At the temperature-induced Mott MIT the orbital radius 119886

119861decreases near 119879 =

119879119888thereby providing the fulfillment of the Mott criterion at a

given level of impurity centres [24 98] The transition fromthe metallic state into the semiconductor state is possible insuch semiconductors as the temperature increases Thus theMIT in manganese dioxide is brought about by temperaturevariation

In conclusion we note that the phase transition describedabove is inverse (reentrant) MIT that is the metallic phaseis low-temperature while the high-temperature state is insu-lating This is rather rare yet not unique and unusualphenomenon In most cases (eg in vanadium dioxide) thelow-temperature phase is insulating and on heating abovea certain temperature 119879

119888 the material becomes metallic for

VO2 this transition temperature is 119879

119888= 340K The inverse

transitions are observed in such compounds as the abovementioned EuO

1minus119910 NiS2Se Y2O3minus119910

and LaMnO3films [24

31 52 85 98 99] Also the high-temperature Mott transi-tion from paramagnetic metal to paramagnetic insulator inV2O3Cr is an inverse transition with the resistivity peak at

119879119888sim 350K for a chromium concentration of around 1 at

[24 51] and in mixed valence CMR-manganites the sharpresistivity peak has been shown to be caused by the AndersonMIT [95]

It is known that many TMOs exhibit electrical switchingassociated with MITs [28] For the anodic oxide films onMn the study of the effect of electrical switching in thin-film Mn-MnO

2-Au sandwich structures showed that the S-

type switching was not observed in contrast to for examplethe similar structures based on oxides of vanadium andsome other transition metals [28] Instead switching withthe N-shaped I-V characteristic occurred after EF at 119879 lt

80K (Figure 18(a)) In addition the EF process in the Mn-based structures was hindered likewise for example for thestructures based on yttrium oxide [31] that is the breakdowntook place more often It should be noted that EF at roomtemperature always led to breakdown and the switchingeffect had never been observed in this case As was arguedin [54] this switching effect was associated with the MIT inMnO2

On the other hand in the films obtained by vacuumsputtering we have observed S-type switching at roomtemperature (Figure 18(b)) The threshold voltage is of theorder of 1 V and almost independent of temperature up to 119879

= 375KThis situation resembles that with yttrium oxide where

both S-type and N-type switching has been observed too[31] One can assume that switching with the S-shapedI-V curves is due to the so-called ldquothermistor effectrdquo Itis well known that the current flowing through a solidgenerates Joule heat resulting in an increased temperatureIn materials with a negative TCR a rising temperatureinduces a current enhancement and an increased powerdissipation resulting in a farther temperature increase Thispositive electrothermal feedback causes the appearance of anNDR and accordingly an S-shaped I-V characteristic [2]

Advances in Condensed Matter Physics 15

minus15

minus10

minus5

0

5

10

15Cu

rren

t (m

A)

0500 10 15minus10 minus05minus15

Voltage (V)

(a)

minus2

minus1

0

1

2

Curr

ent (

mA

)

10 2minus2 minus1

Voltage (V)

(b)

Figure 18 (a) I-V characteristic of anodic oxide film on manganese at T = 77K (b) I-V characteristic of vacuum-deposited MnO2at 119879 =

293K

In some cases this process might by modified by high-fieldeffects such as Schottky injection impact ionization Poole-Frenkel effect and Zener or avalanche breakdown Notethat unlike a conventional thermistor with an Arrhenius-like conductivity law manganese oxide exhibits a weaker119877(119879) dependence characteristic of the hopping conductivitymechanism which seems to account for the observed weaktemperature dependence of the threshold voltage

An alternative mechanism for the S-type switching effectmay be connected with a possible high-temperature usual(ie not inverse)MIT in somemanganese oxide As is knownEF (see Section 22) leads to the formation of a filament ofhighly conducting material a switching channel Similarlyto what is observed for Mo oxide (Section 231) and otherTMOs (Sections 21 and 22) we suppose that the compositionof this channel differs from the material of the initial oxidefilm since its conductivity noticeably exceeds that of anunformed structure In view of such a plentiful set of phasesand crystal structures in the Mn-O system one can supposethat the channelmight consist of nonstoichiometric120573-MnO

2

some other polymorphic modifications of manganese diox-ide or lower Mn oxides which might undergo a MIT underthe action of either temperature or electric field Howeverthis question obviously requires additional investigation inparticularmeasurements of119877(119879)dependences and switchingproperties at higher temperatures If this assumed high-temperature MIT would occur in for example nonstoichio-metric 120573-MnO

2 one could expect observation of double-

NDR I-V characteristics in such samples at low temperaturesanalogously to those in V

2O3Cr (Figure 9) where this effect

is due to the MITs [29] with the only difference being thatin the case of MnO

2this curve should be N-S-shaped (unlike

the S-N-shaped one in Figure 9) since in chromium-dopedvanadium sesquioxide the inverse MIT is high-temperatureas opposed to MnO

2which as we discussed above (see

Figure 17) exhibits the inverse MIT at low temperaturesNote however that the discussed high-temperature MIT

in 120573-MnO2minus119910

may be unobservable under the temperature

change in equilibrium conditions but displays itself onlyunder the applied electric field as the S-type electricalswitching effect because the transition temperature is closeto or higher than the temperature of MnO

2decomposition

(723K) Such a nonequilibrium transition occurs at switchingin those materials where the usual temperature-inducedMITwith a well-defined 119879

119905does not take place for example in

CGSs for which the equilibrium transition temperature 1198791199050

is higher than 119879119892 while in a high electric field 119879

119905(119864) lt 119879

1199050

might be lower than 119879119892 where 119879

119892is the temperature of the

glass-crystal transition and119864 is the electric field strength [30]Summarizing we have studied the electrical properties

(conductivity temperature dependence and Hall and Seebeckeffects) of the 120573 phase of manganese dioxide obtained bypyrolysis thermal vacuum evaporation and anodic oxida-tion The change of conductivity mechanisms dependingon temperature in a range of 450ndash25K has been shownand the metal-insulator phase transition at low (lt90K)temperatures has been revealed The specific feature of thistransition described in terms of the Mott mechanism isthat the metal phase exists at low temperatures while athigher temperatures the material is a semiconductor withthe hopping conductivity over the mixed valence states ofmanganese ions

The low-temperature switching effect with an NDR andN-shaped current-voltage characteristic associated with thephase transition in manganese dioxide has been found in theMOM two-terminal devices based on anodicMn oxide filmsOn the contrary the devices based on vacuum-depositedfilms have been found to exhibit an S-NDR at room andhigher temperatures which is suggested to be caused byeither the thermistor effect or a high-temperature MIT innonstoichiometric 120573-MnO

2

It should be emphasized that the low-temperature MITin 120573-MnO

2with 119879

119905= 70ndash80K is the inverse Mott transition

which is akin for instance to the transition in V2O3Cr

at 119879119905= 190ndash385K (for chromium dopant concentration in

the range of 05ndash18 at) [51] We thus assume that farther

16 Advances in Condensed Matter Physics

5 10 150Voltage (V)

0

1

2

3

4

5

6

7

8Cu

rren

t (m

A)

(a)ΔV

th(V

)

0

1

2

3

1 2 3 4 5 6 7 80W (at )

(b)

Figure 19 I-V curve (a) of Au-V2minus119910

W119910O5times 119899H2O-Au sandwich structure with119910= 003 and119881th scattering as a function of tungsten admixture

percentage 119910 (b) [104 105]

investigations of the phase transition in manganese dioxidedescribed in this paper are a rather interesting and topicalscientific problem since manganese dioxide can serve as amodel object for studying such inverse metal-insulator phasetransitions

Finally we note that the results presented in this sectionindicate the possibility of application of manganese oxide asa material for thin film sandwich switching devices Deviceswith NDR (N- and S-shaped I-V characteristics) have poten-tial applications in microelectronics as switches memoryelements and microsensors (these issues will be discussedin more detail below in Section 4) Particularly manganeseoxide microswitches [82] can be utilized for implementationof neuristors built with Mott-transition-based memristors[100]

24 Effect of Doping It is only natural that the systemsexhibiting the NDR effects possess a high applied potential inelectronics [2 4 8 18 100 101] yet the stage of EF is a weaklink of chain in the technology process Note that the formingprocess may be brought about by laser irradiation [102] notby applying of electric field In the case of laser treatment(or ldquolaser formingrdquo unlike the above described electricalforming) the parameters of the structures are characterizedby the absence of the scatter that is the I-V characteristics ofall structures are almost identical [103] One more demerit tobe avoided is the scatter in switching parameters (the value of119881th first of all) and their instability during operation In thissubsection we discuss the issues concerning the switchingparameter stabilization by means of doping

In the work [104] we have studied the switching effectin the MOM structures on the basis of W-doped V

2O5-gel

filmsThese structures require preliminary EF similar to thatin anodic oxide films resulting in formation of a conducting

channel within the initial dielectric xerogel filmThe channelconsists of vanadiumdioxide and switching is associatedwiththe insulator-to-metal transition in VO

2 As was shown in

[104 105] for the pure (undoped) V2O5-gel the switching

parameters vary in a wide range because the phenomenonof EF is statistical in nature (like electrical breakdown) andits statistical character shows itself as a spread in the observedthreshold voltages of the ensuing structures that is actuallyat multiple measurements 119881th = ⟨119881th⟩ plusmn Δ119881th

It has been shown [104] that the statistical spread in valuesof the threshold parameters can be minimized by means ofdoping (Figure 19) Unsophisticated reasoning could accountfor this result for pure V

2O5-gel electroforming leads to

formation of VO2with 119879

119905= 340K and each switching

event requires heating up and cooling down from roomtemperature to 119879

119905 this thermal cycling can modify the

peripheral regions of the channel which leads to the changeof the switching threshold voltage On the other hand forthe samples with a high concentration of W the MIT issuppressed [104] and switching is degenerated Betweenthese two outermost points an optimum should exist Asone can see from Figure 19 this optimal value correspondsto 3 at of W that is for V

097W003

O2the switching

parameters are the most stableThe transition temperature ofV097

W003

O2is lower than that for pure vanadium dioxide

and hence the magnitude of the aforesaid thermal cyclingis decreased which results in an increase of stability of theswitching parameters

Next we have studied the effect of doping on switchingin AOFs on Ti [29] These films were obtained in 5 watersolution of citric acid (C

6H8O7) in volt-static regime at 119881

119886

= 20V The samples were doped with aluminium by meansof adding soluble Al-containing substances to the electrolyte

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

Films vol 97 no 2 pp 129ndash143 1982[46] R Collongues La Non-Stoechiometrie Masson Paris France

1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

9 no 5 pp 391ndash396 2014[67] B Sun W Zhao Y Liu and P Chen ldquoResistive switching effect

of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

1990[70] S Mukherjee S Karmakar H Sakata and B K Chaudhuri

ldquoLow-temperature metallic behavior of amorphous MoO3-

TeO2thin filmsrdquo Journal of Applied Physics vol 97 no 12 Article

ID 123707 2005[71] AMottaghizadeh Q Yu P L Lang A Zimmers andH Aubin

ldquoMetal oxide resistive switching evolution of the density ofstates across the metal-insulator transitionrdquo Physical ReviewLetters vol 112 no 6 Article ID 066803 2014

[72] R Xie C T Bui B Varghese et al ldquoAn electrically tunedsolid-state thermalmemory based onmetal-insulator transitionof single-crystalline VO

2nanobeamsrdquo Advanced Functional

Materials vol 21 no 9 pp 1602ndash1607 2011

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

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AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

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Physics Research International

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Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

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Soft MatterJournal of

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PhotonicsJournal of

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Journal of

Biophysics

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ThermodynamicsJournal of

4 Advances in Condensed Matter Physics

1

2

3 4

(a)

00 05 10 15 20 250

20

40

60

80

100

Voltage (V)Cu

rren

t (120583

A)

Vth

(b)

Figure 3 (a) The sandwich switching structure (schematic) (1) vanadium metal substrate (2) anodic oxide film (3) Au electrical contactand (4) switching channel (VO

2 as will be shown below in Section 22) (b) the I-V characteristic after EF for one of the samples at room

temperature

initial oxide film because the channel conductivity exceedsthat of an unformed structure by several orders ofmagnitude

Forming does not always result in an S-type characteris-tic In some instances a transition of the structure to a highconductivity state (119877 sim 100Ω) with ohmic behaviour takesplace that is in this case breakdown rather than formingoccurs Breakdown is more probable in Ta

2O5 WO3 HfO

2

and MoO3films while in the V- and Nb-based structures

it is the electroforming that results in the S-shaped I-Vcurves in most cases The anodic films on Ti and Fe holdan intermediate position S-type switching has not beenobserved in Zr Y and Mn oxide films EF of W- Fe- andHf-based structures was carried out at 77 K because at roomtemperature breakdown took place and no switching effectswere observed The characteristic feature of switching in TaMo Hf and to a lesser extent W oxide films is the instabilityof parameters and the gradual disappearance of the S-typeNDRunder the influence of current flow and thermal cycling

The voltage-current characteristic for electroformedvanadium-AOF-metal structure is shown in Figure 3(b) Theparameters of the structures (threshold voltage 119881th andcurrent 119868th resistances of OFF and ON states) may varyby up to an order of magnitude from point to point forthe same specimen Such a wide range of variation of the119881th and 119877off values as well as the absence of correlationbetween these switching parameters and the parameters ofthe sandwich structures (the electrode material and area andthe film thickness) leads to the conclusion that resistanceand threshold parameters are mainly determined by theforming process Conditions of the forming process cannotbe unified in principle because the first stage of forming

is linked to breakdown which is statistical in nature As aresult the diameter and phase composition of the channel(and consequently its effective specific conductivity) varywith position in the sample This accounts for the scatterin the parameters and for the seeming absence of theirthickness dependence The I-V curves for Ti- Nb- and W-based structures are also shown in Figure 4

Similar behaviour has been observed for the other mate-rials On average for 119889 sim 100 nm a typical value of 119881this 1 to 10V that is the threshold field is 105ndash106 Vcm atroom temperature The greatest differences between theseoxides are observed when the temperature dependence oftheir threshold parameters such as119881th is measured Figure 5shows 119881th(119879) curves for the sandwich structures based oniron tungsten vanadium titanium and niobium For Ta

2O5

HfO2 and MoO

3 no reproducible results were obtained

because of instabilities of their voltage-current character-istics with temperature As the temperature increased 119881thdecreased tending to zero at some finite temperature 119879

119900

This is best exhibited by the vanadium and titanium oxidestructures The values of 119879

119900vary considerably for different

oxides but they are nearly identical for different structuresof the same oxide [28] For the Nb-Nb

2O5-metal structures

it was impossible to measure the 119881th(119879) relationship overthe whole temperature range because heating above 300∘Cinduced processes related to diffusion and change in thechannel phase composition leading to degradation of theswitching structure Nevertheless it is evident from Figure 5that for the niobium oxide 119879

119900exceeds 600K

As was mentioned above S-type switching has not beenobserved inZr Y andMnoxide films Instead thesematerialshave sometimes demonstrated N-NDR at 119879 = 293K (Zr and

Advances in Condensed Matter Physics 5

000102030405

Curr

ent (

mA

)

minus01

minus02

minus03

minus04

minus05

minus10minus20 minus05minus15 05 10 15 2000Voltage (V)

(a)

minus7minus6minus5minus4minus3minus2minus1

01234567

Curr

ent (

mA

)

minus15 minus10 minus5 5 10 150Voltage (V)

(b)

minus4

minus2

0

2

4

Curr

ent (

mA

)

minus10 minus6 minus4minus8 minus2 2 4 6 8 100Voltage (V)

(c)

Figure 4 Current-voltage characteristics of MOM structures with AOFs on (a) Ti (b) Nb and (c) W [29]

Y see Figure 6) or at 119879 = 77K (Mn oxide) The process ofelectroforming for these materials was hindered like that forTa Hf and Mo Switching in Mo and Mn oxides will also beadditionally discussed in Section 23 below

22 Switching as an Electrically DrivenMetal-Insulator Transi-tion Next we discuss the process of electroforming in moredetail The initial AOF represents as a rule a highest oxideof the metal (eg Nb

2O5in the case of niobium) However

lower oxides always exist near the AOF-metal interface inthe form of transition layers or as separate inclusions Thiscan be explained in terms of thermodynamics Consider thefollowing reaction

Nb + 2Nb2O5997888rarr 5NbO

2(1)

The change of the Gibbs (isobaric) potential for thisreaction is

Δ119866119903= ]2Δ1198662minus ]1Δ1198661 (2)

where Δ1198661and Δ119866

2are the standard isobaric potentials

of formation and ]1and ]

2are the numbers of moles of

oxides which take part in the reaction For Reaction (1) the

subscripts 1 and 2 in (2) are related to Nb2O5and NbO

2

respectively and Δ119866119903

= minus163 kJmol [28] Since Δ119866119903

lt 0Reaction (1) proceeds spontaneously and hence NbO

2is

always present at the Nb-Nb2O5interface

Transition metals exhibit multiple oxidation states andform a number of oxides Therefore it is obvious that thelower oxide to be formed is mainly that with the mini-mum Δ119866

119903 Figure 7 demonstrates the variation of Δ119866

119903(119909)

for Fe2O3 Nb2O5 V2O5 TiO2 and some other oxides in

reactions similar to (1) where 119909 is the stoichiometric indexof oxygen Δ119866

119903values were calculated using (2) the data

on Δ119866119900 for the calculations were taken from [35] The

minima in these curves correspond to Fe3O4 NbO

2 VO2

and Ti2O3 therefore these oxides form as intermediate

layers between the metal substrate and the correspondingoxide of highest valence Real systems are far from beinga plane parallel structure with two oxide layers hence thesuggested approach is rather oversimplifiedNevertheless theabove considerations show that formation of those oxidesis thermodynamically reasonable whether it is kineticallypossible can only be judged from experiment For exampleas was shown in [33] in AOF on vanadium the vanadiumdioxide layer may be rather thick and only a very thin film

6 Advances in Condensed Matter Physics

00

05

10

15

20

25

30

V (a

u)

1 2

3 4

5

200 300 400 500 600100T (K)

Figure 5 Threshold voltage in arbitrary units 119881 = 119881th(119879)119881th(1198791015840)

for theMOM structures on the basis of different oxides as a functionof ambient temperature (1) Fe (2)W (3)V (4)Ti and (5)Nb anodicoxideData for different samples have been averaged andnormalizedto a certain temperature 119879

1015840 which is different for different oxides[22 27 28]

0

5

10

15

20

25

30

35

Curr

ent (120583

A)

05 10 15 20 2500Voltage (V)

Figure 6 I-V curve with N-NDR of the structure metalY anodicoxidemetal [31]

near the outer boundary is close to the V2O5stoichiometry

The similar ordering of layers evidently exists in iron oxideparticularly it is known that in a thermal oxide of iron theFe3O4phase usually predominates [28] On the other hand

the AOFs on Nb and Ti mainly consist of Nb2O5and TiO

2

and NbO2or Ti2O3layers seem to be relatively thin [27 28]

For the W-WO3system a wide minimum of Δ119866

119903(119909) lies

in the range 119909 = 27ndash30 (Figure 7) the same behaviour seemsto be characteristic of the Mo-MoO

3system The calculation

for manganese oxides yields the minimum at 119909 = 15 that isfor Mn

2O3 The curve Δ119866

119903(119909) for uranium is also presented

just as an example note however that MITs have beenreported for lower uranium oxide U

4O9[36] For Zr Hf Ta

and Y such calculations have not been made because thereexist no clear data on the thermodynamic properties of thelower oxides of those metals

F1

F2F3

T1

T2

T11N1

N2

N3

W1W2

W3

W4

W5U5

V1

V2

V9

V10

V11

U1U2

U3 U4

M4

M1

M2 M3

900

800

700

600

500

400

300

200

100

0

minusΔGr

(kJm

ol)

15 20 25 3010X

V9998400

V3ndashV8

T2998400

Figure 7 Gibbs potential change Δ119866119903(per 1 g atom of metal) for

the reaction of the highest oxide with the metal substrate versus119909 the oxygen stoichiometric index of the lower oxide which isformed in this reaction Symbol indications are as follows (i) IronF1ndashFeO F2ndashFe

3O4 F3ndashFe

2O3 (ii) Niobium N1ndashNbO N2ndashNbO

2

N3ndashNb2O5 (iii) Titanium T1ndashTiO T2ndashTi

2O3 T3ndashT10ndashTi

119899O2119899minus1

(119899 = 3ndash10) T11ndashTiO2 (iv) Vanadium V1ndashVO V2ndashV

2O3 V3ndashV8ndash

V119899O2119899minus1

(119899 = 3ndash8) V9ndashVO2 V10ndashV

6O13 V11ndashV

2O5 (v) Tungsten

W1ndashWO2W2ndashW

18O49W3ndashW

10O29W4ndashW

50O148

W5ndashWO3 (vi)

Manganese M1ndashMnO M2ndashMn3O4 M3ndashMn

2O3 M4ndashMnO

2 (vii)

Uranium U1ndashUO2 U2ndashU

4O9 U3ndashU

3O7 U4ndashU

3O8 U5ndashUO

3 The

points T21015840 and V91015840 characterize a scatter due to the Δ1198660 data

difference [22 28]

During electroforming current-induced heating of thefilm under the electrode leads to a diffusion of both metalfrom the substrate into the film and oxygen from the outerlayer to the inner one Also the transport of metal andoxygen ions due to the applied electric field is possible Sinceduring electroforming (unlike thermal or electrochemicaloxidation) no external oxygen is present no reaction cantake place except the reduction of the highest oxide of AOFThe reduction results in growth of the channel consisting oflower oxide through the film from one electrode to anotherEvidently substances with the minimum Δ119866

119903value (see

Figure 7)will be predominant in the phase composition of thechannelThe current increase after formingmay cause furtherreduction of the channel material leading to a predominanceof the phases such as VO NbO and TiO Many of the lowestoxides of transition metals (mono- and suboxides) exhibitmetallic properties [23] the accumulation of these phases inthe channel will therefore lead to an irreversible increase inconductivity that is to breakdown

The above compounds (VO2 Fe3O4 Ti2O3 and NbO

2)

have one feature in common namely a metal-insulator phasetransition [24] The MIT phenomenon is characterized bythe sharp and reversible change in the conductivity at acertain temperature 119879

119905 for instance vanadium dioxide at

Advances in Condensed Matter Physics 7

1 2

3

0

1

2

3

4

5

6

240 260 280 300 320 340220T (K)

V2 th

(V2)

(a)

1

2

3

(V2th times 04)

420 440 460 480 500 520 540400T (K)

0

1

2

3

4

5

6

7

V2 th

(V2)

(b)

Figure 8 Squared threshold voltage as a function of temperature for (a) vanadium oxide-based switch and (b) titanium oxide (1) (2) and(3) three different samples

119879 lt 340K is a semiconductor at 119879 = 119879119905

= 340K theconductivity abruptly increases by 4-5 orders of magnitudeand above the transition temperature VO

2exhibits metallic

properties ForNbO2119879119905= 1070K Ti

2O3undergoes a gradual

transition in the range 400ndash600K and magnetite (Fe3O4)

is a semiconductor both above and below the Verwey tran-sition temperature (120K) though its resistivity decreaseson heating by two orders of magnitude at 119879 = 119879

119905 For the

switching devices based on these metals the temperatures 119879119900

coincide with the corresponding values of 119879119905(see Figure 5)

This suggests that the switching mechanism is caused by themetal-insulator transition

Electrical switching due to MIT has been first revealedfor vanadium dioxide [16 27 37ndash45] Switching in VO

2

is explained by the current-induced Joule heating of thesample up to 119879 = 119879

119905 which has been confirmed by the

direct IR-radiation measurements of the switching channeltemperature [38 45] In these early works switching hasbeen observed in single crystals [39] and planar thin filmdevices [37 38 45] as well as in vanadate glasses [40 41]VO2-containing ceramics [44] and V

2O5-gel films [42 43]

When as-prepared samples do not consist of pure vanadiumdioxide preliminary electroforming is required resulting inthe formation of the VO

2-containing channel [40 42] The

latter examples as well as the discussed AOFs here supportthe assumption that the formation of vanadium dioxide isthermodynamically preferable at a V

2O5-V interface [22

27] For such samples the threshold voltage decreases withtemperature and reaches zero at 119879 = 119879

119905sim 340K

In this case the switchingmechanismmight be describedin terms of the ldquocritical temperaturerdquo model [29 37] (if theambient temperature is not much lower than 119879

119905)

119881th sim (119879 minus 119879119905)12

(3)

that is the squared threshold voltage linearly tends to zero at119879 rarr 119879

119905 see Figure 8 Switching elements for other transition

metal (FeW Ti and Nb) oxides exhibitingMIT are expected

to show similar behaviour but for different 119879119905rsquos which is

demonstrated by Figure 8(b) for Ti oxideThe switching effect in the WO

3-based sandwich struc-

tures can also be explained in terms of ametal-insulator tran-sition which occurs in nonstoichiometric WO

3minus119910(within a

very narrow interval of variable 119910) at 119879119905ranging from 160 to

280K [46] Because of the narrow interval of ldquoappropriaterdquostoichiometric compositions the S-type I-V characteristicis not likely to appear in tungsten trioxide and in mostcases breakdown occurs instead For switching structureson anodic films on W 119879

119900was found to lie around sim200K

(Figure 5) Therefore 119879119900may turn out to be equal to 119879

119905

Almost no data on MIT in molybdenum oxides are avail-able in the literature except for the transition in Mo

8O23

(MoO2875

) and the switching effect in molybdenum oxidewill be discussed in more detail in the next section Asto Ta and Hf oxides the formation of metastable loweroxides during electroforming should also be possible Theproperties of these oxides are practically unknown but somemetastable oxides of this type have been referred to forexample for the Ta-O system [47] Recently formation ofHfO119909[48] and TaO

119909[49] suboxides has been reported As

to Mn oxides it is known [23] that MnO and Mn3O4are

Mott insulators Mn2O3is a semiconductor and MnO

2is

also a semiconductor but it shows a change in electricalconductivity at 119879 = 119879

119873sim 90K (the Neel temperature) This

might account for the N-NDR effect in Mn oxide this issuewill also be more thoroughly investigated in the next section

Thus the experimental data on the switching effect in119889-metal oxide thin films can be explained in terms of theswitching mechanism driven by the MIT We can state thatin all cases the electrothermal and electrochemical processesduring electroforming are responsible for the switching chan-nel formation The channel consists of a material which canundergo a transition from semiconducting state to metallicstate at a certain temperature 119879

119905 For the V- Ti- Nb- and Fe-

based structures the possibility of formation of the channelsconsisting completely or partly of VO

2 Ti2O3 NbO

2 and

8 Advances in Condensed Matter Physics

Fe3O4 respectively is also confirmed by the thermodynamic

calculations In oxides of W and Mo switching may beassociated with MIT in the channels consisting of WO

3minus119909

and Mo8O23 The S-shaped voltage-current characteristic

is conditioned by the development of an electrothermalinstability in the channel When a voltage is applied thechannel is heated up to 119879 = 119879

119905(at 119881 = 119881th) by the current

and the structure undergoes a transition fromhigh-resistance(OFF) insulating state to low-resistance (ON) metallic state

In high electric fields (105ndash106 Vcm) the possible influ-ence of electronic effects on the MIT should be taken intoaccount A field-induced increase in charge carrier densitywill act to screen Coulomb interactions [12] leading to theelimination of the Mott-Hubbard energy gap at 119879 lt 119879

119905

Moreover a transition of this type may be important in thosematerials where the usual temperature-induced MIT with awell-defined 119879

119905does not take place for example in oxides

of Ta or Hf (and in CGS-based switching structures as well[50]) In the case of vanadium dioxide such a possibilityof the electronically induced MIT was suggested from theinjection experiments [22] and will be discussed also belowin connection with the transition mechanism in VO

2

To summarize the results presented above as well asthe other data on the switching in transition metal oxides[11ndash17 27ndash31] indicate that current instabilities with the S-type NDR exhibit several common features In particularfor each of the investigated materials there is a certain fixedtemperature 119879

119900 above which switching disappears At 119879 lt

119879119900 the threshold voltage decreases as the temperature rises

tending to zero at 119879 = 119879119900 Comparison of these temperatures

with the temperatures of MIT for some compounds (119879119905

=

120K for Fe3O4 sim200K for WO

3minus119909 340K for VO

2 sim500K

for Ti2O3 and 1070K for NbO

2) shows that the switching

effect is associated with the insulator-metal transition in anelectric field The channels consisting of these lower oxidesare formed in initial anodic films during the process ofpreliminary EF

And finally in conclusion of this section we would like todiscuss onemore vanadium oxide where the switching effectsare caused by MITs namely vanadium sesquioxide The I-Vcharacteristics of chromium-doped V

2O3shown in Figure 9

are distinctive in that they exhibit in a certain temperaturerange two regions of negative differential resistance both N-NDR and S-NDR The experimental data on the switchingeffect ofMOM structures based onV

2O3Cr can be explained

in terms of the switching mechanism driven by the variableMIT The S-shaped I-V characteristic is conditioned by thedevelopment of an electrothermal instability in the sampleWhen a voltage is applied the sample is heated by the currentup to 119879 = 119879

1199051(at the threshold voltage 119881 = 119881th119878) and

the structure undergoes a transition from a high-resistance(OFF-1) AFI state to a low-resistance (ON) PM state Asthe current in the ON state increases the sample is furtherheated and at 119879 = 119879

1199052(119868 = 119868th119873) the second transition

to the OFF-2 (or PI) state occurs [51] In the OFF-1 statethe plot of current versus the square root of the appliedvoltage is indicative of a Poole-Frenkel type of conductivityenhancement [52] (Figure 10)

12

34

0

20

40

60

80

100

120

140

160

180

Curr

ent (

mA

)

05 10 15 20 25 3000Voltage (V)

Figure 9 Current-voltage characteristics for V2O3doped with 12

at of Cr at different temperatures 1705 K (1) 1733 K (2) 2210 K(3) and 2655 K (4) [51]

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

Curr

ent (

A)

05 10 15 20 2500Square root of voltage (V05)

150K140K130K120K110K

100K90K80K70K60K

50K40K30K20K10K

Figure 10 Current versus voltage in Poole-Frenkel coordinates fora V2O3-based switching device [52]

23 Switching Effects and Metal-Insulator Transitions in MnandMoOxides In this section we consider electrical switch-ing in oxides of Mn and Mo obtained by vacuum depositionin comparison with those obtained by anodic oxidation [5354] It should be emphasized here that AOFs are (as a ruleexcept for some rare cases) amorphous [32 33] Therefore inMOM structures with anodic films the process of EF similarto that in CGSs usually takes place However in some cases(Mo Mn) as was described in previous sections we havefailed to obtain stable switching with anodic films and herewe present an alternative approach to this problem

Advances in Condensed Matter Physics 9

231 Electrical Switching in Thin Film Structures Based onMolybdenumOxide As inmost TMOs in the molybdenum-oxygen system there exist a number of oxides with variablevalence which are characterized by a wide diversity ofstructures and physical properties [53 55 56] MolybdenumtrioxideMoO

3has a structure based on layers of edge-sharing

distorted MoO6octahedra [23] Similar layered structures

are inherent in lower molybdenum oxides including MoO2

Mo18O52 Mo9O26 Mo8O23 Mo5O14 and Mo

17O47 as well

as 120578- and 120574-Mo4O11[55ndash57]

Stoichiometric MoO3 in its most thermodynamically

stable form 120572-MoO3 is an insulator with a band gap of sim3 eV

[23] During reduction by means of either oxygen deficiencyformation or introducing donor impurity atoms additionaldonor levels near the conduction band bottom appear andthe reduced oxide behaves therefore as a semiconductorPolycrystalline MoO

3 as well as a single crystal has a grey-

yellow colour and the minimum value of the absorption edgeis 440 nm which corresponds to the smallest value of theband gap of 28 eV [58] thus the band gap depends upon thestoichiometry and the crystalline state [53] The conductivityvalues of molybdenum oxides range from dielectric MoO

3

to semiconductor Mo18O52

(resistivity 120588 = 781Ωsdotcm)and down to metal 120578-V]

411

(120588 = 166 times 10minus4Ωsdotcm) [58]Molybdenum dioxide also exhibits metallic properties [2358] and at room temperature 120588 = 88 times 10minus5Ωsdotcm for bulkMoO2samples [55]

Because of their special physical and chemical propertiesmolybdenum oxides are used in various electronic devicessuch as electrochromic displays and indicators reversiblecathodes of lithium batteries gas sensors and memoryelements [55ndash61] Metal-insulator transitions have also beenobserved in some oxides of molybdenum and related com-pounds [62ndash70] In particular Mo

8O23

exhibits a two-stagestructural MIT with formation of a charge-density wave at1198791199051= 315 K and 119879

1199052= 285K [62] However as far as we know

no data are available in the literature concerning thresholdswitching associated with these transitions except for ourwork [53] In this work we have particularly noted thatmemory switching is observed inmany TMOs molybdenumoxides included [4 9 59 60]

The most discussed models in the literature for theReRAMmechanism in oxide structures are those based eitheron the growth and rupture of a metal filament inside theoxide matrix under the action of electric current or onthe redox processes responsible for the formation of somehigh-conductivity or low-conductivity local inclusions cor-responding to particular oxygen stoichiometry [4] The MITideology is also sometimes involved to explain the propertiesof the structures and the memory switching mechanismtherein [71] In any case thememory switching phenomenonseems to be associated with the ion transport [4 9] It isalso appropriate to mention here the works discussing thememory effects in a material with MIT (vanadium dioxide)associated with the presence of hysteresis in the temperaturedependence of conductivity [72]

On the other hand as was shown in the previous sectionmonostable threshold switching (with no memory effects)

associated with the MIT is also characteristic of a numberof TMOs That is why the study of threshold switchingin molybdenum oxide and its possible connection withthe phenomenon of MIT is of considerable scientific andpractical interest

Thinfilm samples ofmolybdenumoxidewere obtained bytwo ways anodic oxidation and thermal vacuum evaporation[53] Anodization of molybdenum was carried out in anacetone-based electrolyte (22 g of benzoic acid plus 40mLof saturated borax aqueous solution per litre of acetone[33 73]) AOFs on Mo might include lower molybdenumoxides for example Mo

4O11andMoO

2with a relatively high

electronic conductivity [53] The fact that the anodic oxideon molybdenum contained lower oxides was confirmed byexperimental data in the work [74] where it was shown thatthe degree of oxidation (valence state) of molybdenum in anAOF is less than six Also this was confirmed theoretically interms of the thermodynamics of the process the formation ofunsaturated oxide MoO

2had been shown to be energetically

more favourable than MoO3[75]

Vacuum deposited film samples were fabricated by ther-mal evaporation of MoO

3powder at residual pressure of

10minus4 Torr onto polished tantalum plates or glass substratesfor electrical and optical studies respectivelyThe thicknessesof the films were determined from the transmission andreflection interference spectra measurements [76] and theywere found to lie in the range from 300 to 800 nm

The XRD pattern of a vacuum-deposited molybdenumoxide sample is presented in Figure 11(a) It is shown thatthe samples represent amorphousMoO

3with a slight oxygen

nonstoichiometry [53] Anodic oxide films on Mo are alsoamorphous (or amorphous-microcrystalline according tothe literature data [73]) but their composition correspondsas described above to ratherMoO

2or other lower oxides and

not to the highest oxide MoO3

Figure 11(b) shows the reflection and transmission spec-tra for one of the samples obtained by vacuum depositionThe experimental data processing using the envelope of theinterference extrema [76] yields the film thickness of (620 plusmn

50) nm and the absorption edge around 120582 asymp 400 nm indi-cates the fact that the oxide phase composition correspondsto MoO

3with a band gap of sim3 eV

Before electroforming initial structures demonstrate thenonlinear and slightly asymmetric current-voltage charac-teristics with no NDR regions When the amplitude of theapplied voltage reaches the forming voltage a sharp andirreversible increase in conductivity is observed and theI(V) curve becomes S-shaped (Figure 12) With increas-ing current the I-V characteristic may change until theparameters of the switching structure are finally stabilizedThe process outlined above is qualitatively similar to theelectroforming of the switching devices based on other TMOs(see Section 22 above) We emphasize once again that thephase composition of the ensuing switching channel mustdiffer from the material of the pristine oxide film becausethe channel conductivity is higher than that of the unformedstructure by several orders of magnitude

The current-voltage characteristics of vacuum-depositedfilms and those of anodic films are qualitatively similar but

10 Advances in Condensed Matter Physics

1

2

20 40 60 8002120579∘

0100200300400500600700800900

I (co

unts

s)

(a)

1

2

3

0

20

40

60

80

100

T (

)

300 400 500 600 700 800 900 1000 1100200Wavelength (nm)

(b)

Figure 11 (a) XRD pattern of the molybdenum oxide film (1) andV]3powder (2) (b) Optical spectra of the sample obtained by vacuum

deposition (1) transmission coefficient of substrate (glass) (2) transmittance and (3) reflectance of Mo oxide film on glass [53]

0 5 10minus5minus10

Voltage (V)

minus016

minus012

minus008

minus004

000

004

008

012

016

Curr

ent (

mA

)

(a)

minus072 072 216 360minus216minus360

Voltage (V)

minus064

minus048

minus032

minus016

000

016

032

048

064

Curr

ent (

mA

)

(b)

Figure 12 Current-voltage characteristics ofMOMstructures with vacuum-deposited (a) and anodic (b)Mo oxide films after electroforming

there is a significant quantitative difference in their thresholdparameters For instance the switching voltage 119881th for theAOF based structures is sim2V (Figure 12(b)) whereas forthe structures on the basis of the films prepared by thermalevaporation119881th is sim10V (Figure 12(a))This difference can beexplained by the difference in thickness of the films

For anodic oxide the thickness can be estimated fromFaradayrsquos law [53]

119889 =

120583119868119886119905

4119890120588119878119873119860

(4)

where 120583 = 128 gmol and 120588 = 65 gcm3 are respectivelythe molar mass and density of V]

2and 119890 and 119873

119860are the

unit charge and Avogadro constant For 119868119886= 70m0 and 119905 =

10min (4) yields 119889 sim 20 nm which is significantly less thanthe typical thickness of the vacuum deposited films and as aresult the threshold voltage for AOFs is also lower than thatfor the films obtained by thermal evaporation

As is discussed in [53] switching is not observed inthinner films obtained by vacuum evaporation (119889 lt 100 nm)

in contrast to ultrathin AOFs A plausible reason for thismight be the fact that relatively thin vacuum depositedfilms contain through-the-thickness conducting defects dueto local stoichiometry variations whereas such defects areimpossible in anodic films because they are grown in highelectric field during anodic oxidation and an appearanceof such defects would interrupt the film growth processThis is similar to what is observed in vanadium oxide inpolycrystalline vanadium dioxide films such pin-hole defectsare usually associated with the grain boundaries which couldundergo local metallization due to strain or nonstoichiom-etry That is why it had been difficult to observe switchingin sandwich MOM structures with sputtered or thermallyoxidized polycrystalline VO

2films and most studies had

been conducted with planar thin-film structures whilst foranodically oxidized VO

2the switching effect has then been

observed in a sandwich structure for the first time in [16]Next we note that unlike the most other TMOs the

process of electroforming in Mo-based structures was hin-dered as was mentioned above in Section 21 that is theconventional electrical breakdown often occurred not the

Advances in Condensed Matter Physics 11

020406080

100120

30 40 50 60 7020Temperature (∘C)

30 40 50 60 7020Temperature (∘C)

0

2

4

6

8

10

12

Thre

shol

d vo

ltage

(V)

5 15minus5minus15

Voltage (V)

minus010

minus005

000005010

Curr

ent (

mA

)

V2 th

(V2)

Figure 13 Threshold voltage as a function of temperature for theTa-MoOx-Au switching structure and the temperature dependenceof (119881th)

2 (lower inset) in compliancewith (3) I-V curve at RT (upperinset)

formation of a switching channel However for the Mooxide films prepared by vacuum deposition the processesof electroforming and switching were more stable whichallowed in this case observation of the transformation of I-V curves at a temperature change It was found that as thetemperature increased the threshold voltage was reducedAt 119879 = 119879

119900sim 55ndash65∘C the NDR region degeneration

commenced at 119879 asymp 60ndash70∘C 119881th rarr 0 and at still highertemperatures the switching effect no longer occurred Inthis case the switching mechanism might be described interms of the ldquocritical temperaturerdquo model (Figure 13) It issupposed [53] that in the case of Mo like in other TMO-based structures formation of a channel also takes placeand this channel should consist of a material exhibiting MITwhich is the reason for switching with an S-shaped current-voltage characteristic (Figure 12)

A brief review of the materials with MIT in the familyof molybdenum compounds presented in [53] shows that themost suitable candidate for the role of such a channel-formingcompound is Mo

8O23

because in this case the value of 1198791199051

almost coincides with the above reported experimentallymeasured 119879

0 It should be noted that formation of other

compounds of molybdenum (eg pyrochlores bronzes sul-fides or chalcogenide glasses) exhibiting MITs with similarorder of magnitude transition temperatures [64ndash68 70] isimpossible because of the lack of the necessary chemicalelements (ie rare earths alkali metals or hydrogen sulfurand tellurium) in the phase composition of both the oxidefilm and the metal electrodes (Au Ta and Mo)

In conclusion the results presented in this subsection onswitching from the HR state to the LR state with an S-NDRin molybdenum oxides obtained by both thermal vacuumdeposition and electrochemical anodic oxidation show thatthe switching effect is due to apparently an insulator-to-metal phase transition in the switching channel consistingcompletely or partly of the lower oxide Mo

8O23 formed in

the initial film during the process of electroforming Thecurrent flowing through the channel heats it up to the MIT

temperature 1198791199051= 315K [62] and the structure switches into

the metallic low-resistance stateThus the channels consisting of this lower oxide are

formed in initial Mo oxide films during preliminary elec-troforming Electrical forming results in the changes inoxygen stoichiometry conditioned by the ionic processes inan electric field close to the MOM structure breakdown fieldThis picture is quite similar to what is observed inmany otherTMOs exhibiting the insulator-to-metal transitions

232 Metal-Insulator Transition and Switching in ManganeseDioxide Manganese dioxide is one of the most interestinginorganic materials because of its wide range of applica-tions In particular nanostructured MnO

2has received great

attention due to its high specific surface area functionalproperties and potential applications as molecular and ionselective membranes in capacitors Li-ion batteries andcatalysts [77] Originally MnO

2has been widely used as a

cathode material for oxide-semiconductor capacitors basedon tantalum niobium and aluminium oxides and the mostimportant properties of the material for this application areits high conductivity and ability to undergo a thermal phasetransition into the lower valence states accompanied by evo-lution of atomic oxygen while the resistance increases by 3-4orders of magnitude (see eg [54] and references therein)Much attention is currently paid to various other propertiesof MnO

2 such as for example the electrochromic effect

[78] thermopower wave phenomenon [79] supercapacitivebehaviour [80] andmemory and threshold switching [54 8182] Also there are a number of papers [83ndash85] describing ananomaly in theMnO

2conductivity near theNeel temperature

which is shown to be associated with the metal-insulatortransition [52] That is why the electrical properties of MnO

2

are of special scientific interest and applied importanceThe most common methods for manganese oxide prepa-

ration are the pyrolytic decomposition of manganese nitrateelectrochemical method hydrothermal synthesis in a mag-netic field and chemical deposition [54 86ndash89] Due to awide range of possible valence states of cations the structureand phase composition of manganese oxides are determinedby the synthesis conditions and process temperature Man-ganese dioxide has many crystallographic forms (120572- 120573- 120574-120575- 120576- and 120582-MnO

2) that connect MnO

6octahedron units to

each other in different ways and have different characters ofspatial alternation of the octahedra filled by Mn atoms andempty octahedra [54 77 90ndash94]

The crystal structure of the 120573-MnO2phase (Figure 14) is a

tetragonal modification of the rutile structural type P4mnmsymmetry group which represents a slightly distorted close-packed hexagonal lattice of oxygen ions [93] Filled octahedraare bound by two common edges in columns oriented alongthe 119888 axis and octahedra of adjacent columns are bound bytheir vertices (Figure 14(c)) Manganese atoms are arrangedin positions 2(a) (000) and oxygen atoms in positions 4(f )(xx0) Because there are vacancies in the oxygen packingthe formula unit can be written as MnO

2minus119910where the

nonstoichiometry index is in the range 119910 = 001ndash010depending on the synthesis method [93]

12 Advances in Condensed Matter Physics

Mn

O

(a)

a

b

c

(b)

O2O4

O1O3

Mn2

Mn1

Mn1998400

O3998400

O4998400

(c)

Figure 14 Crystal structure of manganese dioxide (a) MnO6

octahedron connection in 120573-MnO2(b) [90ndash94] and projection of

octahedron binding onto the ab plane [93]

As to the lower manganese oxides MnO and Mn3O4are

known to be theMott insulatorswith relatively high resistivity[90] and Mn

2O3shows p-type semiconducting properties

MnO2is an n-type semiconductor and antiferromagnetic

with the Neel temperature 119879119873= 925 K [91] Conductivity of

manganese dioxide is higher than that of MnO and Mn2O3

by several orders of magnitude At temperatures above 723Kmanganese dioxide loses oxygen and transforms intoMn

2O3

which is accompanied by the transformation of the crystallinestructure from the tetragonal crystal system of the rutile typeinto the complex large-period cubic lattice (119886 = 94gt) and alarge number of formula units per unit cell [54 92 93]

In this subsection we present the results on electricalproperties of manganese dioxide particularly the natureof the 120573-MnO

2conductivity at low temperatures in its

interrelation with characteristic features of the material crys-talline structure and the metal-insulator phase transitionin this compound as well The effect of electrical switchingwith current-voltage characteristics of both N- and S-typehas been found in thin-film MOM structures on the basisof manganese oxides Possible mechanisms of switching interms of the MIT and thermistor effects are discussed

Mn oxide samples under study have been obtained bythree methods anodic oxidation and vacuum evaporation(thin films) as well as by pyrolysis [54] Thin films ofmanganese dioxide were deposited by means of thermalevaporation onto glass substrates covered by a SnO

2layer

using a VUP-5 vacuum setup the film thickness was 119889 =

250 nmAlso thin films ofmanganese oxidewere obtained byelectrochemical oxidation of metal Mn in the KNO

3-NaNO

3

eutectic melt (see Section 21) at 119879 = 600K at a constantvoltage of about 2V for 3min the current density diminishedfrom 200 to 100mAcm2 during the oxidation process Foranodic oxide films on Mn the value of 119889 was sim100 nm Bulksamples of manganese dioxide were obtained by multipledecomposition (pyrolysis) of manganese nitrate at 119879 = 670Kon a glass-ceramic substrate or on a tantalum sheetmetal withthe subsequent separation from the substrate [92 93] Thetotal coating thickness was about 1mm

The manganese oxide samples were characterized by X-ray diffraction (XRD) using a DRON-6 diffractometer inCuK120572and FeK

120572radiation The characteristics of the atomic

structure of pyrolytic manganese dioxide were refined by thefull-profile analysis of the XRD patterns of polycrystallinesamples [93]The resistivity of pyrolyticMnO

2wasmeasured

in the temperature range 15 to 300K bymeans of a four-probetechnique both DC and AC (in a frequency range from 50 to104Hz) in a Gifford-McMahon cycle cryorefrigerator [54]We also measured electrical conductivity in the range T =293ndash423K the Hall effect in the magnetic field of 23 T andthe Seebeck coefficient (thermoelectromotive force thermo-emf ) The dynamic current-voltage (I-V) characteristics ofthe thin-film MOM structures were measured by oscillo-graphic method using an AC sinusoidal signal

The XRD patterns of the manganese oxide samples arepresented in Figures 15 and 16 The vacuum-deposited filmsare amorphous and represent a mixture of 120573- and 120574-MnO

2

(Figure 16) The results of the full-profile analysis show thatthe pyrolytic MnO

2samples (Figure 15) are composed of

the finely dispersed 120573-MnO2phase with the traces of 120574-

MnO2 120576-MnO

2 and Mn

2O3phases The periods of the

tetragonal unit cell of 120573-MnO2are 119886 = 119887 = 4401 A and

119888 = 2872 A The oxygen coordinates in 4119891 positions (seediscussion of the crystal structure above and Figure 14) arefound to be119909 = 0302 Calculations of the oxygen-manganeseinteratomic distances show [93] that the oxygen octahedron

Advances in Condensed Matter Physics 13

330222

040231

212202

112

130002

220

121

120

111

110

101

020

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 80 100 12002120579∘

Figure 15 XRD (Cu K120572radiation) pattern of pyrolytic MnO

2

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 8002120579∘ Fe

120573-MnO2

120574-MnO2

Experiment

Figure 16 XRD (Fe K120572radiation) pattern of Mn oxide film and

reference spectra of crystalline MnO2samples

is compressed along the (100) direction which connects theoctahedron vertices This deformation results in an increaseof the overlap of electron119901 orbitals of oxygen and119889 orbitals ofmanganese and can form the additional splitting of electronlevels in the crystal field leading to the appearance of unpairedelectrons [94]

The measurements of the conductivity temperaturedependence Hall effect and thermo-emf show that man-ganese dioxide is the electron semiconductor with conductiv-ity of about 1Ωminus1cmminus1 and mobility of sim10 cm2Vsdots The Hallmeasurements give the carrier density ofsim1018 cmminus3 which isclose to the density values in degenerate semiconductorsTheactivation energy of conductivity is sim01 eV and the band gapwidth is equal to 2 eV [90] The estimated value of the Fermienergy from the thermo-emf temperature dependence is inthe range of 002 to 005 eV which also indicates the degener-ate character of the electron gasThe nonstoichiometry indexdetermined by the XRD peaks which are not contributed

by the manganese atoms that is by those with the oddsum of indexes is 119910 = 006 Such nonstoichiometry providesthe concentration of trap states of about 1017-1018 cmminus3which correlates with the above mentioned Hall-effect-basedmeasurements of electron density

Such high vacancy concentration allows us to considerthe nonstoichiometric 120573-MnO

2as a heavily doped semicon-

ductor with a subband of impurity levels which provides afeasibility of the out-of-band electron transfer at low tem-peratures The structural distortions high nonstoichiometryand as a consequence sufficiently high concentration ofimpurity states cause the density state tails near the bandedges similarly to those in heavily doped semiconductorsHowever at room and higher temperatures the conduction isdetermined by the activation mechanism Thus the electronstructure and a low mobility of charge carriers promotethe manifestation of different charge transfer mechanismsin different temperature ranges namely both the hoppingmechanism and the activation one

The electron capturing oxygen vacancies create mixedvalence states of manganese cations (Mn3+ndashMn4+) Interest-ingly the mixed valence of Mn ions is also characteristic ofmanganites Ln

1minus119910Sr119910MnO3[95] where Ln is La or another

rare-earth element possessing the effect of colossal magne-toresistance (CMR) In these compounds the mixed valenceof manganese is attained via doping It had been deemed thatholes introduced by strontium are localized at manganeseions that is the Mn4+ ions with concentration 119910 are formedHowever recent X-ray emission studies have shown that boththe chemical shift and the exchange splitting of the emissionX-ray Mn K

1205731line are almost the same in the range 119910 lt 04ndash

05 as is the case in Mn2O3 and then they decrease quickly

to the values characteristic of MnO2[96] which suggests that

the introduced holes are localized at oxygen atoms in the holedoping region (at relatively low 119910) and atmanganese atoms inthe electron doping region that is at higher 119910 values

The temperature dependence of conductivity is presentedin Figure 17 The resistance peak observed in the figure ina temperature range of 80ndash90K is the result of the phasetransition of 120573-MnO

2from a semiconducting state to a metal

state upon decreasing the temperature to 15 K [54] The tem-perature region of the transition is close to the known Neeltransition from the paramagnetic state into the ferromagneticone for manganese dioxide The temperature dependenceof resistance indicates thus the MIT to occur in MnO

2 In

the temperature range from 300 to 80K (Figure 17) thisdependence does not correspond to the exponential one yetit fits well with the linear dependence in theMott coordinatesln(119877) sim 119879

14 which indicates the hopping conductivitymechanism over the polyvalent states ofmanganese ions witha distance between the centres of 25ndash35gt [92] However inthe temperature range from 90 to 15 K the dependence ofln119877 on ln119879 is almost linear with the slope of about unity(ie 120597 ln119877120597 ln119879 asymp 1) which is characteristic of the metallicconductionThus the character of conductivity ofmanganesedioxide indicates the presence of the MIT at 119879

119888sim 80K (on

cooling)

14 Advances in Condensed Matter Physics

CoolingHeating

40 80 120 160 2000T (K)

0

2

4

6

8

10

Resis

tivity

(Ohm

timescm

)

Figure 17 Temperature dependence of AC (70Hz) resistivity ofpyrolytic MnO

2

In the low temperature region manganese dioxide is anantiferromagnetwith the helical spin ordering [97]The inter-action between the magnetic ions of manganese which leadsto the antiferromagnetic state occurs through the intermedi-ate interaction with diamagnetic oxygen ions which weakensthe exchange interaction The conductivity increases proba-bly due to exceeding the energy of the exchange interactionby the thermal energy as the temperature increases whichleads to an increase in the number of unpaired electrons inthe paramagnetic state As the temperature further increasesthe conductivity continues to rise and the Mott hoppingmechanism of charge transfer becomes predominant Similarcharacter of the temperature dependence in ferromagneticdegenerate semiconductors has previously been described[85 98] for substoichiometric (oxygen-deficient) europiummonoxide The transition from the highly conductive stateinto the insulating state occurs in such semiconductors uponvarying the type of magnetic ordering or its destruction

For EuO1minus119910

lowering the peak magnitude in the 119877(119879)

dependence is associatedwith a decrease in the concentrationof impurities (oxygen vacancies) In magnetic semicon-ductors the phase transition is associated both with themagnetoelectric effects and with the variation in the electricpolarization under the action of the magnetic field at theantiferromagnetic transition [98] The dielectric constant formanganese dioxide is equal to sim10 but the effective dielectricconstant can decrease near 119879

119888by a factor of several times

thereby affecting the mobility of carriers located in the tailsof the density of states near the band edge and promotingtheir delocalization at the phase transition temperatureManganese dioxide also belongs to this group of substanceshowever the phase transition in MnO

2reported here can be

also described in terms of the Mott transition [24]According to the Mott criterion electrons delocalize if

the distance between the atoms 119899minus13 becomes comparable

with their atomic radius 119886119860 where 119886

119860is associated with the

Bohr radius 119886119861= ℏ2120576me2The static permittivity 120576 is replaced

by the effective permittivity which takes into account theexchange interaction of the spins of conduction electronswith orbitalmagneticmoments of atoms At the temperature-induced Mott MIT the orbital radius 119886

119861decreases near 119879 =

119879119888thereby providing the fulfillment of the Mott criterion at a

given level of impurity centres [24 98] The transition fromthe metallic state into the semiconductor state is possible insuch semiconductors as the temperature increases Thus theMIT in manganese dioxide is brought about by temperaturevariation

In conclusion we note that the phase transition describedabove is inverse (reentrant) MIT that is the metallic phaseis low-temperature while the high-temperature state is insu-lating This is rather rare yet not unique and unusualphenomenon In most cases (eg in vanadium dioxide) thelow-temperature phase is insulating and on heating abovea certain temperature 119879

119888 the material becomes metallic for

VO2 this transition temperature is 119879

119888= 340K The inverse

transitions are observed in such compounds as the abovementioned EuO

1minus119910 NiS2Se Y2O3minus119910

and LaMnO3films [24

31 52 85 98 99] Also the high-temperature Mott transi-tion from paramagnetic metal to paramagnetic insulator inV2O3Cr is an inverse transition with the resistivity peak at

119879119888sim 350K for a chromium concentration of around 1 at

[24 51] and in mixed valence CMR-manganites the sharpresistivity peak has been shown to be caused by the AndersonMIT [95]

It is known that many TMOs exhibit electrical switchingassociated with MITs [28] For the anodic oxide films onMn the study of the effect of electrical switching in thin-film Mn-MnO

2-Au sandwich structures showed that the S-

type switching was not observed in contrast to for examplethe similar structures based on oxides of vanadium andsome other transition metals [28] Instead switching withthe N-shaped I-V characteristic occurred after EF at 119879 lt

80K (Figure 18(a)) In addition the EF process in the Mn-based structures was hindered likewise for example for thestructures based on yttrium oxide [31] that is the breakdowntook place more often It should be noted that EF at roomtemperature always led to breakdown and the switchingeffect had never been observed in this case As was arguedin [54] this switching effect was associated with the MIT inMnO2

On the other hand in the films obtained by vacuumsputtering we have observed S-type switching at roomtemperature (Figure 18(b)) The threshold voltage is of theorder of 1 V and almost independent of temperature up to 119879

= 375KThis situation resembles that with yttrium oxide where

both S-type and N-type switching has been observed too[31] One can assume that switching with the S-shapedI-V curves is due to the so-called ldquothermistor effectrdquo Itis well known that the current flowing through a solidgenerates Joule heat resulting in an increased temperatureIn materials with a negative TCR a rising temperatureinduces a current enhancement and an increased powerdissipation resulting in a farther temperature increase Thispositive electrothermal feedback causes the appearance of anNDR and accordingly an S-shaped I-V characteristic [2]

Advances in Condensed Matter Physics 15

minus15

minus10

minus5

0

5

10

15Cu

rren

t (m

A)

0500 10 15minus10 minus05minus15

Voltage (V)

(a)

minus2

minus1

0

1

2

Curr

ent (

mA

)

10 2minus2 minus1

Voltage (V)

(b)

Figure 18 (a) I-V characteristic of anodic oxide film on manganese at T = 77K (b) I-V characteristic of vacuum-deposited MnO2at 119879 =

293K

In some cases this process might by modified by high-fieldeffects such as Schottky injection impact ionization Poole-Frenkel effect and Zener or avalanche breakdown Notethat unlike a conventional thermistor with an Arrhenius-like conductivity law manganese oxide exhibits a weaker119877(119879) dependence characteristic of the hopping conductivitymechanism which seems to account for the observed weaktemperature dependence of the threshold voltage

An alternative mechanism for the S-type switching effectmay be connected with a possible high-temperature usual(ie not inverse)MIT in somemanganese oxide As is knownEF (see Section 22) leads to the formation of a filament ofhighly conducting material a switching channel Similarlyto what is observed for Mo oxide (Section 231) and otherTMOs (Sections 21 and 22) we suppose that the compositionof this channel differs from the material of the initial oxidefilm since its conductivity noticeably exceeds that of anunformed structure In view of such a plentiful set of phasesand crystal structures in the Mn-O system one can supposethat the channelmight consist of nonstoichiometric120573-MnO

2

some other polymorphic modifications of manganese diox-ide or lower Mn oxides which might undergo a MIT underthe action of either temperature or electric field Howeverthis question obviously requires additional investigation inparticularmeasurements of119877(119879)dependences and switchingproperties at higher temperatures If this assumed high-temperature MIT would occur in for example nonstoichio-metric 120573-MnO

2 one could expect observation of double-

NDR I-V characteristics in such samples at low temperaturesanalogously to those in V

2O3Cr (Figure 9) where this effect

is due to the MITs [29] with the only difference being thatin the case of MnO

2this curve should be N-S-shaped (unlike

the S-N-shaped one in Figure 9) since in chromium-dopedvanadium sesquioxide the inverse MIT is high-temperatureas opposed to MnO

2which as we discussed above (see

Figure 17) exhibits the inverse MIT at low temperaturesNote however that the discussed high-temperature MIT

in 120573-MnO2minus119910

may be unobservable under the temperature

change in equilibrium conditions but displays itself onlyunder the applied electric field as the S-type electricalswitching effect because the transition temperature is closeto or higher than the temperature of MnO

2decomposition

(723K) Such a nonequilibrium transition occurs at switchingin those materials where the usual temperature-inducedMITwith a well-defined 119879

119905does not take place for example in

CGSs for which the equilibrium transition temperature 1198791199050

is higher than 119879119892 while in a high electric field 119879

119905(119864) lt 119879

1199050

might be lower than 119879119892 where 119879

119892is the temperature of the

glass-crystal transition and119864 is the electric field strength [30]Summarizing we have studied the electrical properties

(conductivity temperature dependence and Hall and Seebeckeffects) of the 120573 phase of manganese dioxide obtained bypyrolysis thermal vacuum evaporation and anodic oxida-tion The change of conductivity mechanisms dependingon temperature in a range of 450ndash25K has been shownand the metal-insulator phase transition at low (lt90K)temperatures has been revealed The specific feature of thistransition described in terms of the Mott mechanism isthat the metal phase exists at low temperatures while athigher temperatures the material is a semiconductor withthe hopping conductivity over the mixed valence states ofmanganese ions

The low-temperature switching effect with an NDR andN-shaped current-voltage characteristic associated with thephase transition in manganese dioxide has been found in theMOM two-terminal devices based on anodicMn oxide filmsOn the contrary the devices based on vacuum-depositedfilms have been found to exhibit an S-NDR at room andhigher temperatures which is suggested to be caused byeither the thermistor effect or a high-temperature MIT innonstoichiometric 120573-MnO

2

It should be emphasized that the low-temperature MITin 120573-MnO

2with 119879

119905= 70ndash80K is the inverse Mott transition

which is akin for instance to the transition in V2O3Cr

at 119879119905= 190ndash385K (for chromium dopant concentration in

the range of 05ndash18 at) [51] We thus assume that farther

16 Advances in Condensed Matter Physics

5 10 150Voltage (V)

0

1

2

3

4

5

6

7

8Cu

rren

t (m

A)

(a)ΔV

th(V

)

0

1

2

3

1 2 3 4 5 6 7 80W (at )

(b)

Figure 19 I-V curve (a) of Au-V2minus119910

W119910O5times 119899H2O-Au sandwich structure with119910= 003 and119881th scattering as a function of tungsten admixture

percentage 119910 (b) [104 105]

investigations of the phase transition in manganese dioxidedescribed in this paper are a rather interesting and topicalscientific problem since manganese dioxide can serve as amodel object for studying such inverse metal-insulator phasetransitions

Finally we note that the results presented in this sectionindicate the possibility of application of manganese oxide asa material for thin film sandwich switching devices Deviceswith NDR (N- and S-shaped I-V characteristics) have poten-tial applications in microelectronics as switches memoryelements and microsensors (these issues will be discussedin more detail below in Section 4) Particularly manganeseoxide microswitches [82] can be utilized for implementationof neuristors built with Mott-transition-based memristors[100]

24 Effect of Doping It is only natural that the systemsexhibiting the NDR effects possess a high applied potential inelectronics [2 4 8 18 100 101] yet the stage of EF is a weaklink of chain in the technology process Note that the formingprocess may be brought about by laser irradiation [102] notby applying of electric field In the case of laser treatment(or ldquolaser formingrdquo unlike the above described electricalforming) the parameters of the structures are characterizedby the absence of the scatter that is the I-V characteristics ofall structures are almost identical [103] One more demerit tobe avoided is the scatter in switching parameters (the value of119881th first of all) and their instability during operation In thissubsection we discuss the issues concerning the switchingparameter stabilization by means of doping

In the work [104] we have studied the switching effectin the MOM structures on the basis of W-doped V

2O5-gel

filmsThese structures require preliminary EF similar to thatin anodic oxide films resulting in formation of a conducting

channel within the initial dielectric xerogel filmThe channelconsists of vanadiumdioxide and switching is associatedwiththe insulator-to-metal transition in VO

2 As was shown in

[104 105] for the pure (undoped) V2O5-gel the switching

parameters vary in a wide range because the phenomenonof EF is statistical in nature (like electrical breakdown) andits statistical character shows itself as a spread in the observedthreshold voltages of the ensuing structures that is actuallyat multiple measurements 119881th = ⟨119881th⟩ plusmn Δ119881th

It has been shown [104] that the statistical spread in valuesof the threshold parameters can be minimized by means ofdoping (Figure 19) Unsophisticated reasoning could accountfor this result for pure V

2O5-gel electroforming leads to

formation of VO2with 119879

119905= 340K and each switching

event requires heating up and cooling down from roomtemperature to 119879

119905 this thermal cycling can modify the

peripheral regions of the channel which leads to the changeof the switching threshold voltage On the other hand forthe samples with a high concentration of W the MIT issuppressed [104] and switching is degenerated Betweenthese two outermost points an optimum should exist Asone can see from Figure 19 this optimal value correspondsto 3 at of W that is for V

097W003

O2the switching

parameters are the most stableThe transition temperature ofV097

W003

O2is lower than that for pure vanadium dioxide

and hence the magnitude of the aforesaid thermal cyclingis decreased which results in an increase of stability of theswitching parameters

Next we have studied the effect of doping on switchingin AOFs on Ti [29] These films were obtained in 5 watersolution of citric acid (C

6H8O7) in volt-static regime at 119881

119886

= 20V The samples were doped with aluminium by meansof adding soluble Al-containing substances to the electrolyte

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

Films vol 97 no 2 pp 129ndash143 1982[46] R Collongues La Non-Stoechiometrie Masson Paris France

1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

9 no 5 pp 391ndash396 2014[67] B Sun W Zhao Y Liu and P Chen ldquoResistive switching effect

of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

1990[70] S Mukherjee S Karmakar H Sakata and B K Chaudhuri

ldquoLow-temperature metallic behavior of amorphous MoO3-

TeO2thin filmsrdquo Journal of Applied Physics vol 97 no 12 Article

ID 123707 2005[71] AMottaghizadeh Q Yu P L Lang A Zimmers andH Aubin

ldquoMetal oxide resistive switching evolution of the density ofstates across the metal-insulator transitionrdquo Physical ReviewLetters vol 112 no 6 Article ID 066803 2014

[72] R Xie C T Bui B Varghese et al ldquoAn electrically tunedsolid-state thermalmemory based onmetal-insulator transitionof single-crystalline VO

2nanobeamsrdquo Advanced Functional

Materials vol 21 no 9 pp 1602ndash1607 2011

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

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Advances in Condensed Matter Physics 5

000102030405

Curr

ent (

mA

)

minus01

minus02

minus03

minus04

minus05

minus10minus20 minus05minus15 05 10 15 2000Voltage (V)

(a)

minus7minus6minus5minus4minus3minus2minus1

01234567

Curr

ent (

mA

)

minus15 minus10 minus5 5 10 150Voltage (V)

(b)

minus4

minus2

0

2

4

Curr

ent (

mA

)

minus10 minus6 minus4minus8 minus2 2 4 6 8 100Voltage (V)

(c)

Figure 4 Current-voltage characteristics of MOM structures with AOFs on (a) Ti (b) Nb and (c) W [29]

Y see Figure 6) or at 119879 = 77K (Mn oxide) The process ofelectroforming for these materials was hindered like that forTa Hf and Mo Switching in Mo and Mn oxides will also beadditionally discussed in Section 23 below

22 Switching as an Electrically DrivenMetal-Insulator Transi-tion Next we discuss the process of electroforming in moredetail The initial AOF represents as a rule a highest oxideof the metal (eg Nb

2O5in the case of niobium) However

lower oxides always exist near the AOF-metal interface inthe form of transition layers or as separate inclusions Thiscan be explained in terms of thermodynamics Consider thefollowing reaction

Nb + 2Nb2O5997888rarr 5NbO

2(1)

The change of the Gibbs (isobaric) potential for thisreaction is

Δ119866119903= ]2Δ1198662minus ]1Δ1198661 (2)

where Δ1198661and Δ119866

2are the standard isobaric potentials

of formation and ]1and ]

2are the numbers of moles of

oxides which take part in the reaction For Reaction (1) the

subscripts 1 and 2 in (2) are related to Nb2O5and NbO

2

respectively and Δ119866119903

= minus163 kJmol [28] Since Δ119866119903

lt 0Reaction (1) proceeds spontaneously and hence NbO

2is

always present at the Nb-Nb2O5interface

Transition metals exhibit multiple oxidation states andform a number of oxides Therefore it is obvious that thelower oxide to be formed is mainly that with the mini-mum Δ119866

119903 Figure 7 demonstrates the variation of Δ119866

119903(119909)

for Fe2O3 Nb2O5 V2O5 TiO2 and some other oxides in

reactions similar to (1) where 119909 is the stoichiometric indexof oxygen Δ119866

119903values were calculated using (2) the data

on Δ119866119900 for the calculations were taken from [35] The

minima in these curves correspond to Fe3O4 NbO

2 VO2

and Ti2O3 therefore these oxides form as intermediate

layers between the metal substrate and the correspondingoxide of highest valence Real systems are far from beinga plane parallel structure with two oxide layers hence thesuggested approach is rather oversimplifiedNevertheless theabove considerations show that formation of those oxidesis thermodynamically reasonable whether it is kineticallypossible can only be judged from experiment For exampleas was shown in [33] in AOF on vanadium the vanadiumdioxide layer may be rather thick and only a very thin film

6 Advances in Condensed Matter Physics

00

05

10

15

20

25

30

V (a

u)

1 2

3 4

5

200 300 400 500 600100T (K)

Figure 5 Threshold voltage in arbitrary units 119881 = 119881th(119879)119881th(1198791015840)

for theMOM structures on the basis of different oxides as a functionof ambient temperature (1) Fe (2)W (3)V (4)Ti and (5)Nb anodicoxideData for different samples have been averaged andnormalizedto a certain temperature 119879

1015840 which is different for different oxides[22 27 28]

0

5

10

15

20

25

30

35

Curr

ent (120583

A)

05 10 15 20 2500Voltage (V)

Figure 6 I-V curve with N-NDR of the structure metalY anodicoxidemetal [31]

near the outer boundary is close to the V2O5stoichiometry

The similar ordering of layers evidently exists in iron oxideparticularly it is known that in a thermal oxide of iron theFe3O4phase usually predominates [28] On the other hand

the AOFs on Nb and Ti mainly consist of Nb2O5and TiO

2

and NbO2or Ti2O3layers seem to be relatively thin [27 28]

For the W-WO3system a wide minimum of Δ119866

119903(119909) lies

in the range 119909 = 27ndash30 (Figure 7) the same behaviour seemsto be characteristic of the Mo-MoO

3system The calculation

for manganese oxides yields the minimum at 119909 = 15 that isfor Mn

2O3 The curve Δ119866

119903(119909) for uranium is also presented

just as an example note however that MITs have beenreported for lower uranium oxide U

4O9[36] For Zr Hf Ta

and Y such calculations have not been made because thereexist no clear data on the thermodynamic properties of thelower oxides of those metals

F1

F2F3

T1

T2

T11N1

N2

N3

W1W2

W3

W4

W5U5

V1

V2

V9

V10

V11

U1U2

U3 U4

M4

M1

M2 M3

900

800

700

600

500

400

300

200

100

0

minusΔGr

(kJm

ol)

15 20 25 3010X

V9998400

V3ndashV8

T2998400

Figure 7 Gibbs potential change Δ119866119903(per 1 g atom of metal) for

the reaction of the highest oxide with the metal substrate versus119909 the oxygen stoichiometric index of the lower oxide which isformed in this reaction Symbol indications are as follows (i) IronF1ndashFeO F2ndashFe

3O4 F3ndashFe

2O3 (ii) Niobium N1ndashNbO N2ndashNbO

2

N3ndashNb2O5 (iii) Titanium T1ndashTiO T2ndashTi

2O3 T3ndashT10ndashTi

119899O2119899minus1

(119899 = 3ndash10) T11ndashTiO2 (iv) Vanadium V1ndashVO V2ndashV

2O3 V3ndashV8ndash

V119899O2119899minus1

(119899 = 3ndash8) V9ndashVO2 V10ndashV

6O13 V11ndashV

2O5 (v) Tungsten

W1ndashWO2W2ndashW

18O49W3ndashW

10O29W4ndashW

50O148

W5ndashWO3 (vi)

Manganese M1ndashMnO M2ndashMn3O4 M3ndashMn

2O3 M4ndashMnO

2 (vii)

Uranium U1ndashUO2 U2ndashU

4O9 U3ndashU

3O7 U4ndashU

3O8 U5ndashUO

3 The

points T21015840 and V91015840 characterize a scatter due to the Δ1198660 data

difference [22 28]

During electroforming current-induced heating of thefilm under the electrode leads to a diffusion of both metalfrom the substrate into the film and oxygen from the outerlayer to the inner one Also the transport of metal andoxygen ions due to the applied electric field is possible Sinceduring electroforming (unlike thermal or electrochemicaloxidation) no external oxygen is present no reaction cantake place except the reduction of the highest oxide of AOFThe reduction results in growth of the channel consisting oflower oxide through the film from one electrode to anotherEvidently substances with the minimum Δ119866

119903value (see

Figure 7)will be predominant in the phase composition of thechannelThe current increase after formingmay cause furtherreduction of the channel material leading to a predominanceof the phases such as VO NbO and TiO Many of the lowestoxides of transition metals (mono- and suboxides) exhibitmetallic properties [23] the accumulation of these phases inthe channel will therefore lead to an irreversible increase inconductivity that is to breakdown

The above compounds (VO2 Fe3O4 Ti2O3 and NbO

2)

have one feature in common namely a metal-insulator phasetransition [24] The MIT phenomenon is characterized bythe sharp and reversible change in the conductivity at acertain temperature 119879

119905 for instance vanadium dioxide at

Advances in Condensed Matter Physics 7

1 2

3

0

1

2

3

4

5

6

240 260 280 300 320 340220T (K)

V2 th

(V2)

(a)

1

2

3

(V2th times 04)

420 440 460 480 500 520 540400T (K)

0

1

2

3

4

5

6

7

V2 th

(V2)

(b)

Figure 8 Squared threshold voltage as a function of temperature for (a) vanadium oxide-based switch and (b) titanium oxide (1) (2) and(3) three different samples

119879 lt 340K is a semiconductor at 119879 = 119879119905

= 340K theconductivity abruptly increases by 4-5 orders of magnitudeand above the transition temperature VO

2exhibits metallic

properties ForNbO2119879119905= 1070K Ti

2O3undergoes a gradual

transition in the range 400ndash600K and magnetite (Fe3O4)

is a semiconductor both above and below the Verwey tran-sition temperature (120K) though its resistivity decreaseson heating by two orders of magnitude at 119879 = 119879

119905 For the

switching devices based on these metals the temperatures 119879119900

coincide with the corresponding values of 119879119905(see Figure 5)

This suggests that the switching mechanism is caused by themetal-insulator transition

Electrical switching due to MIT has been first revealedfor vanadium dioxide [16 27 37ndash45] Switching in VO

2

is explained by the current-induced Joule heating of thesample up to 119879 = 119879

119905 which has been confirmed by the

direct IR-radiation measurements of the switching channeltemperature [38 45] In these early works switching hasbeen observed in single crystals [39] and planar thin filmdevices [37 38 45] as well as in vanadate glasses [40 41]VO2-containing ceramics [44] and V

2O5-gel films [42 43]

When as-prepared samples do not consist of pure vanadiumdioxide preliminary electroforming is required resulting inthe formation of the VO

2-containing channel [40 42] The

latter examples as well as the discussed AOFs here supportthe assumption that the formation of vanadium dioxide isthermodynamically preferable at a V

2O5-V interface [22

27] For such samples the threshold voltage decreases withtemperature and reaches zero at 119879 = 119879

119905sim 340K

In this case the switchingmechanismmight be describedin terms of the ldquocritical temperaturerdquo model [29 37] (if theambient temperature is not much lower than 119879

119905)

119881th sim (119879 minus 119879119905)12

(3)

that is the squared threshold voltage linearly tends to zero at119879 rarr 119879

119905 see Figure 8 Switching elements for other transition

metal (FeW Ti and Nb) oxides exhibitingMIT are expected

to show similar behaviour but for different 119879119905rsquos which is

demonstrated by Figure 8(b) for Ti oxideThe switching effect in the WO

3-based sandwich struc-

tures can also be explained in terms of ametal-insulator tran-sition which occurs in nonstoichiometric WO

3minus119910(within a

very narrow interval of variable 119910) at 119879119905ranging from 160 to

280K [46] Because of the narrow interval of ldquoappropriaterdquostoichiometric compositions the S-type I-V characteristicis not likely to appear in tungsten trioxide and in mostcases breakdown occurs instead For switching structureson anodic films on W 119879

119900was found to lie around sim200K

(Figure 5) Therefore 119879119900may turn out to be equal to 119879

119905

Almost no data on MIT in molybdenum oxides are avail-able in the literature except for the transition in Mo

8O23

(MoO2875

) and the switching effect in molybdenum oxidewill be discussed in more detail in the next section Asto Ta and Hf oxides the formation of metastable loweroxides during electroforming should also be possible Theproperties of these oxides are practically unknown but somemetastable oxides of this type have been referred to forexample for the Ta-O system [47] Recently formation ofHfO119909[48] and TaO

119909[49] suboxides has been reported As

to Mn oxides it is known [23] that MnO and Mn3O4are

Mott insulators Mn2O3is a semiconductor and MnO

2is

also a semiconductor but it shows a change in electricalconductivity at 119879 = 119879

119873sim 90K (the Neel temperature) This

might account for the N-NDR effect in Mn oxide this issuewill also be more thoroughly investigated in the next section

Thus the experimental data on the switching effect in119889-metal oxide thin films can be explained in terms of theswitching mechanism driven by the MIT We can state thatin all cases the electrothermal and electrochemical processesduring electroforming are responsible for the switching chan-nel formation The channel consists of a material which canundergo a transition from semiconducting state to metallicstate at a certain temperature 119879

119905 For the V- Ti- Nb- and Fe-

based structures the possibility of formation of the channelsconsisting completely or partly of VO

2 Ti2O3 NbO

2 and

8 Advances in Condensed Matter Physics

Fe3O4 respectively is also confirmed by the thermodynamic

calculations In oxides of W and Mo switching may beassociated with MIT in the channels consisting of WO

3minus119909

and Mo8O23 The S-shaped voltage-current characteristic

is conditioned by the development of an electrothermalinstability in the channel When a voltage is applied thechannel is heated up to 119879 = 119879

119905(at 119881 = 119881th) by the current

and the structure undergoes a transition fromhigh-resistance(OFF) insulating state to low-resistance (ON) metallic state

In high electric fields (105ndash106 Vcm) the possible influ-ence of electronic effects on the MIT should be taken intoaccount A field-induced increase in charge carrier densitywill act to screen Coulomb interactions [12] leading to theelimination of the Mott-Hubbard energy gap at 119879 lt 119879

119905

Moreover a transition of this type may be important in thosematerials where the usual temperature-induced MIT with awell-defined 119879

119905does not take place for example in oxides

of Ta or Hf (and in CGS-based switching structures as well[50]) In the case of vanadium dioxide such a possibilityof the electronically induced MIT was suggested from theinjection experiments [22] and will be discussed also belowin connection with the transition mechanism in VO

2

To summarize the results presented above as well asthe other data on the switching in transition metal oxides[11ndash17 27ndash31] indicate that current instabilities with the S-type NDR exhibit several common features In particularfor each of the investigated materials there is a certain fixedtemperature 119879

119900 above which switching disappears At 119879 lt

119879119900 the threshold voltage decreases as the temperature rises

tending to zero at 119879 = 119879119900 Comparison of these temperatures

with the temperatures of MIT for some compounds (119879119905

=

120K for Fe3O4 sim200K for WO

3minus119909 340K for VO

2 sim500K

for Ti2O3 and 1070K for NbO

2) shows that the switching

effect is associated with the insulator-metal transition in anelectric field The channels consisting of these lower oxidesare formed in initial anodic films during the process ofpreliminary EF

And finally in conclusion of this section we would like todiscuss onemore vanadium oxide where the switching effectsare caused by MITs namely vanadium sesquioxide The I-Vcharacteristics of chromium-doped V

2O3shown in Figure 9

are distinctive in that they exhibit in a certain temperaturerange two regions of negative differential resistance both N-NDR and S-NDR The experimental data on the switchingeffect ofMOM structures based onV

2O3Cr can be explained

in terms of the switching mechanism driven by the variableMIT The S-shaped I-V characteristic is conditioned by thedevelopment of an electrothermal instability in the sampleWhen a voltage is applied the sample is heated by the currentup to 119879 = 119879

1199051(at the threshold voltage 119881 = 119881th119878) and

the structure undergoes a transition from a high-resistance(OFF-1) AFI state to a low-resistance (ON) PM state Asthe current in the ON state increases the sample is furtherheated and at 119879 = 119879

1199052(119868 = 119868th119873) the second transition

to the OFF-2 (or PI) state occurs [51] In the OFF-1 statethe plot of current versus the square root of the appliedvoltage is indicative of a Poole-Frenkel type of conductivityenhancement [52] (Figure 10)

12

34

0

20

40

60

80

100

120

140

160

180

Curr

ent (

mA

)

05 10 15 20 25 3000Voltage (V)

Figure 9 Current-voltage characteristics for V2O3doped with 12

at of Cr at different temperatures 1705 K (1) 1733 K (2) 2210 K(3) and 2655 K (4) [51]

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

Curr

ent (

A)

05 10 15 20 2500Square root of voltage (V05)

150K140K130K120K110K

100K90K80K70K60K

50K40K30K20K10K

Figure 10 Current versus voltage in Poole-Frenkel coordinates fora V2O3-based switching device [52]

23 Switching Effects and Metal-Insulator Transitions in MnandMoOxides In this section we consider electrical switch-ing in oxides of Mn and Mo obtained by vacuum depositionin comparison with those obtained by anodic oxidation [5354] It should be emphasized here that AOFs are (as a ruleexcept for some rare cases) amorphous [32 33] Therefore inMOM structures with anodic films the process of EF similarto that in CGSs usually takes place However in some cases(Mo Mn) as was described in previous sections we havefailed to obtain stable switching with anodic films and herewe present an alternative approach to this problem

Advances in Condensed Matter Physics 9

231 Electrical Switching in Thin Film Structures Based onMolybdenumOxide As inmost TMOs in the molybdenum-oxygen system there exist a number of oxides with variablevalence which are characterized by a wide diversity ofstructures and physical properties [53 55 56] MolybdenumtrioxideMoO

3has a structure based on layers of edge-sharing

distorted MoO6octahedra [23] Similar layered structures

are inherent in lower molybdenum oxides including MoO2

Mo18O52 Mo9O26 Mo8O23 Mo5O14 and Mo

17O47 as well

as 120578- and 120574-Mo4O11[55ndash57]

Stoichiometric MoO3 in its most thermodynamically

stable form 120572-MoO3 is an insulator with a band gap of sim3 eV

[23] During reduction by means of either oxygen deficiencyformation or introducing donor impurity atoms additionaldonor levels near the conduction band bottom appear andthe reduced oxide behaves therefore as a semiconductorPolycrystalline MoO

3 as well as a single crystal has a grey-

yellow colour and the minimum value of the absorption edgeis 440 nm which corresponds to the smallest value of theband gap of 28 eV [58] thus the band gap depends upon thestoichiometry and the crystalline state [53] The conductivityvalues of molybdenum oxides range from dielectric MoO

3

to semiconductor Mo18O52

(resistivity 120588 = 781Ωsdotcm)and down to metal 120578-V]

411

(120588 = 166 times 10minus4Ωsdotcm) [58]Molybdenum dioxide also exhibits metallic properties [2358] and at room temperature 120588 = 88 times 10minus5Ωsdotcm for bulkMoO2samples [55]

Because of their special physical and chemical propertiesmolybdenum oxides are used in various electronic devicessuch as electrochromic displays and indicators reversiblecathodes of lithium batteries gas sensors and memoryelements [55ndash61] Metal-insulator transitions have also beenobserved in some oxides of molybdenum and related com-pounds [62ndash70] In particular Mo

8O23

exhibits a two-stagestructural MIT with formation of a charge-density wave at1198791199051= 315 K and 119879

1199052= 285K [62] However as far as we know

no data are available in the literature concerning thresholdswitching associated with these transitions except for ourwork [53] In this work we have particularly noted thatmemory switching is observed inmany TMOs molybdenumoxides included [4 9 59 60]

The most discussed models in the literature for theReRAMmechanism in oxide structures are those based eitheron the growth and rupture of a metal filament inside theoxide matrix under the action of electric current or onthe redox processes responsible for the formation of somehigh-conductivity or low-conductivity local inclusions cor-responding to particular oxygen stoichiometry [4] The MITideology is also sometimes involved to explain the propertiesof the structures and the memory switching mechanismtherein [71] In any case thememory switching phenomenonseems to be associated with the ion transport [4 9] It isalso appropriate to mention here the works discussing thememory effects in a material with MIT (vanadium dioxide)associated with the presence of hysteresis in the temperaturedependence of conductivity [72]

On the other hand as was shown in the previous sectionmonostable threshold switching (with no memory effects)

associated with the MIT is also characteristic of a numberof TMOs That is why the study of threshold switchingin molybdenum oxide and its possible connection withthe phenomenon of MIT is of considerable scientific andpractical interest

Thinfilm samples ofmolybdenumoxidewere obtained bytwo ways anodic oxidation and thermal vacuum evaporation[53] Anodization of molybdenum was carried out in anacetone-based electrolyte (22 g of benzoic acid plus 40mLof saturated borax aqueous solution per litre of acetone[33 73]) AOFs on Mo might include lower molybdenumoxides for example Mo

4O11andMoO

2with a relatively high

electronic conductivity [53] The fact that the anodic oxideon molybdenum contained lower oxides was confirmed byexperimental data in the work [74] where it was shown thatthe degree of oxidation (valence state) of molybdenum in anAOF is less than six Also this was confirmed theoretically interms of the thermodynamics of the process the formation ofunsaturated oxide MoO

2had been shown to be energetically

more favourable than MoO3[75]

Vacuum deposited film samples were fabricated by ther-mal evaporation of MoO

3powder at residual pressure of

10minus4 Torr onto polished tantalum plates or glass substratesfor electrical and optical studies respectivelyThe thicknessesof the films were determined from the transmission andreflection interference spectra measurements [76] and theywere found to lie in the range from 300 to 800 nm

The XRD pattern of a vacuum-deposited molybdenumoxide sample is presented in Figure 11(a) It is shown thatthe samples represent amorphousMoO

3with a slight oxygen

nonstoichiometry [53] Anodic oxide films on Mo are alsoamorphous (or amorphous-microcrystalline according tothe literature data [73]) but their composition correspondsas described above to ratherMoO

2or other lower oxides and

not to the highest oxide MoO3

Figure 11(b) shows the reflection and transmission spec-tra for one of the samples obtained by vacuum depositionThe experimental data processing using the envelope of theinterference extrema [76] yields the film thickness of (620 plusmn

50) nm and the absorption edge around 120582 asymp 400 nm indi-cates the fact that the oxide phase composition correspondsto MoO

3with a band gap of sim3 eV

Before electroforming initial structures demonstrate thenonlinear and slightly asymmetric current-voltage charac-teristics with no NDR regions When the amplitude of theapplied voltage reaches the forming voltage a sharp andirreversible increase in conductivity is observed and theI(V) curve becomes S-shaped (Figure 12) With increas-ing current the I-V characteristic may change until theparameters of the switching structure are finally stabilizedThe process outlined above is qualitatively similar to theelectroforming of the switching devices based on other TMOs(see Section 22 above) We emphasize once again that thephase composition of the ensuing switching channel mustdiffer from the material of the pristine oxide film becausethe channel conductivity is higher than that of the unformedstructure by several orders of magnitude

The current-voltage characteristics of vacuum-depositedfilms and those of anodic films are qualitatively similar but

10 Advances in Condensed Matter Physics

1

2

20 40 60 8002120579∘

0100200300400500600700800900

I (co

unts

s)

(a)

1

2

3

0

20

40

60

80

100

T (

)

300 400 500 600 700 800 900 1000 1100200Wavelength (nm)

(b)

Figure 11 (a) XRD pattern of the molybdenum oxide film (1) andV]3powder (2) (b) Optical spectra of the sample obtained by vacuum

deposition (1) transmission coefficient of substrate (glass) (2) transmittance and (3) reflectance of Mo oxide film on glass [53]

0 5 10minus5minus10

Voltage (V)

minus016

minus012

minus008

minus004

000

004

008

012

016

Curr

ent (

mA

)

(a)

minus072 072 216 360minus216minus360

Voltage (V)

minus064

minus048

minus032

minus016

000

016

032

048

064

Curr

ent (

mA

)

(b)

Figure 12 Current-voltage characteristics ofMOMstructures with vacuum-deposited (a) and anodic (b)Mo oxide films after electroforming

there is a significant quantitative difference in their thresholdparameters For instance the switching voltage 119881th for theAOF based structures is sim2V (Figure 12(b)) whereas forthe structures on the basis of the films prepared by thermalevaporation119881th is sim10V (Figure 12(a))This difference can beexplained by the difference in thickness of the films

For anodic oxide the thickness can be estimated fromFaradayrsquos law [53]

119889 =

120583119868119886119905

4119890120588119878119873119860

(4)

where 120583 = 128 gmol and 120588 = 65 gcm3 are respectivelythe molar mass and density of V]

2and 119890 and 119873

119860are the

unit charge and Avogadro constant For 119868119886= 70m0 and 119905 =

10min (4) yields 119889 sim 20 nm which is significantly less thanthe typical thickness of the vacuum deposited films and as aresult the threshold voltage for AOFs is also lower than thatfor the films obtained by thermal evaporation

As is discussed in [53] switching is not observed inthinner films obtained by vacuum evaporation (119889 lt 100 nm)

in contrast to ultrathin AOFs A plausible reason for thismight be the fact that relatively thin vacuum depositedfilms contain through-the-thickness conducting defects dueto local stoichiometry variations whereas such defects areimpossible in anodic films because they are grown in highelectric field during anodic oxidation and an appearanceof such defects would interrupt the film growth processThis is similar to what is observed in vanadium oxide inpolycrystalline vanadium dioxide films such pin-hole defectsare usually associated with the grain boundaries which couldundergo local metallization due to strain or nonstoichiom-etry That is why it had been difficult to observe switchingin sandwich MOM structures with sputtered or thermallyoxidized polycrystalline VO

2films and most studies had

been conducted with planar thin-film structures whilst foranodically oxidized VO

2the switching effect has then been

observed in a sandwich structure for the first time in [16]Next we note that unlike the most other TMOs the

process of electroforming in Mo-based structures was hin-dered as was mentioned above in Section 21 that is theconventional electrical breakdown often occurred not the

Advances in Condensed Matter Physics 11

020406080

100120

30 40 50 60 7020Temperature (∘C)

30 40 50 60 7020Temperature (∘C)

0

2

4

6

8

10

12

Thre

shol

d vo

ltage

(V)

5 15minus5minus15

Voltage (V)

minus010

minus005

000005010

Curr

ent (

mA

)

V2 th

(V2)

Figure 13 Threshold voltage as a function of temperature for theTa-MoOx-Au switching structure and the temperature dependenceof (119881th)

2 (lower inset) in compliancewith (3) I-V curve at RT (upperinset)

formation of a switching channel However for the Mooxide films prepared by vacuum deposition the processesof electroforming and switching were more stable whichallowed in this case observation of the transformation of I-V curves at a temperature change It was found that as thetemperature increased the threshold voltage was reducedAt 119879 = 119879

119900sim 55ndash65∘C the NDR region degeneration

commenced at 119879 asymp 60ndash70∘C 119881th rarr 0 and at still highertemperatures the switching effect no longer occurred Inthis case the switching mechanism might be described interms of the ldquocritical temperaturerdquo model (Figure 13) It issupposed [53] that in the case of Mo like in other TMO-based structures formation of a channel also takes placeand this channel should consist of a material exhibiting MITwhich is the reason for switching with an S-shaped current-voltage characteristic (Figure 12)

A brief review of the materials with MIT in the familyof molybdenum compounds presented in [53] shows that themost suitable candidate for the role of such a channel-formingcompound is Mo

8O23

because in this case the value of 1198791199051

almost coincides with the above reported experimentallymeasured 119879

0 It should be noted that formation of other

compounds of molybdenum (eg pyrochlores bronzes sul-fides or chalcogenide glasses) exhibiting MITs with similarorder of magnitude transition temperatures [64ndash68 70] isimpossible because of the lack of the necessary chemicalelements (ie rare earths alkali metals or hydrogen sulfurand tellurium) in the phase composition of both the oxidefilm and the metal electrodes (Au Ta and Mo)

In conclusion the results presented in this subsection onswitching from the HR state to the LR state with an S-NDRin molybdenum oxides obtained by both thermal vacuumdeposition and electrochemical anodic oxidation show thatthe switching effect is due to apparently an insulator-to-metal phase transition in the switching channel consistingcompletely or partly of the lower oxide Mo

8O23 formed in

the initial film during the process of electroforming Thecurrent flowing through the channel heats it up to the MIT

temperature 1198791199051= 315K [62] and the structure switches into

the metallic low-resistance stateThus the channels consisting of this lower oxide are

formed in initial Mo oxide films during preliminary elec-troforming Electrical forming results in the changes inoxygen stoichiometry conditioned by the ionic processes inan electric field close to the MOM structure breakdown fieldThis picture is quite similar to what is observed inmany otherTMOs exhibiting the insulator-to-metal transitions

232 Metal-Insulator Transition and Switching in ManganeseDioxide Manganese dioxide is one of the most interestinginorganic materials because of its wide range of applica-tions In particular nanostructured MnO

2has received great

attention due to its high specific surface area functionalproperties and potential applications as molecular and ionselective membranes in capacitors Li-ion batteries andcatalysts [77] Originally MnO

2has been widely used as a

cathode material for oxide-semiconductor capacitors basedon tantalum niobium and aluminium oxides and the mostimportant properties of the material for this application areits high conductivity and ability to undergo a thermal phasetransition into the lower valence states accompanied by evo-lution of atomic oxygen while the resistance increases by 3-4orders of magnitude (see eg [54] and references therein)Much attention is currently paid to various other propertiesof MnO

2 such as for example the electrochromic effect

[78] thermopower wave phenomenon [79] supercapacitivebehaviour [80] andmemory and threshold switching [54 8182] Also there are a number of papers [83ndash85] describing ananomaly in theMnO

2conductivity near theNeel temperature

which is shown to be associated with the metal-insulatortransition [52] That is why the electrical properties of MnO

2

are of special scientific interest and applied importanceThe most common methods for manganese oxide prepa-

ration are the pyrolytic decomposition of manganese nitrateelectrochemical method hydrothermal synthesis in a mag-netic field and chemical deposition [54 86ndash89] Due to awide range of possible valence states of cations the structureand phase composition of manganese oxides are determinedby the synthesis conditions and process temperature Man-ganese dioxide has many crystallographic forms (120572- 120573- 120574-120575- 120576- and 120582-MnO

2) that connect MnO

6octahedron units to

each other in different ways and have different characters ofspatial alternation of the octahedra filled by Mn atoms andempty octahedra [54 77 90ndash94]

The crystal structure of the 120573-MnO2phase (Figure 14) is a

tetragonal modification of the rutile structural type P4mnmsymmetry group which represents a slightly distorted close-packed hexagonal lattice of oxygen ions [93] Filled octahedraare bound by two common edges in columns oriented alongthe 119888 axis and octahedra of adjacent columns are bound bytheir vertices (Figure 14(c)) Manganese atoms are arrangedin positions 2(a) (000) and oxygen atoms in positions 4(f )(xx0) Because there are vacancies in the oxygen packingthe formula unit can be written as MnO

2minus119910where the

nonstoichiometry index is in the range 119910 = 001ndash010depending on the synthesis method [93]

12 Advances in Condensed Matter Physics

Mn

O

(a)

a

b

c

(b)

O2O4

O1O3

Mn2

Mn1

Mn1998400

O3998400

O4998400

(c)

Figure 14 Crystal structure of manganese dioxide (a) MnO6

octahedron connection in 120573-MnO2(b) [90ndash94] and projection of

octahedron binding onto the ab plane [93]

As to the lower manganese oxides MnO and Mn3O4are

known to be theMott insulatorswith relatively high resistivity[90] and Mn

2O3shows p-type semiconducting properties

MnO2is an n-type semiconductor and antiferromagnetic

with the Neel temperature 119879119873= 925 K [91] Conductivity of

manganese dioxide is higher than that of MnO and Mn2O3

by several orders of magnitude At temperatures above 723Kmanganese dioxide loses oxygen and transforms intoMn

2O3

which is accompanied by the transformation of the crystallinestructure from the tetragonal crystal system of the rutile typeinto the complex large-period cubic lattice (119886 = 94gt) and alarge number of formula units per unit cell [54 92 93]

In this subsection we present the results on electricalproperties of manganese dioxide particularly the natureof the 120573-MnO

2conductivity at low temperatures in its

interrelation with characteristic features of the material crys-talline structure and the metal-insulator phase transitionin this compound as well The effect of electrical switchingwith current-voltage characteristics of both N- and S-typehas been found in thin-film MOM structures on the basisof manganese oxides Possible mechanisms of switching interms of the MIT and thermistor effects are discussed

Mn oxide samples under study have been obtained bythree methods anodic oxidation and vacuum evaporation(thin films) as well as by pyrolysis [54] Thin films ofmanganese dioxide were deposited by means of thermalevaporation onto glass substrates covered by a SnO

2layer

using a VUP-5 vacuum setup the film thickness was 119889 =

250 nmAlso thin films ofmanganese oxidewere obtained byelectrochemical oxidation of metal Mn in the KNO

3-NaNO

3

eutectic melt (see Section 21) at 119879 = 600K at a constantvoltage of about 2V for 3min the current density diminishedfrom 200 to 100mAcm2 during the oxidation process Foranodic oxide films on Mn the value of 119889 was sim100 nm Bulksamples of manganese dioxide were obtained by multipledecomposition (pyrolysis) of manganese nitrate at 119879 = 670Kon a glass-ceramic substrate or on a tantalum sheetmetal withthe subsequent separation from the substrate [92 93] Thetotal coating thickness was about 1mm

The manganese oxide samples were characterized by X-ray diffraction (XRD) using a DRON-6 diffractometer inCuK120572and FeK

120572radiation The characteristics of the atomic

structure of pyrolytic manganese dioxide were refined by thefull-profile analysis of the XRD patterns of polycrystallinesamples [93]The resistivity of pyrolyticMnO

2wasmeasured

in the temperature range 15 to 300K bymeans of a four-probetechnique both DC and AC (in a frequency range from 50 to104Hz) in a Gifford-McMahon cycle cryorefrigerator [54]We also measured electrical conductivity in the range T =293ndash423K the Hall effect in the magnetic field of 23 T andthe Seebeck coefficient (thermoelectromotive force thermo-emf ) The dynamic current-voltage (I-V) characteristics ofthe thin-film MOM structures were measured by oscillo-graphic method using an AC sinusoidal signal

The XRD patterns of the manganese oxide samples arepresented in Figures 15 and 16 The vacuum-deposited filmsare amorphous and represent a mixture of 120573- and 120574-MnO

2

(Figure 16) The results of the full-profile analysis show thatthe pyrolytic MnO

2samples (Figure 15) are composed of

the finely dispersed 120573-MnO2phase with the traces of 120574-

MnO2 120576-MnO

2 and Mn

2O3phases The periods of the

tetragonal unit cell of 120573-MnO2are 119886 = 119887 = 4401 A and

119888 = 2872 A The oxygen coordinates in 4119891 positions (seediscussion of the crystal structure above and Figure 14) arefound to be119909 = 0302 Calculations of the oxygen-manganeseinteratomic distances show [93] that the oxygen octahedron

Advances in Condensed Matter Physics 13

330222

040231

212202

112

130002

220

121

120

111

110

101

020

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 80 100 12002120579∘

Figure 15 XRD (Cu K120572radiation) pattern of pyrolytic MnO

2

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 8002120579∘ Fe

120573-MnO2

120574-MnO2

Experiment

Figure 16 XRD (Fe K120572radiation) pattern of Mn oxide film and

reference spectra of crystalline MnO2samples

is compressed along the (100) direction which connects theoctahedron vertices This deformation results in an increaseof the overlap of electron119901 orbitals of oxygen and119889 orbitals ofmanganese and can form the additional splitting of electronlevels in the crystal field leading to the appearance of unpairedelectrons [94]

The measurements of the conductivity temperaturedependence Hall effect and thermo-emf show that man-ganese dioxide is the electron semiconductor with conductiv-ity of about 1Ωminus1cmminus1 and mobility of sim10 cm2Vsdots The Hallmeasurements give the carrier density ofsim1018 cmminus3 which isclose to the density values in degenerate semiconductorsTheactivation energy of conductivity is sim01 eV and the band gapwidth is equal to 2 eV [90] The estimated value of the Fermienergy from the thermo-emf temperature dependence is inthe range of 002 to 005 eV which also indicates the degener-ate character of the electron gasThe nonstoichiometry indexdetermined by the XRD peaks which are not contributed

by the manganese atoms that is by those with the oddsum of indexes is 119910 = 006 Such nonstoichiometry providesthe concentration of trap states of about 1017-1018 cmminus3which correlates with the above mentioned Hall-effect-basedmeasurements of electron density

Such high vacancy concentration allows us to considerthe nonstoichiometric 120573-MnO

2as a heavily doped semicon-

ductor with a subband of impurity levels which provides afeasibility of the out-of-band electron transfer at low tem-peratures The structural distortions high nonstoichiometryand as a consequence sufficiently high concentration ofimpurity states cause the density state tails near the bandedges similarly to those in heavily doped semiconductorsHowever at room and higher temperatures the conduction isdetermined by the activation mechanism Thus the electronstructure and a low mobility of charge carriers promotethe manifestation of different charge transfer mechanismsin different temperature ranges namely both the hoppingmechanism and the activation one

The electron capturing oxygen vacancies create mixedvalence states of manganese cations (Mn3+ndashMn4+) Interest-ingly the mixed valence of Mn ions is also characteristic ofmanganites Ln

1minus119910Sr119910MnO3[95] where Ln is La or another

rare-earth element possessing the effect of colossal magne-toresistance (CMR) In these compounds the mixed valenceof manganese is attained via doping It had been deemed thatholes introduced by strontium are localized at manganeseions that is the Mn4+ ions with concentration 119910 are formedHowever recent X-ray emission studies have shown that boththe chemical shift and the exchange splitting of the emissionX-ray Mn K

1205731line are almost the same in the range 119910 lt 04ndash

05 as is the case in Mn2O3 and then they decrease quickly

to the values characteristic of MnO2[96] which suggests that

the introduced holes are localized at oxygen atoms in the holedoping region (at relatively low 119910) and atmanganese atoms inthe electron doping region that is at higher 119910 values

The temperature dependence of conductivity is presentedin Figure 17 The resistance peak observed in the figure ina temperature range of 80ndash90K is the result of the phasetransition of 120573-MnO

2from a semiconducting state to a metal

state upon decreasing the temperature to 15 K [54] The tem-perature region of the transition is close to the known Neeltransition from the paramagnetic state into the ferromagneticone for manganese dioxide The temperature dependenceof resistance indicates thus the MIT to occur in MnO

2 In

the temperature range from 300 to 80K (Figure 17) thisdependence does not correspond to the exponential one yetit fits well with the linear dependence in theMott coordinatesln(119877) sim 119879

14 which indicates the hopping conductivitymechanism over the polyvalent states ofmanganese ions witha distance between the centres of 25ndash35gt [92] However inthe temperature range from 90 to 15 K the dependence ofln119877 on ln119879 is almost linear with the slope of about unity(ie 120597 ln119877120597 ln119879 asymp 1) which is characteristic of the metallicconductionThus the character of conductivity ofmanganesedioxide indicates the presence of the MIT at 119879

119888sim 80K (on

cooling)

14 Advances in Condensed Matter Physics

CoolingHeating

40 80 120 160 2000T (K)

0

2

4

6

8

10

Resis

tivity

(Ohm

timescm

)

Figure 17 Temperature dependence of AC (70Hz) resistivity ofpyrolytic MnO

2

In the low temperature region manganese dioxide is anantiferromagnetwith the helical spin ordering [97]The inter-action between the magnetic ions of manganese which leadsto the antiferromagnetic state occurs through the intermedi-ate interaction with diamagnetic oxygen ions which weakensthe exchange interaction The conductivity increases proba-bly due to exceeding the energy of the exchange interactionby the thermal energy as the temperature increases whichleads to an increase in the number of unpaired electrons inthe paramagnetic state As the temperature further increasesthe conductivity continues to rise and the Mott hoppingmechanism of charge transfer becomes predominant Similarcharacter of the temperature dependence in ferromagneticdegenerate semiconductors has previously been described[85 98] for substoichiometric (oxygen-deficient) europiummonoxide The transition from the highly conductive stateinto the insulating state occurs in such semiconductors uponvarying the type of magnetic ordering or its destruction

For EuO1minus119910

lowering the peak magnitude in the 119877(119879)

dependence is associatedwith a decrease in the concentrationof impurities (oxygen vacancies) In magnetic semicon-ductors the phase transition is associated both with themagnetoelectric effects and with the variation in the electricpolarization under the action of the magnetic field at theantiferromagnetic transition [98] The dielectric constant formanganese dioxide is equal to sim10 but the effective dielectricconstant can decrease near 119879

119888by a factor of several times

thereby affecting the mobility of carriers located in the tailsof the density of states near the band edge and promotingtheir delocalization at the phase transition temperatureManganese dioxide also belongs to this group of substanceshowever the phase transition in MnO

2reported here can be

also described in terms of the Mott transition [24]According to the Mott criterion electrons delocalize if

the distance between the atoms 119899minus13 becomes comparable

with their atomic radius 119886119860 where 119886

119860is associated with the

Bohr radius 119886119861= ℏ2120576me2The static permittivity 120576 is replaced

by the effective permittivity which takes into account theexchange interaction of the spins of conduction electronswith orbitalmagneticmoments of atoms At the temperature-induced Mott MIT the orbital radius 119886

119861decreases near 119879 =

119879119888thereby providing the fulfillment of the Mott criterion at a

given level of impurity centres [24 98] The transition fromthe metallic state into the semiconductor state is possible insuch semiconductors as the temperature increases Thus theMIT in manganese dioxide is brought about by temperaturevariation

In conclusion we note that the phase transition describedabove is inverse (reentrant) MIT that is the metallic phaseis low-temperature while the high-temperature state is insu-lating This is rather rare yet not unique and unusualphenomenon In most cases (eg in vanadium dioxide) thelow-temperature phase is insulating and on heating abovea certain temperature 119879

119888 the material becomes metallic for

VO2 this transition temperature is 119879

119888= 340K The inverse

transitions are observed in such compounds as the abovementioned EuO

1minus119910 NiS2Se Y2O3minus119910

and LaMnO3films [24

31 52 85 98 99] Also the high-temperature Mott transi-tion from paramagnetic metal to paramagnetic insulator inV2O3Cr is an inverse transition with the resistivity peak at

119879119888sim 350K for a chromium concentration of around 1 at

[24 51] and in mixed valence CMR-manganites the sharpresistivity peak has been shown to be caused by the AndersonMIT [95]

It is known that many TMOs exhibit electrical switchingassociated with MITs [28] For the anodic oxide films onMn the study of the effect of electrical switching in thin-film Mn-MnO

2-Au sandwich structures showed that the S-

type switching was not observed in contrast to for examplethe similar structures based on oxides of vanadium andsome other transition metals [28] Instead switching withthe N-shaped I-V characteristic occurred after EF at 119879 lt

80K (Figure 18(a)) In addition the EF process in the Mn-based structures was hindered likewise for example for thestructures based on yttrium oxide [31] that is the breakdowntook place more often It should be noted that EF at roomtemperature always led to breakdown and the switchingeffect had never been observed in this case As was arguedin [54] this switching effect was associated with the MIT inMnO2

On the other hand in the films obtained by vacuumsputtering we have observed S-type switching at roomtemperature (Figure 18(b)) The threshold voltage is of theorder of 1 V and almost independent of temperature up to 119879

= 375KThis situation resembles that with yttrium oxide where

both S-type and N-type switching has been observed too[31] One can assume that switching with the S-shapedI-V curves is due to the so-called ldquothermistor effectrdquo Itis well known that the current flowing through a solidgenerates Joule heat resulting in an increased temperatureIn materials with a negative TCR a rising temperatureinduces a current enhancement and an increased powerdissipation resulting in a farther temperature increase Thispositive electrothermal feedback causes the appearance of anNDR and accordingly an S-shaped I-V characteristic [2]

Advances in Condensed Matter Physics 15

minus15

minus10

minus5

0

5

10

15Cu

rren

t (m

A)

0500 10 15minus10 minus05minus15

Voltage (V)

(a)

minus2

minus1

0

1

2

Curr

ent (

mA

)

10 2minus2 minus1

Voltage (V)

(b)

Figure 18 (a) I-V characteristic of anodic oxide film on manganese at T = 77K (b) I-V characteristic of vacuum-deposited MnO2at 119879 =

293K

In some cases this process might by modified by high-fieldeffects such as Schottky injection impact ionization Poole-Frenkel effect and Zener or avalanche breakdown Notethat unlike a conventional thermistor with an Arrhenius-like conductivity law manganese oxide exhibits a weaker119877(119879) dependence characteristic of the hopping conductivitymechanism which seems to account for the observed weaktemperature dependence of the threshold voltage

An alternative mechanism for the S-type switching effectmay be connected with a possible high-temperature usual(ie not inverse)MIT in somemanganese oxide As is knownEF (see Section 22) leads to the formation of a filament ofhighly conducting material a switching channel Similarlyto what is observed for Mo oxide (Section 231) and otherTMOs (Sections 21 and 22) we suppose that the compositionof this channel differs from the material of the initial oxidefilm since its conductivity noticeably exceeds that of anunformed structure In view of such a plentiful set of phasesand crystal structures in the Mn-O system one can supposethat the channelmight consist of nonstoichiometric120573-MnO

2

some other polymorphic modifications of manganese diox-ide or lower Mn oxides which might undergo a MIT underthe action of either temperature or electric field Howeverthis question obviously requires additional investigation inparticularmeasurements of119877(119879)dependences and switchingproperties at higher temperatures If this assumed high-temperature MIT would occur in for example nonstoichio-metric 120573-MnO

2 one could expect observation of double-

NDR I-V characteristics in such samples at low temperaturesanalogously to those in V

2O3Cr (Figure 9) where this effect

is due to the MITs [29] with the only difference being thatin the case of MnO

2this curve should be N-S-shaped (unlike

the S-N-shaped one in Figure 9) since in chromium-dopedvanadium sesquioxide the inverse MIT is high-temperatureas opposed to MnO

2which as we discussed above (see

Figure 17) exhibits the inverse MIT at low temperaturesNote however that the discussed high-temperature MIT

in 120573-MnO2minus119910

may be unobservable under the temperature

change in equilibrium conditions but displays itself onlyunder the applied electric field as the S-type electricalswitching effect because the transition temperature is closeto or higher than the temperature of MnO

2decomposition

(723K) Such a nonequilibrium transition occurs at switchingin those materials where the usual temperature-inducedMITwith a well-defined 119879

119905does not take place for example in

CGSs for which the equilibrium transition temperature 1198791199050

is higher than 119879119892 while in a high electric field 119879

119905(119864) lt 119879

1199050

might be lower than 119879119892 where 119879

119892is the temperature of the

glass-crystal transition and119864 is the electric field strength [30]Summarizing we have studied the electrical properties

(conductivity temperature dependence and Hall and Seebeckeffects) of the 120573 phase of manganese dioxide obtained bypyrolysis thermal vacuum evaporation and anodic oxida-tion The change of conductivity mechanisms dependingon temperature in a range of 450ndash25K has been shownand the metal-insulator phase transition at low (lt90K)temperatures has been revealed The specific feature of thistransition described in terms of the Mott mechanism isthat the metal phase exists at low temperatures while athigher temperatures the material is a semiconductor withthe hopping conductivity over the mixed valence states ofmanganese ions

The low-temperature switching effect with an NDR andN-shaped current-voltage characteristic associated with thephase transition in manganese dioxide has been found in theMOM two-terminal devices based on anodicMn oxide filmsOn the contrary the devices based on vacuum-depositedfilms have been found to exhibit an S-NDR at room andhigher temperatures which is suggested to be caused byeither the thermistor effect or a high-temperature MIT innonstoichiometric 120573-MnO

2

It should be emphasized that the low-temperature MITin 120573-MnO

2with 119879

119905= 70ndash80K is the inverse Mott transition

which is akin for instance to the transition in V2O3Cr

at 119879119905= 190ndash385K (for chromium dopant concentration in

the range of 05ndash18 at) [51] We thus assume that farther

16 Advances in Condensed Matter Physics

5 10 150Voltage (V)

0

1

2

3

4

5

6

7

8Cu

rren

t (m

A)

(a)ΔV

th(V

)

0

1

2

3

1 2 3 4 5 6 7 80W (at )

(b)

Figure 19 I-V curve (a) of Au-V2minus119910

W119910O5times 119899H2O-Au sandwich structure with119910= 003 and119881th scattering as a function of tungsten admixture

percentage 119910 (b) [104 105]

investigations of the phase transition in manganese dioxidedescribed in this paper are a rather interesting and topicalscientific problem since manganese dioxide can serve as amodel object for studying such inverse metal-insulator phasetransitions

Finally we note that the results presented in this sectionindicate the possibility of application of manganese oxide asa material for thin film sandwich switching devices Deviceswith NDR (N- and S-shaped I-V characteristics) have poten-tial applications in microelectronics as switches memoryelements and microsensors (these issues will be discussedin more detail below in Section 4) Particularly manganeseoxide microswitches [82] can be utilized for implementationof neuristors built with Mott-transition-based memristors[100]

24 Effect of Doping It is only natural that the systemsexhibiting the NDR effects possess a high applied potential inelectronics [2 4 8 18 100 101] yet the stage of EF is a weaklink of chain in the technology process Note that the formingprocess may be brought about by laser irradiation [102] notby applying of electric field In the case of laser treatment(or ldquolaser formingrdquo unlike the above described electricalforming) the parameters of the structures are characterizedby the absence of the scatter that is the I-V characteristics ofall structures are almost identical [103] One more demerit tobe avoided is the scatter in switching parameters (the value of119881th first of all) and their instability during operation In thissubsection we discuss the issues concerning the switchingparameter stabilization by means of doping

In the work [104] we have studied the switching effectin the MOM structures on the basis of W-doped V

2O5-gel

filmsThese structures require preliminary EF similar to thatin anodic oxide films resulting in formation of a conducting

channel within the initial dielectric xerogel filmThe channelconsists of vanadiumdioxide and switching is associatedwiththe insulator-to-metal transition in VO

2 As was shown in

[104 105] for the pure (undoped) V2O5-gel the switching

parameters vary in a wide range because the phenomenonof EF is statistical in nature (like electrical breakdown) andits statistical character shows itself as a spread in the observedthreshold voltages of the ensuing structures that is actuallyat multiple measurements 119881th = ⟨119881th⟩ plusmn Δ119881th

It has been shown [104] that the statistical spread in valuesof the threshold parameters can be minimized by means ofdoping (Figure 19) Unsophisticated reasoning could accountfor this result for pure V

2O5-gel electroforming leads to

formation of VO2with 119879

119905= 340K and each switching

event requires heating up and cooling down from roomtemperature to 119879

119905 this thermal cycling can modify the

peripheral regions of the channel which leads to the changeof the switching threshold voltage On the other hand forthe samples with a high concentration of W the MIT issuppressed [104] and switching is degenerated Betweenthese two outermost points an optimum should exist Asone can see from Figure 19 this optimal value correspondsto 3 at of W that is for V

097W003

O2the switching

parameters are the most stableThe transition temperature ofV097

W003

O2is lower than that for pure vanadium dioxide

and hence the magnitude of the aforesaid thermal cyclingis decreased which results in an increase of stability of theswitching parameters

Next we have studied the effect of doping on switchingin AOFs on Ti [29] These films were obtained in 5 watersolution of citric acid (C

6H8O7) in volt-static regime at 119881

119886

= 20V The samples were doped with aluminium by meansof adding soluble Al-containing substances to the electrolyte

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

Films vol 97 no 2 pp 129ndash143 1982[46] R Collongues La Non-Stoechiometrie Masson Paris France

1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

9 no 5 pp 391ndash396 2014[67] B Sun W Zhao Y Liu and P Chen ldquoResistive switching effect

of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

1990[70] S Mukherjee S Karmakar H Sakata and B K Chaudhuri

ldquoLow-temperature metallic behavior of amorphous MoO3-

TeO2thin filmsrdquo Journal of Applied Physics vol 97 no 12 Article

ID 123707 2005[71] AMottaghizadeh Q Yu P L Lang A Zimmers andH Aubin

ldquoMetal oxide resistive switching evolution of the density ofstates across the metal-insulator transitionrdquo Physical ReviewLetters vol 112 no 6 Article ID 066803 2014

[72] R Xie C T Bui B Varghese et al ldquoAn electrically tunedsolid-state thermalmemory based onmetal-insulator transitionof single-crystalline VO

2nanobeamsrdquo Advanced Functional

Materials vol 21 no 9 pp 1602ndash1607 2011

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

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GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

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Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

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AerodynamicsJournal of

Volume 2014

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PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

6 Advances in Condensed Matter Physics

00

05

10

15

20

25

30

V (a

u)

1 2

3 4

5

200 300 400 500 600100T (K)

Figure 5 Threshold voltage in arbitrary units 119881 = 119881th(119879)119881th(1198791015840)

for theMOM structures on the basis of different oxides as a functionof ambient temperature (1) Fe (2)W (3)V (4)Ti and (5)Nb anodicoxideData for different samples have been averaged andnormalizedto a certain temperature 119879

1015840 which is different for different oxides[22 27 28]

0

5

10

15

20

25

30

35

Curr

ent (120583

A)

05 10 15 20 2500Voltage (V)

Figure 6 I-V curve with N-NDR of the structure metalY anodicoxidemetal [31]

near the outer boundary is close to the V2O5stoichiometry

The similar ordering of layers evidently exists in iron oxideparticularly it is known that in a thermal oxide of iron theFe3O4phase usually predominates [28] On the other hand

the AOFs on Nb and Ti mainly consist of Nb2O5and TiO

2

and NbO2or Ti2O3layers seem to be relatively thin [27 28]

For the W-WO3system a wide minimum of Δ119866

119903(119909) lies

in the range 119909 = 27ndash30 (Figure 7) the same behaviour seemsto be characteristic of the Mo-MoO

3system The calculation

for manganese oxides yields the minimum at 119909 = 15 that isfor Mn

2O3 The curve Δ119866

119903(119909) for uranium is also presented

just as an example note however that MITs have beenreported for lower uranium oxide U

4O9[36] For Zr Hf Ta

and Y such calculations have not been made because thereexist no clear data on the thermodynamic properties of thelower oxides of those metals

F1

F2F3

T1

T2

T11N1

N2

N3

W1W2

W3

W4

W5U5

V1

V2

V9

V10

V11

U1U2

U3 U4

M4

M1

M2 M3

900

800

700

600

500

400

300

200

100

0

minusΔGr

(kJm

ol)

15 20 25 3010X

V9998400

V3ndashV8

T2998400

Figure 7 Gibbs potential change Δ119866119903(per 1 g atom of metal) for

the reaction of the highest oxide with the metal substrate versus119909 the oxygen stoichiometric index of the lower oxide which isformed in this reaction Symbol indications are as follows (i) IronF1ndashFeO F2ndashFe

3O4 F3ndashFe

2O3 (ii) Niobium N1ndashNbO N2ndashNbO

2

N3ndashNb2O5 (iii) Titanium T1ndashTiO T2ndashTi

2O3 T3ndashT10ndashTi

119899O2119899minus1

(119899 = 3ndash10) T11ndashTiO2 (iv) Vanadium V1ndashVO V2ndashV

2O3 V3ndashV8ndash

V119899O2119899minus1

(119899 = 3ndash8) V9ndashVO2 V10ndashV

6O13 V11ndashV

2O5 (v) Tungsten

W1ndashWO2W2ndashW

18O49W3ndashW

10O29W4ndashW

50O148

W5ndashWO3 (vi)

Manganese M1ndashMnO M2ndashMn3O4 M3ndashMn

2O3 M4ndashMnO

2 (vii)

Uranium U1ndashUO2 U2ndashU

4O9 U3ndashU

3O7 U4ndashU

3O8 U5ndashUO

3 The

points T21015840 and V91015840 characterize a scatter due to the Δ1198660 data

difference [22 28]

During electroforming current-induced heating of thefilm under the electrode leads to a diffusion of both metalfrom the substrate into the film and oxygen from the outerlayer to the inner one Also the transport of metal andoxygen ions due to the applied electric field is possible Sinceduring electroforming (unlike thermal or electrochemicaloxidation) no external oxygen is present no reaction cantake place except the reduction of the highest oxide of AOFThe reduction results in growth of the channel consisting oflower oxide through the film from one electrode to anotherEvidently substances with the minimum Δ119866

119903value (see

Figure 7)will be predominant in the phase composition of thechannelThe current increase after formingmay cause furtherreduction of the channel material leading to a predominanceof the phases such as VO NbO and TiO Many of the lowestoxides of transition metals (mono- and suboxides) exhibitmetallic properties [23] the accumulation of these phases inthe channel will therefore lead to an irreversible increase inconductivity that is to breakdown

The above compounds (VO2 Fe3O4 Ti2O3 and NbO

2)

have one feature in common namely a metal-insulator phasetransition [24] The MIT phenomenon is characterized bythe sharp and reversible change in the conductivity at acertain temperature 119879

119905 for instance vanadium dioxide at

Advances in Condensed Matter Physics 7

1 2

3

0

1

2

3

4

5

6

240 260 280 300 320 340220T (K)

V2 th

(V2)

(a)

1

2

3

(V2th times 04)

420 440 460 480 500 520 540400T (K)

0

1

2

3

4

5

6

7

V2 th

(V2)

(b)

Figure 8 Squared threshold voltage as a function of temperature for (a) vanadium oxide-based switch and (b) titanium oxide (1) (2) and(3) three different samples

119879 lt 340K is a semiconductor at 119879 = 119879119905

= 340K theconductivity abruptly increases by 4-5 orders of magnitudeand above the transition temperature VO

2exhibits metallic

properties ForNbO2119879119905= 1070K Ti

2O3undergoes a gradual

transition in the range 400ndash600K and magnetite (Fe3O4)

is a semiconductor both above and below the Verwey tran-sition temperature (120K) though its resistivity decreaseson heating by two orders of magnitude at 119879 = 119879

119905 For the

switching devices based on these metals the temperatures 119879119900

coincide with the corresponding values of 119879119905(see Figure 5)

This suggests that the switching mechanism is caused by themetal-insulator transition

Electrical switching due to MIT has been first revealedfor vanadium dioxide [16 27 37ndash45] Switching in VO

2

is explained by the current-induced Joule heating of thesample up to 119879 = 119879

119905 which has been confirmed by the

direct IR-radiation measurements of the switching channeltemperature [38 45] In these early works switching hasbeen observed in single crystals [39] and planar thin filmdevices [37 38 45] as well as in vanadate glasses [40 41]VO2-containing ceramics [44] and V

2O5-gel films [42 43]

When as-prepared samples do not consist of pure vanadiumdioxide preliminary electroforming is required resulting inthe formation of the VO

2-containing channel [40 42] The

latter examples as well as the discussed AOFs here supportthe assumption that the formation of vanadium dioxide isthermodynamically preferable at a V

2O5-V interface [22

27] For such samples the threshold voltage decreases withtemperature and reaches zero at 119879 = 119879

119905sim 340K

In this case the switchingmechanismmight be describedin terms of the ldquocritical temperaturerdquo model [29 37] (if theambient temperature is not much lower than 119879

119905)

119881th sim (119879 minus 119879119905)12

(3)

that is the squared threshold voltage linearly tends to zero at119879 rarr 119879

119905 see Figure 8 Switching elements for other transition

metal (FeW Ti and Nb) oxides exhibitingMIT are expected

to show similar behaviour but for different 119879119905rsquos which is

demonstrated by Figure 8(b) for Ti oxideThe switching effect in the WO

3-based sandwich struc-

tures can also be explained in terms of ametal-insulator tran-sition which occurs in nonstoichiometric WO

3minus119910(within a

very narrow interval of variable 119910) at 119879119905ranging from 160 to

280K [46] Because of the narrow interval of ldquoappropriaterdquostoichiometric compositions the S-type I-V characteristicis not likely to appear in tungsten trioxide and in mostcases breakdown occurs instead For switching structureson anodic films on W 119879

119900was found to lie around sim200K

(Figure 5) Therefore 119879119900may turn out to be equal to 119879

119905

Almost no data on MIT in molybdenum oxides are avail-able in the literature except for the transition in Mo

8O23

(MoO2875

) and the switching effect in molybdenum oxidewill be discussed in more detail in the next section Asto Ta and Hf oxides the formation of metastable loweroxides during electroforming should also be possible Theproperties of these oxides are practically unknown but somemetastable oxides of this type have been referred to forexample for the Ta-O system [47] Recently formation ofHfO119909[48] and TaO

119909[49] suboxides has been reported As

to Mn oxides it is known [23] that MnO and Mn3O4are

Mott insulators Mn2O3is a semiconductor and MnO

2is

also a semiconductor but it shows a change in electricalconductivity at 119879 = 119879

119873sim 90K (the Neel temperature) This

might account for the N-NDR effect in Mn oxide this issuewill also be more thoroughly investigated in the next section

Thus the experimental data on the switching effect in119889-metal oxide thin films can be explained in terms of theswitching mechanism driven by the MIT We can state thatin all cases the electrothermal and electrochemical processesduring electroforming are responsible for the switching chan-nel formation The channel consists of a material which canundergo a transition from semiconducting state to metallicstate at a certain temperature 119879

119905 For the V- Ti- Nb- and Fe-

based structures the possibility of formation of the channelsconsisting completely or partly of VO

2 Ti2O3 NbO

2 and

8 Advances in Condensed Matter Physics

Fe3O4 respectively is also confirmed by the thermodynamic

calculations In oxides of W and Mo switching may beassociated with MIT in the channels consisting of WO

3minus119909

and Mo8O23 The S-shaped voltage-current characteristic

is conditioned by the development of an electrothermalinstability in the channel When a voltage is applied thechannel is heated up to 119879 = 119879

119905(at 119881 = 119881th) by the current

and the structure undergoes a transition fromhigh-resistance(OFF) insulating state to low-resistance (ON) metallic state

In high electric fields (105ndash106 Vcm) the possible influ-ence of electronic effects on the MIT should be taken intoaccount A field-induced increase in charge carrier densitywill act to screen Coulomb interactions [12] leading to theelimination of the Mott-Hubbard energy gap at 119879 lt 119879

119905

Moreover a transition of this type may be important in thosematerials where the usual temperature-induced MIT with awell-defined 119879

119905does not take place for example in oxides

of Ta or Hf (and in CGS-based switching structures as well[50]) In the case of vanadium dioxide such a possibilityof the electronically induced MIT was suggested from theinjection experiments [22] and will be discussed also belowin connection with the transition mechanism in VO

2

To summarize the results presented above as well asthe other data on the switching in transition metal oxides[11ndash17 27ndash31] indicate that current instabilities with the S-type NDR exhibit several common features In particularfor each of the investigated materials there is a certain fixedtemperature 119879

119900 above which switching disappears At 119879 lt

119879119900 the threshold voltage decreases as the temperature rises

tending to zero at 119879 = 119879119900 Comparison of these temperatures

with the temperatures of MIT for some compounds (119879119905

=

120K for Fe3O4 sim200K for WO

3minus119909 340K for VO

2 sim500K

for Ti2O3 and 1070K for NbO

2) shows that the switching

effect is associated with the insulator-metal transition in anelectric field The channels consisting of these lower oxidesare formed in initial anodic films during the process ofpreliminary EF

And finally in conclusion of this section we would like todiscuss onemore vanadium oxide where the switching effectsare caused by MITs namely vanadium sesquioxide The I-Vcharacteristics of chromium-doped V

2O3shown in Figure 9

are distinctive in that they exhibit in a certain temperaturerange two regions of negative differential resistance both N-NDR and S-NDR The experimental data on the switchingeffect ofMOM structures based onV

2O3Cr can be explained

in terms of the switching mechanism driven by the variableMIT The S-shaped I-V characteristic is conditioned by thedevelopment of an electrothermal instability in the sampleWhen a voltage is applied the sample is heated by the currentup to 119879 = 119879

1199051(at the threshold voltage 119881 = 119881th119878) and

the structure undergoes a transition from a high-resistance(OFF-1) AFI state to a low-resistance (ON) PM state Asthe current in the ON state increases the sample is furtherheated and at 119879 = 119879

1199052(119868 = 119868th119873) the second transition

to the OFF-2 (or PI) state occurs [51] In the OFF-1 statethe plot of current versus the square root of the appliedvoltage is indicative of a Poole-Frenkel type of conductivityenhancement [52] (Figure 10)

12

34

0

20

40

60

80

100

120

140

160

180

Curr

ent (

mA

)

05 10 15 20 25 3000Voltage (V)

Figure 9 Current-voltage characteristics for V2O3doped with 12

at of Cr at different temperatures 1705 K (1) 1733 K (2) 2210 K(3) and 2655 K (4) [51]

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

Curr

ent (

A)

05 10 15 20 2500Square root of voltage (V05)

150K140K130K120K110K

100K90K80K70K60K

50K40K30K20K10K

Figure 10 Current versus voltage in Poole-Frenkel coordinates fora V2O3-based switching device [52]

23 Switching Effects and Metal-Insulator Transitions in MnandMoOxides In this section we consider electrical switch-ing in oxides of Mn and Mo obtained by vacuum depositionin comparison with those obtained by anodic oxidation [5354] It should be emphasized here that AOFs are (as a ruleexcept for some rare cases) amorphous [32 33] Therefore inMOM structures with anodic films the process of EF similarto that in CGSs usually takes place However in some cases(Mo Mn) as was described in previous sections we havefailed to obtain stable switching with anodic films and herewe present an alternative approach to this problem

Advances in Condensed Matter Physics 9

231 Electrical Switching in Thin Film Structures Based onMolybdenumOxide As inmost TMOs in the molybdenum-oxygen system there exist a number of oxides with variablevalence which are characterized by a wide diversity ofstructures and physical properties [53 55 56] MolybdenumtrioxideMoO

3has a structure based on layers of edge-sharing

distorted MoO6octahedra [23] Similar layered structures

are inherent in lower molybdenum oxides including MoO2

Mo18O52 Mo9O26 Mo8O23 Mo5O14 and Mo

17O47 as well

as 120578- and 120574-Mo4O11[55ndash57]

Stoichiometric MoO3 in its most thermodynamically

stable form 120572-MoO3 is an insulator with a band gap of sim3 eV

[23] During reduction by means of either oxygen deficiencyformation or introducing donor impurity atoms additionaldonor levels near the conduction band bottom appear andthe reduced oxide behaves therefore as a semiconductorPolycrystalline MoO

3 as well as a single crystal has a grey-

yellow colour and the minimum value of the absorption edgeis 440 nm which corresponds to the smallest value of theband gap of 28 eV [58] thus the band gap depends upon thestoichiometry and the crystalline state [53] The conductivityvalues of molybdenum oxides range from dielectric MoO

3

to semiconductor Mo18O52

(resistivity 120588 = 781Ωsdotcm)and down to metal 120578-V]

411

(120588 = 166 times 10minus4Ωsdotcm) [58]Molybdenum dioxide also exhibits metallic properties [2358] and at room temperature 120588 = 88 times 10minus5Ωsdotcm for bulkMoO2samples [55]

Because of their special physical and chemical propertiesmolybdenum oxides are used in various electronic devicessuch as electrochromic displays and indicators reversiblecathodes of lithium batteries gas sensors and memoryelements [55ndash61] Metal-insulator transitions have also beenobserved in some oxides of molybdenum and related com-pounds [62ndash70] In particular Mo

8O23

exhibits a two-stagestructural MIT with formation of a charge-density wave at1198791199051= 315 K and 119879

1199052= 285K [62] However as far as we know

no data are available in the literature concerning thresholdswitching associated with these transitions except for ourwork [53] In this work we have particularly noted thatmemory switching is observed inmany TMOs molybdenumoxides included [4 9 59 60]

The most discussed models in the literature for theReRAMmechanism in oxide structures are those based eitheron the growth and rupture of a metal filament inside theoxide matrix under the action of electric current or onthe redox processes responsible for the formation of somehigh-conductivity or low-conductivity local inclusions cor-responding to particular oxygen stoichiometry [4] The MITideology is also sometimes involved to explain the propertiesof the structures and the memory switching mechanismtherein [71] In any case thememory switching phenomenonseems to be associated with the ion transport [4 9] It isalso appropriate to mention here the works discussing thememory effects in a material with MIT (vanadium dioxide)associated with the presence of hysteresis in the temperaturedependence of conductivity [72]

On the other hand as was shown in the previous sectionmonostable threshold switching (with no memory effects)

associated with the MIT is also characteristic of a numberof TMOs That is why the study of threshold switchingin molybdenum oxide and its possible connection withthe phenomenon of MIT is of considerable scientific andpractical interest

Thinfilm samples ofmolybdenumoxidewere obtained bytwo ways anodic oxidation and thermal vacuum evaporation[53] Anodization of molybdenum was carried out in anacetone-based electrolyte (22 g of benzoic acid plus 40mLof saturated borax aqueous solution per litre of acetone[33 73]) AOFs on Mo might include lower molybdenumoxides for example Mo

4O11andMoO

2with a relatively high

electronic conductivity [53] The fact that the anodic oxideon molybdenum contained lower oxides was confirmed byexperimental data in the work [74] where it was shown thatthe degree of oxidation (valence state) of molybdenum in anAOF is less than six Also this was confirmed theoretically interms of the thermodynamics of the process the formation ofunsaturated oxide MoO

2had been shown to be energetically

more favourable than MoO3[75]

Vacuum deposited film samples were fabricated by ther-mal evaporation of MoO

3powder at residual pressure of

10minus4 Torr onto polished tantalum plates or glass substratesfor electrical and optical studies respectivelyThe thicknessesof the films were determined from the transmission andreflection interference spectra measurements [76] and theywere found to lie in the range from 300 to 800 nm

The XRD pattern of a vacuum-deposited molybdenumoxide sample is presented in Figure 11(a) It is shown thatthe samples represent amorphousMoO

3with a slight oxygen

nonstoichiometry [53] Anodic oxide films on Mo are alsoamorphous (or amorphous-microcrystalline according tothe literature data [73]) but their composition correspondsas described above to ratherMoO

2or other lower oxides and

not to the highest oxide MoO3

Figure 11(b) shows the reflection and transmission spec-tra for one of the samples obtained by vacuum depositionThe experimental data processing using the envelope of theinterference extrema [76] yields the film thickness of (620 plusmn

50) nm and the absorption edge around 120582 asymp 400 nm indi-cates the fact that the oxide phase composition correspondsto MoO

3with a band gap of sim3 eV

Before electroforming initial structures demonstrate thenonlinear and slightly asymmetric current-voltage charac-teristics with no NDR regions When the amplitude of theapplied voltage reaches the forming voltage a sharp andirreversible increase in conductivity is observed and theI(V) curve becomes S-shaped (Figure 12) With increas-ing current the I-V characteristic may change until theparameters of the switching structure are finally stabilizedThe process outlined above is qualitatively similar to theelectroforming of the switching devices based on other TMOs(see Section 22 above) We emphasize once again that thephase composition of the ensuing switching channel mustdiffer from the material of the pristine oxide film becausethe channel conductivity is higher than that of the unformedstructure by several orders of magnitude

The current-voltage characteristics of vacuum-depositedfilms and those of anodic films are qualitatively similar but

10 Advances in Condensed Matter Physics

1

2

20 40 60 8002120579∘

0100200300400500600700800900

I (co

unts

s)

(a)

1

2

3

0

20

40

60

80

100

T (

)

300 400 500 600 700 800 900 1000 1100200Wavelength (nm)

(b)

Figure 11 (a) XRD pattern of the molybdenum oxide film (1) andV]3powder (2) (b) Optical spectra of the sample obtained by vacuum

deposition (1) transmission coefficient of substrate (glass) (2) transmittance and (3) reflectance of Mo oxide film on glass [53]

0 5 10minus5minus10

Voltage (V)

minus016

minus012

minus008

minus004

000

004

008

012

016

Curr

ent (

mA

)

(a)

minus072 072 216 360minus216minus360

Voltage (V)

minus064

minus048

minus032

minus016

000

016

032

048

064

Curr

ent (

mA

)

(b)

Figure 12 Current-voltage characteristics ofMOMstructures with vacuum-deposited (a) and anodic (b)Mo oxide films after electroforming

there is a significant quantitative difference in their thresholdparameters For instance the switching voltage 119881th for theAOF based structures is sim2V (Figure 12(b)) whereas forthe structures on the basis of the films prepared by thermalevaporation119881th is sim10V (Figure 12(a))This difference can beexplained by the difference in thickness of the films

For anodic oxide the thickness can be estimated fromFaradayrsquos law [53]

119889 =

120583119868119886119905

4119890120588119878119873119860

(4)

where 120583 = 128 gmol and 120588 = 65 gcm3 are respectivelythe molar mass and density of V]

2and 119890 and 119873

119860are the

unit charge and Avogadro constant For 119868119886= 70m0 and 119905 =

10min (4) yields 119889 sim 20 nm which is significantly less thanthe typical thickness of the vacuum deposited films and as aresult the threshold voltage for AOFs is also lower than thatfor the films obtained by thermal evaporation

As is discussed in [53] switching is not observed inthinner films obtained by vacuum evaporation (119889 lt 100 nm)

in contrast to ultrathin AOFs A plausible reason for thismight be the fact that relatively thin vacuum depositedfilms contain through-the-thickness conducting defects dueto local stoichiometry variations whereas such defects areimpossible in anodic films because they are grown in highelectric field during anodic oxidation and an appearanceof such defects would interrupt the film growth processThis is similar to what is observed in vanadium oxide inpolycrystalline vanadium dioxide films such pin-hole defectsare usually associated with the grain boundaries which couldundergo local metallization due to strain or nonstoichiom-etry That is why it had been difficult to observe switchingin sandwich MOM structures with sputtered or thermallyoxidized polycrystalline VO

2films and most studies had

been conducted with planar thin-film structures whilst foranodically oxidized VO

2the switching effect has then been

observed in a sandwich structure for the first time in [16]Next we note that unlike the most other TMOs the

process of electroforming in Mo-based structures was hin-dered as was mentioned above in Section 21 that is theconventional electrical breakdown often occurred not the

Advances in Condensed Matter Physics 11

020406080

100120

30 40 50 60 7020Temperature (∘C)

30 40 50 60 7020Temperature (∘C)

0

2

4

6

8

10

12

Thre

shol

d vo

ltage

(V)

5 15minus5minus15

Voltage (V)

minus010

minus005

000005010

Curr

ent (

mA

)

V2 th

(V2)

Figure 13 Threshold voltage as a function of temperature for theTa-MoOx-Au switching structure and the temperature dependenceof (119881th)

2 (lower inset) in compliancewith (3) I-V curve at RT (upperinset)

formation of a switching channel However for the Mooxide films prepared by vacuum deposition the processesof electroforming and switching were more stable whichallowed in this case observation of the transformation of I-V curves at a temperature change It was found that as thetemperature increased the threshold voltage was reducedAt 119879 = 119879

119900sim 55ndash65∘C the NDR region degeneration

commenced at 119879 asymp 60ndash70∘C 119881th rarr 0 and at still highertemperatures the switching effect no longer occurred Inthis case the switching mechanism might be described interms of the ldquocritical temperaturerdquo model (Figure 13) It issupposed [53] that in the case of Mo like in other TMO-based structures formation of a channel also takes placeand this channel should consist of a material exhibiting MITwhich is the reason for switching with an S-shaped current-voltage characteristic (Figure 12)

A brief review of the materials with MIT in the familyof molybdenum compounds presented in [53] shows that themost suitable candidate for the role of such a channel-formingcompound is Mo

8O23

because in this case the value of 1198791199051

almost coincides with the above reported experimentallymeasured 119879

0 It should be noted that formation of other

compounds of molybdenum (eg pyrochlores bronzes sul-fides or chalcogenide glasses) exhibiting MITs with similarorder of magnitude transition temperatures [64ndash68 70] isimpossible because of the lack of the necessary chemicalelements (ie rare earths alkali metals or hydrogen sulfurand tellurium) in the phase composition of both the oxidefilm and the metal electrodes (Au Ta and Mo)

In conclusion the results presented in this subsection onswitching from the HR state to the LR state with an S-NDRin molybdenum oxides obtained by both thermal vacuumdeposition and electrochemical anodic oxidation show thatthe switching effect is due to apparently an insulator-to-metal phase transition in the switching channel consistingcompletely or partly of the lower oxide Mo

8O23 formed in

the initial film during the process of electroforming Thecurrent flowing through the channel heats it up to the MIT

temperature 1198791199051= 315K [62] and the structure switches into

the metallic low-resistance stateThus the channels consisting of this lower oxide are

formed in initial Mo oxide films during preliminary elec-troforming Electrical forming results in the changes inoxygen stoichiometry conditioned by the ionic processes inan electric field close to the MOM structure breakdown fieldThis picture is quite similar to what is observed inmany otherTMOs exhibiting the insulator-to-metal transitions

232 Metal-Insulator Transition and Switching in ManganeseDioxide Manganese dioxide is one of the most interestinginorganic materials because of its wide range of applica-tions In particular nanostructured MnO

2has received great

attention due to its high specific surface area functionalproperties and potential applications as molecular and ionselective membranes in capacitors Li-ion batteries andcatalysts [77] Originally MnO

2has been widely used as a

cathode material for oxide-semiconductor capacitors basedon tantalum niobium and aluminium oxides and the mostimportant properties of the material for this application areits high conductivity and ability to undergo a thermal phasetransition into the lower valence states accompanied by evo-lution of atomic oxygen while the resistance increases by 3-4orders of magnitude (see eg [54] and references therein)Much attention is currently paid to various other propertiesof MnO

2 such as for example the electrochromic effect

[78] thermopower wave phenomenon [79] supercapacitivebehaviour [80] andmemory and threshold switching [54 8182] Also there are a number of papers [83ndash85] describing ananomaly in theMnO

2conductivity near theNeel temperature

which is shown to be associated with the metal-insulatortransition [52] That is why the electrical properties of MnO

2

are of special scientific interest and applied importanceThe most common methods for manganese oxide prepa-

ration are the pyrolytic decomposition of manganese nitrateelectrochemical method hydrothermal synthesis in a mag-netic field and chemical deposition [54 86ndash89] Due to awide range of possible valence states of cations the structureand phase composition of manganese oxides are determinedby the synthesis conditions and process temperature Man-ganese dioxide has many crystallographic forms (120572- 120573- 120574-120575- 120576- and 120582-MnO

2) that connect MnO

6octahedron units to

each other in different ways and have different characters ofspatial alternation of the octahedra filled by Mn atoms andempty octahedra [54 77 90ndash94]

The crystal structure of the 120573-MnO2phase (Figure 14) is a

tetragonal modification of the rutile structural type P4mnmsymmetry group which represents a slightly distorted close-packed hexagonal lattice of oxygen ions [93] Filled octahedraare bound by two common edges in columns oriented alongthe 119888 axis and octahedra of adjacent columns are bound bytheir vertices (Figure 14(c)) Manganese atoms are arrangedin positions 2(a) (000) and oxygen atoms in positions 4(f )(xx0) Because there are vacancies in the oxygen packingthe formula unit can be written as MnO

2minus119910where the

nonstoichiometry index is in the range 119910 = 001ndash010depending on the synthesis method [93]

12 Advances in Condensed Matter Physics

Mn

O

(a)

a

b

c

(b)

O2O4

O1O3

Mn2

Mn1

Mn1998400

O3998400

O4998400

(c)

Figure 14 Crystal structure of manganese dioxide (a) MnO6

octahedron connection in 120573-MnO2(b) [90ndash94] and projection of

octahedron binding onto the ab plane [93]

As to the lower manganese oxides MnO and Mn3O4are

known to be theMott insulatorswith relatively high resistivity[90] and Mn

2O3shows p-type semiconducting properties

MnO2is an n-type semiconductor and antiferromagnetic

with the Neel temperature 119879119873= 925 K [91] Conductivity of

manganese dioxide is higher than that of MnO and Mn2O3

by several orders of magnitude At temperatures above 723Kmanganese dioxide loses oxygen and transforms intoMn

2O3

which is accompanied by the transformation of the crystallinestructure from the tetragonal crystal system of the rutile typeinto the complex large-period cubic lattice (119886 = 94gt) and alarge number of formula units per unit cell [54 92 93]

In this subsection we present the results on electricalproperties of manganese dioxide particularly the natureof the 120573-MnO

2conductivity at low temperatures in its

interrelation with characteristic features of the material crys-talline structure and the metal-insulator phase transitionin this compound as well The effect of electrical switchingwith current-voltage characteristics of both N- and S-typehas been found in thin-film MOM structures on the basisof manganese oxides Possible mechanisms of switching interms of the MIT and thermistor effects are discussed

Mn oxide samples under study have been obtained bythree methods anodic oxidation and vacuum evaporation(thin films) as well as by pyrolysis [54] Thin films ofmanganese dioxide were deposited by means of thermalevaporation onto glass substrates covered by a SnO

2layer

using a VUP-5 vacuum setup the film thickness was 119889 =

250 nmAlso thin films ofmanganese oxidewere obtained byelectrochemical oxidation of metal Mn in the KNO

3-NaNO

3

eutectic melt (see Section 21) at 119879 = 600K at a constantvoltage of about 2V for 3min the current density diminishedfrom 200 to 100mAcm2 during the oxidation process Foranodic oxide films on Mn the value of 119889 was sim100 nm Bulksamples of manganese dioxide were obtained by multipledecomposition (pyrolysis) of manganese nitrate at 119879 = 670Kon a glass-ceramic substrate or on a tantalum sheetmetal withthe subsequent separation from the substrate [92 93] Thetotal coating thickness was about 1mm

The manganese oxide samples were characterized by X-ray diffraction (XRD) using a DRON-6 diffractometer inCuK120572and FeK

120572radiation The characteristics of the atomic

structure of pyrolytic manganese dioxide were refined by thefull-profile analysis of the XRD patterns of polycrystallinesamples [93]The resistivity of pyrolyticMnO

2wasmeasured

in the temperature range 15 to 300K bymeans of a four-probetechnique both DC and AC (in a frequency range from 50 to104Hz) in a Gifford-McMahon cycle cryorefrigerator [54]We also measured electrical conductivity in the range T =293ndash423K the Hall effect in the magnetic field of 23 T andthe Seebeck coefficient (thermoelectromotive force thermo-emf ) The dynamic current-voltage (I-V) characteristics ofthe thin-film MOM structures were measured by oscillo-graphic method using an AC sinusoidal signal

The XRD patterns of the manganese oxide samples arepresented in Figures 15 and 16 The vacuum-deposited filmsare amorphous and represent a mixture of 120573- and 120574-MnO

2

(Figure 16) The results of the full-profile analysis show thatthe pyrolytic MnO

2samples (Figure 15) are composed of

the finely dispersed 120573-MnO2phase with the traces of 120574-

MnO2 120576-MnO

2 and Mn

2O3phases The periods of the

tetragonal unit cell of 120573-MnO2are 119886 = 119887 = 4401 A and

119888 = 2872 A The oxygen coordinates in 4119891 positions (seediscussion of the crystal structure above and Figure 14) arefound to be119909 = 0302 Calculations of the oxygen-manganeseinteratomic distances show [93] that the oxygen octahedron

Advances in Condensed Matter Physics 13

330222

040231

212202

112

130002

220

121

120

111

110

101

020

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 80 100 12002120579∘

Figure 15 XRD (Cu K120572radiation) pattern of pyrolytic MnO

2

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 8002120579∘ Fe

120573-MnO2

120574-MnO2

Experiment

Figure 16 XRD (Fe K120572radiation) pattern of Mn oxide film and

reference spectra of crystalline MnO2samples

is compressed along the (100) direction which connects theoctahedron vertices This deformation results in an increaseof the overlap of electron119901 orbitals of oxygen and119889 orbitals ofmanganese and can form the additional splitting of electronlevels in the crystal field leading to the appearance of unpairedelectrons [94]

The measurements of the conductivity temperaturedependence Hall effect and thermo-emf show that man-ganese dioxide is the electron semiconductor with conductiv-ity of about 1Ωminus1cmminus1 and mobility of sim10 cm2Vsdots The Hallmeasurements give the carrier density ofsim1018 cmminus3 which isclose to the density values in degenerate semiconductorsTheactivation energy of conductivity is sim01 eV and the band gapwidth is equal to 2 eV [90] The estimated value of the Fermienergy from the thermo-emf temperature dependence is inthe range of 002 to 005 eV which also indicates the degener-ate character of the electron gasThe nonstoichiometry indexdetermined by the XRD peaks which are not contributed

by the manganese atoms that is by those with the oddsum of indexes is 119910 = 006 Such nonstoichiometry providesthe concentration of trap states of about 1017-1018 cmminus3which correlates with the above mentioned Hall-effect-basedmeasurements of electron density

Such high vacancy concentration allows us to considerthe nonstoichiometric 120573-MnO

2as a heavily doped semicon-

ductor with a subband of impurity levels which provides afeasibility of the out-of-band electron transfer at low tem-peratures The structural distortions high nonstoichiometryand as a consequence sufficiently high concentration ofimpurity states cause the density state tails near the bandedges similarly to those in heavily doped semiconductorsHowever at room and higher temperatures the conduction isdetermined by the activation mechanism Thus the electronstructure and a low mobility of charge carriers promotethe manifestation of different charge transfer mechanismsin different temperature ranges namely both the hoppingmechanism and the activation one

The electron capturing oxygen vacancies create mixedvalence states of manganese cations (Mn3+ndashMn4+) Interest-ingly the mixed valence of Mn ions is also characteristic ofmanganites Ln

1minus119910Sr119910MnO3[95] where Ln is La or another

rare-earth element possessing the effect of colossal magne-toresistance (CMR) In these compounds the mixed valenceof manganese is attained via doping It had been deemed thatholes introduced by strontium are localized at manganeseions that is the Mn4+ ions with concentration 119910 are formedHowever recent X-ray emission studies have shown that boththe chemical shift and the exchange splitting of the emissionX-ray Mn K

1205731line are almost the same in the range 119910 lt 04ndash

05 as is the case in Mn2O3 and then they decrease quickly

to the values characteristic of MnO2[96] which suggests that

the introduced holes are localized at oxygen atoms in the holedoping region (at relatively low 119910) and atmanganese atoms inthe electron doping region that is at higher 119910 values

The temperature dependence of conductivity is presentedin Figure 17 The resistance peak observed in the figure ina temperature range of 80ndash90K is the result of the phasetransition of 120573-MnO

2from a semiconducting state to a metal

state upon decreasing the temperature to 15 K [54] The tem-perature region of the transition is close to the known Neeltransition from the paramagnetic state into the ferromagneticone for manganese dioxide The temperature dependenceof resistance indicates thus the MIT to occur in MnO

2 In

the temperature range from 300 to 80K (Figure 17) thisdependence does not correspond to the exponential one yetit fits well with the linear dependence in theMott coordinatesln(119877) sim 119879

14 which indicates the hopping conductivitymechanism over the polyvalent states ofmanganese ions witha distance between the centres of 25ndash35gt [92] However inthe temperature range from 90 to 15 K the dependence ofln119877 on ln119879 is almost linear with the slope of about unity(ie 120597 ln119877120597 ln119879 asymp 1) which is characteristic of the metallicconductionThus the character of conductivity ofmanganesedioxide indicates the presence of the MIT at 119879

119888sim 80K (on

cooling)

14 Advances in Condensed Matter Physics

CoolingHeating

40 80 120 160 2000T (K)

0

2

4

6

8

10

Resis

tivity

(Ohm

timescm

)

Figure 17 Temperature dependence of AC (70Hz) resistivity ofpyrolytic MnO

2

In the low temperature region manganese dioxide is anantiferromagnetwith the helical spin ordering [97]The inter-action between the magnetic ions of manganese which leadsto the antiferromagnetic state occurs through the intermedi-ate interaction with diamagnetic oxygen ions which weakensthe exchange interaction The conductivity increases proba-bly due to exceeding the energy of the exchange interactionby the thermal energy as the temperature increases whichleads to an increase in the number of unpaired electrons inthe paramagnetic state As the temperature further increasesthe conductivity continues to rise and the Mott hoppingmechanism of charge transfer becomes predominant Similarcharacter of the temperature dependence in ferromagneticdegenerate semiconductors has previously been described[85 98] for substoichiometric (oxygen-deficient) europiummonoxide The transition from the highly conductive stateinto the insulating state occurs in such semiconductors uponvarying the type of magnetic ordering or its destruction

For EuO1minus119910

lowering the peak magnitude in the 119877(119879)

dependence is associatedwith a decrease in the concentrationof impurities (oxygen vacancies) In magnetic semicon-ductors the phase transition is associated both with themagnetoelectric effects and with the variation in the electricpolarization under the action of the magnetic field at theantiferromagnetic transition [98] The dielectric constant formanganese dioxide is equal to sim10 but the effective dielectricconstant can decrease near 119879

119888by a factor of several times

thereby affecting the mobility of carriers located in the tailsof the density of states near the band edge and promotingtheir delocalization at the phase transition temperatureManganese dioxide also belongs to this group of substanceshowever the phase transition in MnO

2reported here can be

also described in terms of the Mott transition [24]According to the Mott criterion electrons delocalize if

the distance between the atoms 119899minus13 becomes comparable

with their atomic radius 119886119860 where 119886

119860is associated with the

Bohr radius 119886119861= ℏ2120576me2The static permittivity 120576 is replaced

by the effective permittivity which takes into account theexchange interaction of the spins of conduction electronswith orbitalmagneticmoments of atoms At the temperature-induced Mott MIT the orbital radius 119886

119861decreases near 119879 =

119879119888thereby providing the fulfillment of the Mott criterion at a

given level of impurity centres [24 98] The transition fromthe metallic state into the semiconductor state is possible insuch semiconductors as the temperature increases Thus theMIT in manganese dioxide is brought about by temperaturevariation

In conclusion we note that the phase transition describedabove is inverse (reentrant) MIT that is the metallic phaseis low-temperature while the high-temperature state is insu-lating This is rather rare yet not unique and unusualphenomenon In most cases (eg in vanadium dioxide) thelow-temperature phase is insulating and on heating abovea certain temperature 119879

119888 the material becomes metallic for

VO2 this transition temperature is 119879

119888= 340K The inverse

transitions are observed in such compounds as the abovementioned EuO

1minus119910 NiS2Se Y2O3minus119910

and LaMnO3films [24

31 52 85 98 99] Also the high-temperature Mott transi-tion from paramagnetic metal to paramagnetic insulator inV2O3Cr is an inverse transition with the resistivity peak at

119879119888sim 350K for a chromium concentration of around 1 at

[24 51] and in mixed valence CMR-manganites the sharpresistivity peak has been shown to be caused by the AndersonMIT [95]

It is known that many TMOs exhibit electrical switchingassociated with MITs [28] For the anodic oxide films onMn the study of the effect of electrical switching in thin-film Mn-MnO

2-Au sandwich structures showed that the S-

type switching was not observed in contrast to for examplethe similar structures based on oxides of vanadium andsome other transition metals [28] Instead switching withthe N-shaped I-V characteristic occurred after EF at 119879 lt

80K (Figure 18(a)) In addition the EF process in the Mn-based structures was hindered likewise for example for thestructures based on yttrium oxide [31] that is the breakdowntook place more often It should be noted that EF at roomtemperature always led to breakdown and the switchingeffect had never been observed in this case As was arguedin [54] this switching effect was associated with the MIT inMnO2

On the other hand in the films obtained by vacuumsputtering we have observed S-type switching at roomtemperature (Figure 18(b)) The threshold voltage is of theorder of 1 V and almost independent of temperature up to 119879

= 375KThis situation resembles that with yttrium oxide where

both S-type and N-type switching has been observed too[31] One can assume that switching with the S-shapedI-V curves is due to the so-called ldquothermistor effectrdquo Itis well known that the current flowing through a solidgenerates Joule heat resulting in an increased temperatureIn materials with a negative TCR a rising temperatureinduces a current enhancement and an increased powerdissipation resulting in a farther temperature increase Thispositive electrothermal feedback causes the appearance of anNDR and accordingly an S-shaped I-V characteristic [2]

Advances in Condensed Matter Physics 15

minus15

minus10

minus5

0

5

10

15Cu

rren

t (m

A)

0500 10 15minus10 minus05minus15

Voltage (V)

(a)

minus2

minus1

0

1

2

Curr

ent (

mA

)

10 2minus2 minus1

Voltage (V)

(b)

Figure 18 (a) I-V characteristic of anodic oxide film on manganese at T = 77K (b) I-V characteristic of vacuum-deposited MnO2at 119879 =

293K

In some cases this process might by modified by high-fieldeffects such as Schottky injection impact ionization Poole-Frenkel effect and Zener or avalanche breakdown Notethat unlike a conventional thermistor with an Arrhenius-like conductivity law manganese oxide exhibits a weaker119877(119879) dependence characteristic of the hopping conductivitymechanism which seems to account for the observed weaktemperature dependence of the threshold voltage

An alternative mechanism for the S-type switching effectmay be connected with a possible high-temperature usual(ie not inverse)MIT in somemanganese oxide As is knownEF (see Section 22) leads to the formation of a filament ofhighly conducting material a switching channel Similarlyto what is observed for Mo oxide (Section 231) and otherTMOs (Sections 21 and 22) we suppose that the compositionof this channel differs from the material of the initial oxidefilm since its conductivity noticeably exceeds that of anunformed structure In view of such a plentiful set of phasesand crystal structures in the Mn-O system one can supposethat the channelmight consist of nonstoichiometric120573-MnO

2

some other polymorphic modifications of manganese diox-ide or lower Mn oxides which might undergo a MIT underthe action of either temperature or electric field Howeverthis question obviously requires additional investigation inparticularmeasurements of119877(119879)dependences and switchingproperties at higher temperatures If this assumed high-temperature MIT would occur in for example nonstoichio-metric 120573-MnO

2 one could expect observation of double-

NDR I-V characteristics in such samples at low temperaturesanalogously to those in V

2O3Cr (Figure 9) where this effect

is due to the MITs [29] with the only difference being thatin the case of MnO

2this curve should be N-S-shaped (unlike

the S-N-shaped one in Figure 9) since in chromium-dopedvanadium sesquioxide the inverse MIT is high-temperatureas opposed to MnO

2which as we discussed above (see

Figure 17) exhibits the inverse MIT at low temperaturesNote however that the discussed high-temperature MIT

in 120573-MnO2minus119910

may be unobservable under the temperature

change in equilibrium conditions but displays itself onlyunder the applied electric field as the S-type electricalswitching effect because the transition temperature is closeto or higher than the temperature of MnO

2decomposition

(723K) Such a nonequilibrium transition occurs at switchingin those materials where the usual temperature-inducedMITwith a well-defined 119879

119905does not take place for example in

CGSs for which the equilibrium transition temperature 1198791199050

is higher than 119879119892 while in a high electric field 119879

119905(119864) lt 119879

1199050

might be lower than 119879119892 where 119879

119892is the temperature of the

glass-crystal transition and119864 is the electric field strength [30]Summarizing we have studied the electrical properties

(conductivity temperature dependence and Hall and Seebeckeffects) of the 120573 phase of manganese dioxide obtained bypyrolysis thermal vacuum evaporation and anodic oxida-tion The change of conductivity mechanisms dependingon temperature in a range of 450ndash25K has been shownand the metal-insulator phase transition at low (lt90K)temperatures has been revealed The specific feature of thistransition described in terms of the Mott mechanism isthat the metal phase exists at low temperatures while athigher temperatures the material is a semiconductor withthe hopping conductivity over the mixed valence states ofmanganese ions

The low-temperature switching effect with an NDR andN-shaped current-voltage characteristic associated with thephase transition in manganese dioxide has been found in theMOM two-terminal devices based on anodicMn oxide filmsOn the contrary the devices based on vacuum-depositedfilms have been found to exhibit an S-NDR at room andhigher temperatures which is suggested to be caused byeither the thermistor effect or a high-temperature MIT innonstoichiometric 120573-MnO

2

It should be emphasized that the low-temperature MITin 120573-MnO

2with 119879

119905= 70ndash80K is the inverse Mott transition

which is akin for instance to the transition in V2O3Cr

at 119879119905= 190ndash385K (for chromium dopant concentration in

the range of 05ndash18 at) [51] We thus assume that farther

16 Advances in Condensed Matter Physics

5 10 150Voltage (V)

0

1

2

3

4

5

6

7

8Cu

rren

t (m

A)

(a)ΔV

th(V

)

0

1

2

3

1 2 3 4 5 6 7 80W (at )

(b)

Figure 19 I-V curve (a) of Au-V2minus119910

W119910O5times 119899H2O-Au sandwich structure with119910= 003 and119881th scattering as a function of tungsten admixture

percentage 119910 (b) [104 105]

investigations of the phase transition in manganese dioxidedescribed in this paper are a rather interesting and topicalscientific problem since manganese dioxide can serve as amodel object for studying such inverse metal-insulator phasetransitions

Finally we note that the results presented in this sectionindicate the possibility of application of manganese oxide asa material for thin film sandwich switching devices Deviceswith NDR (N- and S-shaped I-V characteristics) have poten-tial applications in microelectronics as switches memoryelements and microsensors (these issues will be discussedin more detail below in Section 4) Particularly manganeseoxide microswitches [82] can be utilized for implementationof neuristors built with Mott-transition-based memristors[100]

24 Effect of Doping It is only natural that the systemsexhibiting the NDR effects possess a high applied potential inelectronics [2 4 8 18 100 101] yet the stage of EF is a weaklink of chain in the technology process Note that the formingprocess may be brought about by laser irradiation [102] notby applying of electric field In the case of laser treatment(or ldquolaser formingrdquo unlike the above described electricalforming) the parameters of the structures are characterizedby the absence of the scatter that is the I-V characteristics ofall structures are almost identical [103] One more demerit tobe avoided is the scatter in switching parameters (the value of119881th first of all) and their instability during operation In thissubsection we discuss the issues concerning the switchingparameter stabilization by means of doping

In the work [104] we have studied the switching effectin the MOM structures on the basis of W-doped V

2O5-gel

filmsThese structures require preliminary EF similar to thatin anodic oxide films resulting in formation of a conducting

channel within the initial dielectric xerogel filmThe channelconsists of vanadiumdioxide and switching is associatedwiththe insulator-to-metal transition in VO

2 As was shown in

[104 105] for the pure (undoped) V2O5-gel the switching

parameters vary in a wide range because the phenomenonof EF is statistical in nature (like electrical breakdown) andits statistical character shows itself as a spread in the observedthreshold voltages of the ensuing structures that is actuallyat multiple measurements 119881th = ⟨119881th⟩ plusmn Δ119881th

It has been shown [104] that the statistical spread in valuesof the threshold parameters can be minimized by means ofdoping (Figure 19) Unsophisticated reasoning could accountfor this result for pure V

2O5-gel electroforming leads to

formation of VO2with 119879

119905= 340K and each switching

event requires heating up and cooling down from roomtemperature to 119879

119905 this thermal cycling can modify the

peripheral regions of the channel which leads to the changeof the switching threshold voltage On the other hand forthe samples with a high concentration of W the MIT issuppressed [104] and switching is degenerated Betweenthese two outermost points an optimum should exist Asone can see from Figure 19 this optimal value correspondsto 3 at of W that is for V

097W003

O2the switching

parameters are the most stableThe transition temperature ofV097

W003

O2is lower than that for pure vanadium dioxide

and hence the magnitude of the aforesaid thermal cyclingis decreased which results in an increase of stability of theswitching parameters

Next we have studied the effect of doping on switchingin AOFs on Ti [29] These films were obtained in 5 watersolution of citric acid (C

6H8O7) in volt-static regime at 119881

119886

= 20V The samples were doped with aluminium by meansof adding soluble Al-containing substances to the electrolyte

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

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[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

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[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

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Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

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tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

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4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

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03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

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2CCNT

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2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

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2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

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1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

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3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

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[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

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2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

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24 Advances in Condensed Matter Physics

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2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

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[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

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2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

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2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

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FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

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AstrophysicsJournal of

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Solid State PhysicsJournal of

 Computational  Methods in Physics

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Soft MatterJournal of

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ThermodynamicsJournal of

Advances in Condensed Matter Physics 7

1 2

3

0

1

2

3

4

5

6

240 260 280 300 320 340220T (K)

V2 th

(V2)

(a)

1

2

3

(V2th times 04)

420 440 460 480 500 520 540400T (K)

0

1

2

3

4

5

6

7

V2 th

(V2)

(b)

Figure 8 Squared threshold voltage as a function of temperature for (a) vanadium oxide-based switch and (b) titanium oxide (1) (2) and(3) three different samples

119879 lt 340K is a semiconductor at 119879 = 119879119905

= 340K theconductivity abruptly increases by 4-5 orders of magnitudeand above the transition temperature VO

2exhibits metallic

properties ForNbO2119879119905= 1070K Ti

2O3undergoes a gradual

transition in the range 400ndash600K and magnetite (Fe3O4)

is a semiconductor both above and below the Verwey tran-sition temperature (120K) though its resistivity decreaseson heating by two orders of magnitude at 119879 = 119879

119905 For the

switching devices based on these metals the temperatures 119879119900

coincide with the corresponding values of 119879119905(see Figure 5)

This suggests that the switching mechanism is caused by themetal-insulator transition

Electrical switching due to MIT has been first revealedfor vanadium dioxide [16 27 37ndash45] Switching in VO

2

is explained by the current-induced Joule heating of thesample up to 119879 = 119879

119905 which has been confirmed by the

direct IR-radiation measurements of the switching channeltemperature [38 45] In these early works switching hasbeen observed in single crystals [39] and planar thin filmdevices [37 38 45] as well as in vanadate glasses [40 41]VO2-containing ceramics [44] and V

2O5-gel films [42 43]

When as-prepared samples do not consist of pure vanadiumdioxide preliminary electroforming is required resulting inthe formation of the VO

2-containing channel [40 42] The

latter examples as well as the discussed AOFs here supportthe assumption that the formation of vanadium dioxide isthermodynamically preferable at a V

2O5-V interface [22

27] For such samples the threshold voltage decreases withtemperature and reaches zero at 119879 = 119879

119905sim 340K

In this case the switchingmechanismmight be describedin terms of the ldquocritical temperaturerdquo model [29 37] (if theambient temperature is not much lower than 119879

119905)

119881th sim (119879 minus 119879119905)12

(3)

that is the squared threshold voltage linearly tends to zero at119879 rarr 119879

119905 see Figure 8 Switching elements for other transition

metal (FeW Ti and Nb) oxides exhibitingMIT are expected

to show similar behaviour but for different 119879119905rsquos which is

demonstrated by Figure 8(b) for Ti oxideThe switching effect in the WO

3-based sandwich struc-

tures can also be explained in terms of ametal-insulator tran-sition which occurs in nonstoichiometric WO

3minus119910(within a

very narrow interval of variable 119910) at 119879119905ranging from 160 to

280K [46] Because of the narrow interval of ldquoappropriaterdquostoichiometric compositions the S-type I-V characteristicis not likely to appear in tungsten trioxide and in mostcases breakdown occurs instead For switching structureson anodic films on W 119879

119900was found to lie around sim200K

(Figure 5) Therefore 119879119900may turn out to be equal to 119879

119905

Almost no data on MIT in molybdenum oxides are avail-able in the literature except for the transition in Mo

8O23

(MoO2875

) and the switching effect in molybdenum oxidewill be discussed in more detail in the next section Asto Ta and Hf oxides the formation of metastable loweroxides during electroforming should also be possible Theproperties of these oxides are practically unknown but somemetastable oxides of this type have been referred to forexample for the Ta-O system [47] Recently formation ofHfO119909[48] and TaO

119909[49] suboxides has been reported As

to Mn oxides it is known [23] that MnO and Mn3O4are

Mott insulators Mn2O3is a semiconductor and MnO

2is

also a semiconductor but it shows a change in electricalconductivity at 119879 = 119879

119873sim 90K (the Neel temperature) This

might account for the N-NDR effect in Mn oxide this issuewill also be more thoroughly investigated in the next section

Thus the experimental data on the switching effect in119889-metal oxide thin films can be explained in terms of theswitching mechanism driven by the MIT We can state thatin all cases the electrothermal and electrochemical processesduring electroforming are responsible for the switching chan-nel formation The channel consists of a material which canundergo a transition from semiconducting state to metallicstate at a certain temperature 119879

119905 For the V- Ti- Nb- and Fe-

based structures the possibility of formation of the channelsconsisting completely or partly of VO

2 Ti2O3 NbO

2 and

8 Advances in Condensed Matter Physics

Fe3O4 respectively is also confirmed by the thermodynamic

calculations In oxides of W and Mo switching may beassociated with MIT in the channels consisting of WO

3minus119909

and Mo8O23 The S-shaped voltage-current characteristic

is conditioned by the development of an electrothermalinstability in the channel When a voltage is applied thechannel is heated up to 119879 = 119879

119905(at 119881 = 119881th) by the current

and the structure undergoes a transition fromhigh-resistance(OFF) insulating state to low-resistance (ON) metallic state

In high electric fields (105ndash106 Vcm) the possible influ-ence of electronic effects on the MIT should be taken intoaccount A field-induced increase in charge carrier densitywill act to screen Coulomb interactions [12] leading to theelimination of the Mott-Hubbard energy gap at 119879 lt 119879

119905

Moreover a transition of this type may be important in thosematerials where the usual temperature-induced MIT with awell-defined 119879

119905does not take place for example in oxides

of Ta or Hf (and in CGS-based switching structures as well[50]) In the case of vanadium dioxide such a possibilityof the electronically induced MIT was suggested from theinjection experiments [22] and will be discussed also belowin connection with the transition mechanism in VO

2

To summarize the results presented above as well asthe other data on the switching in transition metal oxides[11ndash17 27ndash31] indicate that current instabilities with the S-type NDR exhibit several common features In particularfor each of the investigated materials there is a certain fixedtemperature 119879

119900 above which switching disappears At 119879 lt

119879119900 the threshold voltage decreases as the temperature rises

tending to zero at 119879 = 119879119900 Comparison of these temperatures

with the temperatures of MIT for some compounds (119879119905

=

120K for Fe3O4 sim200K for WO

3minus119909 340K for VO

2 sim500K

for Ti2O3 and 1070K for NbO

2) shows that the switching

effect is associated with the insulator-metal transition in anelectric field The channels consisting of these lower oxidesare formed in initial anodic films during the process ofpreliminary EF

And finally in conclusion of this section we would like todiscuss onemore vanadium oxide where the switching effectsare caused by MITs namely vanadium sesquioxide The I-Vcharacteristics of chromium-doped V

2O3shown in Figure 9

are distinctive in that they exhibit in a certain temperaturerange two regions of negative differential resistance both N-NDR and S-NDR The experimental data on the switchingeffect ofMOM structures based onV

2O3Cr can be explained

in terms of the switching mechanism driven by the variableMIT The S-shaped I-V characteristic is conditioned by thedevelopment of an electrothermal instability in the sampleWhen a voltage is applied the sample is heated by the currentup to 119879 = 119879

1199051(at the threshold voltage 119881 = 119881th119878) and

the structure undergoes a transition from a high-resistance(OFF-1) AFI state to a low-resistance (ON) PM state Asthe current in the ON state increases the sample is furtherheated and at 119879 = 119879

1199052(119868 = 119868th119873) the second transition

to the OFF-2 (or PI) state occurs [51] In the OFF-1 statethe plot of current versus the square root of the appliedvoltage is indicative of a Poole-Frenkel type of conductivityenhancement [52] (Figure 10)

12

34

0

20

40

60

80

100

120

140

160

180

Curr

ent (

mA

)

05 10 15 20 25 3000Voltage (V)

Figure 9 Current-voltage characteristics for V2O3doped with 12

at of Cr at different temperatures 1705 K (1) 1733 K (2) 2210 K(3) and 2655 K (4) [51]

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

Curr

ent (

A)

05 10 15 20 2500Square root of voltage (V05)

150K140K130K120K110K

100K90K80K70K60K

50K40K30K20K10K

Figure 10 Current versus voltage in Poole-Frenkel coordinates fora V2O3-based switching device [52]

23 Switching Effects and Metal-Insulator Transitions in MnandMoOxides In this section we consider electrical switch-ing in oxides of Mn and Mo obtained by vacuum depositionin comparison with those obtained by anodic oxidation [5354] It should be emphasized here that AOFs are (as a ruleexcept for some rare cases) amorphous [32 33] Therefore inMOM structures with anodic films the process of EF similarto that in CGSs usually takes place However in some cases(Mo Mn) as was described in previous sections we havefailed to obtain stable switching with anodic films and herewe present an alternative approach to this problem

Advances in Condensed Matter Physics 9

231 Electrical Switching in Thin Film Structures Based onMolybdenumOxide As inmost TMOs in the molybdenum-oxygen system there exist a number of oxides with variablevalence which are characterized by a wide diversity ofstructures and physical properties [53 55 56] MolybdenumtrioxideMoO

3has a structure based on layers of edge-sharing

distorted MoO6octahedra [23] Similar layered structures

are inherent in lower molybdenum oxides including MoO2

Mo18O52 Mo9O26 Mo8O23 Mo5O14 and Mo

17O47 as well

as 120578- and 120574-Mo4O11[55ndash57]

Stoichiometric MoO3 in its most thermodynamically

stable form 120572-MoO3 is an insulator with a band gap of sim3 eV

[23] During reduction by means of either oxygen deficiencyformation or introducing donor impurity atoms additionaldonor levels near the conduction band bottom appear andthe reduced oxide behaves therefore as a semiconductorPolycrystalline MoO

3 as well as a single crystal has a grey-

yellow colour and the minimum value of the absorption edgeis 440 nm which corresponds to the smallest value of theband gap of 28 eV [58] thus the band gap depends upon thestoichiometry and the crystalline state [53] The conductivityvalues of molybdenum oxides range from dielectric MoO

3

to semiconductor Mo18O52

(resistivity 120588 = 781Ωsdotcm)and down to metal 120578-V]

411

(120588 = 166 times 10minus4Ωsdotcm) [58]Molybdenum dioxide also exhibits metallic properties [2358] and at room temperature 120588 = 88 times 10minus5Ωsdotcm for bulkMoO2samples [55]

Because of their special physical and chemical propertiesmolybdenum oxides are used in various electronic devicessuch as electrochromic displays and indicators reversiblecathodes of lithium batteries gas sensors and memoryelements [55ndash61] Metal-insulator transitions have also beenobserved in some oxides of molybdenum and related com-pounds [62ndash70] In particular Mo

8O23

exhibits a two-stagestructural MIT with formation of a charge-density wave at1198791199051= 315 K and 119879

1199052= 285K [62] However as far as we know

no data are available in the literature concerning thresholdswitching associated with these transitions except for ourwork [53] In this work we have particularly noted thatmemory switching is observed inmany TMOs molybdenumoxides included [4 9 59 60]

The most discussed models in the literature for theReRAMmechanism in oxide structures are those based eitheron the growth and rupture of a metal filament inside theoxide matrix under the action of electric current or onthe redox processes responsible for the formation of somehigh-conductivity or low-conductivity local inclusions cor-responding to particular oxygen stoichiometry [4] The MITideology is also sometimes involved to explain the propertiesof the structures and the memory switching mechanismtherein [71] In any case thememory switching phenomenonseems to be associated with the ion transport [4 9] It isalso appropriate to mention here the works discussing thememory effects in a material with MIT (vanadium dioxide)associated with the presence of hysteresis in the temperaturedependence of conductivity [72]

On the other hand as was shown in the previous sectionmonostable threshold switching (with no memory effects)

associated with the MIT is also characteristic of a numberof TMOs That is why the study of threshold switchingin molybdenum oxide and its possible connection withthe phenomenon of MIT is of considerable scientific andpractical interest

Thinfilm samples ofmolybdenumoxidewere obtained bytwo ways anodic oxidation and thermal vacuum evaporation[53] Anodization of molybdenum was carried out in anacetone-based electrolyte (22 g of benzoic acid plus 40mLof saturated borax aqueous solution per litre of acetone[33 73]) AOFs on Mo might include lower molybdenumoxides for example Mo

4O11andMoO

2with a relatively high

electronic conductivity [53] The fact that the anodic oxideon molybdenum contained lower oxides was confirmed byexperimental data in the work [74] where it was shown thatthe degree of oxidation (valence state) of molybdenum in anAOF is less than six Also this was confirmed theoretically interms of the thermodynamics of the process the formation ofunsaturated oxide MoO

2had been shown to be energetically

more favourable than MoO3[75]

Vacuum deposited film samples were fabricated by ther-mal evaporation of MoO

3powder at residual pressure of

10minus4 Torr onto polished tantalum plates or glass substratesfor electrical and optical studies respectivelyThe thicknessesof the films were determined from the transmission andreflection interference spectra measurements [76] and theywere found to lie in the range from 300 to 800 nm

The XRD pattern of a vacuum-deposited molybdenumoxide sample is presented in Figure 11(a) It is shown thatthe samples represent amorphousMoO

3with a slight oxygen

nonstoichiometry [53] Anodic oxide films on Mo are alsoamorphous (or amorphous-microcrystalline according tothe literature data [73]) but their composition correspondsas described above to ratherMoO

2or other lower oxides and

not to the highest oxide MoO3

Figure 11(b) shows the reflection and transmission spec-tra for one of the samples obtained by vacuum depositionThe experimental data processing using the envelope of theinterference extrema [76] yields the film thickness of (620 plusmn

50) nm and the absorption edge around 120582 asymp 400 nm indi-cates the fact that the oxide phase composition correspondsto MoO

3with a band gap of sim3 eV

Before electroforming initial structures demonstrate thenonlinear and slightly asymmetric current-voltage charac-teristics with no NDR regions When the amplitude of theapplied voltage reaches the forming voltage a sharp andirreversible increase in conductivity is observed and theI(V) curve becomes S-shaped (Figure 12) With increas-ing current the I-V characteristic may change until theparameters of the switching structure are finally stabilizedThe process outlined above is qualitatively similar to theelectroforming of the switching devices based on other TMOs(see Section 22 above) We emphasize once again that thephase composition of the ensuing switching channel mustdiffer from the material of the pristine oxide film becausethe channel conductivity is higher than that of the unformedstructure by several orders of magnitude

The current-voltage characteristics of vacuum-depositedfilms and those of anodic films are qualitatively similar but

10 Advances in Condensed Matter Physics

1

2

20 40 60 8002120579∘

0100200300400500600700800900

I (co

unts

s)

(a)

1

2

3

0

20

40

60

80

100

T (

)

300 400 500 600 700 800 900 1000 1100200Wavelength (nm)

(b)

Figure 11 (a) XRD pattern of the molybdenum oxide film (1) andV]3powder (2) (b) Optical spectra of the sample obtained by vacuum

deposition (1) transmission coefficient of substrate (glass) (2) transmittance and (3) reflectance of Mo oxide film on glass [53]

0 5 10minus5minus10

Voltage (V)

minus016

minus012

minus008

minus004

000

004

008

012

016

Curr

ent (

mA

)

(a)

minus072 072 216 360minus216minus360

Voltage (V)

minus064

minus048

minus032

minus016

000

016

032

048

064

Curr

ent (

mA

)

(b)

Figure 12 Current-voltage characteristics ofMOMstructures with vacuum-deposited (a) and anodic (b)Mo oxide films after electroforming

there is a significant quantitative difference in their thresholdparameters For instance the switching voltage 119881th for theAOF based structures is sim2V (Figure 12(b)) whereas forthe structures on the basis of the films prepared by thermalevaporation119881th is sim10V (Figure 12(a))This difference can beexplained by the difference in thickness of the films

For anodic oxide the thickness can be estimated fromFaradayrsquos law [53]

119889 =

120583119868119886119905

4119890120588119878119873119860

(4)

where 120583 = 128 gmol and 120588 = 65 gcm3 are respectivelythe molar mass and density of V]

2and 119890 and 119873

119860are the

unit charge and Avogadro constant For 119868119886= 70m0 and 119905 =

10min (4) yields 119889 sim 20 nm which is significantly less thanthe typical thickness of the vacuum deposited films and as aresult the threshold voltage for AOFs is also lower than thatfor the films obtained by thermal evaporation

As is discussed in [53] switching is not observed inthinner films obtained by vacuum evaporation (119889 lt 100 nm)

in contrast to ultrathin AOFs A plausible reason for thismight be the fact that relatively thin vacuum depositedfilms contain through-the-thickness conducting defects dueto local stoichiometry variations whereas such defects areimpossible in anodic films because they are grown in highelectric field during anodic oxidation and an appearanceof such defects would interrupt the film growth processThis is similar to what is observed in vanadium oxide inpolycrystalline vanadium dioxide films such pin-hole defectsare usually associated with the grain boundaries which couldundergo local metallization due to strain or nonstoichiom-etry That is why it had been difficult to observe switchingin sandwich MOM structures with sputtered or thermallyoxidized polycrystalline VO

2films and most studies had

been conducted with planar thin-film structures whilst foranodically oxidized VO

2the switching effect has then been

observed in a sandwich structure for the first time in [16]Next we note that unlike the most other TMOs the

process of electroforming in Mo-based structures was hin-dered as was mentioned above in Section 21 that is theconventional electrical breakdown often occurred not the

Advances in Condensed Matter Physics 11

020406080

100120

30 40 50 60 7020Temperature (∘C)

30 40 50 60 7020Temperature (∘C)

0

2

4

6

8

10

12

Thre

shol

d vo

ltage

(V)

5 15minus5minus15

Voltage (V)

minus010

minus005

000005010

Curr

ent (

mA

)

V2 th

(V2)

Figure 13 Threshold voltage as a function of temperature for theTa-MoOx-Au switching structure and the temperature dependenceof (119881th)

2 (lower inset) in compliancewith (3) I-V curve at RT (upperinset)

formation of a switching channel However for the Mooxide films prepared by vacuum deposition the processesof electroforming and switching were more stable whichallowed in this case observation of the transformation of I-V curves at a temperature change It was found that as thetemperature increased the threshold voltage was reducedAt 119879 = 119879

119900sim 55ndash65∘C the NDR region degeneration

commenced at 119879 asymp 60ndash70∘C 119881th rarr 0 and at still highertemperatures the switching effect no longer occurred Inthis case the switching mechanism might be described interms of the ldquocritical temperaturerdquo model (Figure 13) It issupposed [53] that in the case of Mo like in other TMO-based structures formation of a channel also takes placeand this channel should consist of a material exhibiting MITwhich is the reason for switching with an S-shaped current-voltage characteristic (Figure 12)

A brief review of the materials with MIT in the familyof molybdenum compounds presented in [53] shows that themost suitable candidate for the role of such a channel-formingcompound is Mo

8O23

because in this case the value of 1198791199051

almost coincides with the above reported experimentallymeasured 119879

0 It should be noted that formation of other

compounds of molybdenum (eg pyrochlores bronzes sul-fides or chalcogenide glasses) exhibiting MITs with similarorder of magnitude transition temperatures [64ndash68 70] isimpossible because of the lack of the necessary chemicalelements (ie rare earths alkali metals or hydrogen sulfurand tellurium) in the phase composition of both the oxidefilm and the metal electrodes (Au Ta and Mo)

In conclusion the results presented in this subsection onswitching from the HR state to the LR state with an S-NDRin molybdenum oxides obtained by both thermal vacuumdeposition and electrochemical anodic oxidation show thatthe switching effect is due to apparently an insulator-to-metal phase transition in the switching channel consistingcompletely or partly of the lower oxide Mo

8O23 formed in

the initial film during the process of electroforming Thecurrent flowing through the channel heats it up to the MIT

temperature 1198791199051= 315K [62] and the structure switches into

the metallic low-resistance stateThus the channels consisting of this lower oxide are

formed in initial Mo oxide films during preliminary elec-troforming Electrical forming results in the changes inoxygen stoichiometry conditioned by the ionic processes inan electric field close to the MOM structure breakdown fieldThis picture is quite similar to what is observed inmany otherTMOs exhibiting the insulator-to-metal transitions

232 Metal-Insulator Transition and Switching in ManganeseDioxide Manganese dioxide is one of the most interestinginorganic materials because of its wide range of applica-tions In particular nanostructured MnO

2has received great

attention due to its high specific surface area functionalproperties and potential applications as molecular and ionselective membranes in capacitors Li-ion batteries andcatalysts [77] Originally MnO

2has been widely used as a

cathode material for oxide-semiconductor capacitors basedon tantalum niobium and aluminium oxides and the mostimportant properties of the material for this application areits high conductivity and ability to undergo a thermal phasetransition into the lower valence states accompanied by evo-lution of atomic oxygen while the resistance increases by 3-4orders of magnitude (see eg [54] and references therein)Much attention is currently paid to various other propertiesof MnO

2 such as for example the electrochromic effect

[78] thermopower wave phenomenon [79] supercapacitivebehaviour [80] andmemory and threshold switching [54 8182] Also there are a number of papers [83ndash85] describing ananomaly in theMnO

2conductivity near theNeel temperature

which is shown to be associated with the metal-insulatortransition [52] That is why the electrical properties of MnO

2

are of special scientific interest and applied importanceThe most common methods for manganese oxide prepa-

ration are the pyrolytic decomposition of manganese nitrateelectrochemical method hydrothermal synthesis in a mag-netic field and chemical deposition [54 86ndash89] Due to awide range of possible valence states of cations the structureand phase composition of manganese oxides are determinedby the synthesis conditions and process temperature Man-ganese dioxide has many crystallographic forms (120572- 120573- 120574-120575- 120576- and 120582-MnO

2) that connect MnO

6octahedron units to

each other in different ways and have different characters ofspatial alternation of the octahedra filled by Mn atoms andempty octahedra [54 77 90ndash94]

The crystal structure of the 120573-MnO2phase (Figure 14) is a

tetragonal modification of the rutile structural type P4mnmsymmetry group which represents a slightly distorted close-packed hexagonal lattice of oxygen ions [93] Filled octahedraare bound by two common edges in columns oriented alongthe 119888 axis and octahedra of adjacent columns are bound bytheir vertices (Figure 14(c)) Manganese atoms are arrangedin positions 2(a) (000) and oxygen atoms in positions 4(f )(xx0) Because there are vacancies in the oxygen packingthe formula unit can be written as MnO

2minus119910where the

nonstoichiometry index is in the range 119910 = 001ndash010depending on the synthesis method [93]

12 Advances in Condensed Matter Physics

Mn

O

(a)

a

b

c

(b)

O2O4

O1O3

Mn2

Mn1

Mn1998400

O3998400

O4998400

(c)

Figure 14 Crystal structure of manganese dioxide (a) MnO6

octahedron connection in 120573-MnO2(b) [90ndash94] and projection of

octahedron binding onto the ab plane [93]

As to the lower manganese oxides MnO and Mn3O4are

known to be theMott insulatorswith relatively high resistivity[90] and Mn

2O3shows p-type semiconducting properties

MnO2is an n-type semiconductor and antiferromagnetic

with the Neel temperature 119879119873= 925 K [91] Conductivity of

manganese dioxide is higher than that of MnO and Mn2O3

by several orders of magnitude At temperatures above 723Kmanganese dioxide loses oxygen and transforms intoMn

2O3

which is accompanied by the transformation of the crystallinestructure from the tetragonal crystal system of the rutile typeinto the complex large-period cubic lattice (119886 = 94gt) and alarge number of formula units per unit cell [54 92 93]

In this subsection we present the results on electricalproperties of manganese dioxide particularly the natureof the 120573-MnO

2conductivity at low temperatures in its

interrelation with characteristic features of the material crys-talline structure and the metal-insulator phase transitionin this compound as well The effect of electrical switchingwith current-voltage characteristics of both N- and S-typehas been found in thin-film MOM structures on the basisof manganese oxides Possible mechanisms of switching interms of the MIT and thermistor effects are discussed

Mn oxide samples under study have been obtained bythree methods anodic oxidation and vacuum evaporation(thin films) as well as by pyrolysis [54] Thin films ofmanganese dioxide were deposited by means of thermalevaporation onto glass substrates covered by a SnO

2layer

using a VUP-5 vacuum setup the film thickness was 119889 =

250 nmAlso thin films ofmanganese oxidewere obtained byelectrochemical oxidation of metal Mn in the KNO

3-NaNO

3

eutectic melt (see Section 21) at 119879 = 600K at a constantvoltage of about 2V for 3min the current density diminishedfrom 200 to 100mAcm2 during the oxidation process Foranodic oxide films on Mn the value of 119889 was sim100 nm Bulksamples of manganese dioxide were obtained by multipledecomposition (pyrolysis) of manganese nitrate at 119879 = 670Kon a glass-ceramic substrate or on a tantalum sheetmetal withthe subsequent separation from the substrate [92 93] Thetotal coating thickness was about 1mm

The manganese oxide samples were characterized by X-ray diffraction (XRD) using a DRON-6 diffractometer inCuK120572and FeK

120572radiation The characteristics of the atomic

structure of pyrolytic manganese dioxide were refined by thefull-profile analysis of the XRD patterns of polycrystallinesamples [93]The resistivity of pyrolyticMnO

2wasmeasured

in the temperature range 15 to 300K bymeans of a four-probetechnique both DC and AC (in a frequency range from 50 to104Hz) in a Gifford-McMahon cycle cryorefrigerator [54]We also measured electrical conductivity in the range T =293ndash423K the Hall effect in the magnetic field of 23 T andthe Seebeck coefficient (thermoelectromotive force thermo-emf ) The dynamic current-voltage (I-V) characteristics ofthe thin-film MOM structures were measured by oscillo-graphic method using an AC sinusoidal signal

The XRD patterns of the manganese oxide samples arepresented in Figures 15 and 16 The vacuum-deposited filmsare amorphous and represent a mixture of 120573- and 120574-MnO

2

(Figure 16) The results of the full-profile analysis show thatthe pyrolytic MnO

2samples (Figure 15) are composed of

the finely dispersed 120573-MnO2phase with the traces of 120574-

MnO2 120576-MnO

2 and Mn

2O3phases The periods of the

tetragonal unit cell of 120573-MnO2are 119886 = 119887 = 4401 A and

119888 = 2872 A The oxygen coordinates in 4119891 positions (seediscussion of the crystal structure above and Figure 14) arefound to be119909 = 0302 Calculations of the oxygen-manganeseinteratomic distances show [93] that the oxygen octahedron

Advances in Condensed Matter Physics 13

330222

040231

212202

112

130002

220

121

120

111

110

101

020

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 80 100 12002120579∘

Figure 15 XRD (Cu K120572radiation) pattern of pyrolytic MnO

2

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 8002120579∘ Fe

120573-MnO2

120574-MnO2

Experiment

Figure 16 XRD (Fe K120572radiation) pattern of Mn oxide film and

reference spectra of crystalline MnO2samples

is compressed along the (100) direction which connects theoctahedron vertices This deformation results in an increaseof the overlap of electron119901 orbitals of oxygen and119889 orbitals ofmanganese and can form the additional splitting of electronlevels in the crystal field leading to the appearance of unpairedelectrons [94]

The measurements of the conductivity temperaturedependence Hall effect and thermo-emf show that man-ganese dioxide is the electron semiconductor with conductiv-ity of about 1Ωminus1cmminus1 and mobility of sim10 cm2Vsdots The Hallmeasurements give the carrier density ofsim1018 cmminus3 which isclose to the density values in degenerate semiconductorsTheactivation energy of conductivity is sim01 eV and the band gapwidth is equal to 2 eV [90] The estimated value of the Fermienergy from the thermo-emf temperature dependence is inthe range of 002 to 005 eV which also indicates the degener-ate character of the electron gasThe nonstoichiometry indexdetermined by the XRD peaks which are not contributed

by the manganese atoms that is by those with the oddsum of indexes is 119910 = 006 Such nonstoichiometry providesthe concentration of trap states of about 1017-1018 cmminus3which correlates with the above mentioned Hall-effect-basedmeasurements of electron density

Such high vacancy concentration allows us to considerthe nonstoichiometric 120573-MnO

2as a heavily doped semicon-

ductor with a subband of impurity levels which provides afeasibility of the out-of-band electron transfer at low tem-peratures The structural distortions high nonstoichiometryand as a consequence sufficiently high concentration ofimpurity states cause the density state tails near the bandedges similarly to those in heavily doped semiconductorsHowever at room and higher temperatures the conduction isdetermined by the activation mechanism Thus the electronstructure and a low mobility of charge carriers promotethe manifestation of different charge transfer mechanismsin different temperature ranges namely both the hoppingmechanism and the activation one

The electron capturing oxygen vacancies create mixedvalence states of manganese cations (Mn3+ndashMn4+) Interest-ingly the mixed valence of Mn ions is also characteristic ofmanganites Ln

1minus119910Sr119910MnO3[95] where Ln is La or another

rare-earth element possessing the effect of colossal magne-toresistance (CMR) In these compounds the mixed valenceof manganese is attained via doping It had been deemed thatholes introduced by strontium are localized at manganeseions that is the Mn4+ ions with concentration 119910 are formedHowever recent X-ray emission studies have shown that boththe chemical shift and the exchange splitting of the emissionX-ray Mn K

1205731line are almost the same in the range 119910 lt 04ndash

05 as is the case in Mn2O3 and then they decrease quickly

to the values characteristic of MnO2[96] which suggests that

the introduced holes are localized at oxygen atoms in the holedoping region (at relatively low 119910) and atmanganese atoms inthe electron doping region that is at higher 119910 values

The temperature dependence of conductivity is presentedin Figure 17 The resistance peak observed in the figure ina temperature range of 80ndash90K is the result of the phasetransition of 120573-MnO

2from a semiconducting state to a metal

state upon decreasing the temperature to 15 K [54] The tem-perature region of the transition is close to the known Neeltransition from the paramagnetic state into the ferromagneticone for manganese dioxide The temperature dependenceof resistance indicates thus the MIT to occur in MnO

2 In

the temperature range from 300 to 80K (Figure 17) thisdependence does not correspond to the exponential one yetit fits well with the linear dependence in theMott coordinatesln(119877) sim 119879

14 which indicates the hopping conductivitymechanism over the polyvalent states ofmanganese ions witha distance between the centres of 25ndash35gt [92] However inthe temperature range from 90 to 15 K the dependence ofln119877 on ln119879 is almost linear with the slope of about unity(ie 120597 ln119877120597 ln119879 asymp 1) which is characteristic of the metallicconductionThus the character of conductivity ofmanganesedioxide indicates the presence of the MIT at 119879

119888sim 80K (on

cooling)

14 Advances in Condensed Matter Physics

CoolingHeating

40 80 120 160 2000T (K)

0

2

4

6

8

10

Resis

tivity

(Ohm

timescm

)

Figure 17 Temperature dependence of AC (70Hz) resistivity ofpyrolytic MnO

2

In the low temperature region manganese dioxide is anantiferromagnetwith the helical spin ordering [97]The inter-action between the magnetic ions of manganese which leadsto the antiferromagnetic state occurs through the intermedi-ate interaction with diamagnetic oxygen ions which weakensthe exchange interaction The conductivity increases proba-bly due to exceeding the energy of the exchange interactionby the thermal energy as the temperature increases whichleads to an increase in the number of unpaired electrons inthe paramagnetic state As the temperature further increasesthe conductivity continues to rise and the Mott hoppingmechanism of charge transfer becomes predominant Similarcharacter of the temperature dependence in ferromagneticdegenerate semiconductors has previously been described[85 98] for substoichiometric (oxygen-deficient) europiummonoxide The transition from the highly conductive stateinto the insulating state occurs in such semiconductors uponvarying the type of magnetic ordering or its destruction

For EuO1minus119910

lowering the peak magnitude in the 119877(119879)

dependence is associatedwith a decrease in the concentrationof impurities (oxygen vacancies) In magnetic semicon-ductors the phase transition is associated both with themagnetoelectric effects and with the variation in the electricpolarization under the action of the magnetic field at theantiferromagnetic transition [98] The dielectric constant formanganese dioxide is equal to sim10 but the effective dielectricconstant can decrease near 119879

119888by a factor of several times

thereby affecting the mobility of carriers located in the tailsof the density of states near the band edge and promotingtheir delocalization at the phase transition temperatureManganese dioxide also belongs to this group of substanceshowever the phase transition in MnO

2reported here can be

also described in terms of the Mott transition [24]According to the Mott criterion electrons delocalize if

the distance between the atoms 119899minus13 becomes comparable

with their atomic radius 119886119860 where 119886

119860is associated with the

Bohr radius 119886119861= ℏ2120576me2The static permittivity 120576 is replaced

by the effective permittivity which takes into account theexchange interaction of the spins of conduction electronswith orbitalmagneticmoments of atoms At the temperature-induced Mott MIT the orbital radius 119886

119861decreases near 119879 =

119879119888thereby providing the fulfillment of the Mott criterion at a

given level of impurity centres [24 98] The transition fromthe metallic state into the semiconductor state is possible insuch semiconductors as the temperature increases Thus theMIT in manganese dioxide is brought about by temperaturevariation

In conclusion we note that the phase transition describedabove is inverse (reentrant) MIT that is the metallic phaseis low-temperature while the high-temperature state is insu-lating This is rather rare yet not unique and unusualphenomenon In most cases (eg in vanadium dioxide) thelow-temperature phase is insulating and on heating abovea certain temperature 119879

119888 the material becomes metallic for

VO2 this transition temperature is 119879

119888= 340K The inverse

transitions are observed in such compounds as the abovementioned EuO

1minus119910 NiS2Se Y2O3minus119910

and LaMnO3films [24

31 52 85 98 99] Also the high-temperature Mott transi-tion from paramagnetic metal to paramagnetic insulator inV2O3Cr is an inverse transition with the resistivity peak at

119879119888sim 350K for a chromium concentration of around 1 at

[24 51] and in mixed valence CMR-manganites the sharpresistivity peak has been shown to be caused by the AndersonMIT [95]

It is known that many TMOs exhibit electrical switchingassociated with MITs [28] For the anodic oxide films onMn the study of the effect of electrical switching in thin-film Mn-MnO

2-Au sandwich structures showed that the S-

type switching was not observed in contrast to for examplethe similar structures based on oxides of vanadium andsome other transition metals [28] Instead switching withthe N-shaped I-V characteristic occurred after EF at 119879 lt

80K (Figure 18(a)) In addition the EF process in the Mn-based structures was hindered likewise for example for thestructures based on yttrium oxide [31] that is the breakdowntook place more often It should be noted that EF at roomtemperature always led to breakdown and the switchingeffect had never been observed in this case As was arguedin [54] this switching effect was associated with the MIT inMnO2

On the other hand in the films obtained by vacuumsputtering we have observed S-type switching at roomtemperature (Figure 18(b)) The threshold voltage is of theorder of 1 V and almost independent of temperature up to 119879

= 375KThis situation resembles that with yttrium oxide where

both S-type and N-type switching has been observed too[31] One can assume that switching with the S-shapedI-V curves is due to the so-called ldquothermistor effectrdquo Itis well known that the current flowing through a solidgenerates Joule heat resulting in an increased temperatureIn materials with a negative TCR a rising temperatureinduces a current enhancement and an increased powerdissipation resulting in a farther temperature increase Thispositive electrothermal feedback causes the appearance of anNDR and accordingly an S-shaped I-V characteristic [2]

Advances in Condensed Matter Physics 15

minus15

minus10

minus5

0

5

10

15Cu

rren

t (m

A)

0500 10 15minus10 minus05minus15

Voltage (V)

(a)

minus2

minus1

0

1

2

Curr

ent (

mA

)

10 2minus2 minus1

Voltage (V)

(b)

Figure 18 (a) I-V characteristic of anodic oxide film on manganese at T = 77K (b) I-V characteristic of vacuum-deposited MnO2at 119879 =

293K

In some cases this process might by modified by high-fieldeffects such as Schottky injection impact ionization Poole-Frenkel effect and Zener or avalanche breakdown Notethat unlike a conventional thermistor with an Arrhenius-like conductivity law manganese oxide exhibits a weaker119877(119879) dependence characteristic of the hopping conductivitymechanism which seems to account for the observed weaktemperature dependence of the threshold voltage

An alternative mechanism for the S-type switching effectmay be connected with a possible high-temperature usual(ie not inverse)MIT in somemanganese oxide As is knownEF (see Section 22) leads to the formation of a filament ofhighly conducting material a switching channel Similarlyto what is observed for Mo oxide (Section 231) and otherTMOs (Sections 21 and 22) we suppose that the compositionof this channel differs from the material of the initial oxidefilm since its conductivity noticeably exceeds that of anunformed structure In view of such a plentiful set of phasesand crystal structures in the Mn-O system one can supposethat the channelmight consist of nonstoichiometric120573-MnO

2

some other polymorphic modifications of manganese diox-ide or lower Mn oxides which might undergo a MIT underthe action of either temperature or electric field Howeverthis question obviously requires additional investigation inparticularmeasurements of119877(119879)dependences and switchingproperties at higher temperatures If this assumed high-temperature MIT would occur in for example nonstoichio-metric 120573-MnO

2 one could expect observation of double-

NDR I-V characteristics in such samples at low temperaturesanalogously to those in V

2O3Cr (Figure 9) where this effect

is due to the MITs [29] with the only difference being thatin the case of MnO

2this curve should be N-S-shaped (unlike

the S-N-shaped one in Figure 9) since in chromium-dopedvanadium sesquioxide the inverse MIT is high-temperatureas opposed to MnO

2which as we discussed above (see

Figure 17) exhibits the inverse MIT at low temperaturesNote however that the discussed high-temperature MIT

in 120573-MnO2minus119910

may be unobservable under the temperature

change in equilibrium conditions but displays itself onlyunder the applied electric field as the S-type electricalswitching effect because the transition temperature is closeto or higher than the temperature of MnO

2decomposition

(723K) Such a nonequilibrium transition occurs at switchingin those materials where the usual temperature-inducedMITwith a well-defined 119879

119905does not take place for example in

CGSs for which the equilibrium transition temperature 1198791199050

is higher than 119879119892 while in a high electric field 119879

119905(119864) lt 119879

1199050

might be lower than 119879119892 where 119879

119892is the temperature of the

glass-crystal transition and119864 is the electric field strength [30]Summarizing we have studied the electrical properties

(conductivity temperature dependence and Hall and Seebeckeffects) of the 120573 phase of manganese dioxide obtained bypyrolysis thermal vacuum evaporation and anodic oxida-tion The change of conductivity mechanisms dependingon temperature in a range of 450ndash25K has been shownand the metal-insulator phase transition at low (lt90K)temperatures has been revealed The specific feature of thistransition described in terms of the Mott mechanism isthat the metal phase exists at low temperatures while athigher temperatures the material is a semiconductor withthe hopping conductivity over the mixed valence states ofmanganese ions

The low-temperature switching effect with an NDR andN-shaped current-voltage characteristic associated with thephase transition in manganese dioxide has been found in theMOM two-terminal devices based on anodicMn oxide filmsOn the contrary the devices based on vacuum-depositedfilms have been found to exhibit an S-NDR at room andhigher temperatures which is suggested to be caused byeither the thermistor effect or a high-temperature MIT innonstoichiometric 120573-MnO

2

It should be emphasized that the low-temperature MITin 120573-MnO

2with 119879

119905= 70ndash80K is the inverse Mott transition

which is akin for instance to the transition in V2O3Cr

at 119879119905= 190ndash385K (for chromium dopant concentration in

the range of 05ndash18 at) [51] We thus assume that farther

16 Advances in Condensed Matter Physics

5 10 150Voltage (V)

0

1

2

3

4

5

6

7

8Cu

rren

t (m

A)

(a)ΔV

th(V

)

0

1

2

3

1 2 3 4 5 6 7 80W (at )

(b)

Figure 19 I-V curve (a) of Au-V2minus119910

W119910O5times 119899H2O-Au sandwich structure with119910= 003 and119881th scattering as a function of tungsten admixture

percentage 119910 (b) [104 105]

investigations of the phase transition in manganese dioxidedescribed in this paper are a rather interesting and topicalscientific problem since manganese dioxide can serve as amodel object for studying such inverse metal-insulator phasetransitions

Finally we note that the results presented in this sectionindicate the possibility of application of manganese oxide asa material for thin film sandwich switching devices Deviceswith NDR (N- and S-shaped I-V characteristics) have poten-tial applications in microelectronics as switches memoryelements and microsensors (these issues will be discussedin more detail below in Section 4) Particularly manganeseoxide microswitches [82] can be utilized for implementationof neuristors built with Mott-transition-based memristors[100]

24 Effect of Doping It is only natural that the systemsexhibiting the NDR effects possess a high applied potential inelectronics [2 4 8 18 100 101] yet the stage of EF is a weaklink of chain in the technology process Note that the formingprocess may be brought about by laser irradiation [102] notby applying of electric field In the case of laser treatment(or ldquolaser formingrdquo unlike the above described electricalforming) the parameters of the structures are characterizedby the absence of the scatter that is the I-V characteristics ofall structures are almost identical [103] One more demerit tobe avoided is the scatter in switching parameters (the value of119881th first of all) and their instability during operation In thissubsection we discuss the issues concerning the switchingparameter stabilization by means of doping

In the work [104] we have studied the switching effectin the MOM structures on the basis of W-doped V

2O5-gel

filmsThese structures require preliminary EF similar to thatin anodic oxide films resulting in formation of a conducting

channel within the initial dielectric xerogel filmThe channelconsists of vanadiumdioxide and switching is associatedwiththe insulator-to-metal transition in VO

2 As was shown in

[104 105] for the pure (undoped) V2O5-gel the switching

parameters vary in a wide range because the phenomenonof EF is statistical in nature (like electrical breakdown) andits statistical character shows itself as a spread in the observedthreshold voltages of the ensuing structures that is actuallyat multiple measurements 119881th = ⟨119881th⟩ plusmn Δ119881th

It has been shown [104] that the statistical spread in valuesof the threshold parameters can be minimized by means ofdoping (Figure 19) Unsophisticated reasoning could accountfor this result for pure V

2O5-gel electroforming leads to

formation of VO2with 119879

119905= 340K and each switching

event requires heating up and cooling down from roomtemperature to 119879

119905 this thermal cycling can modify the

peripheral regions of the channel which leads to the changeof the switching threshold voltage On the other hand forthe samples with a high concentration of W the MIT issuppressed [104] and switching is degenerated Betweenthese two outermost points an optimum should exist Asone can see from Figure 19 this optimal value correspondsto 3 at of W that is for V

097W003

O2the switching

parameters are the most stableThe transition temperature ofV097

W003

O2is lower than that for pure vanadium dioxide

and hence the magnitude of the aforesaid thermal cyclingis decreased which results in an increase of stability of theswitching parameters

Next we have studied the effect of doping on switchingin AOFs on Ti [29] These films were obtained in 5 watersolution of citric acid (C

6H8O7) in volt-static regime at 119881

119886

= 20V The samples were doped with aluminium by meansof adding soluble Al-containing substances to the electrolyte

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

Films vol 97 no 2 pp 129ndash143 1982[46] R Collongues La Non-Stoechiometrie Masson Paris France

1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

9 no 5 pp 391ndash396 2014[67] B Sun W Zhao Y Liu and P Chen ldquoResistive switching effect

of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

1990[70] S Mukherjee S Karmakar H Sakata and B K Chaudhuri

ldquoLow-temperature metallic behavior of amorphous MoO3-

TeO2thin filmsrdquo Journal of Applied Physics vol 97 no 12 Article

ID 123707 2005[71] AMottaghizadeh Q Yu P L Lang A Zimmers andH Aubin

ldquoMetal oxide resistive switching evolution of the density ofstates across the metal-insulator transitionrdquo Physical ReviewLetters vol 112 no 6 Article ID 066803 2014

[72] R Xie C T Bui B Varghese et al ldquoAn electrically tunedsolid-state thermalmemory based onmetal-insulator transitionof single-crystalline VO

2nanobeamsrdquo Advanced Functional

Materials vol 21 no 9 pp 1602ndash1607 2011

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

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GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

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Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

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PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

8 Advances in Condensed Matter Physics

Fe3O4 respectively is also confirmed by the thermodynamic

calculations In oxides of W and Mo switching may beassociated with MIT in the channels consisting of WO

3minus119909

and Mo8O23 The S-shaped voltage-current characteristic

is conditioned by the development of an electrothermalinstability in the channel When a voltage is applied thechannel is heated up to 119879 = 119879

119905(at 119881 = 119881th) by the current

and the structure undergoes a transition fromhigh-resistance(OFF) insulating state to low-resistance (ON) metallic state

In high electric fields (105ndash106 Vcm) the possible influ-ence of electronic effects on the MIT should be taken intoaccount A field-induced increase in charge carrier densitywill act to screen Coulomb interactions [12] leading to theelimination of the Mott-Hubbard energy gap at 119879 lt 119879

119905

Moreover a transition of this type may be important in thosematerials where the usual temperature-induced MIT with awell-defined 119879

119905does not take place for example in oxides

of Ta or Hf (and in CGS-based switching structures as well[50]) In the case of vanadium dioxide such a possibilityof the electronically induced MIT was suggested from theinjection experiments [22] and will be discussed also belowin connection with the transition mechanism in VO

2

To summarize the results presented above as well asthe other data on the switching in transition metal oxides[11ndash17 27ndash31] indicate that current instabilities with the S-type NDR exhibit several common features In particularfor each of the investigated materials there is a certain fixedtemperature 119879

119900 above which switching disappears At 119879 lt

119879119900 the threshold voltage decreases as the temperature rises

tending to zero at 119879 = 119879119900 Comparison of these temperatures

with the temperatures of MIT for some compounds (119879119905

=

120K for Fe3O4 sim200K for WO

3minus119909 340K for VO

2 sim500K

for Ti2O3 and 1070K for NbO

2) shows that the switching

effect is associated with the insulator-metal transition in anelectric field The channels consisting of these lower oxidesare formed in initial anodic films during the process ofpreliminary EF

And finally in conclusion of this section we would like todiscuss onemore vanadium oxide where the switching effectsare caused by MITs namely vanadium sesquioxide The I-Vcharacteristics of chromium-doped V

2O3shown in Figure 9

are distinctive in that they exhibit in a certain temperaturerange two regions of negative differential resistance both N-NDR and S-NDR The experimental data on the switchingeffect ofMOM structures based onV

2O3Cr can be explained

in terms of the switching mechanism driven by the variableMIT The S-shaped I-V characteristic is conditioned by thedevelopment of an electrothermal instability in the sampleWhen a voltage is applied the sample is heated by the currentup to 119879 = 119879

1199051(at the threshold voltage 119881 = 119881th119878) and

the structure undergoes a transition from a high-resistance(OFF-1) AFI state to a low-resistance (ON) PM state Asthe current in the ON state increases the sample is furtherheated and at 119879 = 119879

1199052(119868 = 119868th119873) the second transition

to the OFF-2 (or PI) state occurs [51] In the OFF-1 statethe plot of current versus the square root of the appliedvoltage is indicative of a Poole-Frenkel type of conductivityenhancement [52] (Figure 10)

12

34

0

20

40

60

80

100

120

140

160

180

Curr

ent (

mA

)

05 10 15 20 25 3000Voltage (V)

Figure 9 Current-voltage characteristics for V2O3doped with 12

at of Cr at different temperatures 1705 K (1) 1733 K (2) 2210 K(3) and 2655 K (4) [51]

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

Curr

ent (

A)

05 10 15 20 2500Square root of voltage (V05)

150K140K130K120K110K

100K90K80K70K60K

50K40K30K20K10K

Figure 10 Current versus voltage in Poole-Frenkel coordinates fora V2O3-based switching device [52]

23 Switching Effects and Metal-Insulator Transitions in MnandMoOxides In this section we consider electrical switch-ing in oxides of Mn and Mo obtained by vacuum depositionin comparison with those obtained by anodic oxidation [5354] It should be emphasized here that AOFs are (as a ruleexcept for some rare cases) amorphous [32 33] Therefore inMOM structures with anodic films the process of EF similarto that in CGSs usually takes place However in some cases(Mo Mn) as was described in previous sections we havefailed to obtain stable switching with anodic films and herewe present an alternative approach to this problem

Advances in Condensed Matter Physics 9

231 Electrical Switching in Thin Film Structures Based onMolybdenumOxide As inmost TMOs in the molybdenum-oxygen system there exist a number of oxides with variablevalence which are characterized by a wide diversity ofstructures and physical properties [53 55 56] MolybdenumtrioxideMoO

3has a structure based on layers of edge-sharing

distorted MoO6octahedra [23] Similar layered structures

are inherent in lower molybdenum oxides including MoO2

Mo18O52 Mo9O26 Mo8O23 Mo5O14 and Mo

17O47 as well

as 120578- and 120574-Mo4O11[55ndash57]

Stoichiometric MoO3 in its most thermodynamically

stable form 120572-MoO3 is an insulator with a band gap of sim3 eV

[23] During reduction by means of either oxygen deficiencyformation or introducing donor impurity atoms additionaldonor levels near the conduction band bottom appear andthe reduced oxide behaves therefore as a semiconductorPolycrystalline MoO

3 as well as a single crystal has a grey-

yellow colour and the minimum value of the absorption edgeis 440 nm which corresponds to the smallest value of theband gap of 28 eV [58] thus the band gap depends upon thestoichiometry and the crystalline state [53] The conductivityvalues of molybdenum oxides range from dielectric MoO

3

to semiconductor Mo18O52

(resistivity 120588 = 781Ωsdotcm)and down to metal 120578-V]

411

(120588 = 166 times 10minus4Ωsdotcm) [58]Molybdenum dioxide also exhibits metallic properties [2358] and at room temperature 120588 = 88 times 10minus5Ωsdotcm for bulkMoO2samples [55]

Because of their special physical and chemical propertiesmolybdenum oxides are used in various electronic devicessuch as electrochromic displays and indicators reversiblecathodes of lithium batteries gas sensors and memoryelements [55ndash61] Metal-insulator transitions have also beenobserved in some oxides of molybdenum and related com-pounds [62ndash70] In particular Mo

8O23

exhibits a two-stagestructural MIT with formation of a charge-density wave at1198791199051= 315 K and 119879

1199052= 285K [62] However as far as we know

no data are available in the literature concerning thresholdswitching associated with these transitions except for ourwork [53] In this work we have particularly noted thatmemory switching is observed inmany TMOs molybdenumoxides included [4 9 59 60]

The most discussed models in the literature for theReRAMmechanism in oxide structures are those based eitheron the growth and rupture of a metal filament inside theoxide matrix under the action of electric current or onthe redox processes responsible for the formation of somehigh-conductivity or low-conductivity local inclusions cor-responding to particular oxygen stoichiometry [4] The MITideology is also sometimes involved to explain the propertiesof the structures and the memory switching mechanismtherein [71] In any case thememory switching phenomenonseems to be associated with the ion transport [4 9] It isalso appropriate to mention here the works discussing thememory effects in a material with MIT (vanadium dioxide)associated with the presence of hysteresis in the temperaturedependence of conductivity [72]

On the other hand as was shown in the previous sectionmonostable threshold switching (with no memory effects)

associated with the MIT is also characteristic of a numberof TMOs That is why the study of threshold switchingin molybdenum oxide and its possible connection withthe phenomenon of MIT is of considerable scientific andpractical interest

Thinfilm samples ofmolybdenumoxidewere obtained bytwo ways anodic oxidation and thermal vacuum evaporation[53] Anodization of molybdenum was carried out in anacetone-based electrolyte (22 g of benzoic acid plus 40mLof saturated borax aqueous solution per litre of acetone[33 73]) AOFs on Mo might include lower molybdenumoxides for example Mo

4O11andMoO

2with a relatively high

electronic conductivity [53] The fact that the anodic oxideon molybdenum contained lower oxides was confirmed byexperimental data in the work [74] where it was shown thatthe degree of oxidation (valence state) of molybdenum in anAOF is less than six Also this was confirmed theoretically interms of the thermodynamics of the process the formation ofunsaturated oxide MoO

2had been shown to be energetically

more favourable than MoO3[75]

Vacuum deposited film samples were fabricated by ther-mal evaporation of MoO

3powder at residual pressure of

10minus4 Torr onto polished tantalum plates or glass substratesfor electrical and optical studies respectivelyThe thicknessesof the films were determined from the transmission andreflection interference spectra measurements [76] and theywere found to lie in the range from 300 to 800 nm

The XRD pattern of a vacuum-deposited molybdenumoxide sample is presented in Figure 11(a) It is shown thatthe samples represent amorphousMoO

3with a slight oxygen

nonstoichiometry [53] Anodic oxide films on Mo are alsoamorphous (or amorphous-microcrystalline according tothe literature data [73]) but their composition correspondsas described above to ratherMoO

2or other lower oxides and

not to the highest oxide MoO3

Figure 11(b) shows the reflection and transmission spec-tra for one of the samples obtained by vacuum depositionThe experimental data processing using the envelope of theinterference extrema [76] yields the film thickness of (620 plusmn

50) nm and the absorption edge around 120582 asymp 400 nm indi-cates the fact that the oxide phase composition correspondsto MoO

3with a band gap of sim3 eV

Before electroforming initial structures demonstrate thenonlinear and slightly asymmetric current-voltage charac-teristics with no NDR regions When the amplitude of theapplied voltage reaches the forming voltage a sharp andirreversible increase in conductivity is observed and theI(V) curve becomes S-shaped (Figure 12) With increas-ing current the I-V characteristic may change until theparameters of the switching structure are finally stabilizedThe process outlined above is qualitatively similar to theelectroforming of the switching devices based on other TMOs(see Section 22 above) We emphasize once again that thephase composition of the ensuing switching channel mustdiffer from the material of the pristine oxide film becausethe channel conductivity is higher than that of the unformedstructure by several orders of magnitude

The current-voltage characteristics of vacuum-depositedfilms and those of anodic films are qualitatively similar but

10 Advances in Condensed Matter Physics

1

2

20 40 60 8002120579∘

0100200300400500600700800900

I (co

unts

s)

(a)

1

2

3

0

20

40

60

80

100

T (

)

300 400 500 600 700 800 900 1000 1100200Wavelength (nm)

(b)

Figure 11 (a) XRD pattern of the molybdenum oxide film (1) andV]3powder (2) (b) Optical spectra of the sample obtained by vacuum

deposition (1) transmission coefficient of substrate (glass) (2) transmittance and (3) reflectance of Mo oxide film on glass [53]

0 5 10minus5minus10

Voltage (V)

minus016

minus012

minus008

minus004

000

004

008

012

016

Curr

ent (

mA

)

(a)

minus072 072 216 360minus216minus360

Voltage (V)

minus064

minus048

minus032

minus016

000

016

032

048

064

Curr

ent (

mA

)

(b)

Figure 12 Current-voltage characteristics ofMOMstructures with vacuum-deposited (a) and anodic (b)Mo oxide films after electroforming

there is a significant quantitative difference in their thresholdparameters For instance the switching voltage 119881th for theAOF based structures is sim2V (Figure 12(b)) whereas forthe structures on the basis of the films prepared by thermalevaporation119881th is sim10V (Figure 12(a))This difference can beexplained by the difference in thickness of the films

For anodic oxide the thickness can be estimated fromFaradayrsquos law [53]

119889 =

120583119868119886119905

4119890120588119878119873119860

(4)

where 120583 = 128 gmol and 120588 = 65 gcm3 are respectivelythe molar mass and density of V]

2and 119890 and 119873

119860are the

unit charge and Avogadro constant For 119868119886= 70m0 and 119905 =

10min (4) yields 119889 sim 20 nm which is significantly less thanthe typical thickness of the vacuum deposited films and as aresult the threshold voltage for AOFs is also lower than thatfor the films obtained by thermal evaporation

As is discussed in [53] switching is not observed inthinner films obtained by vacuum evaporation (119889 lt 100 nm)

in contrast to ultrathin AOFs A plausible reason for thismight be the fact that relatively thin vacuum depositedfilms contain through-the-thickness conducting defects dueto local stoichiometry variations whereas such defects areimpossible in anodic films because they are grown in highelectric field during anodic oxidation and an appearanceof such defects would interrupt the film growth processThis is similar to what is observed in vanadium oxide inpolycrystalline vanadium dioxide films such pin-hole defectsare usually associated with the grain boundaries which couldundergo local metallization due to strain or nonstoichiom-etry That is why it had been difficult to observe switchingin sandwich MOM structures with sputtered or thermallyoxidized polycrystalline VO

2films and most studies had

been conducted with planar thin-film structures whilst foranodically oxidized VO

2the switching effect has then been

observed in a sandwich structure for the first time in [16]Next we note that unlike the most other TMOs the

process of electroforming in Mo-based structures was hin-dered as was mentioned above in Section 21 that is theconventional electrical breakdown often occurred not the

Advances in Condensed Matter Physics 11

020406080

100120

30 40 50 60 7020Temperature (∘C)

30 40 50 60 7020Temperature (∘C)

0

2

4

6

8

10

12

Thre

shol

d vo

ltage

(V)

5 15minus5minus15

Voltage (V)

minus010

minus005

000005010

Curr

ent (

mA

)

V2 th

(V2)

Figure 13 Threshold voltage as a function of temperature for theTa-MoOx-Au switching structure and the temperature dependenceof (119881th)

2 (lower inset) in compliancewith (3) I-V curve at RT (upperinset)

formation of a switching channel However for the Mooxide films prepared by vacuum deposition the processesof electroforming and switching were more stable whichallowed in this case observation of the transformation of I-V curves at a temperature change It was found that as thetemperature increased the threshold voltage was reducedAt 119879 = 119879

119900sim 55ndash65∘C the NDR region degeneration

commenced at 119879 asymp 60ndash70∘C 119881th rarr 0 and at still highertemperatures the switching effect no longer occurred Inthis case the switching mechanism might be described interms of the ldquocritical temperaturerdquo model (Figure 13) It issupposed [53] that in the case of Mo like in other TMO-based structures formation of a channel also takes placeand this channel should consist of a material exhibiting MITwhich is the reason for switching with an S-shaped current-voltage characteristic (Figure 12)

A brief review of the materials with MIT in the familyof molybdenum compounds presented in [53] shows that themost suitable candidate for the role of such a channel-formingcompound is Mo

8O23

because in this case the value of 1198791199051

almost coincides with the above reported experimentallymeasured 119879

0 It should be noted that formation of other

compounds of molybdenum (eg pyrochlores bronzes sul-fides or chalcogenide glasses) exhibiting MITs with similarorder of magnitude transition temperatures [64ndash68 70] isimpossible because of the lack of the necessary chemicalelements (ie rare earths alkali metals or hydrogen sulfurand tellurium) in the phase composition of both the oxidefilm and the metal electrodes (Au Ta and Mo)

In conclusion the results presented in this subsection onswitching from the HR state to the LR state with an S-NDRin molybdenum oxides obtained by both thermal vacuumdeposition and electrochemical anodic oxidation show thatthe switching effect is due to apparently an insulator-to-metal phase transition in the switching channel consistingcompletely or partly of the lower oxide Mo

8O23 formed in

the initial film during the process of electroforming Thecurrent flowing through the channel heats it up to the MIT

temperature 1198791199051= 315K [62] and the structure switches into

the metallic low-resistance stateThus the channels consisting of this lower oxide are

formed in initial Mo oxide films during preliminary elec-troforming Electrical forming results in the changes inoxygen stoichiometry conditioned by the ionic processes inan electric field close to the MOM structure breakdown fieldThis picture is quite similar to what is observed inmany otherTMOs exhibiting the insulator-to-metal transitions

232 Metal-Insulator Transition and Switching in ManganeseDioxide Manganese dioxide is one of the most interestinginorganic materials because of its wide range of applica-tions In particular nanostructured MnO

2has received great

attention due to its high specific surface area functionalproperties and potential applications as molecular and ionselective membranes in capacitors Li-ion batteries andcatalysts [77] Originally MnO

2has been widely used as a

cathode material for oxide-semiconductor capacitors basedon tantalum niobium and aluminium oxides and the mostimportant properties of the material for this application areits high conductivity and ability to undergo a thermal phasetransition into the lower valence states accompanied by evo-lution of atomic oxygen while the resistance increases by 3-4orders of magnitude (see eg [54] and references therein)Much attention is currently paid to various other propertiesof MnO

2 such as for example the electrochromic effect

[78] thermopower wave phenomenon [79] supercapacitivebehaviour [80] andmemory and threshold switching [54 8182] Also there are a number of papers [83ndash85] describing ananomaly in theMnO

2conductivity near theNeel temperature

which is shown to be associated with the metal-insulatortransition [52] That is why the electrical properties of MnO

2

are of special scientific interest and applied importanceThe most common methods for manganese oxide prepa-

ration are the pyrolytic decomposition of manganese nitrateelectrochemical method hydrothermal synthesis in a mag-netic field and chemical deposition [54 86ndash89] Due to awide range of possible valence states of cations the structureand phase composition of manganese oxides are determinedby the synthesis conditions and process temperature Man-ganese dioxide has many crystallographic forms (120572- 120573- 120574-120575- 120576- and 120582-MnO

2) that connect MnO

6octahedron units to

each other in different ways and have different characters ofspatial alternation of the octahedra filled by Mn atoms andempty octahedra [54 77 90ndash94]

The crystal structure of the 120573-MnO2phase (Figure 14) is a

tetragonal modification of the rutile structural type P4mnmsymmetry group which represents a slightly distorted close-packed hexagonal lattice of oxygen ions [93] Filled octahedraare bound by two common edges in columns oriented alongthe 119888 axis and octahedra of adjacent columns are bound bytheir vertices (Figure 14(c)) Manganese atoms are arrangedin positions 2(a) (000) and oxygen atoms in positions 4(f )(xx0) Because there are vacancies in the oxygen packingthe formula unit can be written as MnO

2minus119910where the

nonstoichiometry index is in the range 119910 = 001ndash010depending on the synthesis method [93]

12 Advances in Condensed Matter Physics

Mn

O

(a)

a

b

c

(b)

O2O4

O1O3

Mn2

Mn1

Mn1998400

O3998400

O4998400

(c)

Figure 14 Crystal structure of manganese dioxide (a) MnO6

octahedron connection in 120573-MnO2(b) [90ndash94] and projection of

octahedron binding onto the ab plane [93]

As to the lower manganese oxides MnO and Mn3O4are

known to be theMott insulatorswith relatively high resistivity[90] and Mn

2O3shows p-type semiconducting properties

MnO2is an n-type semiconductor and antiferromagnetic

with the Neel temperature 119879119873= 925 K [91] Conductivity of

manganese dioxide is higher than that of MnO and Mn2O3

by several orders of magnitude At temperatures above 723Kmanganese dioxide loses oxygen and transforms intoMn

2O3

which is accompanied by the transformation of the crystallinestructure from the tetragonal crystal system of the rutile typeinto the complex large-period cubic lattice (119886 = 94gt) and alarge number of formula units per unit cell [54 92 93]

In this subsection we present the results on electricalproperties of manganese dioxide particularly the natureof the 120573-MnO

2conductivity at low temperatures in its

interrelation with characteristic features of the material crys-talline structure and the metal-insulator phase transitionin this compound as well The effect of electrical switchingwith current-voltage characteristics of both N- and S-typehas been found in thin-film MOM structures on the basisof manganese oxides Possible mechanisms of switching interms of the MIT and thermistor effects are discussed

Mn oxide samples under study have been obtained bythree methods anodic oxidation and vacuum evaporation(thin films) as well as by pyrolysis [54] Thin films ofmanganese dioxide were deposited by means of thermalevaporation onto glass substrates covered by a SnO

2layer

using a VUP-5 vacuum setup the film thickness was 119889 =

250 nmAlso thin films ofmanganese oxidewere obtained byelectrochemical oxidation of metal Mn in the KNO

3-NaNO

3

eutectic melt (see Section 21) at 119879 = 600K at a constantvoltage of about 2V for 3min the current density diminishedfrom 200 to 100mAcm2 during the oxidation process Foranodic oxide films on Mn the value of 119889 was sim100 nm Bulksamples of manganese dioxide were obtained by multipledecomposition (pyrolysis) of manganese nitrate at 119879 = 670Kon a glass-ceramic substrate or on a tantalum sheetmetal withthe subsequent separation from the substrate [92 93] Thetotal coating thickness was about 1mm

The manganese oxide samples were characterized by X-ray diffraction (XRD) using a DRON-6 diffractometer inCuK120572and FeK

120572radiation The characteristics of the atomic

structure of pyrolytic manganese dioxide were refined by thefull-profile analysis of the XRD patterns of polycrystallinesamples [93]The resistivity of pyrolyticMnO

2wasmeasured

in the temperature range 15 to 300K bymeans of a four-probetechnique both DC and AC (in a frequency range from 50 to104Hz) in a Gifford-McMahon cycle cryorefrigerator [54]We also measured electrical conductivity in the range T =293ndash423K the Hall effect in the magnetic field of 23 T andthe Seebeck coefficient (thermoelectromotive force thermo-emf ) The dynamic current-voltage (I-V) characteristics ofthe thin-film MOM structures were measured by oscillo-graphic method using an AC sinusoidal signal

The XRD patterns of the manganese oxide samples arepresented in Figures 15 and 16 The vacuum-deposited filmsare amorphous and represent a mixture of 120573- and 120574-MnO

2

(Figure 16) The results of the full-profile analysis show thatthe pyrolytic MnO

2samples (Figure 15) are composed of

the finely dispersed 120573-MnO2phase with the traces of 120574-

MnO2 120576-MnO

2 and Mn

2O3phases The periods of the

tetragonal unit cell of 120573-MnO2are 119886 = 119887 = 4401 A and

119888 = 2872 A The oxygen coordinates in 4119891 positions (seediscussion of the crystal structure above and Figure 14) arefound to be119909 = 0302 Calculations of the oxygen-manganeseinteratomic distances show [93] that the oxygen octahedron

Advances in Condensed Matter Physics 13

330222

040231

212202

112

130002

220

121

120

111

110

101

020

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 80 100 12002120579∘

Figure 15 XRD (Cu K120572radiation) pattern of pyrolytic MnO

2

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 8002120579∘ Fe

120573-MnO2

120574-MnO2

Experiment

Figure 16 XRD (Fe K120572radiation) pattern of Mn oxide film and

reference spectra of crystalline MnO2samples

is compressed along the (100) direction which connects theoctahedron vertices This deformation results in an increaseof the overlap of electron119901 orbitals of oxygen and119889 orbitals ofmanganese and can form the additional splitting of electronlevels in the crystal field leading to the appearance of unpairedelectrons [94]

The measurements of the conductivity temperaturedependence Hall effect and thermo-emf show that man-ganese dioxide is the electron semiconductor with conductiv-ity of about 1Ωminus1cmminus1 and mobility of sim10 cm2Vsdots The Hallmeasurements give the carrier density ofsim1018 cmminus3 which isclose to the density values in degenerate semiconductorsTheactivation energy of conductivity is sim01 eV and the band gapwidth is equal to 2 eV [90] The estimated value of the Fermienergy from the thermo-emf temperature dependence is inthe range of 002 to 005 eV which also indicates the degener-ate character of the electron gasThe nonstoichiometry indexdetermined by the XRD peaks which are not contributed

by the manganese atoms that is by those with the oddsum of indexes is 119910 = 006 Such nonstoichiometry providesthe concentration of trap states of about 1017-1018 cmminus3which correlates with the above mentioned Hall-effect-basedmeasurements of electron density

Such high vacancy concentration allows us to considerthe nonstoichiometric 120573-MnO

2as a heavily doped semicon-

ductor with a subband of impurity levels which provides afeasibility of the out-of-band electron transfer at low tem-peratures The structural distortions high nonstoichiometryand as a consequence sufficiently high concentration ofimpurity states cause the density state tails near the bandedges similarly to those in heavily doped semiconductorsHowever at room and higher temperatures the conduction isdetermined by the activation mechanism Thus the electronstructure and a low mobility of charge carriers promotethe manifestation of different charge transfer mechanismsin different temperature ranges namely both the hoppingmechanism and the activation one

The electron capturing oxygen vacancies create mixedvalence states of manganese cations (Mn3+ndashMn4+) Interest-ingly the mixed valence of Mn ions is also characteristic ofmanganites Ln

1minus119910Sr119910MnO3[95] where Ln is La or another

rare-earth element possessing the effect of colossal magne-toresistance (CMR) In these compounds the mixed valenceof manganese is attained via doping It had been deemed thatholes introduced by strontium are localized at manganeseions that is the Mn4+ ions with concentration 119910 are formedHowever recent X-ray emission studies have shown that boththe chemical shift and the exchange splitting of the emissionX-ray Mn K

1205731line are almost the same in the range 119910 lt 04ndash

05 as is the case in Mn2O3 and then they decrease quickly

to the values characteristic of MnO2[96] which suggests that

the introduced holes are localized at oxygen atoms in the holedoping region (at relatively low 119910) and atmanganese atoms inthe electron doping region that is at higher 119910 values

The temperature dependence of conductivity is presentedin Figure 17 The resistance peak observed in the figure ina temperature range of 80ndash90K is the result of the phasetransition of 120573-MnO

2from a semiconducting state to a metal

state upon decreasing the temperature to 15 K [54] The tem-perature region of the transition is close to the known Neeltransition from the paramagnetic state into the ferromagneticone for manganese dioxide The temperature dependenceof resistance indicates thus the MIT to occur in MnO

2 In

the temperature range from 300 to 80K (Figure 17) thisdependence does not correspond to the exponential one yetit fits well with the linear dependence in theMott coordinatesln(119877) sim 119879

14 which indicates the hopping conductivitymechanism over the polyvalent states ofmanganese ions witha distance between the centres of 25ndash35gt [92] However inthe temperature range from 90 to 15 K the dependence ofln119877 on ln119879 is almost linear with the slope of about unity(ie 120597 ln119877120597 ln119879 asymp 1) which is characteristic of the metallicconductionThus the character of conductivity ofmanganesedioxide indicates the presence of the MIT at 119879

119888sim 80K (on

cooling)

14 Advances in Condensed Matter Physics

CoolingHeating

40 80 120 160 2000T (K)

0

2

4

6

8

10

Resis

tivity

(Ohm

timescm

)

Figure 17 Temperature dependence of AC (70Hz) resistivity ofpyrolytic MnO

2

In the low temperature region manganese dioxide is anantiferromagnetwith the helical spin ordering [97]The inter-action between the magnetic ions of manganese which leadsto the antiferromagnetic state occurs through the intermedi-ate interaction with diamagnetic oxygen ions which weakensthe exchange interaction The conductivity increases proba-bly due to exceeding the energy of the exchange interactionby the thermal energy as the temperature increases whichleads to an increase in the number of unpaired electrons inthe paramagnetic state As the temperature further increasesthe conductivity continues to rise and the Mott hoppingmechanism of charge transfer becomes predominant Similarcharacter of the temperature dependence in ferromagneticdegenerate semiconductors has previously been described[85 98] for substoichiometric (oxygen-deficient) europiummonoxide The transition from the highly conductive stateinto the insulating state occurs in such semiconductors uponvarying the type of magnetic ordering or its destruction

For EuO1minus119910

lowering the peak magnitude in the 119877(119879)

dependence is associatedwith a decrease in the concentrationof impurities (oxygen vacancies) In magnetic semicon-ductors the phase transition is associated both with themagnetoelectric effects and with the variation in the electricpolarization under the action of the magnetic field at theantiferromagnetic transition [98] The dielectric constant formanganese dioxide is equal to sim10 but the effective dielectricconstant can decrease near 119879

119888by a factor of several times

thereby affecting the mobility of carriers located in the tailsof the density of states near the band edge and promotingtheir delocalization at the phase transition temperatureManganese dioxide also belongs to this group of substanceshowever the phase transition in MnO

2reported here can be

also described in terms of the Mott transition [24]According to the Mott criterion electrons delocalize if

the distance between the atoms 119899minus13 becomes comparable

with their atomic radius 119886119860 where 119886

119860is associated with the

Bohr radius 119886119861= ℏ2120576me2The static permittivity 120576 is replaced

by the effective permittivity which takes into account theexchange interaction of the spins of conduction electronswith orbitalmagneticmoments of atoms At the temperature-induced Mott MIT the orbital radius 119886

119861decreases near 119879 =

119879119888thereby providing the fulfillment of the Mott criterion at a

given level of impurity centres [24 98] The transition fromthe metallic state into the semiconductor state is possible insuch semiconductors as the temperature increases Thus theMIT in manganese dioxide is brought about by temperaturevariation

In conclusion we note that the phase transition describedabove is inverse (reentrant) MIT that is the metallic phaseis low-temperature while the high-temperature state is insu-lating This is rather rare yet not unique and unusualphenomenon In most cases (eg in vanadium dioxide) thelow-temperature phase is insulating and on heating abovea certain temperature 119879

119888 the material becomes metallic for

VO2 this transition temperature is 119879

119888= 340K The inverse

transitions are observed in such compounds as the abovementioned EuO

1minus119910 NiS2Se Y2O3minus119910

and LaMnO3films [24

31 52 85 98 99] Also the high-temperature Mott transi-tion from paramagnetic metal to paramagnetic insulator inV2O3Cr is an inverse transition with the resistivity peak at

119879119888sim 350K for a chromium concentration of around 1 at

[24 51] and in mixed valence CMR-manganites the sharpresistivity peak has been shown to be caused by the AndersonMIT [95]

It is known that many TMOs exhibit electrical switchingassociated with MITs [28] For the anodic oxide films onMn the study of the effect of electrical switching in thin-film Mn-MnO

2-Au sandwich structures showed that the S-

type switching was not observed in contrast to for examplethe similar structures based on oxides of vanadium andsome other transition metals [28] Instead switching withthe N-shaped I-V characteristic occurred after EF at 119879 lt

80K (Figure 18(a)) In addition the EF process in the Mn-based structures was hindered likewise for example for thestructures based on yttrium oxide [31] that is the breakdowntook place more often It should be noted that EF at roomtemperature always led to breakdown and the switchingeffect had never been observed in this case As was arguedin [54] this switching effect was associated with the MIT inMnO2

On the other hand in the films obtained by vacuumsputtering we have observed S-type switching at roomtemperature (Figure 18(b)) The threshold voltage is of theorder of 1 V and almost independent of temperature up to 119879

= 375KThis situation resembles that with yttrium oxide where

both S-type and N-type switching has been observed too[31] One can assume that switching with the S-shapedI-V curves is due to the so-called ldquothermistor effectrdquo Itis well known that the current flowing through a solidgenerates Joule heat resulting in an increased temperatureIn materials with a negative TCR a rising temperatureinduces a current enhancement and an increased powerdissipation resulting in a farther temperature increase Thispositive electrothermal feedback causes the appearance of anNDR and accordingly an S-shaped I-V characteristic [2]

Advances in Condensed Matter Physics 15

minus15

minus10

minus5

0

5

10

15Cu

rren

t (m

A)

0500 10 15minus10 minus05minus15

Voltage (V)

(a)

minus2

minus1

0

1

2

Curr

ent (

mA

)

10 2minus2 minus1

Voltage (V)

(b)

Figure 18 (a) I-V characteristic of anodic oxide film on manganese at T = 77K (b) I-V characteristic of vacuum-deposited MnO2at 119879 =

293K

In some cases this process might by modified by high-fieldeffects such as Schottky injection impact ionization Poole-Frenkel effect and Zener or avalanche breakdown Notethat unlike a conventional thermistor with an Arrhenius-like conductivity law manganese oxide exhibits a weaker119877(119879) dependence characteristic of the hopping conductivitymechanism which seems to account for the observed weaktemperature dependence of the threshold voltage

An alternative mechanism for the S-type switching effectmay be connected with a possible high-temperature usual(ie not inverse)MIT in somemanganese oxide As is knownEF (see Section 22) leads to the formation of a filament ofhighly conducting material a switching channel Similarlyto what is observed for Mo oxide (Section 231) and otherTMOs (Sections 21 and 22) we suppose that the compositionof this channel differs from the material of the initial oxidefilm since its conductivity noticeably exceeds that of anunformed structure In view of such a plentiful set of phasesand crystal structures in the Mn-O system one can supposethat the channelmight consist of nonstoichiometric120573-MnO

2

some other polymorphic modifications of manganese diox-ide or lower Mn oxides which might undergo a MIT underthe action of either temperature or electric field Howeverthis question obviously requires additional investigation inparticularmeasurements of119877(119879)dependences and switchingproperties at higher temperatures If this assumed high-temperature MIT would occur in for example nonstoichio-metric 120573-MnO

2 one could expect observation of double-

NDR I-V characteristics in such samples at low temperaturesanalogously to those in V

2O3Cr (Figure 9) where this effect

is due to the MITs [29] with the only difference being thatin the case of MnO

2this curve should be N-S-shaped (unlike

the S-N-shaped one in Figure 9) since in chromium-dopedvanadium sesquioxide the inverse MIT is high-temperatureas opposed to MnO

2which as we discussed above (see

Figure 17) exhibits the inverse MIT at low temperaturesNote however that the discussed high-temperature MIT

in 120573-MnO2minus119910

may be unobservable under the temperature

change in equilibrium conditions but displays itself onlyunder the applied electric field as the S-type electricalswitching effect because the transition temperature is closeto or higher than the temperature of MnO

2decomposition

(723K) Such a nonequilibrium transition occurs at switchingin those materials where the usual temperature-inducedMITwith a well-defined 119879

119905does not take place for example in

CGSs for which the equilibrium transition temperature 1198791199050

is higher than 119879119892 while in a high electric field 119879

119905(119864) lt 119879

1199050

might be lower than 119879119892 where 119879

119892is the temperature of the

glass-crystal transition and119864 is the electric field strength [30]Summarizing we have studied the electrical properties

(conductivity temperature dependence and Hall and Seebeckeffects) of the 120573 phase of manganese dioxide obtained bypyrolysis thermal vacuum evaporation and anodic oxida-tion The change of conductivity mechanisms dependingon temperature in a range of 450ndash25K has been shownand the metal-insulator phase transition at low (lt90K)temperatures has been revealed The specific feature of thistransition described in terms of the Mott mechanism isthat the metal phase exists at low temperatures while athigher temperatures the material is a semiconductor withthe hopping conductivity over the mixed valence states ofmanganese ions

The low-temperature switching effect with an NDR andN-shaped current-voltage characteristic associated with thephase transition in manganese dioxide has been found in theMOM two-terminal devices based on anodicMn oxide filmsOn the contrary the devices based on vacuum-depositedfilms have been found to exhibit an S-NDR at room andhigher temperatures which is suggested to be caused byeither the thermistor effect or a high-temperature MIT innonstoichiometric 120573-MnO

2

It should be emphasized that the low-temperature MITin 120573-MnO

2with 119879

119905= 70ndash80K is the inverse Mott transition

which is akin for instance to the transition in V2O3Cr

at 119879119905= 190ndash385K (for chromium dopant concentration in

the range of 05ndash18 at) [51] We thus assume that farther

16 Advances in Condensed Matter Physics

5 10 150Voltage (V)

0

1

2

3

4

5

6

7

8Cu

rren

t (m

A)

(a)ΔV

th(V

)

0

1

2

3

1 2 3 4 5 6 7 80W (at )

(b)

Figure 19 I-V curve (a) of Au-V2minus119910

W119910O5times 119899H2O-Au sandwich structure with119910= 003 and119881th scattering as a function of tungsten admixture

percentage 119910 (b) [104 105]

investigations of the phase transition in manganese dioxidedescribed in this paper are a rather interesting and topicalscientific problem since manganese dioxide can serve as amodel object for studying such inverse metal-insulator phasetransitions

Finally we note that the results presented in this sectionindicate the possibility of application of manganese oxide asa material for thin film sandwich switching devices Deviceswith NDR (N- and S-shaped I-V characteristics) have poten-tial applications in microelectronics as switches memoryelements and microsensors (these issues will be discussedin more detail below in Section 4) Particularly manganeseoxide microswitches [82] can be utilized for implementationof neuristors built with Mott-transition-based memristors[100]

24 Effect of Doping It is only natural that the systemsexhibiting the NDR effects possess a high applied potential inelectronics [2 4 8 18 100 101] yet the stage of EF is a weaklink of chain in the technology process Note that the formingprocess may be brought about by laser irradiation [102] notby applying of electric field In the case of laser treatment(or ldquolaser formingrdquo unlike the above described electricalforming) the parameters of the structures are characterizedby the absence of the scatter that is the I-V characteristics ofall structures are almost identical [103] One more demerit tobe avoided is the scatter in switching parameters (the value of119881th first of all) and their instability during operation In thissubsection we discuss the issues concerning the switchingparameter stabilization by means of doping

In the work [104] we have studied the switching effectin the MOM structures on the basis of W-doped V

2O5-gel

filmsThese structures require preliminary EF similar to thatin anodic oxide films resulting in formation of a conducting

channel within the initial dielectric xerogel filmThe channelconsists of vanadiumdioxide and switching is associatedwiththe insulator-to-metal transition in VO

2 As was shown in

[104 105] for the pure (undoped) V2O5-gel the switching

parameters vary in a wide range because the phenomenonof EF is statistical in nature (like electrical breakdown) andits statistical character shows itself as a spread in the observedthreshold voltages of the ensuing structures that is actuallyat multiple measurements 119881th = ⟨119881th⟩ plusmn Δ119881th

It has been shown [104] that the statistical spread in valuesof the threshold parameters can be minimized by means ofdoping (Figure 19) Unsophisticated reasoning could accountfor this result for pure V

2O5-gel electroforming leads to

formation of VO2with 119879

119905= 340K and each switching

event requires heating up and cooling down from roomtemperature to 119879

119905 this thermal cycling can modify the

peripheral regions of the channel which leads to the changeof the switching threshold voltage On the other hand forthe samples with a high concentration of W the MIT issuppressed [104] and switching is degenerated Betweenthese two outermost points an optimum should exist Asone can see from Figure 19 this optimal value correspondsto 3 at of W that is for V

097W003

O2the switching

parameters are the most stableThe transition temperature ofV097

W003

O2is lower than that for pure vanadium dioxide

and hence the magnitude of the aforesaid thermal cyclingis decreased which results in an increase of stability of theswitching parameters

Next we have studied the effect of doping on switchingin AOFs on Ti [29] These films were obtained in 5 watersolution of citric acid (C

6H8O7) in volt-static regime at 119881

119886

= 20V The samples were doped with aluminium by meansof adding soluble Al-containing substances to the electrolyte

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

Films vol 97 no 2 pp 129ndash143 1982[46] R Collongues La Non-Stoechiometrie Masson Paris France

1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

9 no 5 pp 391ndash396 2014[67] B Sun W Zhao Y Liu and P Chen ldquoResistive switching effect

of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

1990[70] S Mukherjee S Karmakar H Sakata and B K Chaudhuri

ldquoLow-temperature metallic behavior of amorphous MoO3-

TeO2thin filmsrdquo Journal of Applied Physics vol 97 no 12 Article

ID 123707 2005[71] AMottaghizadeh Q Yu P L Lang A Zimmers andH Aubin

ldquoMetal oxide resistive switching evolution of the density ofstates across the metal-insulator transitionrdquo Physical ReviewLetters vol 112 no 6 Article ID 066803 2014

[72] R Xie C T Bui B Varghese et al ldquoAn electrically tunedsolid-state thermalmemory based onmetal-insulator transitionof single-crystalline VO

2nanobeamsrdquo Advanced Functional

Materials vol 21 no 9 pp 1602ndash1607 2011

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

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FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

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AstronomyAdvances in

International Journal of

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Superconductivity

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AstrophysicsJournal of

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Physics Research International

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Solid State PhysicsJournal of

 Computational  Methods in Physics

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

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PhotonicsJournal of

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Biophysics

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ThermodynamicsJournal of

Advances in Condensed Matter Physics 9

231 Electrical Switching in Thin Film Structures Based onMolybdenumOxide As inmost TMOs in the molybdenum-oxygen system there exist a number of oxides with variablevalence which are characterized by a wide diversity ofstructures and physical properties [53 55 56] MolybdenumtrioxideMoO

3has a structure based on layers of edge-sharing

distorted MoO6octahedra [23] Similar layered structures

are inherent in lower molybdenum oxides including MoO2

Mo18O52 Mo9O26 Mo8O23 Mo5O14 and Mo

17O47 as well

as 120578- and 120574-Mo4O11[55ndash57]

Stoichiometric MoO3 in its most thermodynamically

stable form 120572-MoO3 is an insulator with a band gap of sim3 eV

[23] During reduction by means of either oxygen deficiencyformation or introducing donor impurity atoms additionaldonor levels near the conduction band bottom appear andthe reduced oxide behaves therefore as a semiconductorPolycrystalline MoO

3 as well as a single crystal has a grey-

yellow colour and the minimum value of the absorption edgeis 440 nm which corresponds to the smallest value of theband gap of 28 eV [58] thus the band gap depends upon thestoichiometry and the crystalline state [53] The conductivityvalues of molybdenum oxides range from dielectric MoO

3

to semiconductor Mo18O52

(resistivity 120588 = 781Ωsdotcm)and down to metal 120578-V]

411

(120588 = 166 times 10minus4Ωsdotcm) [58]Molybdenum dioxide also exhibits metallic properties [2358] and at room temperature 120588 = 88 times 10minus5Ωsdotcm for bulkMoO2samples [55]

Because of their special physical and chemical propertiesmolybdenum oxides are used in various electronic devicessuch as electrochromic displays and indicators reversiblecathodes of lithium batteries gas sensors and memoryelements [55ndash61] Metal-insulator transitions have also beenobserved in some oxides of molybdenum and related com-pounds [62ndash70] In particular Mo

8O23

exhibits a two-stagestructural MIT with formation of a charge-density wave at1198791199051= 315 K and 119879

1199052= 285K [62] However as far as we know

no data are available in the literature concerning thresholdswitching associated with these transitions except for ourwork [53] In this work we have particularly noted thatmemory switching is observed inmany TMOs molybdenumoxides included [4 9 59 60]

The most discussed models in the literature for theReRAMmechanism in oxide structures are those based eitheron the growth and rupture of a metal filament inside theoxide matrix under the action of electric current or onthe redox processes responsible for the formation of somehigh-conductivity or low-conductivity local inclusions cor-responding to particular oxygen stoichiometry [4] The MITideology is also sometimes involved to explain the propertiesof the structures and the memory switching mechanismtherein [71] In any case thememory switching phenomenonseems to be associated with the ion transport [4 9] It isalso appropriate to mention here the works discussing thememory effects in a material with MIT (vanadium dioxide)associated with the presence of hysteresis in the temperaturedependence of conductivity [72]

On the other hand as was shown in the previous sectionmonostable threshold switching (with no memory effects)

associated with the MIT is also characteristic of a numberof TMOs That is why the study of threshold switchingin molybdenum oxide and its possible connection withthe phenomenon of MIT is of considerable scientific andpractical interest

Thinfilm samples ofmolybdenumoxidewere obtained bytwo ways anodic oxidation and thermal vacuum evaporation[53] Anodization of molybdenum was carried out in anacetone-based electrolyte (22 g of benzoic acid plus 40mLof saturated borax aqueous solution per litre of acetone[33 73]) AOFs on Mo might include lower molybdenumoxides for example Mo

4O11andMoO

2with a relatively high

electronic conductivity [53] The fact that the anodic oxideon molybdenum contained lower oxides was confirmed byexperimental data in the work [74] where it was shown thatthe degree of oxidation (valence state) of molybdenum in anAOF is less than six Also this was confirmed theoretically interms of the thermodynamics of the process the formation ofunsaturated oxide MoO

2had been shown to be energetically

more favourable than MoO3[75]

Vacuum deposited film samples were fabricated by ther-mal evaporation of MoO

3powder at residual pressure of

10minus4 Torr onto polished tantalum plates or glass substratesfor electrical and optical studies respectivelyThe thicknessesof the films were determined from the transmission andreflection interference spectra measurements [76] and theywere found to lie in the range from 300 to 800 nm

The XRD pattern of a vacuum-deposited molybdenumoxide sample is presented in Figure 11(a) It is shown thatthe samples represent amorphousMoO

3with a slight oxygen

nonstoichiometry [53] Anodic oxide films on Mo are alsoamorphous (or amorphous-microcrystalline according tothe literature data [73]) but their composition correspondsas described above to ratherMoO

2or other lower oxides and

not to the highest oxide MoO3

Figure 11(b) shows the reflection and transmission spec-tra for one of the samples obtained by vacuum depositionThe experimental data processing using the envelope of theinterference extrema [76] yields the film thickness of (620 plusmn

50) nm and the absorption edge around 120582 asymp 400 nm indi-cates the fact that the oxide phase composition correspondsto MoO

3with a band gap of sim3 eV

Before electroforming initial structures demonstrate thenonlinear and slightly asymmetric current-voltage charac-teristics with no NDR regions When the amplitude of theapplied voltage reaches the forming voltage a sharp andirreversible increase in conductivity is observed and theI(V) curve becomes S-shaped (Figure 12) With increas-ing current the I-V characteristic may change until theparameters of the switching structure are finally stabilizedThe process outlined above is qualitatively similar to theelectroforming of the switching devices based on other TMOs(see Section 22 above) We emphasize once again that thephase composition of the ensuing switching channel mustdiffer from the material of the pristine oxide film becausethe channel conductivity is higher than that of the unformedstructure by several orders of magnitude

The current-voltage characteristics of vacuum-depositedfilms and those of anodic films are qualitatively similar but

10 Advances in Condensed Matter Physics

1

2

20 40 60 8002120579∘

0100200300400500600700800900

I (co

unts

s)

(a)

1

2

3

0

20

40

60

80

100

T (

)

300 400 500 600 700 800 900 1000 1100200Wavelength (nm)

(b)

Figure 11 (a) XRD pattern of the molybdenum oxide film (1) andV]3powder (2) (b) Optical spectra of the sample obtained by vacuum

deposition (1) transmission coefficient of substrate (glass) (2) transmittance and (3) reflectance of Mo oxide film on glass [53]

0 5 10minus5minus10

Voltage (V)

minus016

minus012

minus008

minus004

000

004

008

012

016

Curr

ent (

mA

)

(a)

minus072 072 216 360minus216minus360

Voltage (V)

minus064

minus048

minus032

minus016

000

016

032

048

064

Curr

ent (

mA

)

(b)

Figure 12 Current-voltage characteristics ofMOMstructures with vacuum-deposited (a) and anodic (b)Mo oxide films after electroforming

there is a significant quantitative difference in their thresholdparameters For instance the switching voltage 119881th for theAOF based structures is sim2V (Figure 12(b)) whereas forthe structures on the basis of the films prepared by thermalevaporation119881th is sim10V (Figure 12(a))This difference can beexplained by the difference in thickness of the films

For anodic oxide the thickness can be estimated fromFaradayrsquos law [53]

119889 =

120583119868119886119905

4119890120588119878119873119860

(4)

where 120583 = 128 gmol and 120588 = 65 gcm3 are respectivelythe molar mass and density of V]

2and 119890 and 119873

119860are the

unit charge and Avogadro constant For 119868119886= 70m0 and 119905 =

10min (4) yields 119889 sim 20 nm which is significantly less thanthe typical thickness of the vacuum deposited films and as aresult the threshold voltage for AOFs is also lower than thatfor the films obtained by thermal evaporation

As is discussed in [53] switching is not observed inthinner films obtained by vacuum evaporation (119889 lt 100 nm)

in contrast to ultrathin AOFs A plausible reason for thismight be the fact that relatively thin vacuum depositedfilms contain through-the-thickness conducting defects dueto local stoichiometry variations whereas such defects areimpossible in anodic films because they are grown in highelectric field during anodic oxidation and an appearanceof such defects would interrupt the film growth processThis is similar to what is observed in vanadium oxide inpolycrystalline vanadium dioxide films such pin-hole defectsare usually associated with the grain boundaries which couldundergo local metallization due to strain or nonstoichiom-etry That is why it had been difficult to observe switchingin sandwich MOM structures with sputtered or thermallyoxidized polycrystalline VO

2films and most studies had

been conducted with planar thin-film structures whilst foranodically oxidized VO

2the switching effect has then been

observed in a sandwich structure for the first time in [16]Next we note that unlike the most other TMOs the

process of electroforming in Mo-based structures was hin-dered as was mentioned above in Section 21 that is theconventional electrical breakdown often occurred not the

Advances in Condensed Matter Physics 11

020406080

100120

30 40 50 60 7020Temperature (∘C)

30 40 50 60 7020Temperature (∘C)

0

2

4

6

8

10

12

Thre

shol

d vo

ltage

(V)

5 15minus5minus15

Voltage (V)

minus010

minus005

000005010

Curr

ent (

mA

)

V2 th

(V2)

Figure 13 Threshold voltage as a function of temperature for theTa-MoOx-Au switching structure and the temperature dependenceof (119881th)

2 (lower inset) in compliancewith (3) I-V curve at RT (upperinset)

formation of a switching channel However for the Mooxide films prepared by vacuum deposition the processesof electroforming and switching were more stable whichallowed in this case observation of the transformation of I-V curves at a temperature change It was found that as thetemperature increased the threshold voltage was reducedAt 119879 = 119879

119900sim 55ndash65∘C the NDR region degeneration

commenced at 119879 asymp 60ndash70∘C 119881th rarr 0 and at still highertemperatures the switching effect no longer occurred Inthis case the switching mechanism might be described interms of the ldquocritical temperaturerdquo model (Figure 13) It issupposed [53] that in the case of Mo like in other TMO-based structures formation of a channel also takes placeand this channel should consist of a material exhibiting MITwhich is the reason for switching with an S-shaped current-voltage characteristic (Figure 12)

A brief review of the materials with MIT in the familyof molybdenum compounds presented in [53] shows that themost suitable candidate for the role of such a channel-formingcompound is Mo

8O23

because in this case the value of 1198791199051

almost coincides with the above reported experimentallymeasured 119879

0 It should be noted that formation of other

compounds of molybdenum (eg pyrochlores bronzes sul-fides or chalcogenide glasses) exhibiting MITs with similarorder of magnitude transition temperatures [64ndash68 70] isimpossible because of the lack of the necessary chemicalelements (ie rare earths alkali metals or hydrogen sulfurand tellurium) in the phase composition of both the oxidefilm and the metal electrodes (Au Ta and Mo)

In conclusion the results presented in this subsection onswitching from the HR state to the LR state with an S-NDRin molybdenum oxides obtained by both thermal vacuumdeposition and electrochemical anodic oxidation show thatthe switching effect is due to apparently an insulator-to-metal phase transition in the switching channel consistingcompletely or partly of the lower oxide Mo

8O23 formed in

the initial film during the process of electroforming Thecurrent flowing through the channel heats it up to the MIT

temperature 1198791199051= 315K [62] and the structure switches into

the metallic low-resistance stateThus the channels consisting of this lower oxide are

formed in initial Mo oxide films during preliminary elec-troforming Electrical forming results in the changes inoxygen stoichiometry conditioned by the ionic processes inan electric field close to the MOM structure breakdown fieldThis picture is quite similar to what is observed inmany otherTMOs exhibiting the insulator-to-metal transitions

232 Metal-Insulator Transition and Switching in ManganeseDioxide Manganese dioxide is one of the most interestinginorganic materials because of its wide range of applica-tions In particular nanostructured MnO

2has received great

attention due to its high specific surface area functionalproperties and potential applications as molecular and ionselective membranes in capacitors Li-ion batteries andcatalysts [77] Originally MnO

2has been widely used as a

cathode material for oxide-semiconductor capacitors basedon tantalum niobium and aluminium oxides and the mostimportant properties of the material for this application areits high conductivity and ability to undergo a thermal phasetransition into the lower valence states accompanied by evo-lution of atomic oxygen while the resistance increases by 3-4orders of magnitude (see eg [54] and references therein)Much attention is currently paid to various other propertiesof MnO

2 such as for example the electrochromic effect

[78] thermopower wave phenomenon [79] supercapacitivebehaviour [80] andmemory and threshold switching [54 8182] Also there are a number of papers [83ndash85] describing ananomaly in theMnO

2conductivity near theNeel temperature

which is shown to be associated with the metal-insulatortransition [52] That is why the electrical properties of MnO

2

are of special scientific interest and applied importanceThe most common methods for manganese oxide prepa-

ration are the pyrolytic decomposition of manganese nitrateelectrochemical method hydrothermal synthesis in a mag-netic field and chemical deposition [54 86ndash89] Due to awide range of possible valence states of cations the structureand phase composition of manganese oxides are determinedby the synthesis conditions and process temperature Man-ganese dioxide has many crystallographic forms (120572- 120573- 120574-120575- 120576- and 120582-MnO

2) that connect MnO

6octahedron units to

each other in different ways and have different characters ofspatial alternation of the octahedra filled by Mn atoms andempty octahedra [54 77 90ndash94]

The crystal structure of the 120573-MnO2phase (Figure 14) is a

tetragonal modification of the rutile structural type P4mnmsymmetry group which represents a slightly distorted close-packed hexagonal lattice of oxygen ions [93] Filled octahedraare bound by two common edges in columns oriented alongthe 119888 axis and octahedra of adjacent columns are bound bytheir vertices (Figure 14(c)) Manganese atoms are arrangedin positions 2(a) (000) and oxygen atoms in positions 4(f )(xx0) Because there are vacancies in the oxygen packingthe formula unit can be written as MnO

2minus119910where the

nonstoichiometry index is in the range 119910 = 001ndash010depending on the synthesis method [93]

12 Advances in Condensed Matter Physics

Mn

O

(a)

a

b

c

(b)

O2O4

O1O3

Mn2

Mn1

Mn1998400

O3998400

O4998400

(c)

Figure 14 Crystal structure of manganese dioxide (a) MnO6

octahedron connection in 120573-MnO2(b) [90ndash94] and projection of

octahedron binding onto the ab plane [93]

As to the lower manganese oxides MnO and Mn3O4are

known to be theMott insulatorswith relatively high resistivity[90] and Mn

2O3shows p-type semiconducting properties

MnO2is an n-type semiconductor and antiferromagnetic

with the Neel temperature 119879119873= 925 K [91] Conductivity of

manganese dioxide is higher than that of MnO and Mn2O3

by several orders of magnitude At temperatures above 723Kmanganese dioxide loses oxygen and transforms intoMn

2O3

which is accompanied by the transformation of the crystallinestructure from the tetragonal crystal system of the rutile typeinto the complex large-period cubic lattice (119886 = 94gt) and alarge number of formula units per unit cell [54 92 93]

In this subsection we present the results on electricalproperties of manganese dioxide particularly the natureof the 120573-MnO

2conductivity at low temperatures in its

interrelation with characteristic features of the material crys-talline structure and the metal-insulator phase transitionin this compound as well The effect of electrical switchingwith current-voltage characteristics of both N- and S-typehas been found in thin-film MOM structures on the basisof manganese oxides Possible mechanisms of switching interms of the MIT and thermistor effects are discussed

Mn oxide samples under study have been obtained bythree methods anodic oxidation and vacuum evaporation(thin films) as well as by pyrolysis [54] Thin films ofmanganese dioxide were deposited by means of thermalevaporation onto glass substrates covered by a SnO

2layer

using a VUP-5 vacuum setup the film thickness was 119889 =

250 nmAlso thin films ofmanganese oxidewere obtained byelectrochemical oxidation of metal Mn in the KNO

3-NaNO

3

eutectic melt (see Section 21) at 119879 = 600K at a constantvoltage of about 2V for 3min the current density diminishedfrom 200 to 100mAcm2 during the oxidation process Foranodic oxide films on Mn the value of 119889 was sim100 nm Bulksamples of manganese dioxide were obtained by multipledecomposition (pyrolysis) of manganese nitrate at 119879 = 670Kon a glass-ceramic substrate or on a tantalum sheetmetal withthe subsequent separation from the substrate [92 93] Thetotal coating thickness was about 1mm

The manganese oxide samples were characterized by X-ray diffraction (XRD) using a DRON-6 diffractometer inCuK120572and FeK

120572radiation The characteristics of the atomic

structure of pyrolytic manganese dioxide were refined by thefull-profile analysis of the XRD patterns of polycrystallinesamples [93]The resistivity of pyrolyticMnO

2wasmeasured

in the temperature range 15 to 300K bymeans of a four-probetechnique both DC and AC (in a frequency range from 50 to104Hz) in a Gifford-McMahon cycle cryorefrigerator [54]We also measured electrical conductivity in the range T =293ndash423K the Hall effect in the magnetic field of 23 T andthe Seebeck coefficient (thermoelectromotive force thermo-emf ) The dynamic current-voltage (I-V) characteristics ofthe thin-film MOM structures were measured by oscillo-graphic method using an AC sinusoidal signal

The XRD patterns of the manganese oxide samples arepresented in Figures 15 and 16 The vacuum-deposited filmsare amorphous and represent a mixture of 120573- and 120574-MnO

2

(Figure 16) The results of the full-profile analysis show thatthe pyrolytic MnO

2samples (Figure 15) are composed of

the finely dispersed 120573-MnO2phase with the traces of 120574-

MnO2 120576-MnO

2 and Mn

2O3phases The periods of the

tetragonal unit cell of 120573-MnO2are 119886 = 119887 = 4401 A and

119888 = 2872 A The oxygen coordinates in 4119891 positions (seediscussion of the crystal structure above and Figure 14) arefound to be119909 = 0302 Calculations of the oxygen-manganeseinteratomic distances show [93] that the oxygen octahedron

Advances in Condensed Matter Physics 13

330222

040231

212202

112

130002

220

121

120

111

110

101

020

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 80 100 12002120579∘

Figure 15 XRD (Cu K120572radiation) pattern of pyrolytic MnO

2

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 8002120579∘ Fe

120573-MnO2

120574-MnO2

Experiment

Figure 16 XRD (Fe K120572radiation) pattern of Mn oxide film and

reference spectra of crystalline MnO2samples

is compressed along the (100) direction which connects theoctahedron vertices This deformation results in an increaseof the overlap of electron119901 orbitals of oxygen and119889 orbitals ofmanganese and can form the additional splitting of electronlevels in the crystal field leading to the appearance of unpairedelectrons [94]

The measurements of the conductivity temperaturedependence Hall effect and thermo-emf show that man-ganese dioxide is the electron semiconductor with conductiv-ity of about 1Ωminus1cmminus1 and mobility of sim10 cm2Vsdots The Hallmeasurements give the carrier density ofsim1018 cmminus3 which isclose to the density values in degenerate semiconductorsTheactivation energy of conductivity is sim01 eV and the band gapwidth is equal to 2 eV [90] The estimated value of the Fermienergy from the thermo-emf temperature dependence is inthe range of 002 to 005 eV which also indicates the degener-ate character of the electron gasThe nonstoichiometry indexdetermined by the XRD peaks which are not contributed

by the manganese atoms that is by those with the oddsum of indexes is 119910 = 006 Such nonstoichiometry providesthe concentration of trap states of about 1017-1018 cmminus3which correlates with the above mentioned Hall-effect-basedmeasurements of electron density

Such high vacancy concentration allows us to considerthe nonstoichiometric 120573-MnO

2as a heavily doped semicon-

ductor with a subband of impurity levels which provides afeasibility of the out-of-band electron transfer at low tem-peratures The structural distortions high nonstoichiometryand as a consequence sufficiently high concentration ofimpurity states cause the density state tails near the bandedges similarly to those in heavily doped semiconductorsHowever at room and higher temperatures the conduction isdetermined by the activation mechanism Thus the electronstructure and a low mobility of charge carriers promotethe manifestation of different charge transfer mechanismsin different temperature ranges namely both the hoppingmechanism and the activation one

The electron capturing oxygen vacancies create mixedvalence states of manganese cations (Mn3+ndashMn4+) Interest-ingly the mixed valence of Mn ions is also characteristic ofmanganites Ln

1minus119910Sr119910MnO3[95] where Ln is La or another

rare-earth element possessing the effect of colossal magne-toresistance (CMR) In these compounds the mixed valenceof manganese is attained via doping It had been deemed thatholes introduced by strontium are localized at manganeseions that is the Mn4+ ions with concentration 119910 are formedHowever recent X-ray emission studies have shown that boththe chemical shift and the exchange splitting of the emissionX-ray Mn K

1205731line are almost the same in the range 119910 lt 04ndash

05 as is the case in Mn2O3 and then they decrease quickly

to the values characteristic of MnO2[96] which suggests that

the introduced holes are localized at oxygen atoms in the holedoping region (at relatively low 119910) and atmanganese atoms inthe electron doping region that is at higher 119910 values

The temperature dependence of conductivity is presentedin Figure 17 The resistance peak observed in the figure ina temperature range of 80ndash90K is the result of the phasetransition of 120573-MnO

2from a semiconducting state to a metal

state upon decreasing the temperature to 15 K [54] The tem-perature region of the transition is close to the known Neeltransition from the paramagnetic state into the ferromagneticone for manganese dioxide The temperature dependenceof resistance indicates thus the MIT to occur in MnO

2 In

the temperature range from 300 to 80K (Figure 17) thisdependence does not correspond to the exponential one yetit fits well with the linear dependence in theMott coordinatesln(119877) sim 119879

14 which indicates the hopping conductivitymechanism over the polyvalent states ofmanganese ions witha distance between the centres of 25ndash35gt [92] However inthe temperature range from 90 to 15 K the dependence ofln119877 on ln119879 is almost linear with the slope of about unity(ie 120597 ln119877120597 ln119879 asymp 1) which is characteristic of the metallicconductionThus the character of conductivity ofmanganesedioxide indicates the presence of the MIT at 119879

119888sim 80K (on

cooling)

14 Advances in Condensed Matter Physics

CoolingHeating

40 80 120 160 2000T (K)

0

2

4

6

8

10

Resis

tivity

(Ohm

timescm

)

Figure 17 Temperature dependence of AC (70Hz) resistivity ofpyrolytic MnO

2

In the low temperature region manganese dioxide is anantiferromagnetwith the helical spin ordering [97]The inter-action between the magnetic ions of manganese which leadsto the antiferromagnetic state occurs through the intermedi-ate interaction with diamagnetic oxygen ions which weakensthe exchange interaction The conductivity increases proba-bly due to exceeding the energy of the exchange interactionby the thermal energy as the temperature increases whichleads to an increase in the number of unpaired electrons inthe paramagnetic state As the temperature further increasesthe conductivity continues to rise and the Mott hoppingmechanism of charge transfer becomes predominant Similarcharacter of the temperature dependence in ferromagneticdegenerate semiconductors has previously been described[85 98] for substoichiometric (oxygen-deficient) europiummonoxide The transition from the highly conductive stateinto the insulating state occurs in such semiconductors uponvarying the type of magnetic ordering or its destruction

For EuO1minus119910

lowering the peak magnitude in the 119877(119879)

dependence is associatedwith a decrease in the concentrationof impurities (oxygen vacancies) In magnetic semicon-ductors the phase transition is associated both with themagnetoelectric effects and with the variation in the electricpolarization under the action of the magnetic field at theantiferromagnetic transition [98] The dielectric constant formanganese dioxide is equal to sim10 but the effective dielectricconstant can decrease near 119879

119888by a factor of several times

thereby affecting the mobility of carriers located in the tailsof the density of states near the band edge and promotingtheir delocalization at the phase transition temperatureManganese dioxide also belongs to this group of substanceshowever the phase transition in MnO

2reported here can be

also described in terms of the Mott transition [24]According to the Mott criterion electrons delocalize if

the distance between the atoms 119899minus13 becomes comparable

with their atomic radius 119886119860 where 119886

119860is associated with the

Bohr radius 119886119861= ℏ2120576me2The static permittivity 120576 is replaced

by the effective permittivity which takes into account theexchange interaction of the spins of conduction electronswith orbitalmagneticmoments of atoms At the temperature-induced Mott MIT the orbital radius 119886

119861decreases near 119879 =

119879119888thereby providing the fulfillment of the Mott criterion at a

given level of impurity centres [24 98] The transition fromthe metallic state into the semiconductor state is possible insuch semiconductors as the temperature increases Thus theMIT in manganese dioxide is brought about by temperaturevariation

In conclusion we note that the phase transition describedabove is inverse (reentrant) MIT that is the metallic phaseis low-temperature while the high-temperature state is insu-lating This is rather rare yet not unique and unusualphenomenon In most cases (eg in vanadium dioxide) thelow-temperature phase is insulating and on heating abovea certain temperature 119879

119888 the material becomes metallic for

VO2 this transition temperature is 119879

119888= 340K The inverse

transitions are observed in such compounds as the abovementioned EuO

1minus119910 NiS2Se Y2O3minus119910

and LaMnO3films [24

31 52 85 98 99] Also the high-temperature Mott transi-tion from paramagnetic metal to paramagnetic insulator inV2O3Cr is an inverse transition with the resistivity peak at

119879119888sim 350K for a chromium concentration of around 1 at

[24 51] and in mixed valence CMR-manganites the sharpresistivity peak has been shown to be caused by the AndersonMIT [95]

It is known that many TMOs exhibit electrical switchingassociated with MITs [28] For the anodic oxide films onMn the study of the effect of electrical switching in thin-film Mn-MnO

2-Au sandwich structures showed that the S-

type switching was not observed in contrast to for examplethe similar structures based on oxides of vanadium andsome other transition metals [28] Instead switching withthe N-shaped I-V characteristic occurred after EF at 119879 lt

80K (Figure 18(a)) In addition the EF process in the Mn-based structures was hindered likewise for example for thestructures based on yttrium oxide [31] that is the breakdowntook place more often It should be noted that EF at roomtemperature always led to breakdown and the switchingeffect had never been observed in this case As was arguedin [54] this switching effect was associated with the MIT inMnO2

On the other hand in the films obtained by vacuumsputtering we have observed S-type switching at roomtemperature (Figure 18(b)) The threshold voltage is of theorder of 1 V and almost independent of temperature up to 119879

= 375KThis situation resembles that with yttrium oxide where

both S-type and N-type switching has been observed too[31] One can assume that switching with the S-shapedI-V curves is due to the so-called ldquothermistor effectrdquo Itis well known that the current flowing through a solidgenerates Joule heat resulting in an increased temperatureIn materials with a negative TCR a rising temperatureinduces a current enhancement and an increased powerdissipation resulting in a farther temperature increase Thispositive electrothermal feedback causes the appearance of anNDR and accordingly an S-shaped I-V characteristic [2]

Advances in Condensed Matter Physics 15

minus15

minus10

minus5

0

5

10

15Cu

rren

t (m

A)

0500 10 15minus10 minus05minus15

Voltage (V)

(a)

minus2

minus1

0

1

2

Curr

ent (

mA

)

10 2minus2 minus1

Voltage (V)

(b)

Figure 18 (a) I-V characteristic of anodic oxide film on manganese at T = 77K (b) I-V characteristic of vacuum-deposited MnO2at 119879 =

293K

In some cases this process might by modified by high-fieldeffects such as Schottky injection impact ionization Poole-Frenkel effect and Zener or avalanche breakdown Notethat unlike a conventional thermistor with an Arrhenius-like conductivity law manganese oxide exhibits a weaker119877(119879) dependence characteristic of the hopping conductivitymechanism which seems to account for the observed weaktemperature dependence of the threshold voltage

An alternative mechanism for the S-type switching effectmay be connected with a possible high-temperature usual(ie not inverse)MIT in somemanganese oxide As is knownEF (see Section 22) leads to the formation of a filament ofhighly conducting material a switching channel Similarlyto what is observed for Mo oxide (Section 231) and otherTMOs (Sections 21 and 22) we suppose that the compositionof this channel differs from the material of the initial oxidefilm since its conductivity noticeably exceeds that of anunformed structure In view of such a plentiful set of phasesand crystal structures in the Mn-O system one can supposethat the channelmight consist of nonstoichiometric120573-MnO

2

some other polymorphic modifications of manganese diox-ide or lower Mn oxides which might undergo a MIT underthe action of either temperature or electric field Howeverthis question obviously requires additional investigation inparticularmeasurements of119877(119879)dependences and switchingproperties at higher temperatures If this assumed high-temperature MIT would occur in for example nonstoichio-metric 120573-MnO

2 one could expect observation of double-

NDR I-V characteristics in such samples at low temperaturesanalogously to those in V

2O3Cr (Figure 9) where this effect

is due to the MITs [29] with the only difference being thatin the case of MnO

2this curve should be N-S-shaped (unlike

the S-N-shaped one in Figure 9) since in chromium-dopedvanadium sesquioxide the inverse MIT is high-temperatureas opposed to MnO

2which as we discussed above (see

Figure 17) exhibits the inverse MIT at low temperaturesNote however that the discussed high-temperature MIT

in 120573-MnO2minus119910

may be unobservable under the temperature

change in equilibrium conditions but displays itself onlyunder the applied electric field as the S-type electricalswitching effect because the transition temperature is closeto or higher than the temperature of MnO

2decomposition

(723K) Such a nonequilibrium transition occurs at switchingin those materials where the usual temperature-inducedMITwith a well-defined 119879

119905does not take place for example in

CGSs for which the equilibrium transition temperature 1198791199050

is higher than 119879119892 while in a high electric field 119879

119905(119864) lt 119879

1199050

might be lower than 119879119892 where 119879

119892is the temperature of the

glass-crystal transition and119864 is the electric field strength [30]Summarizing we have studied the electrical properties

(conductivity temperature dependence and Hall and Seebeckeffects) of the 120573 phase of manganese dioxide obtained bypyrolysis thermal vacuum evaporation and anodic oxida-tion The change of conductivity mechanisms dependingon temperature in a range of 450ndash25K has been shownand the metal-insulator phase transition at low (lt90K)temperatures has been revealed The specific feature of thistransition described in terms of the Mott mechanism isthat the metal phase exists at low temperatures while athigher temperatures the material is a semiconductor withthe hopping conductivity over the mixed valence states ofmanganese ions

The low-temperature switching effect with an NDR andN-shaped current-voltage characteristic associated with thephase transition in manganese dioxide has been found in theMOM two-terminal devices based on anodicMn oxide filmsOn the contrary the devices based on vacuum-depositedfilms have been found to exhibit an S-NDR at room andhigher temperatures which is suggested to be caused byeither the thermistor effect or a high-temperature MIT innonstoichiometric 120573-MnO

2

It should be emphasized that the low-temperature MITin 120573-MnO

2with 119879

119905= 70ndash80K is the inverse Mott transition

which is akin for instance to the transition in V2O3Cr

at 119879119905= 190ndash385K (for chromium dopant concentration in

the range of 05ndash18 at) [51] We thus assume that farther

16 Advances in Condensed Matter Physics

5 10 150Voltage (V)

0

1

2

3

4

5

6

7

8Cu

rren

t (m

A)

(a)ΔV

th(V

)

0

1

2

3

1 2 3 4 5 6 7 80W (at )

(b)

Figure 19 I-V curve (a) of Au-V2minus119910

W119910O5times 119899H2O-Au sandwich structure with119910= 003 and119881th scattering as a function of tungsten admixture

percentage 119910 (b) [104 105]

investigations of the phase transition in manganese dioxidedescribed in this paper are a rather interesting and topicalscientific problem since manganese dioxide can serve as amodel object for studying such inverse metal-insulator phasetransitions

Finally we note that the results presented in this sectionindicate the possibility of application of manganese oxide asa material for thin film sandwich switching devices Deviceswith NDR (N- and S-shaped I-V characteristics) have poten-tial applications in microelectronics as switches memoryelements and microsensors (these issues will be discussedin more detail below in Section 4) Particularly manganeseoxide microswitches [82] can be utilized for implementationof neuristors built with Mott-transition-based memristors[100]

24 Effect of Doping It is only natural that the systemsexhibiting the NDR effects possess a high applied potential inelectronics [2 4 8 18 100 101] yet the stage of EF is a weaklink of chain in the technology process Note that the formingprocess may be brought about by laser irradiation [102] notby applying of electric field In the case of laser treatment(or ldquolaser formingrdquo unlike the above described electricalforming) the parameters of the structures are characterizedby the absence of the scatter that is the I-V characteristics ofall structures are almost identical [103] One more demerit tobe avoided is the scatter in switching parameters (the value of119881th first of all) and their instability during operation In thissubsection we discuss the issues concerning the switchingparameter stabilization by means of doping

In the work [104] we have studied the switching effectin the MOM structures on the basis of W-doped V

2O5-gel

filmsThese structures require preliminary EF similar to thatin anodic oxide films resulting in formation of a conducting

channel within the initial dielectric xerogel filmThe channelconsists of vanadiumdioxide and switching is associatedwiththe insulator-to-metal transition in VO

2 As was shown in

[104 105] for the pure (undoped) V2O5-gel the switching

parameters vary in a wide range because the phenomenonof EF is statistical in nature (like electrical breakdown) andits statistical character shows itself as a spread in the observedthreshold voltages of the ensuing structures that is actuallyat multiple measurements 119881th = ⟨119881th⟩ plusmn Δ119881th

It has been shown [104] that the statistical spread in valuesof the threshold parameters can be minimized by means ofdoping (Figure 19) Unsophisticated reasoning could accountfor this result for pure V

2O5-gel electroforming leads to

formation of VO2with 119879

119905= 340K and each switching

event requires heating up and cooling down from roomtemperature to 119879

119905 this thermal cycling can modify the

peripheral regions of the channel which leads to the changeof the switching threshold voltage On the other hand forthe samples with a high concentration of W the MIT issuppressed [104] and switching is degenerated Betweenthese two outermost points an optimum should exist Asone can see from Figure 19 this optimal value correspondsto 3 at of W that is for V

097W003

O2the switching

parameters are the most stableThe transition temperature ofV097

W003

O2is lower than that for pure vanadium dioxide

and hence the magnitude of the aforesaid thermal cyclingis decreased which results in an increase of stability of theswitching parameters

Next we have studied the effect of doping on switchingin AOFs on Ti [29] These films were obtained in 5 watersolution of citric acid (C

6H8O7) in volt-static regime at 119881

119886

= 20V The samples were doped with aluminium by meansof adding soluble Al-containing substances to the electrolyte

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

Films vol 97 no 2 pp 129ndash143 1982[46] R Collongues La Non-Stoechiometrie Masson Paris France

1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

9 no 5 pp 391ndash396 2014[67] B Sun W Zhao Y Liu and P Chen ldquoResistive switching effect

of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

1990[70] S Mukherjee S Karmakar H Sakata and B K Chaudhuri

ldquoLow-temperature metallic behavior of amorphous MoO3-

TeO2thin filmsrdquo Journal of Applied Physics vol 97 no 12 Article

ID 123707 2005[71] AMottaghizadeh Q Yu P L Lang A Zimmers andH Aubin

ldquoMetal oxide resistive switching evolution of the density ofstates across the metal-insulator transitionrdquo Physical ReviewLetters vol 112 no 6 Article ID 066803 2014

[72] R Xie C T Bui B Varghese et al ldquoAn electrically tunedsolid-state thermalmemory based onmetal-insulator transitionof single-crystalline VO

2nanobeamsrdquo Advanced Functional

Materials vol 21 no 9 pp 1602ndash1607 2011

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

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ThermodynamicsJournal of

10 Advances in Condensed Matter Physics

1

2

20 40 60 8002120579∘

0100200300400500600700800900

I (co

unts

s)

(a)

1

2

3

0

20

40

60

80

100

T (

)

300 400 500 600 700 800 900 1000 1100200Wavelength (nm)

(b)

Figure 11 (a) XRD pattern of the molybdenum oxide film (1) andV]3powder (2) (b) Optical spectra of the sample obtained by vacuum

deposition (1) transmission coefficient of substrate (glass) (2) transmittance and (3) reflectance of Mo oxide film on glass [53]

0 5 10minus5minus10

Voltage (V)

minus016

minus012

minus008

minus004

000

004

008

012

016

Curr

ent (

mA

)

(a)

minus072 072 216 360minus216minus360

Voltage (V)

minus064

minus048

minus032

minus016

000

016

032

048

064

Curr

ent (

mA

)

(b)

Figure 12 Current-voltage characteristics ofMOMstructures with vacuum-deposited (a) and anodic (b)Mo oxide films after electroforming

there is a significant quantitative difference in their thresholdparameters For instance the switching voltage 119881th for theAOF based structures is sim2V (Figure 12(b)) whereas forthe structures on the basis of the films prepared by thermalevaporation119881th is sim10V (Figure 12(a))This difference can beexplained by the difference in thickness of the films

For anodic oxide the thickness can be estimated fromFaradayrsquos law [53]

119889 =

120583119868119886119905

4119890120588119878119873119860

(4)

where 120583 = 128 gmol and 120588 = 65 gcm3 are respectivelythe molar mass and density of V]

2and 119890 and 119873

119860are the

unit charge and Avogadro constant For 119868119886= 70m0 and 119905 =

10min (4) yields 119889 sim 20 nm which is significantly less thanthe typical thickness of the vacuum deposited films and as aresult the threshold voltage for AOFs is also lower than thatfor the films obtained by thermal evaporation

As is discussed in [53] switching is not observed inthinner films obtained by vacuum evaporation (119889 lt 100 nm)

in contrast to ultrathin AOFs A plausible reason for thismight be the fact that relatively thin vacuum depositedfilms contain through-the-thickness conducting defects dueto local stoichiometry variations whereas such defects areimpossible in anodic films because they are grown in highelectric field during anodic oxidation and an appearanceof such defects would interrupt the film growth processThis is similar to what is observed in vanadium oxide inpolycrystalline vanadium dioxide films such pin-hole defectsare usually associated with the grain boundaries which couldundergo local metallization due to strain or nonstoichiom-etry That is why it had been difficult to observe switchingin sandwich MOM structures with sputtered or thermallyoxidized polycrystalline VO

2films and most studies had

been conducted with planar thin-film structures whilst foranodically oxidized VO

2the switching effect has then been

observed in a sandwich structure for the first time in [16]Next we note that unlike the most other TMOs the

process of electroforming in Mo-based structures was hin-dered as was mentioned above in Section 21 that is theconventional electrical breakdown often occurred not the

Advances in Condensed Matter Physics 11

020406080

100120

30 40 50 60 7020Temperature (∘C)

30 40 50 60 7020Temperature (∘C)

0

2

4

6

8

10

12

Thre

shol

d vo

ltage

(V)

5 15minus5minus15

Voltage (V)

minus010

minus005

000005010

Curr

ent (

mA

)

V2 th

(V2)

Figure 13 Threshold voltage as a function of temperature for theTa-MoOx-Au switching structure and the temperature dependenceof (119881th)

2 (lower inset) in compliancewith (3) I-V curve at RT (upperinset)

formation of a switching channel However for the Mooxide films prepared by vacuum deposition the processesof electroforming and switching were more stable whichallowed in this case observation of the transformation of I-V curves at a temperature change It was found that as thetemperature increased the threshold voltage was reducedAt 119879 = 119879

119900sim 55ndash65∘C the NDR region degeneration

commenced at 119879 asymp 60ndash70∘C 119881th rarr 0 and at still highertemperatures the switching effect no longer occurred Inthis case the switching mechanism might be described interms of the ldquocritical temperaturerdquo model (Figure 13) It issupposed [53] that in the case of Mo like in other TMO-based structures formation of a channel also takes placeand this channel should consist of a material exhibiting MITwhich is the reason for switching with an S-shaped current-voltage characteristic (Figure 12)

A brief review of the materials with MIT in the familyof molybdenum compounds presented in [53] shows that themost suitable candidate for the role of such a channel-formingcompound is Mo

8O23

because in this case the value of 1198791199051

almost coincides with the above reported experimentallymeasured 119879

0 It should be noted that formation of other

compounds of molybdenum (eg pyrochlores bronzes sul-fides or chalcogenide glasses) exhibiting MITs with similarorder of magnitude transition temperatures [64ndash68 70] isimpossible because of the lack of the necessary chemicalelements (ie rare earths alkali metals or hydrogen sulfurand tellurium) in the phase composition of both the oxidefilm and the metal electrodes (Au Ta and Mo)

In conclusion the results presented in this subsection onswitching from the HR state to the LR state with an S-NDRin molybdenum oxides obtained by both thermal vacuumdeposition and electrochemical anodic oxidation show thatthe switching effect is due to apparently an insulator-to-metal phase transition in the switching channel consistingcompletely or partly of the lower oxide Mo

8O23 formed in

the initial film during the process of electroforming Thecurrent flowing through the channel heats it up to the MIT

temperature 1198791199051= 315K [62] and the structure switches into

the metallic low-resistance stateThus the channels consisting of this lower oxide are

formed in initial Mo oxide films during preliminary elec-troforming Electrical forming results in the changes inoxygen stoichiometry conditioned by the ionic processes inan electric field close to the MOM structure breakdown fieldThis picture is quite similar to what is observed inmany otherTMOs exhibiting the insulator-to-metal transitions

232 Metal-Insulator Transition and Switching in ManganeseDioxide Manganese dioxide is one of the most interestinginorganic materials because of its wide range of applica-tions In particular nanostructured MnO

2has received great

attention due to its high specific surface area functionalproperties and potential applications as molecular and ionselective membranes in capacitors Li-ion batteries andcatalysts [77] Originally MnO

2has been widely used as a

cathode material for oxide-semiconductor capacitors basedon tantalum niobium and aluminium oxides and the mostimportant properties of the material for this application areits high conductivity and ability to undergo a thermal phasetransition into the lower valence states accompanied by evo-lution of atomic oxygen while the resistance increases by 3-4orders of magnitude (see eg [54] and references therein)Much attention is currently paid to various other propertiesof MnO

2 such as for example the electrochromic effect

[78] thermopower wave phenomenon [79] supercapacitivebehaviour [80] andmemory and threshold switching [54 8182] Also there are a number of papers [83ndash85] describing ananomaly in theMnO

2conductivity near theNeel temperature

which is shown to be associated with the metal-insulatortransition [52] That is why the electrical properties of MnO

2

are of special scientific interest and applied importanceThe most common methods for manganese oxide prepa-

ration are the pyrolytic decomposition of manganese nitrateelectrochemical method hydrothermal synthesis in a mag-netic field and chemical deposition [54 86ndash89] Due to awide range of possible valence states of cations the structureand phase composition of manganese oxides are determinedby the synthesis conditions and process temperature Man-ganese dioxide has many crystallographic forms (120572- 120573- 120574-120575- 120576- and 120582-MnO

2) that connect MnO

6octahedron units to

each other in different ways and have different characters ofspatial alternation of the octahedra filled by Mn atoms andempty octahedra [54 77 90ndash94]

The crystal structure of the 120573-MnO2phase (Figure 14) is a

tetragonal modification of the rutile structural type P4mnmsymmetry group which represents a slightly distorted close-packed hexagonal lattice of oxygen ions [93] Filled octahedraare bound by two common edges in columns oriented alongthe 119888 axis and octahedra of adjacent columns are bound bytheir vertices (Figure 14(c)) Manganese atoms are arrangedin positions 2(a) (000) and oxygen atoms in positions 4(f )(xx0) Because there are vacancies in the oxygen packingthe formula unit can be written as MnO

2minus119910where the

nonstoichiometry index is in the range 119910 = 001ndash010depending on the synthesis method [93]

12 Advances in Condensed Matter Physics

Mn

O

(a)

a

b

c

(b)

O2O4

O1O3

Mn2

Mn1

Mn1998400

O3998400

O4998400

(c)

Figure 14 Crystal structure of manganese dioxide (a) MnO6

octahedron connection in 120573-MnO2(b) [90ndash94] and projection of

octahedron binding onto the ab plane [93]

As to the lower manganese oxides MnO and Mn3O4are

known to be theMott insulatorswith relatively high resistivity[90] and Mn

2O3shows p-type semiconducting properties

MnO2is an n-type semiconductor and antiferromagnetic

with the Neel temperature 119879119873= 925 K [91] Conductivity of

manganese dioxide is higher than that of MnO and Mn2O3

by several orders of magnitude At temperatures above 723Kmanganese dioxide loses oxygen and transforms intoMn

2O3

which is accompanied by the transformation of the crystallinestructure from the tetragonal crystal system of the rutile typeinto the complex large-period cubic lattice (119886 = 94gt) and alarge number of formula units per unit cell [54 92 93]

In this subsection we present the results on electricalproperties of manganese dioxide particularly the natureof the 120573-MnO

2conductivity at low temperatures in its

interrelation with characteristic features of the material crys-talline structure and the metal-insulator phase transitionin this compound as well The effect of electrical switchingwith current-voltage characteristics of both N- and S-typehas been found in thin-film MOM structures on the basisof manganese oxides Possible mechanisms of switching interms of the MIT and thermistor effects are discussed

Mn oxide samples under study have been obtained bythree methods anodic oxidation and vacuum evaporation(thin films) as well as by pyrolysis [54] Thin films ofmanganese dioxide were deposited by means of thermalevaporation onto glass substrates covered by a SnO

2layer

using a VUP-5 vacuum setup the film thickness was 119889 =

250 nmAlso thin films ofmanganese oxidewere obtained byelectrochemical oxidation of metal Mn in the KNO

3-NaNO

3

eutectic melt (see Section 21) at 119879 = 600K at a constantvoltage of about 2V for 3min the current density diminishedfrom 200 to 100mAcm2 during the oxidation process Foranodic oxide films on Mn the value of 119889 was sim100 nm Bulksamples of manganese dioxide were obtained by multipledecomposition (pyrolysis) of manganese nitrate at 119879 = 670Kon a glass-ceramic substrate or on a tantalum sheetmetal withthe subsequent separation from the substrate [92 93] Thetotal coating thickness was about 1mm

The manganese oxide samples were characterized by X-ray diffraction (XRD) using a DRON-6 diffractometer inCuK120572and FeK

120572radiation The characteristics of the atomic

structure of pyrolytic manganese dioxide were refined by thefull-profile analysis of the XRD patterns of polycrystallinesamples [93]The resistivity of pyrolyticMnO

2wasmeasured

in the temperature range 15 to 300K bymeans of a four-probetechnique both DC and AC (in a frequency range from 50 to104Hz) in a Gifford-McMahon cycle cryorefrigerator [54]We also measured electrical conductivity in the range T =293ndash423K the Hall effect in the magnetic field of 23 T andthe Seebeck coefficient (thermoelectromotive force thermo-emf ) The dynamic current-voltage (I-V) characteristics ofthe thin-film MOM structures were measured by oscillo-graphic method using an AC sinusoidal signal

The XRD patterns of the manganese oxide samples arepresented in Figures 15 and 16 The vacuum-deposited filmsare amorphous and represent a mixture of 120573- and 120574-MnO

2

(Figure 16) The results of the full-profile analysis show thatthe pyrolytic MnO

2samples (Figure 15) are composed of

the finely dispersed 120573-MnO2phase with the traces of 120574-

MnO2 120576-MnO

2 and Mn

2O3phases The periods of the

tetragonal unit cell of 120573-MnO2are 119886 = 119887 = 4401 A and

119888 = 2872 A The oxygen coordinates in 4119891 positions (seediscussion of the crystal structure above and Figure 14) arefound to be119909 = 0302 Calculations of the oxygen-manganeseinteratomic distances show [93] that the oxygen octahedron

Advances in Condensed Matter Physics 13

330222

040231

212202

112

130002

220

121

120

111

110

101

020

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 80 100 12002120579∘

Figure 15 XRD (Cu K120572radiation) pattern of pyrolytic MnO

2

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 8002120579∘ Fe

120573-MnO2

120574-MnO2

Experiment

Figure 16 XRD (Fe K120572radiation) pattern of Mn oxide film and

reference spectra of crystalline MnO2samples

is compressed along the (100) direction which connects theoctahedron vertices This deformation results in an increaseof the overlap of electron119901 orbitals of oxygen and119889 orbitals ofmanganese and can form the additional splitting of electronlevels in the crystal field leading to the appearance of unpairedelectrons [94]

The measurements of the conductivity temperaturedependence Hall effect and thermo-emf show that man-ganese dioxide is the electron semiconductor with conductiv-ity of about 1Ωminus1cmminus1 and mobility of sim10 cm2Vsdots The Hallmeasurements give the carrier density ofsim1018 cmminus3 which isclose to the density values in degenerate semiconductorsTheactivation energy of conductivity is sim01 eV and the band gapwidth is equal to 2 eV [90] The estimated value of the Fermienergy from the thermo-emf temperature dependence is inthe range of 002 to 005 eV which also indicates the degener-ate character of the electron gasThe nonstoichiometry indexdetermined by the XRD peaks which are not contributed

by the manganese atoms that is by those with the oddsum of indexes is 119910 = 006 Such nonstoichiometry providesthe concentration of trap states of about 1017-1018 cmminus3which correlates with the above mentioned Hall-effect-basedmeasurements of electron density

Such high vacancy concentration allows us to considerthe nonstoichiometric 120573-MnO

2as a heavily doped semicon-

ductor with a subband of impurity levels which provides afeasibility of the out-of-band electron transfer at low tem-peratures The structural distortions high nonstoichiometryand as a consequence sufficiently high concentration ofimpurity states cause the density state tails near the bandedges similarly to those in heavily doped semiconductorsHowever at room and higher temperatures the conduction isdetermined by the activation mechanism Thus the electronstructure and a low mobility of charge carriers promotethe manifestation of different charge transfer mechanismsin different temperature ranges namely both the hoppingmechanism and the activation one

The electron capturing oxygen vacancies create mixedvalence states of manganese cations (Mn3+ndashMn4+) Interest-ingly the mixed valence of Mn ions is also characteristic ofmanganites Ln

1minus119910Sr119910MnO3[95] where Ln is La or another

rare-earth element possessing the effect of colossal magne-toresistance (CMR) In these compounds the mixed valenceof manganese is attained via doping It had been deemed thatholes introduced by strontium are localized at manganeseions that is the Mn4+ ions with concentration 119910 are formedHowever recent X-ray emission studies have shown that boththe chemical shift and the exchange splitting of the emissionX-ray Mn K

1205731line are almost the same in the range 119910 lt 04ndash

05 as is the case in Mn2O3 and then they decrease quickly

to the values characteristic of MnO2[96] which suggests that

the introduced holes are localized at oxygen atoms in the holedoping region (at relatively low 119910) and atmanganese atoms inthe electron doping region that is at higher 119910 values

The temperature dependence of conductivity is presentedin Figure 17 The resistance peak observed in the figure ina temperature range of 80ndash90K is the result of the phasetransition of 120573-MnO

2from a semiconducting state to a metal

state upon decreasing the temperature to 15 K [54] The tem-perature region of the transition is close to the known Neeltransition from the paramagnetic state into the ferromagneticone for manganese dioxide The temperature dependenceof resistance indicates thus the MIT to occur in MnO

2 In

the temperature range from 300 to 80K (Figure 17) thisdependence does not correspond to the exponential one yetit fits well with the linear dependence in theMott coordinatesln(119877) sim 119879

14 which indicates the hopping conductivitymechanism over the polyvalent states ofmanganese ions witha distance between the centres of 25ndash35gt [92] However inthe temperature range from 90 to 15 K the dependence ofln119877 on ln119879 is almost linear with the slope of about unity(ie 120597 ln119877120597 ln119879 asymp 1) which is characteristic of the metallicconductionThus the character of conductivity ofmanganesedioxide indicates the presence of the MIT at 119879

119888sim 80K (on

cooling)

14 Advances in Condensed Matter Physics

CoolingHeating

40 80 120 160 2000T (K)

0

2

4

6

8

10

Resis

tivity

(Ohm

timescm

)

Figure 17 Temperature dependence of AC (70Hz) resistivity ofpyrolytic MnO

2

In the low temperature region manganese dioxide is anantiferromagnetwith the helical spin ordering [97]The inter-action between the magnetic ions of manganese which leadsto the antiferromagnetic state occurs through the intermedi-ate interaction with diamagnetic oxygen ions which weakensthe exchange interaction The conductivity increases proba-bly due to exceeding the energy of the exchange interactionby the thermal energy as the temperature increases whichleads to an increase in the number of unpaired electrons inthe paramagnetic state As the temperature further increasesthe conductivity continues to rise and the Mott hoppingmechanism of charge transfer becomes predominant Similarcharacter of the temperature dependence in ferromagneticdegenerate semiconductors has previously been described[85 98] for substoichiometric (oxygen-deficient) europiummonoxide The transition from the highly conductive stateinto the insulating state occurs in such semiconductors uponvarying the type of magnetic ordering or its destruction

For EuO1minus119910

lowering the peak magnitude in the 119877(119879)

dependence is associatedwith a decrease in the concentrationof impurities (oxygen vacancies) In magnetic semicon-ductors the phase transition is associated both with themagnetoelectric effects and with the variation in the electricpolarization under the action of the magnetic field at theantiferromagnetic transition [98] The dielectric constant formanganese dioxide is equal to sim10 but the effective dielectricconstant can decrease near 119879

119888by a factor of several times

thereby affecting the mobility of carriers located in the tailsof the density of states near the band edge and promotingtheir delocalization at the phase transition temperatureManganese dioxide also belongs to this group of substanceshowever the phase transition in MnO

2reported here can be

also described in terms of the Mott transition [24]According to the Mott criterion electrons delocalize if

the distance between the atoms 119899minus13 becomes comparable

with their atomic radius 119886119860 where 119886

119860is associated with the

Bohr radius 119886119861= ℏ2120576me2The static permittivity 120576 is replaced

by the effective permittivity which takes into account theexchange interaction of the spins of conduction electronswith orbitalmagneticmoments of atoms At the temperature-induced Mott MIT the orbital radius 119886

119861decreases near 119879 =

119879119888thereby providing the fulfillment of the Mott criterion at a

given level of impurity centres [24 98] The transition fromthe metallic state into the semiconductor state is possible insuch semiconductors as the temperature increases Thus theMIT in manganese dioxide is brought about by temperaturevariation

In conclusion we note that the phase transition describedabove is inverse (reentrant) MIT that is the metallic phaseis low-temperature while the high-temperature state is insu-lating This is rather rare yet not unique and unusualphenomenon In most cases (eg in vanadium dioxide) thelow-temperature phase is insulating and on heating abovea certain temperature 119879

119888 the material becomes metallic for

VO2 this transition temperature is 119879

119888= 340K The inverse

transitions are observed in such compounds as the abovementioned EuO

1minus119910 NiS2Se Y2O3minus119910

and LaMnO3films [24

31 52 85 98 99] Also the high-temperature Mott transi-tion from paramagnetic metal to paramagnetic insulator inV2O3Cr is an inverse transition with the resistivity peak at

119879119888sim 350K for a chromium concentration of around 1 at

[24 51] and in mixed valence CMR-manganites the sharpresistivity peak has been shown to be caused by the AndersonMIT [95]

It is known that many TMOs exhibit electrical switchingassociated with MITs [28] For the anodic oxide films onMn the study of the effect of electrical switching in thin-film Mn-MnO

2-Au sandwich structures showed that the S-

type switching was not observed in contrast to for examplethe similar structures based on oxides of vanadium andsome other transition metals [28] Instead switching withthe N-shaped I-V characteristic occurred after EF at 119879 lt

80K (Figure 18(a)) In addition the EF process in the Mn-based structures was hindered likewise for example for thestructures based on yttrium oxide [31] that is the breakdowntook place more often It should be noted that EF at roomtemperature always led to breakdown and the switchingeffect had never been observed in this case As was arguedin [54] this switching effect was associated with the MIT inMnO2

On the other hand in the films obtained by vacuumsputtering we have observed S-type switching at roomtemperature (Figure 18(b)) The threshold voltage is of theorder of 1 V and almost independent of temperature up to 119879

= 375KThis situation resembles that with yttrium oxide where

both S-type and N-type switching has been observed too[31] One can assume that switching with the S-shapedI-V curves is due to the so-called ldquothermistor effectrdquo Itis well known that the current flowing through a solidgenerates Joule heat resulting in an increased temperatureIn materials with a negative TCR a rising temperatureinduces a current enhancement and an increased powerdissipation resulting in a farther temperature increase Thispositive electrothermal feedback causes the appearance of anNDR and accordingly an S-shaped I-V characteristic [2]

Advances in Condensed Matter Physics 15

minus15

minus10

minus5

0

5

10

15Cu

rren

t (m

A)

0500 10 15minus10 minus05minus15

Voltage (V)

(a)

minus2

minus1

0

1

2

Curr

ent (

mA

)

10 2minus2 minus1

Voltage (V)

(b)

Figure 18 (a) I-V characteristic of anodic oxide film on manganese at T = 77K (b) I-V characteristic of vacuum-deposited MnO2at 119879 =

293K

In some cases this process might by modified by high-fieldeffects such as Schottky injection impact ionization Poole-Frenkel effect and Zener or avalanche breakdown Notethat unlike a conventional thermistor with an Arrhenius-like conductivity law manganese oxide exhibits a weaker119877(119879) dependence characteristic of the hopping conductivitymechanism which seems to account for the observed weaktemperature dependence of the threshold voltage

An alternative mechanism for the S-type switching effectmay be connected with a possible high-temperature usual(ie not inverse)MIT in somemanganese oxide As is knownEF (see Section 22) leads to the formation of a filament ofhighly conducting material a switching channel Similarlyto what is observed for Mo oxide (Section 231) and otherTMOs (Sections 21 and 22) we suppose that the compositionof this channel differs from the material of the initial oxidefilm since its conductivity noticeably exceeds that of anunformed structure In view of such a plentiful set of phasesand crystal structures in the Mn-O system one can supposethat the channelmight consist of nonstoichiometric120573-MnO

2

some other polymorphic modifications of manganese diox-ide or lower Mn oxides which might undergo a MIT underthe action of either temperature or electric field Howeverthis question obviously requires additional investigation inparticularmeasurements of119877(119879)dependences and switchingproperties at higher temperatures If this assumed high-temperature MIT would occur in for example nonstoichio-metric 120573-MnO

2 one could expect observation of double-

NDR I-V characteristics in such samples at low temperaturesanalogously to those in V

2O3Cr (Figure 9) where this effect

is due to the MITs [29] with the only difference being thatin the case of MnO

2this curve should be N-S-shaped (unlike

the S-N-shaped one in Figure 9) since in chromium-dopedvanadium sesquioxide the inverse MIT is high-temperatureas opposed to MnO

2which as we discussed above (see

Figure 17) exhibits the inverse MIT at low temperaturesNote however that the discussed high-temperature MIT

in 120573-MnO2minus119910

may be unobservable under the temperature

change in equilibrium conditions but displays itself onlyunder the applied electric field as the S-type electricalswitching effect because the transition temperature is closeto or higher than the temperature of MnO

2decomposition

(723K) Such a nonequilibrium transition occurs at switchingin those materials where the usual temperature-inducedMITwith a well-defined 119879

119905does not take place for example in

CGSs for which the equilibrium transition temperature 1198791199050

is higher than 119879119892 while in a high electric field 119879

119905(119864) lt 119879

1199050

might be lower than 119879119892 where 119879

119892is the temperature of the

glass-crystal transition and119864 is the electric field strength [30]Summarizing we have studied the electrical properties

(conductivity temperature dependence and Hall and Seebeckeffects) of the 120573 phase of manganese dioxide obtained bypyrolysis thermal vacuum evaporation and anodic oxida-tion The change of conductivity mechanisms dependingon temperature in a range of 450ndash25K has been shownand the metal-insulator phase transition at low (lt90K)temperatures has been revealed The specific feature of thistransition described in terms of the Mott mechanism isthat the metal phase exists at low temperatures while athigher temperatures the material is a semiconductor withthe hopping conductivity over the mixed valence states ofmanganese ions

The low-temperature switching effect with an NDR andN-shaped current-voltage characteristic associated with thephase transition in manganese dioxide has been found in theMOM two-terminal devices based on anodicMn oxide filmsOn the contrary the devices based on vacuum-depositedfilms have been found to exhibit an S-NDR at room andhigher temperatures which is suggested to be caused byeither the thermistor effect or a high-temperature MIT innonstoichiometric 120573-MnO

2

It should be emphasized that the low-temperature MITin 120573-MnO

2with 119879

119905= 70ndash80K is the inverse Mott transition

which is akin for instance to the transition in V2O3Cr

at 119879119905= 190ndash385K (for chromium dopant concentration in

the range of 05ndash18 at) [51] We thus assume that farther

16 Advances in Condensed Matter Physics

5 10 150Voltage (V)

0

1

2

3

4

5

6

7

8Cu

rren

t (m

A)

(a)ΔV

th(V

)

0

1

2

3

1 2 3 4 5 6 7 80W (at )

(b)

Figure 19 I-V curve (a) of Au-V2minus119910

W119910O5times 119899H2O-Au sandwich structure with119910= 003 and119881th scattering as a function of tungsten admixture

percentage 119910 (b) [104 105]

investigations of the phase transition in manganese dioxidedescribed in this paper are a rather interesting and topicalscientific problem since manganese dioxide can serve as amodel object for studying such inverse metal-insulator phasetransitions

Finally we note that the results presented in this sectionindicate the possibility of application of manganese oxide asa material for thin film sandwich switching devices Deviceswith NDR (N- and S-shaped I-V characteristics) have poten-tial applications in microelectronics as switches memoryelements and microsensors (these issues will be discussedin more detail below in Section 4) Particularly manganeseoxide microswitches [82] can be utilized for implementationof neuristors built with Mott-transition-based memristors[100]

24 Effect of Doping It is only natural that the systemsexhibiting the NDR effects possess a high applied potential inelectronics [2 4 8 18 100 101] yet the stage of EF is a weaklink of chain in the technology process Note that the formingprocess may be brought about by laser irradiation [102] notby applying of electric field In the case of laser treatment(or ldquolaser formingrdquo unlike the above described electricalforming) the parameters of the structures are characterizedby the absence of the scatter that is the I-V characteristics ofall structures are almost identical [103] One more demerit tobe avoided is the scatter in switching parameters (the value of119881th first of all) and their instability during operation In thissubsection we discuss the issues concerning the switchingparameter stabilization by means of doping

In the work [104] we have studied the switching effectin the MOM structures on the basis of W-doped V

2O5-gel

filmsThese structures require preliminary EF similar to thatin anodic oxide films resulting in formation of a conducting

channel within the initial dielectric xerogel filmThe channelconsists of vanadiumdioxide and switching is associatedwiththe insulator-to-metal transition in VO

2 As was shown in

[104 105] for the pure (undoped) V2O5-gel the switching

parameters vary in a wide range because the phenomenonof EF is statistical in nature (like electrical breakdown) andits statistical character shows itself as a spread in the observedthreshold voltages of the ensuing structures that is actuallyat multiple measurements 119881th = ⟨119881th⟩ plusmn Δ119881th

It has been shown [104] that the statistical spread in valuesof the threshold parameters can be minimized by means ofdoping (Figure 19) Unsophisticated reasoning could accountfor this result for pure V

2O5-gel electroforming leads to

formation of VO2with 119879

119905= 340K and each switching

event requires heating up and cooling down from roomtemperature to 119879

119905 this thermal cycling can modify the

peripheral regions of the channel which leads to the changeof the switching threshold voltage On the other hand forthe samples with a high concentration of W the MIT issuppressed [104] and switching is degenerated Betweenthese two outermost points an optimum should exist Asone can see from Figure 19 this optimal value correspondsto 3 at of W that is for V

097W003

O2the switching

parameters are the most stableThe transition temperature ofV097

W003

O2is lower than that for pure vanadium dioxide

and hence the magnitude of the aforesaid thermal cyclingis decreased which results in an increase of stability of theswitching parameters

Next we have studied the effect of doping on switchingin AOFs on Ti [29] These films were obtained in 5 watersolution of citric acid (C

6H8O7) in volt-static regime at 119881

119886

= 20V The samples were doped with aluminium by meansof adding soluble Al-containing substances to the electrolyte

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

Films vol 97 no 2 pp 129ndash143 1982[46] R Collongues La Non-Stoechiometrie Masson Paris France

1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

9 no 5 pp 391ndash396 2014[67] B Sun W Zhao Y Liu and P Chen ldquoResistive switching effect

of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

1990[70] S Mukherjee S Karmakar H Sakata and B K Chaudhuri

ldquoLow-temperature metallic behavior of amorphous MoO3-

TeO2thin filmsrdquo Journal of Applied Physics vol 97 no 12 Article

ID 123707 2005[71] AMottaghizadeh Q Yu P L Lang A Zimmers andH Aubin

ldquoMetal oxide resistive switching evolution of the density ofstates across the metal-insulator transitionrdquo Physical ReviewLetters vol 112 no 6 Article ID 066803 2014

[72] R Xie C T Bui B Varghese et al ldquoAn electrically tunedsolid-state thermalmemory based onmetal-insulator transitionof single-crystalline VO

2nanobeamsrdquo Advanced Functional

Materials vol 21 no 9 pp 1602ndash1607 2011

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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FluidsJournal of

Atomic and Molecular Physics

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

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AstronomyAdvances in

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Superconductivity

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Physics Research International

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Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

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AerodynamicsJournal of

Volume 2014

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PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

Advances in Condensed Matter Physics 11

020406080

100120

30 40 50 60 7020Temperature (∘C)

30 40 50 60 7020Temperature (∘C)

0

2

4

6

8

10

12

Thre

shol

d vo

ltage

(V)

5 15minus5minus15

Voltage (V)

minus010

minus005

000005010

Curr

ent (

mA

)

V2 th

(V2)

Figure 13 Threshold voltage as a function of temperature for theTa-MoOx-Au switching structure and the temperature dependenceof (119881th)

2 (lower inset) in compliancewith (3) I-V curve at RT (upperinset)

formation of a switching channel However for the Mooxide films prepared by vacuum deposition the processesof electroforming and switching were more stable whichallowed in this case observation of the transformation of I-V curves at a temperature change It was found that as thetemperature increased the threshold voltage was reducedAt 119879 = 119879

119900sim 55ndash65∘C the NDR region degeneration

commenced at 119879 asymp 60ndash70∘C 119881th rarr 0 and at still highertemperatures the switching effect no longer occurred Inthis case the switching mechanism might be described interms of the ldquocritical temperaturerdquo model (Figure 13) It issupposed [53] that in the case of Mo like in other TMO-based structures formation of a channel also takes placeand this channel should consist of a material exhibiting MITwhich is the reason for switching with an S-shaped current-voltage characteristic (Figure 12)

A brief review of the materials with MIT in the familyof molybdenum compounds presented in [53] shows that themost suitable candidate for the role of such a channel-formingcompound is Mo

8O23

because in this case the value of 1198791199051

almost coincides with the above reported experimentallymeasured 119879

0 It should be noted that formation of other

compounds of molybdenum (eg pyrochlores bronzes sul-fides or chalcogenide glasses) exhibiting MITs with similarorder of magnitude transition temperatures [64ndash68 70] isimpossible because of the lack of the necessary chemicalelements (ie rare earths alkali metals or hydrogen sulfurand tellurium) in the phase composition of both the oxidefilm and the metal electrodes (Au Ta and Mo)

In conclusion the results presented in this subsection onswitching from the HR state to the LR state with an S-NDRin molybdenum oxides obtained by both thermal vacuumdeposition and electrochemical anodic oxidation show thatthe switching effect is due to apparently an insulator-to-metal phase transition in the switching channel consistingcompletely or partly of the lower oxide Mo

8O23 formed in

the initial film during the process of electroforming Thecurrent flowing through the channel heats it up to the MIT

temperature 1198791199051= 315K [62] and the structure switches into

the metallic low-resistance stateThus the channels consisting of this lower oxide are

formed in initial Mo oxide films during preliminary elec-troforming Electrical forming results in the changes inoxygen stoichiometry conditioned by the ionic processes inan electric field close to the MOM structure breakdown fieldThis picture is quite similar to what is observed inmany otherTMOs exhibiting the insulator-to-metal transitions

232 Metal-Insulator Transition and Switching in ManganeseDioxide Manganese dioxide is one of the most interestinginorganic materials because of its wide range of applica-tions In particular nanostructured MnO

2has received great

attention due to its high specific surface area functionalproperties and potential applications as molecular and ionselective membranes in capacitors Li-ion batteries andcatalysts [77] Originally MnO

2has been widely used as a

cathode material for oxide-semiconductor capacitors basedon tantalum niobium and aluminium oxides and the mostimportant properties of the material for this application areits high conductivity and ability to undergo a thermal phasetransition into the lower valence states accompanied by evo-lution of atomic oxygen while the resistance increases by 3-4orders of magnitude (see eg [54] and references therein)Much attention is currently paid to various other propertiesof MnO

2 such as for example the electrochromic effect

[78] thermopower wave phenomenon [79] supercapacitivebehaviour [80] andmemory and threshold switching [54 8182] Also there are a number of papers [83ndash85] describing ananomaly in theMnO

2conductivity near theNeel temperature

which is shown to be associated with the metal-insulatortransition [52] That is why the electrical properties of MnO

2

are of special scientific interest and applied importanceThe most common methods for manganese oxide prepa-

ration are the pyrolytic decomposition of manganese nitrateelectrochemical method hydrothermal synthesis in a mag-netic field and chemical deposition [54 86ndash89] Due to awide range of possible valence states of cations the structureand phase composition of manganese oxides are determinedby the synthesis conditions and process temperature Man-ganese dioxide has many crystallographic forms (120572- 120573- 120574-120575- 120576- and 120582-MnO

2) that connect MnO

6octahedron units to

each other in different ways and have different characters ofspatial alternation of the octahedra filled by Mn atoms andempty octahedra [54 77 90ndash94]

The crystal structure of the 120573-MnO2phase (Figure 14) is a

tetragonal modification of the rutile structural type P4mnmsymmetry group which represents a slightly distorted close-packed hexagonal lattice of oxygen ions [93] Filled octahedraare bound by two common edges in columns oriented alongthe 119888 axis and octahedra of adjacent columns are bound bytheir vertices (Figure 14(c)) Manganese atoms are arrangedin positions 2(a) (000) and oxygen atoms in positions 4(f )(xx0) Because there are vacancies in the oxygen packingthe formula unit can be written as MnO

2minus119910where the

nonstoichiometry index is in the range 119910 = 001ndash010depending on the synthesis method [93]

12 Advances in Condensed Matter Physics

Mn

O

(a)

a

b

c

(b)

O2O4

O1O3

Mn2

Mn1

Mn1998400

O3998400

O4998400

(c)

Figure 14 Crystal structure of manganese dioxide (a) MnO6

octahedron connection in 120573-MnO2(b) [90ndash94] and projection of

octahedron binding onto the ab plane [93]

As to the lower manganese oxides MnO and Mn3O4are

known to be theMott insulatorswith relatively high resistivity[90] and Mn

2O3shows p-type semiconducting properties

MnO2is an n-type semiconductor and antiferromagnetic

with the Neel temperature 119879119873= 925 K [91] Conductivity of

manganese dioxide is higher than that of MnO and Mn2O3

by several orders of magnitude At temperatures above 723Kmanganese dioxide loses oxygen and transforms intoMn

2O3

which is accompanied by the transformation of the crystallinestructure from the tetragonal crystal system of the rutile typeinto the complex large-period cubic lattice (119886 = 94gt) and alarge number of formula units per unit cell [54 92 93]

In this subsection we present the results on electricalproperties of manganese dioxide particularly the natureof the 120573-MnO

2conductivity at low temperatures in its

interrelation with characteristic features of the material crys-talline structure and the metal-insulator phase transitionin this compound as well The effect of electrical switchingwith current-voltage characteristics of both N- and S-typehas been found in thin-film MOM structures on the basisof manganese oxides Possible mechanisms of switching interms of the MIT and thermistor effects are discussed

Mn oxide samples under study have been obtained bythree methods anodic oxidation and vacuum evaporation(thin films) as well as by pyrolysis [54] Thin films ofmanganese dioxide were deposited by means of thermalevaporation onto glass substrates covered by a SnO

2layer

using a VUP-5 vacuum setup the film thickness was 119889 =

250 nmAlso thin films ofmanganese oxidewere obtained byelectrochemical oxidation of metal Mn in the KNO

3-NaNO

3

eutectic melt (see Section 21) at 119879 = 600K at a constantvoltage of about 2V for 3min the current density diminishedfrom 200 to 100mAcm2 during the oxidation process Foranodic oxide films on Mn the value of 119889 was sim100 nm Bulksamples of manganese dioxide were obtained by multipledecomposition (pyrolysis) of manganese nitrate at 119879 = 670Kon a glass-ceramic substrate or on a tantalum sheetmetal withthe subsequent separation from the substrate [92 93] Thetotal coating thickness was about 1mm

The manganese oxide samples were characterized by X-ray diffraction (XRD) using a DRON-6 diffractometer inCuK120572and FeK

120572radiation The characteristics of the atomic

structure of pyrolytic manganese dioxide were refined by thefull-profile analysis of the XRD patterns of polycrystallinesamples [93]The resistivity of pyrolyticMnO

2wasmeasured

in the temperature range 15 to 300K bymeans of a four-probetechnique both DC and AC (in a frequency range from 50 to104Hz) in a Gifford-McMahon cycle cryorefrigerator [54]We also measured electrical conductivity in the range T =293ndash423K the Hall effect in the magnetic field of 23 T andthe Seebeck coefficient (thermoelectromotive force thermo-emf ) The dynamic current-voltage (I-V) characteristics ofthe thin-film MOM structures were measured by oscillo-graphic method using an AC sinusoidal signal

The XRD patterns of the manganese oxide samples arepresented in Figures 15 and 16 The vacuum-deposited filmsare amorphous and represent a mixture of 120573- and 120574-MnO

2

(Figure 16) The results of the full-profile analysis show thatthe pyrolytic MnO

2samples (Figure 15) are composed of

the finely dispersed 120573-MnO2phase with the traces of 120574-

MnO2 120576-MnO

2 and Mn

2O3phases The periods of the

tetragonal unit cell of 120573-MnO2are 119886 = 119887 = 4401 A and

119888 = 2872 A The oxygen coordinates in 4119891 positions (seediscussion of the crystal structure above and Figure 14) arefound to be119909 = 0302 Calculations of the oxygen-manganeseinteratomic distances show [93] that the oxygen octahedron

Advances in Condensed Matter Physics 13

330222

040231

212202

112

130002

220

121

120

111

110

101

020

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 80 100 12002120579∘

Figure 15 XRD (Cu K120572radiation) pattern of pyrolytic MnO

2

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 8002120579∘ Fe

120573-MnO2

120574-MnO2

Experiment

Figure 16 XRD (Fe K120572radiation) pattern of Mn oxide film and

reference spectra of crystalline MnO2samples

is compressed along the (100) direction which connects theoctahedron vertices This deformation results in an increaseof the overlap of electron119901 orbitals of oxygen and119889 orbitals ofmanganese and can form the additional splitting of electronlevels in the crystal field leading to the appearance of unpairedelectrons [94]

The measurements of the conductivity temperaturedependence Hall effect and thermo-emf show that man-ganese dioxide is the electron semiconductor with conductiv-ity of about 1Ωminus1cmminus1 and mobility of sim10 cm2Vsdots The Hallmeasurements give the carrier density ofsim1018 cmminus3 which isclose to the density values in degenerate semiconductorsTheactivation energy of conductivity is sim01 eV and the band gapwidth is equal to 2 eV [90] The estimated value of the Fermienergy from the thermo-emf temperature dependence is inthe range of 002 to 005 eV which also indicates the degener-ate character of the electron gasThe nonstoichiometry indexdetermined by the XRD peaks which are not contributed

by the manganese atoms that is by those with the oddsum of indexes is 119910 = 006 Such nonstoichiometry providesthe concentration of trap states of about 1017-1018 cmminus3which correlates with the above mentioned Hall-effect-basedmeasurements of electron density

Such high vacancy concentration allows us to considerthe nonstoichiometric 120573-MnO

2as a heavily doped semicon-

ductor with a subband of impurity levels which provides afeasibility of the out-of-band electron transfer at low tem-peratures The structural distortions high nonstoichiometryand as a consequence sufficiently high concentration ofimpurity states cause the density state tails near the bandedges similarly to those in heavily doped semiconductorsHowever at room and higher temperatures the conduction isdetermined by the activation mechanism Thus the electronstructure and a low mobility of charge carriers promotethe manifestation of different charge transfer mechanismsin different temperature ranges namely both the hoppingmechanism and the activation one

The electron capturing oxygen vacancies create mixedvalence states of manganese cations (Mn3+ndashMn4+) Interest-ingly the mixed valence of Mn ions is also characteristic ofmanganites Ln

1minus119910Sr119910MnO3[95] where Ln is La or another

rare-earth element possessing the effect of colossal magne-toresistance (CMR) In these compounds the mixed valenceof manganese is attained via doping It had been deemed thatholes introduced by strontium are localized at manganeseions that is the Mn4+ ions with concentration 119910 are formedHowever recent X-ray emission studies have shown that boththe chemical shift and the exchange splitting of the emissionX-ray Mn K

1205731line are almost the same in the range 119910 lt 04ndash

05 as is the case in Mn2O3 and then they decrease quickly

to the values characteristic of MnO2[96] which suggests that

the introduced holes are localized at oxygen atoms in the holedoping region (at relatively low 119910) and atmanganese atoms inthe electron doping region that is at higher 119910 values

The temperature dependence of conductivity is presentedin Figure 17 The resistance peak observed in the figure ina temperature range of 80ndash90K is the result of the phasetransition of 120573-MnO

2from a semiconducting state to a metal

state upon decreasing the temperature to 15 K [54] The tem-perature region of the transition is close to the known Neeltransition from the paramagnetic state into the ferromagneticone for manganese dioxide The temperature dependenceof resistance indicates thus the MIT to occur in MnO

2 In

the temperature range from 300 to 80K (Figure 17) thisdependence does not correspond to the exponential one yetit fits well with the linear dependence in theMott coordinatesln(119877) sim 119879

14 which indicates the hopping conductivitymechanism over the polyvalent states ofmanganese ions witha distance between the centres of 25ndash35gt [92] However inthe temperature range from 90 to 15 K the dependence ofln119877 on ln119879 is almost linear with the slope of about unity(ie 120597 ln119877120597 ln119879 asymp 1) which is characteristic of the metallicconductionThus the character of conductivity ofmanganesedioxide indicates the presence of the MIT at 119879

119888sim 80K (on

cooling)

14 Advances in Condensed Matter Physics

CoolingHeating

40 80 120 160 2000T (K)

0

2

4

6

8

10

Resis

tivity

(Ohm

timescm

)

Figure 17 Temperature dependence of AC (70Hz) resistivity ofpyrolytic MnO

2

In the low temperature region manganese dioxide is anantiferromagnetwith the helical spin ordering [97]The inter-action between the magnetic ions of manganese which leadsto the antiferromagnetic state occurs through the intermedi-ate interaction with diamagnetic oxygen ions which weakensthe exchange interaction The conductivity increases proba-bly due to exceeding the energy of the exchange interactionby the thermal energy as the temperature increases whichleads to an increase in the number of unpaired electrons inthe paramagnetic state As the temperature further increasesthe conductivity continues to rise and the Mott hoppingmechanism of charge transfer becomes predominant Similarcharacter of the temperature dependence in ferromagneticdegenerate semiconductors has previously been described[85 98] for substoichiometric (oxygen-deficient) europiummonoxide The transition from the highly conductive stateinto the insulating state occurs in such semiconductors uponvarying the type of magnetic ordering or its destruction

For EuO1minus119910

lowering the peak magnitude in the 119877(119879)

dependence is associatedwith a decrease in the concentrationof impurities (oxygen vacancies) In magnetic semicon-ductors the phase transition is associated both with themagnetoelectric effects and with the variation in the electricpolarization under the action of the magnetic field at theantiferromagnetic transition [98] The dielectric constant formanganese dioxide is equal to sim10 but the effective dielectricconstant can decrease near 119879

119888by a factor of several times

thereby affecting the mobility of carriers located in the tailsof the density of states near the band edge and promotingtheir delocalization at the phase transition temperatureManganese dioxide also belongs to this group of substanceshowever the phase transition in MnO

2reported here can be

also described in terms of the Mott transition [24]According to the Mott criterion electrons delocalize if

the distance between the atoms 119899minus13 becomes comparable

with their atomic radius 119886119860 where 119886

119860is associated with the

Bohr radius 119886119861= ℏ2120576me2The static permittivity 120576 is replaced

by the effective permittivity which takes into account theexchange interaction of the spins of conduction electronswith orbitalmagneticmoments of atoms At the temperature-induced Mott MIT the orbital radius 119886

119861decreases near 119879 =

119879119888thereby providing the fulfillment of the Mott criterion at a

given level of impurity centres [24 98] The transition fromthe metallic state into the semiconductor state is possible insuch semiconductors as the temperature increases Thus theMIT in manganese dioxide is brought about by temperaturevariation

In conclusion we note that the phase transition describedabove is inverse (reentrant) MIT that is the metallic phaseis low-temperature while the high-temperature state is insu-lating This is rather rare yet not unique and unusualphenomenon In most cases (eg in vanadium dioxide) thelow-temperature phase is insulating and on heating abovea certain temperature 119879

119888 the material becomes metallic for

VO2 this transition temperature is 119879

119888= 340K The inverse

transitions are observed in such compounds as the abovementioned EuO

1minus119910 NiS2Se Y2O3minus119910

and LaMnO3films [24

31 52 85 98 99] Also the high-temperature Mott transi-tion from paramagnetic metal to paramagnetic insulator inV2O3Cr is an inverse transition with the resistivity peak at

119879119888sim 350K for a chromium concentration of around 1 at

[24 51] and in mixed valence CMR-manganites the sharpresistivity peak has been shown to be caused by the AndersonMIT [95]

It is known that many TMOs exhibit electrical switchingassociated with MITs [28] For the anodic oxide films onMn the study of the effect of electrical switching in thin-film Mn-MnO

2-Au sandwich structures showed that the S-

type switching was not observed in contrast to for examplethe similar structures based on oxides of vanadium andsome other transition metals [28] Instead switching withthe N-shaped I-V characteristic occurred after EF at 119879 lt

80K (Figure 18(a)) In addition the EF process in the Mn-based structures was hindered likewise for example for thestructures based on yttrium oxide [31] that is the breakdowntook place more often It should be noted that EF at roomtemperature always led to breakdown and the switchingeffect had never been observed in this case As was arguedin [54] this switching effect was associated with the MIT inMnO2

On the other hand in the films obtained by vacuumsputtering we have observed S-type switching at roomtemperature (Figure 18(b)) The threshold voltage is of theorder of 1 V and almost independent of temperature up to 119879

= 375KThis situation resembles that with yttrium oxide where

both S-type and N-type switching has been observed too[31] One can assume that switching with the S-shapedI-V curves is due to the so-called ldquothermistor effectrdquo Itis well known that the current flowing through a solidgenerates Joule heat resulting in an increased temperatureIn materials with a negative TCR a rising temperatureinduces a current enhancement and an increased powerdissipation resulting in a farther temperature increase Thispositive electrothermal feedback causes the appearance of anNDR and accordingly an S-shaped I-V characteristic [2]

Advances in Condensed Matter Physics 15

minus15

minus10

minus5

0

5

10

15Cu

rren

t (m

A)

0500 10 15minus10 minus05minus15

Voltage (V)

(a)

minus2

minus1

0

1

2

Curr

ent (

mA

)

10 2minus2 minus1

Voltage (V)

(b)

Figure 18 (a) I-V characteristic of anodic oxide film on manganese at T = 77K (b) I-V characteristic of vacuum-deposited MnO2at 119879 =

293K

In some cases this process might by modified by high-fieldeffects such as Schottky injection impact ionization Poole-Frenkel effect and Zener or avalanche breakdown Notethat unlike a conventional thermistor with an Arrhenius-like conductivity law manganese oxide exhibits a weaker119877(119879) dependence characteristic of the hopping conductivitymechanism which seems to account for the observed weaktemperature dependence of the threshold voltage

An alternative mechanism for the S-type switching effectmay be connected with a possible high-temperature usual(ie not inverse)MIT in somemanganese oxide As is knownEF (see Section 22) leads to the formation of a filament ofhighly conducting material a switching channel Similarlyto what is observed for Mo oxide (Section 231) and otherTMOs (Sections 21 and 22) we suppose that the compositionof this channel differs from the material of the initial oxidefilm since its conductivity noticeably exceeds that of anunformed structure In view of such a plentiful set of phasesand crystal structures in the Mn-O system one can supposethat the channelmight consist of nonstoichiometric120573-MnO

2

some other polymorphic modifications of manganese diox-ide or lower Mn oxides which might undergo a MIT underthe action of either temperature or electric field Howeverthis question obviously requires additional investigation inparticularmeasurements of119877(119879)dependences and switchingproperties at higher temperatures If this assumed high-temperature MIT would occur in for example nonstoichio-metric 120573-MnO

2 one could expect observation of double-

NDR I-V characteristics in such samples at low temperaturesanalogously to those in V

2O3Cr (Figure 9) where this effect

is due to the MITs [29] with the only difference being thatin the case of MnO

2this curve should be N-S-shaped (unlike

the S-N-shaped one in Figure 9) since in chromium-dopedvanadium sesquioxide the inverse MIT is high-temperatureas opposed to MnO

2which as we discussed above (see

Figure 17) exhibits the inverse MIT at low temperaturesNote however that the discussed high-temperature MIT

in 120573-MnO2minus119910

may be unobservable under the temperature

change in equilibrium conditions but displays itself onlyunder the applied electric field as the S-type electricalswitching effect because the transition temperature is closeto or higher than the temperature of MnO

2decomposition

(723K) Such a nonequilibrium transition occurs at switchingin those materials where the usual temperature-inducedMITwith a well-defined 119879

119905does not take place for example in

CGSs for which the equilibrium transition temperature 1198791199050

is higher than 119879119892 while in a high electric field 119879

119905(119864) lt 119879

1199050

might be lower than 119879119892 where 119879

119892is the temperature of the

glass-crystal transition and119864 is the electric field strength [30]Summarizing we have studied the electrical properties

(conductivity temperature dependence and Hall and Seebeckeffects) of the 120573 phase of manganese dioxide obtained bypyrolysis thermal vacuum evaporation and anodic oxida-tion The change of conductivity mechanisms dependingon temperature in a range of 450ndash25K has been shownand the metal-insulator phase transition at low (lt90K)temperatures has been revealed The specific feature of thistransition described in terms of the Mott mechanism isthat the metal phase exists at low temperatures while athigher temperatures the material is a semiconductor withthe hopping conductivity over the mixed valence states ofmanganese ions

The low-temperature switching effect with an NDR andN-shaped current-voltage characteristic associated with thephase transition in manganese dioxide has been found in theMOM two-terminal devices based on anodicMn oxide filmsOn the contrary the devices based on vacuum-depositedfilms have been found to exhibit an S-NDR at room andhigher temperatures which is suggested to be caused byeither the thermistor effect or a high-temperature MIT innonstoichiometric 120573-MnO

2

It should be emphasized that the low-temperature MITin 120573-MnO

2with 119879

119905= 70ndash80K is the inverse Mott transition

which is akin for instance to the transition in V2O3Cr

at 119879119905= 190ndash385K (for chromium dopant concentration in

the range of 05ndash18 at) [51] We thus assume that farther

16 Advances in Condensed Matter Physics

5 10 150Voltage (V)

0

1

2

3

4

5

6

7

8Cu

rren

t (m

A)

(a)ΔV

th(V

)

0

1

2

3

1 2 3 4 5 6 7 80W (at )

(b)

Figure 19 I-V curve (a) of Au-V2minus119910

W119910O5times 119899H2O-Au sandwich structure with119910= 003 and119881th scattering as a function of tungsten admixture

percentage 119910 (b) [104 105]

investigations of the phase transition in manganese dioxidedescribed in this paper are a rather interesting and topicalscientific problem since manganese dioxide can serve as amodel object for studying such inverse metal-insulator phasetransitions

Finally we note that the results presented in this sectionindicate the possibility of application of manganese oxide asa material for thin film sandwich switching devices Deviceswith NDR (N- and S-shaped I-V characteristics) have poten-tial applications in microelectronics as switches memoryelements and microsensors (these issues will be discussedin more detail below in Section 4) Particularly manganeseoxide microswitches [82] can be utilized for implementationof neuristors built with Mott-transition-based memristors[100]

24 Effect of Doping It is only natural that the systemsexhibiting the NDR effects possess a high applied potential inelectronics [2 4 8 18 100 101] yet the stage of EF is a weaklink of chain in the technology process Note that the formingprocess may be brought about by laser irradiation [102] notby applying of electric field In the case of laser treatment(or ldquolaser formingrdquo unlike the above described electricalforming) the parameters of the structures are characterizedby the absence of the scatter that is the I-V characteristics ofall structures are almost identical [103] One more demerit tobe avoided is the scatter in switching parameters (the value of119881th first of all) and their instability during operation In thissubsection we discuss the issues concerning the switchingparameter stabilization by means of doping

In the work [104] we have studied the switching effectin the MOM structures on the basis of W-doped V

2O5-gel

filmsThese structures require preliminary EF similar to thatin anodic oxide films resulting in formation of a conducting

channel within the initial dielectric xerogel filmThe channelconsists of vanadiumdioxide and switching is associatedwiththe insulator-to-metal transition in VO

2 As was shown in

[104 105] for the pure (undoped) V2O5-gel the switching

parameters vary in a wide range because the phenomenonof EF is statistical in nature (like electrical breakdown) andits statistical character shows itself as a spread in the observedthreshold voltages of the ensuing structures that is actuallyat multiple measurements 119881th = ⟨119881th⟩ plusmn Δ119881th

It has been shown [104] that the statistical spread in valuesof the threshold parameters can be minimized by means ofdoping (Figure 19) Unsophisticated reasoning could accountfor this result for pure V

2O5-gel electroforming leads to

formation of VO2with 119879

119905= 340K and each switching

event requires heating up and cooling down from roomtemperature to 119879

119905 this thermal cycling can modify the

peripheral regions of the channel which leads to the changeof the switching threshold voltage On the other hand forthe samples with a high concentration of W the MIT issuppressed [104] and switching is degenerated Betweenthese two outermost points an optimum should exist Asone can see from Figure 19 this optimal value correspondsto 3 at of W that is for V

097W003

O2the switching

parameters are the most stableThe transition temperature ofV097

W003

O2is lower than that for pure vanadium dioxide

and hence the magnitude of the aforesaid thermal cyclingis decreased which results in an increase of stability of theswitching parameters

Next we have studied the effect of doping on switchingin AOFs on Ti [29] These films were obtained in 5 watersolution of citric acid (C

6H8O7) in volt-static regime at 119881

119886

= 20V The samples were doped with aluminium by meansof adding soluble Al-containing substances to the electrolyte

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

Films vol 97 no 2 pp 129ndash143 1982[46] R Collongues La Non-Stoechiometrie Masson Paris France

1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

9 no 5 pp 391ndash396 2014[67] B Sun W Zhao Y Liu and P Chen ldquoResistive switching effect

of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

1990[70] S Mukherjee S Karmakar H Sakata and B K Chaudhuri

ldquoLow-temperature metallic behavior of amorphous MoO3-

TeO2thin filmsrdquo Journal of Applied Physics vol 97 no 12 Article

ID 123707 2005[71] AMottaghizadeh Q Yu P L Lang A Zimmers andH Aubin

ldquoMetal oxide resistive switching evolution of the density ofstates across the metal-insulator transitionrdquo Physical ReviewLetters vol 112 no 6 Article ID 066803 2014

[72] R Xie C T Bui B Varghese et al ldquoAn electrically tunedsolid-state thermalmemory based onmetal-insulator transitionof single-crystalline VO

2nanobeamsrdquo Advanced Functional

Materials vol 21 no 9 pp 1602ndash1607 2011

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

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GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

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Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

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AerodynamicsJournal of

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PhotonicsJournal of

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Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

12 Advances in Condensed Matter Physics

Mn

O

(a)

a

b

c

(b)

O2O4

O1O3

Mn2

Mn1

Mn1998400

O3998400

O4998400

(c)

Figure 14 Crystal structure of manganese dioxide (a) MnO6

octahedron connection in 120573-MnO2(b) [90ndash94] and projection of

octahedron binding onto the ab plane [93]

As to the lower manganese oxides MnO and Mn3O4are

known to be theMott insulatorswith relatively high resistivity[90] and Mn

2O3shows p-type semiconducting properties

MnO2is an n-type semiconductor and antiferromagnetic

with the Neel temperature 119879119873= 925 K [91] Conductivity of

manganese dioxide is higher than that of MnO and Mn2O3

by several orders of magnitude At temperatures above 723Kmanganese dioxide loses oxygen and transforms intoMn

2O3

which is accompanied by the transformation of the crystallinestructure from the tetragonal crystal system of the rutile typeinto the complex large-period cubic lattice (119886 = 94gt) and alarge number of formula units per unit cell [54 92 93]

In this subsection we present the results on electricalproperties of manganese dioxide particularly the natureof the 120573-MnO

2conductivity at low temperatures in its

interrelation with characteristic features of the material crys-talline structure and the metal-insulator phase transitionin this compound as well The effect of electrical switchingwith current-voltage characteristics of both N- and S-typehas been found in thin-film MOM structures on the basisof manganese oxides Possible mechanisms of switching interms of the MIT and thermistor effects are discussed

Mn oxide samples under study have been obtained bythree methods anodic oxidation and vacuum evaporation(thin films) as well as by pyrolysis [54] Thin films ofmanganese dioxide were deposited by means of thermalevaporation onto glass substrates covered by a SnO

2layer

using a VUP-5 vacuum setup the film thickness was 119889 =

250 nmAlso thin films ofmanganese oxidewere obtained byelectrochemical oxidation of metal Mn in the KNO

3-NaNO

3

eutectic melt (see Section 21) at 119879 = 600K at a constantvoltage of about 2V for 3min the current density diminishedfrom 200 to 100mAcm2 during the oxidation process Foranodic oxide films on Mn the value of 119889 was sim100 nm Bulksamples of manganese dioxide were obtained by multipledecomposition (pyrolysis) of manganese nitrate at 119879 = 670Kon a glass-ceramic substrate or on a tantalum sheetmetal withthe subsequent separation from the substrate [92 93] Thetotal coating thickness was about 1mm

The manganese oxide samples were characterized by X-ray diffraction (XRD) using a DRON-6 diffractometer inCuK120572and FeK

120572radiation The characteristics of the atomic

structure of pyrolytic manganese dioxide were refined by thefull-profile analysis of the XRD patterns of polycrystallinesamples [93]The resistivity of pyrolyticMnO

2wasmeasured

in the temperature range 15 to 300K bymeans of a four-probetechnique both DC and AC (in a frequency range from 50 to104Hz) in a Gifford-McMahon cycle cryorefrigerator [54]We also measured electrical conductivity in the range T =293ndash423K the Hall effect in the magnetic field of 23 T andthe Seebeck coefficient (thermoelectromotive force thermo-emf ) The dynamic current-voltage (I-V) characteristics ofthe thin-film MOM structures were measured by oscillo-graphic method using an AC sinusoidal signal

The XRD patterns of the manganese oxide samples arepresented in Figures 15 and 16 The vacuum-deposited filmsare amorphous and represent a mixture of 120573- and 120574-MnO

2

(Figure 16) The results of the full-profile analysis show thatthe pyrolytic MnO

2samples (Figure 15) are composed of

the finely dispersed 120573-MnO2phase with the traces of 120574-

MnO2 120576-MnO

2 and Mn

2O3phases The periods of the

tetragonal unit cell of 120573-MnO2are 119886 = 119887 = 4401 A and

119888 = 2872 A The oxygen coordinates in 4119891 positions (seediscussion of the crystal structure above and Figure 14) arefound to be119909 = 0302 Calculations of the oxygen-manganeseinteratomic distances show [93] that the oxygen octahedron

Advances in Condensed Matter Physics 13

330222

040231

212202

112

130002

220

121

120

111

110

101

020

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 80 100 12002120579∘

Figure 15 XRD (Cu K120572radiation) pattern of pyrolytic MnO

2

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 8002120579∘ Fe

120573-MnO2

120574-MnO2

Experiment

Figure 16 XRD (Fe K120572radiation) pattern of Mn oxide film and

reference spectra of crystalline MnO2samples

is compressed along the (100) direction which connects theoctahedron vertices This deformation results in an increaseof the overlap of electron119901 orbitals of oxygen and119889 orbitals ofmanganese and can form the additional splitting of electronlevels in the crystal field leading to the appearance of unpairedelectrons [94]

The measurements of the conductivity temperaturedependence Hall effect and thermo-emf show that man-ganese dioxide is the electron semiconductor with conductiv-ity of about 1Ωminus1cmminus1 and mobility of sim10 cm2Vsdots The Hallmeasurements give the carrier density ofsim1018 cmminus3 which isclose to the density values in degenerate semiconductorsTheactivation energy of conductivity is sim01 eV and the band gapwidth is equal to 2 eV [90] The estimated value of the Fermienergy from the thermo-emf temperature dependence is inthe range of 002 to 005 eV which also indicates the degener-ate character of the electron gasThe nonstoichiometry indexdetermined by the XRD peaks which are not contributed

by the manganese atoms that is by those with the oddsum of indexes is 119910 = 006 Such nonstoichiometry providesthe concentration of trap states of about 1017-1018 cmminus3which correlates with the above mentioned Hall-effect-basedmeasurements of electron density

Such high vacancy concentration allows us to considerthe nonstoichiometric 120573-MnO

2as a heavily doped semicon-

ductor with a subband of impurity levels which provides afeasibility of the out-of-band electron transfer at low tem-peratures The structural distortions high nonstoichiometryand as a consequence sufficiently high concentration ofimpurity states cause the density state tails near the bandedges similarly to those in heavily doped semiconductorsHowever at room and higher temperatures the conduction isdetermined by the activation mechanism Thus the electronstructure and a low mobility of charge carriers promotethe manifestation of different charge transfer mechanismsin different temperature ranges namely both the hoppingmechanism and the activation one

The electron capturing oxygen vacancies create mixedvalence states of manganese cations (Mn3+ndashMn4+) Interest-ingly the mixed valence of Mn ions is also characteristic ofmanganites Ln

1minus119910Sr119910MnO3[95] where Ln is La or another

rare-earth element possessing the effect of colossal magne-toresistance (CMR) In these compounds the mixed valenceof manganese is attained via doping It had been deemed thatholes introduced by strontium are localized at manganeseions that is the Mn4+ ions with concentration 119910 are formedHowever recent X-ray emission studies have shown that boththe chemical shift and the exchange splitting of the emissionX-ray Mn K

1205731line are almost the same in the range 119910 lt 04ndash

05 as is the case in Mn2O3 and then they decrease quickly

to the values characteristic of MnO2[96] which suggests that

the introduced holes are localized at oxygen atoms in the holedoping region (at relatively low 119910) and atmanganese atoms inthe electron doping region that is at higher 119910 values

The temperature dependence of conductivity is presentedin Figure 17 The resistance peak observed in the figure ina temperature range of 80ndash90K is the result of the phasetransition of 120573-MnO

2from a semiconducting state to a metal

state upon decreasing the temperature to 15 K [54] The tem-perature region of the transition is close to the known Neeltransition from the paramagnetic state into the ferromagneticone for manganese dioxide The temperature dependenceof resistance indicates thus the MIT to occur in MnO

2 In

the temperature range from 300 to 80K (Figure 17) thisdependence does not correspond to the exponential one yetit fits well with the linear dependence in theMott coordinatesln(119877) sim 119879

14 which indicates the hopping conductivitymechanism over the polyvalent states ofmanganese ions witha distance between the centres of 25ndash35gt [92] However inthe temperature range from 90 to 15 K the dependence ofln119877 on ln119879 is almost linear with the slope of about unity(ie 120597 ln119877120597 ln119879 asymp 1) which is characteristic of the metallicconductionThus the character of conductivity ofmanganesedioxide indicates the presence of the MIT at 119879

119888sim 80K (on

cooling)

14 Advances in Condensed Matter Physics

CoolingHeating

40 80 120 160 2000T (K)

0

2

4

6

8

10

Resis

tivity

(Ohm

timescm

)

Figure 17 Temperature dependence of AC (70Hz) resistivity ofpyrolytic MnO

2

In the low temperature region manganese dioxide is anantiferromagnetwith the helical spin ordering [97]The inter-action between the magnetic ions of manganese which leadsto the antiferromagnetic state occurs through the intermedi-ate interaction with diamagnetic oxygen ions which weakensthe exchange interaction The conductivity increases proba-bly due to exceeding the energy of the exchange interactionby the thermal energy as the temperature increases whichleads to an increase in the number of unpaired electrons inthe paramagnetic state As the temperature further increasesthe conductivity continues to rise and the Mott hoppingmechanism of charge transfer becomes predominant Similarcharacter of the temperature dependence in ferromagneticdegenerate semiconductors has previously been described[85 98] for substoichiometric (oxygen-deficient) europiummonoxide The transition from the highly conductive stateinto the insulating state occurs in such semiconductors uponvarying the type of magnetic ordering or its destruction

For EuO1minus119910

lowering the peak magnitude in the 119877(119879)

dependence is associatedwith a decrease in the concentrationof impurities (oxygen vacancies) In magnetic semicon-ductors the phase transition is associated both with themagnetoelectric effects and with the variation in the electricpolarization under the action of the magnetic field at theantiferromagnetic transition [98] The dielectric constant formanganese dioxide is equal to sim10 but the effective dielectricconstant can decrease near 119879

119888by a factor of several times

thereby affecting the mobility of carriers located in the tailsof the density of states near the band edge and promotingtheir delocalization at the phase transition temperatureManganese dioxide also belongs to this group of substanceshowever the phase transition in MnO

2reported here can be

also described in terms of the Mott transition [24]According to the Mott criterion electrons delocalize if

the distance between the atoms 119899minus13 becomes comparable

with their atomic radius 119886119860 where 119886

119860is associated with the

Bohr radius 119886119861= ℏ2120576me2The static permittivity 120576 is replaced

by the effective permittivity which takes into account theexchange interaction of the spins of conduction electronswith orbitalmagneticmoments of atoms At the temperature-induced Mott MIT the orbital radius 119886

119861decreases near 119879 =

119879119888thereby providing the fulfillment of the Mott criterion at a

given level of impurity centres [24 98] The transition fromthe metallic state into the semiconductor state is possible insuch semiconductors as the temperature increases Thus theMIT in manganese dioxide is brought about by temperaturevariation

In conclusion we note that the phase transition describedabove is inverse (reentrant) MIT that is the metallic phaseis low-temperature while the high-temperature state is insu-lating This is rather rare yet not unique and unusualphenomenon In most cases (eg in vanadium dioxide) thelow-temperature phase is insulating and on heating abovea certain temperature 119879

119888 the material becomes metallic for

VO2 this transition temperature is 119879

119888= 340K The inverse

transitions are observed in such compounds as the abovementioned EuO

1minus119910 NiS2Se Y2O3minus119910

and LaMnO3films [24

31 52 85 98 99] Also the high-temperature Mott transi-tion from paramagnetic metal to paramagnetic insulator inV2O3Cr is an inverse transition with the resistivity peak at

119879119888sim 350K for a chromium concentration of around 1 at

[24 51] and in mixed valence CMR-manganites the sharpresistivity peak has been shown to be caused by the AndersonMIT [95]

It is known that many TMOs exhibit electrical switchingassociated with MITs [28] For the anodic oxide films onMn the study of the effect of electrical switching in thin-film Mn-MnO

2-Au sandwich structures showed that the S-

type switching was not observed in contrast to for examplethe similar structures based on oxides of vanadium andsome other transition metals [28] Instead switching withthe N-shaped I-V characteristic occurred after EF at 119879 lt

80K (Figure 18(a)) In addition the EF process in the Mn-based structures was hindered likewise for example for thestructures based on yttrium oxide [31] that is the breakdowntook place more often It should be noted that EF at roomtemperature always led to breakdown and the switchingeffect had never been observed in this case As was arguedin [54] this switching effect was associated with the MIT inMnO2

On the other hand in the films obtained by vacuumsputtering we have observed S-type switching at roomtemperature (Figure 18(b)) The threshold voltage is of theorder of 1 V and almost independent of temperature up to 119879

= 375KThis situation resembles that with yttrium oxide where

both S-type and N-type switching has been observed too[31] One can assume that switching with the S-shapedI-V curves is due to the so-called ldquothermistor effectrdquo Itis well known that the current flowing through a solidgenerates Joule heat resulting in an increased temperatureIn materials with a negative TCR a rising temperatureinduces a current enhancement and an increased powerdissipation resulting in a farther temperature increase Thispositive electrothermal feedback causes the appearance of anNDR and accordingly an S-shaped I-V characteristic [2]

Advances in Condensed Matter Physics 15

minus15

minus10

minus5

0

5

10

15Cu

rren

t (m

A)

0500 10 15minus10 minus05minus15

Voltage (V)

(a)

minus2

minus1

0

1

2

Curr

ent (

mA

)

10 2minus2 minus1

Voltage (V)

(b)

Figure 18 (a) I-V characteristic of anodic oxide film on manganese at T = 77K (b) I-V characteristic of vacuum-deposited MnO2at 119879 =

293K

In some cases this process might by modified by high-fieldeffects such as Schottky injection impact ionization Poole-Frenkel effect and Zener or avalanche breakdown Notethat unlike a conventional thermistor with an Arrhenius-like conductivity law manganese oxide exhibits a weaker119877(119879) dependence characteristic of the hopping conductivitymechanism which seems to account for the observed weaktemperature dependence of the threshold voltage

An alternative mechanism for the S-type switching effectmay be connected with a possible high-temperature usual(ie not inverse)MIT in somemanganese oxide As is knownEF (see Section 22) leads to the formation of a filament ofhighly conducting material a switching channel Similarlyto what is observed for Mo oxide (Section 231) and otherTMOs (Sections 21 and 22) we suppose that the compositionof this channel differs from the material of the initial oxidefilm since its conductivity noticeably exceeds that of anunformed structure In view of such a plentiful set of phasesand crystal structures in the Mn-O system one can supposethat the channelmight consist of nonstoichiometric120573-MnO

2

some other polymorphic modifications of manganese diox-ide or lower Mn oxides which might undergo a MIT underthe action of either temperature or electric field Howeverthis question obviously requires additional investigation inparticularmeasurements of119877(119879)dependences and switchingproperties at higher temperatures If this assumed high-temperature MIT would occur in for example nonstoichio-metric 120573-MnO

2 one could expect observation of double-

NDR I-V characteristics in such samples at low temperaturesanalogously to those in V

2O3Cr (Figure 9) where this effect

is due to the MITs [29] with the only difference being thatin the case of MnO

2this curve should be N-S-shaped (unlike

the S-N-shaped one in Figure 9) since in chromium-dopedvanadium sesquioxide the inverse MIT is high-temperatureas opposed to MnO

2which as we discussed above (see

Figure 17) exhibits the inverse MIT at low temperaturesNote however that the discussed high-temperature MIT

in 120573-MnO2minus119910

may be unobservable under the temperature

change in equilibrium conditions but displays itself onlyunder the applied electric field as the S-type electricalswitching effect because the transition temperature is closeto or higher than the temperature of MnO

2decomposition

(723K) Such a nonequilibrium transition occurs at switchingin those materials where the usual temperature-inducedMITwith a well-defined 119879

119905does not take place for example in

CGSs for which the equilibrium transition temperature 1198791199050

is higher than 119879119892 while in a high electric field 119879

119905(119864) lt 119879

1199050

might be lower than 119879119892 where 119879

119892is the temperature of the

glass-crystal transition and119864 is the electric field strength [30]Summarizing we have studied the electrical properties

(conductivity temperature dependence and Hall and Seebeckeffects) of the 120573 phase of manganese dioxide obtained bypyrolysis thermal vacuum evaporation and anodic oxida-tion The change of conductivity mechanisms dependingon temperature in a range of 450ndash25K has been shownand the metal-insulator phase transition at low (lt90K)temperatures has been revealed The specific feature of thistransition described in terms of the Mott mechanism isthat the metal phase exists at low temperatures while athigher temperatures the material is a semiconductor withthe hopping conductivity over the mixed valence states ofmanganese ions

The low-temperature switching effect with an NDR andN-shaped current-voltage characteristic associated with thephase transition in manganese dioxide has been found in theMOM two-terminal devices based on anodicMn oxide filmsOn the contrary the devices based on vacuum-depositedfilms have been found to exhibit an S-NDR at room andhigher temperatures which is suggested to be caused byeither the thermistor effect or a high-temperature MIT innonstoichiometric 120573-MnO

2

It should be emphasized that the low-temperature MITin 120573-MnO

2with 119879

119905= 70ndash80K is the inverse Mott transition

which is akin for instance to the transition in V2O3Cr

at 119879119905= 190ndash385K (for chromium dopant concentration in

the range of 05ndash18 at) [51] We thus assume that farther

16 Advances in Condensed Matter Physics

5 10 150Voltage (V)

0

1

2

3

4

5

6

7

8Cu

rren

t (m

A)

(a)ΔV

th(V

)

0

1

2

3

1 2 3 4 5 6 7 80W (at )

(b)

Figure 19 I-V curve (a) of Au-V2minus119910

W119910O5times 119899H2O-Au sandwich structure with119910= 003 and119881th scattering as a function of tungsten admixture

percentage 119910 (b) [104 105]

investigations of the phase transition in manganese dioxidedescribed in this paper are a rather interesting and topicalscientific problem since manganese dioxide can serve as amodel object for studying such inverse metal-insulator phasetransitions

Finally we note that the results presented in this sectionindicate the possibility of application of manganese oxide asa material for thin film sandwich switching devices Deviceswith NDR (N- and S-shaped I-V characteristics) have poten-tial applications in microelectronics as switches memoryelements and microsensors (these issues will be discussedin more detail below in Section 4) Particularly manganeseoxide microswitches [82] can be utilized for implementationof neuristors built with Mott-transition-based memristors[100]

24 Effect of Doping It is only natural that the systemsexhibiting the NDR effects possess a high applied potential inelectronics [2 4 8 18 100 101] yet the stage of EF is a weaklink of chain in the technology process Note that the formingprocess may be brought about by laser irradiation [102] notby applying of electric field In the case of laser treatment(or ldquolaser formingrdquo unlike the above described electricalforming) the parameters of the structures are characterizedby the absence of the scatter that is the I-V characteristics ofall structures are almost identical [103] One more demerit tobe avoided is the scatter in switching parameters (the value of119881th first of all) and their instability during operation In thissubsection we discuss the issues concerning the switchingparameter stabilization by means of doping

In the work [104] we have studied the switching effectin the MOM structures on the basis of W-doped V

2O5-gel

filmsThese structures require preliminary EF similar to thatin anodic oxide films resulting in formation of a conducting

channel within the initial dielectric xerogel filmThe channelconsists of vanadiumdioxide and switching is associatedwiththe insulator-to-metal transition in VO

2 As was shown in

[104 105] for the pure (undoped) V2O5-gel the switching

parameters vary in a wide range because the phenomenonof EF is statistical in nature (like electrical breakdown) andits statistical character shows itself as a spread in the observedthreshold voltages of the ensuing structures that is actuallyat multiple measurements 119881th = ⟨119881th⟩ plusmn Δ119881th

It has been shown [104] that the statistical spread in valuesof the threshold parameters can be minimized by means ofdoping (Figure 19) Unsophisticated reasoning could accountfor this result for pure V

2O5-gel electroforming leads to

formation of VO2with 119879

119905= 340K and each switching

event requires heating up and cooling down from roomtemperature to 119879

119905 this thermal cycling can modify the

peripheral regions of the channel which leads to the changeof the switching threshold voltage On the other hand forthe samples with a high concentration of W the MIT issuppressed [104] and switching is degenerated Betweenthese two outermost points an optimum should exist Asone can see from Figure 19 this optimal value correspondsto 3 at of W that is for V

097W003

O2the switching

parameters are the most stableThe transition temperature ofV097

W003

O2is lower than that for pure vanadium dioxide

and hence the magnitude of the aforesaid thermal cyclingis decreased which results in an increase of stability of theswitching parameters

Next we have studied the effect of doping on switchingin AOFs on Ti [29] These films were obtained in 5 watersolution of citric acid (C

6H8O7) in volt-static regime at 119881

119886

= 20V The samples were doped with aluminium by meansof adding soluble Al-containing substances to the electrolyte

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

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1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

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of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

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ldquoLow-temperature metallic behavior of amorphous MoO3-

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Materials vol 21 no 9 pp 1602ndash1607 2011

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[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

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wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

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2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

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[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

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PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

Advances in Condensed Matter Physics 13

330222

040231

212202

112

130002

220

121

120

111

110

101

020

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 80 100 12002120579∘

Figure 15 XRD (Cu K120572radiation) pattern of pyrolytic MnO

2

0

200

400

600

800

1000

I (co

unts

s)

20 40 60 8002120579∘ Fe

120573-MnO2

120574-MnO2

Experiment

Figure 16 XRD (Fe K120572radiation) pattern of Mn oxide film and

reference spectra of crystalline MnO2samples

is compressed along the (100) direction which connects theoctahedron vertices This deformation results in an increaseof the overlap of electron119901 orbitals of oxygen and119889 orbitals ofmanganese and can form the additional splitting of electronlevels in the crystal field leading to the appearance of unpairedelectrons [94]

The measurements of the conductivity temperaturedependence Hall effect and thermo-emf show that man-ganese dioxide is the electron semiconductor with conductiv-ity of about 1Ωminus1cmminus1 and mobility of sim10 cm2Vsdots The Hallmeasurements give the carrier density ofsim1018 cmminus3 which isclose to the density values in degenerate semiconductorsTheactivation energy of conductivity is sim01 eV and the band gapwidth is equal to 2 eV [90] The estimated value of the Fermienergy from the thermo-emf temperature dependence is inthe range of 002 to 005 eV which also indicates the degener-ate character of the electron gasThe nonstoichiometry indexdetermined by the XRD peaks which are not contributed

by the manganese atoms that is by those with the oddsum of indexes is 119910 = 006 Such nonstoichiometry providesthe concentration of trap states of about 1017-1018 cmminus3which correlates with the above mentioned Hall-effect-basedmeasurements of electron density

Such high vacancy concentration allows us to considerthe nonstoichiometric 120573-MnO

2as a heavily doped semicon-

ductor with a subband of impurity levels which provides afeasibility of the out-of-band electron transfer at low tem-peratures The structural distortions high nonstoichiometryand as a consequence sufficiently high concentration ofimpurity states cause the density state tails near the bandedges similarly to those in heavily doped semiconductorsHowever at room and higher temperatures the conduction isdetermined by the activation mechanism Thus the electronstructure and a low mobility of charge carriers promotethe manifestation of different charge transfer mechanismsin different temperature ranges namely both the hoppingmechanism and the activation one

The electron capturing oxygen vacancies create mixedvalence states of manganese cations (Mn3+ndashMn4+) Interest-ingly the mixed valence of Mn ions is also characteristic ofmanganites Ln

1minus119910Sr119910MnO3[95] where Ln is La or another

rare-earth element possessing the effect of colossal magne-toresistance (CMR) In these compounds the mixed valenceof manganese is attained via doping It had been deemed thatholes introduced by strontium are localized at manganeseions that is the Mn4+ ions with concentration 119910 are formedHowever recent X-ray emission studies have shown that boththe chemical shift and the exchange splitting of the emissionX-ray Mn K

1205731line are almost the same in the range 119910 lt 04ndash

05 as is the case in Mn2O3 and then they decrease quickly

to the values characteristic of MnO2[96] which suggests that

the introduced holes are localized at oxygen atoms in the holedoping region (at relatively low 119910) and atmanganese atoms inthe electron doping region that is at higher 119910 values

The temperature dependence of conductivity is presentedin Figure 17 The resistance peak observed in the figure ina temperature range of 80ndash90K is the result of the phasetransition of 120573-MnO

2from a semiconducting state to a metal

state upon decreasing the temperature to 15 K [54] The tem-perature region of the transition is close to the known Neeltransition from the paramagnetic state into the ferromagneticone for manganese dioxide The temperature dependenceof resistance indicates thus the MIT to occur in MnO

2 In

the temperature range from 300 to 80K (Figure 17) thisdependence does not correspond to the exponential one yetit fits well with the linear dependence in theMott coordinatesln(119877) sim 119879

14 which indicates the hopping conductivitymechanism over the polyvalent states ofmanganese ions witha distance between the centres of 25ndash35gt [92] However inthe temperature range from 90 to 15 K the dependence ofln119877 on ln119879 is almost linear with the slope of about unity(ie 120597 ln119877120597 ln119879 asymp 1) which is characteristic of the metallicconductionThus the character of conductivity ofmanganesedioxide indicates the presence of the MIT at 119879

119888sim 80K (on

cooling)

14 Advances in Condensed Matter Physics

CoolingHeating

40 80 120 160 2000T (K)

0

2

4

6

8

10

Resis

tivity

(Ohm

timescm

)

Figure 17 Temperature dependence of AC (70Hz) resistivity ofpyrolytic MnO

2

In the low temperature region manganese dioxide is anantiferromagnetwith the helical spin ordering [97]The inter-action between the magnetic ions of manganese which leadsto the antiferromagnetic state occurs through the intermedi-ate interaction with diamagnetic oxygen ions which weakensthe exchange interaction The conductivity increases proba-bly due to exceeding the energy of the exchange interactionby the thermal energy as the temperature increases whichleads to an increase in the number of unpaired electrons inthe paramagnetic state As the temperature further increasesthe conductivity continues to rise and the Mott hoppingmechanism of charge transfer becomes predominant Similarcharacter of the temperature dependence in ferromagneticdegenerate semiconductors has previously been described[85 98] for substoichiometric (oxygen-deficient) europiummonoxide The transition from the highly conductive stateinto the insulating state occurs in such semiconductors uponvarying the type of magnetic ordering or its destruction

For EuO1minus119910

lowering the peak magnitude in the 119877(119879)

dependence is associatedwith a decrease in the concentrationof impurities (oxygen vacancies) In magnetic semicon-ductors the phase transition is associated both with themagnetoelectric effects and with the variation in the electricpolarization under the action of the magnetic field at theantiferromagnetic transition [98] The dielectric constant formanganese dioxide is equal to sim10 but the effective dielectricconstant can decrease near 119879

119888by a factor of several times

thereby affecting the mobility of carriers located in the tailsof the density of states near the band edge and promotingtheir delocalization at the phase transition temperatureManganese dioxide also belongs to this group of substanceshowever the phase transition in MnO

2reported here can be

also described in terms of the Mott transition [24]According to the Mott criterion electrons delocalize if

the distance between the atoms 119899minus13 becomes comparable

with their atomic radius 119886119860 where 119886

119860is associated with the

Bohr radius 119886119861= ℏ2120576me2The static permittivity 120576 is replaced

by the effective permittivity which takes into account theexchange interaction of the spins of conduction electronswith orbitalmagneticmoments of atoms At the temperature-induced Mott MIT the orbital radius 119886

119861decreases near 119879 =

119879119888thereby providing the fulfillment of the Mott criterion at a

given level of impurity centres [24 98] The transition fromthe metallic state into the semiconductor state is possible insuch semiconductors as the temperature increases Thus theMIT in manganese dioxide is brought about by temperaturevariation

In conclusion we note that the phase transition describedabove is inverse (reentrant) MIT that is the metallic phaseis low-temperature while the high-temperature state is insu-lating This is rather rare yet not unique and unusualphenomenon In most cases (eg in vanadium dioxide) thelow-temperature phase is insulating and on heating abovea certain temperature 119879

119888 the material becomes metallic for

VO2 this transition temperature is 119879

119888= 340K The inverse

transitions are observed in such compounds as the abovementioned EuO

1minus119910 NiS2Se Y2O3minus119910

and LaMnO3films [24

31 52 85 98 99] Also the high-temperature Mott transi-tion from paramagnetic metal to paramagnetic insulator inV2O3Cr is an inverse transition with the resistivity peak at

119879119888sim 350K for a chromium concentration of around 1 at

[24 51] and in mixed valence CMR-manganites the sharpresistivity peak has been shown to be caused by the AndersonMIT [95]

It is known that many TMOs exhibit electrical switchingassociated with MITs [28] For the anodic oxide films onMn the study of the effect of electrical switching in thin-film Mn-MnO

2-Au sandwich structures showed that the S-

type switching was not observed in contrast to for examplethe similar structures based on oxides of vanadium andsome other transition metals [28] Instead switching withthe N-shaped I-V characteristic occurred after EF at 119879 lt

80K (Figure 18(a)) In addition the EF process in the Mn-based structures was hindered likewise for example for thestructures based on yttrium oxide [31] that is the breakdowntook place more often It should be noted that EF at roomtemperature always led to breakdown and the switchingeffect had never been observed in this case As was arguedin [54] this switching effect was associated with the MIT inMnO2

On the other hand in the films obtained by vacuumsputtering we have observed S-type switching at roomtemperature (Figure 18(b)) The threshold voltage is of theorder of 1 V and almost independent of temperature up to 119879

= 375KThis situation resembles that with yttrium oxide where

both S-type and N-type switching has been observed too[31] One can assume that switching with the S-shapedI-V curves is due to the so-called ldquothermistor effectrdquo Itis well known that the current flowing through a solidgenerates Joule heat resulting in an increased temperatureIn materials with a negative TCR a rising temperatureinduces a current enhancement and an increased powerdissipation resulting in a farther temperature increase Thispositive electrothermal feedback causes the appearance of anNDR and accordingly an S-shaped I-V characteristic [2]

Advances in Condensed Matter Physics 15

minus15

minus10

minus5

0

5

10

15Cu

rren

t (m

A)

0500 10 15minus10 minus05minus15

Voltage (V)

(a)

minus2

minus1

0

1

2

Curr

ent (

mA

)

10 2minus2 minus1

Voltage (V)

(b)

Figure 18 (a) I-V characteristic of anodic oxide film on manganese at T = 77K (b) I-V characteristic of vacuum-deposited MnO2at 119879 =

293K

In some cases this process might by modified by high-fieldeffects such as Schottky injection impact ionization Poole-Frenkel effect and Zener or avalanche breakdown Notethat unlike a conventional thermistor with an Arrhenius-like conductivity law manganese oxide exhibits a weaker119877(119879) dependence characteristic of the hopping conductivitymechanism which seems to account for the observed weaktemperature dependence of the threshold voltage

An alternative mechanism for the S-type switching effectmay be connected with a possible high-temperature usual(ie not inverse)MIT in somemanganese oxide As is knownEF (see Section 22) leads to the formation of a filament ofhighly conducting material a switching channel Similarlyto what is observed for Mo oxide (Section 231) and otherTMOs (Sections 21 and 22) we suppose that the compositionof this channel differs from the material of the initial oxidefilm since its conductivity noticeably exceeds that of anunformed structure In view of such a plentiful set of phasesand crystal structures in the Mn-O system one can supposethat the channelmight consist of nonstoichiometric120573-MnO

2

some other polymorphic modifications of manganese diox-ide or lower Mn oxides which might undergo a MIT underthe action of either temperature or electric field Howeverthis question obviously requires additional investigation inparticularmeasurements of119877(119879)dependences and switchingproperties at higher temperatures If this assumed high-temperature MIT would occur in for example nonstoichio-metric 120573-MnO

2 one could expect observation of double-

NDR I-V characteristics in such samples at low temperaturesanalogously to those in V

2O3Cr (Figure 9) where this effect

is due to the MITs [29] with the only difference being thatin the case of MnO

2this curve should be N-S-shaped (unlike

the S-N-shaped one in Figure 9) since in chromium-dopedvanadium sesquioxide the inverse MIT is high-temperatureas opposed to MnO

2which as we discussed above (see

Figure 17) exhibits the inverse MIT at low temperaturesNote however that the discussed high-temperature MIT

in 120573-MnO2minus119910

may be unobservable under the temperature

change in equilibrium conditions but displays itself onlyunder the applied electric field as the S-type electricalswitching effect because the transition temperature is closeto or higher than the temperature of MnO

2decomposition

(723K) Such a nonequilibrium transition occurs at switchingin those materials where the usual temperature-inducedMITwith a well-defined 119879

119905does not take place for example in

CGSs for which the equilibrium transition temperature 1198791199050

is higher than 119879119892 while in a high electric field 119879

119905(119864) lt 119879

1199050

might be lower than 119879119892 where 119879

119892is the temperature of the

glass-crystal transition and119864 is the electric field strength [30]Summarizing we have studied the electrical properties

(conductivity temperature dependence and Hall and Seebeckeffects) of the 120573 phase of manganese dioxide obtained bypyrolysis thermal vacuum evaporation and anodic oxida-tion The change of conductivity mechanisms dependingon temperature in a range of 450ndash25K has been shownand the metal-insulator phase transition at low (lt90K)temperatures has been revealed The specific feature of thistransition described in terms of the Mott mechanism isthat the metal phase exists at low temperatures while athigher temperatures the material is a semiconductor withthe hopping conductivity over the mixed valence states ofmanganese ions

The low-temperature switching effect with an NDR andN-shaped current-voltage characteristic associated with thephase transition in manganese dioxide has been found in theMOM two-terminal devices based on anodicMn oxide filmsOn the contrary the devices based on vacuum-depositedfilms have been found to exhibit an S-NDR at room andhigher temperatures which is suggested to be caused byeither the thermistor effect or a high-temperature MIT innonstoichiometric 120573-MnO

2

It should be emphasized that the low-temperature MITin 120573-MnO

2with 119879

119905= 70ndash80K is the inverse Mott transition

which is akin for instance to the transition in V2O3Cr

at 119879119905= 190ndash385K (for chromium dopant concentration in

the range of 05ndash18 at) [51] We thus assume that farther

16 Advances in Condensed Matter Physics

5 10 150Voltage (V)

0

1

2

3

4

5

6

7

8Cu

rren

t (m

A)

(a)ΔV

th(V

)

0

1

2

3

1 2 3 4 5 6 7 80W (at )

(b)

Figure 19 I-V curve (a) of Au-V2minus119910

W119910O5times 119899H2O-Au sandwich structure with119910= 003 and119881th scattering as a function of tungsten admixture

percentage 119910 (b) [104 105]

investigations of the phase transition in manganese dioxidedescribed in this paper are a rather interesting and topicalscientific problem since manganese dioxide can serve as amodel object for studying such inverse metal-insulator phasetransitions

Finally we note that the results presented in this sectionindicate the possibility of application of manganese oxide asa material for thin film sandwich switching devices Deviceswith NDR (N- and S-shaped I-V characteristics) have poten-tial applications in microelectronics as switches memoryelements and microsensors (these issues will be discussedin more detail below in Section 4) Particularly manganeseoxide microswitches [82] can be utilized for implementationof neuristors built with Mott-transition-based memristors[100]

24 Effect of Doping It is only natural that the systemsexhibiting the NDR effects possess a high applied potential inelectronics [2 4 8 18 100 101] yet the stage of EF is a weaklink of chain in the technology process Note that the formingprocess may be brought about by laser irradiation [102] notby applying of electric field In the case of laser treatment(or ldquolaser formingrdquo unlike the above described electricalforming) the parameters of the structures are characterizedby the absence of the scatter that is the I-V characteristics ofall structures are almost identical [103] One more demerit tobe avoided is the scatter in switching parameters (the value of119881th first of all) and their instability during operation In thissubsection we discuss the issues concerning the switchingparameter stabilization by means of doping

In the work [104] we have studied the switching effectin the MOM structures on the basis of W-doped V

2O5-gel

filmsThese structures require preliminary EF similar to thatin anodic oxide films resulting in formation of a conducting

channel within the initial dielectric xerogel filmThe channelconsists of vanadiumdioxide and switching is associatedwiththe insulator-to-metal transition in VO

2 As was shown in

[104 105] for the pure (undoped) V2O5-gel the switching

parameters vary in a wide range because the phenomenonof EF is statistical in nature (like electrical breakdown) andits statistical character shows itself as a spread in the observedthreshold voltages of the ensuing structures that is actuallyat multiple measurements 119881th = ⟨119881th⟩ plusmn Δ119881th

It has been shown [104] that the statistical spread in valuesof the threshold parameters can be minimized by means ofdoping (Figure 19) Unsophisticated reasoning could accountfor this result for pure V

2O5-gel electroforming leads to

formation of VO2with 119879

119905= 340K and each switching

event requires heating up and cooling down from roomtemperature to 119879

119905 this thermal cycling can modify the

peripheral regions of the channel which leads to the changeof the switching threshold voltage On the other hand forthe samples with a high concentration of W the MIT issuppressed [104] and switching is degenerated Betweenthese two outermost points an optimum should exist Asone can see from Figure 19 this optimal value correspondsto 3 at of W that is for V

097W003

O2the switching

parameters are the most stableThe transition temperature ofV097

W003

O2is lower than that for pure vanadium dioxide

and hence the magnitude of the aforesaid thermal cyclingis decreased which results in an increase of stability of theswitching parameters

Next we have studied the effect of doping on switchingin AOFs on Ti [29] These films were obtained in 5 watersolution of citric acid (C

6H8O7) in volt-static regime at 119881

119886

= 20V The samples were doped with aluminium by meansof adding soluble Al-containing substances to the electrolyte

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

Films vol 97 no 2 pp 129ndash143 1982[46] R Collongues La Non-Stoechiometrie Masson Paris France

1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

9 no 5 pp 391ndash396 2014[67] B Sun W Zhao Y Liu and P Chen ldquoResistive switching effect

of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

1990[70] S Mukherjee S Karmakar H Sakata and B K Chaudhuri

ldquoLow-temperature metallic behavior of amorphous MoO3-

TeO2thin filmsrdquo Journal of Applied Physics vol 97 no 12 Article

ID 123707 2005[71] AMottaghizadeh Q Yu P L Lang A Zimmers andH Aubin

ldquoMetal oxide resistive switching evolution of the density ofstates across the metal-insulator transitionrdquo Physical ReviewLetters vol 112 no 6 Article ID 066803 2014

[72] R Xie C T Bui B Varghese et al ldquoAn electrically tunedsolid-state thermalmemory based onmetal-insulator transitionof single-crystalline VO

2nanobeamsrdquo Advanced Functional

Materials vol 21 no 9 pp 1602ndash1607 2011

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

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Statistical MechanicsInternational Journal of

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GravityJournal of

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AstrophysicsJournal of

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Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

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AerodynamicsJournal of

Volume 2014

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PhotonicsJournal of

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Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

14 Advances in Condensed Matter Physics

CoolingHeating

40 80 120 160 2000T (K)

0

2

4

6

8

10

Resis

tivity

(Ohm

timescm

)

Figure 17 Temperature dependence of AC (70Hz) resistivity ofpyrolytic MnO

2

In the low temperature region manganese dioxide is anantiferromagnetwith the helical spin ordering [97]The inter-action between the magnetic ions of manganese which leadsto the antiferromagnetic state occurs through the intermedi-ate interaction with diamagnetic oxygen ions which weakensthe exchange interaction The conductivity increases proba-bly due to exceeding the energy of the exchange interactionby the thermal energy as the temperature increases whichleads to an increase in the number of unpaired electrons inthe paramagnetic state As the temperature further increasesthe conductivity continues to rise and the Mott hoppingmechanism of charge transfer becomes predominant Similarcharacter of the temperature dependence in ferromagneticdegenerate semiconductors has previously been described[85 98] for substoichiometric (oxygen-deficient) europiummonoxide The transition from the highly conductive stateinto the insulating state occurs in such semiconductors uponvarying the type of magnetic ordering or its destruction

For EuO1minus119910

lowering the peak magnitude in the 119877(119879)

dependence is associatedwith a decrease in the concentrationof impurities (oxygen vacancies) In magnetic semicon-ductors the phase transition is associated both with themagnetoelectric effects and with the variation in the electricpolarization under the action of the magnetic field at theantiferromagnetic transition [98] The dielectric constant formanganese dioxide is equal to sim10 but the effective dielectricconstant can decrease near 119879

119888by a factor of several times

thereby affecting the mobility of carriers located in the tailsof the density of states near the band edge and promotingtheir delocalization at the phase transition temperatureManganese dioxide also belongs to this group of substanceshowever the phase transition in MnO

2reported here can be

also described in terms of the Mott transition [24]According to the Mott criterion electrons delocalize if

the distance between the atoms 119899minus13 becomes comparable

with their atomic radius 119886119860 where 119886

119860is associated with the

Bohr radius 119886119861= ℏ2120576me2The static permittivity 120576 is replaced

by the effective permittivity which takes into account theexchange interaction of the spins of conduction electronswith orbitalmagneticmoments of atoms At the temperature-induced Mott MIT the orbital radius 119886

119861decreases near 119879 =

119879119888thereby providing the fulfillment of the Mott criterion at a

given level of impurity centres [24 98] The transition fromthe metallic state into the semiconductor state is possible insuch semiconductors as the temperature increases Thus theMIT in manganese dioxide is brought about by temperaturevariation

In conclusion we note that the phase transition describedabove is inverse (reentrant) MIT that is the metallic phaseis low-temperature while the high-temperature state is insu-lating This is rather rare yet not unique and unusualphenomenon In most cases (eg in vanadium dioxide) thelow-temperature phase is insulating and on heating abovea certain temperature 119879

119888 the material becomes metallic for

VO2 this transition temperature is 119879

119888= 340K The inverse

transitions are observed in such compounds as the abovementioned EuO

1minus119910 NiS2Se Y2O3minus119910

and LaMnO3films [24

31 52 85 98 99] Also the high-temperature Mott transi-tion from paramagnetic metal to paramagnetic insulator inV2O3Cr is an inverse transition with the resistivity peak at

119879119888sim 350K for a chromium concentration of around 1 at

[24 51] and in mixed valence CMR-manganites the sharpresistivity peak has been shown to be caused by the AndersonMIT [95]

It is known that many TMOs exhibit electrical switchingassociated with MITs [28] For the anodic oxide films onMn the study of the effect of electrical switching in thin-film Mn-MnO

2-Au sandwich structures showed that the S-

type switching was not observed in contrast to for examplethe similar structures based on oxides of vanadium andsome other transition metals [28] Instead switching withthe N-shaped I-V characteristic occurred after EF at 119879 lt

80K (Figure 18(a)) In addition the EF process in the Mn-based structures was hindered likewise for example for thestructures based on yttrium oxide [31] that is the breakdowntook place more often It should be noted that EF at roomtemperature always led to breakdown and the switchingeffect had never been observed in this case As was arguedin [54] this switching effect was associated with the MIT inMnO2

On the other hand in the films obtained by vacuumsputtering we have observed S-type switching at roomtemperature (Figure 18(b)) The threshold voltage is of theorder of 1 V and almost independent of temperature up to 119879

= 375KThis situation resembles that with yttrium oxide where

both S-type and N-type switching has been observed too[31] One can assume that switching with the S-shapedI-V curves is due to the so-called ldquothermistor effectrdquo Itis well known that the current flowing through a solidgenerates Joule heat resulting in an increased temperatureIn materials with a negative TCR a rising temperatureinduces a current enhancement and an increased powerdissipation resulting in a farther temperature increase Thispositive electrothermal feedback causes the appearance of anNDR and accordingly an S-shaped I-V characteristic [2]

Advances in Condensed Matter Physics 15

minus15

minus10

minus5

0

5

10

15Cu

rren

t (m

A)

0500 10 15minus10 minus05minus15

Voltage (V)

(a)

minus2

minus1

0

1

2

Curr

ent (

mA

)

10 2minus2 minus1

Voltage (V)

(b)

Figure 18 (a) I-V characteristic of anodic oxide film on manganese at T = 77K (b) I-V characteristic of vacuum-deposited MnO2at 119879 =

293K

In some cases this process might by modified by high-fieldeffects such as Schottky injection impact ionization Poole-Frenkel effect and Zener or avalanche breakdown Notethat unlike a conventional thermistor with an Arrhenius-like conductivity law manganese oxide exhibits a weaker119877(119879) dependence characteristic of the hopping conductivitymechanism which seems to account for the observed weaktemperature dependence of the threshold voltage

An alternative mechanism for the S-type switching effectmay be connected with a possible high-temperature usual(ie not inverse)MIT in somemanganese oxide As is knownEF (see Section 22) leads to the formation of a filament ofhighly conducting material a switching channel Similarlyto what is observed for Mo oxide (Section 231) and otherTMOs (Sections 21 and 22) we suppose that the compositionof this channel differs from the material of the initial oxidefilm since its conductivity noticeably exceeds that of anunformed structure In view of such a plentiful set of phasesand crystal structures in the Mn-O system one can supposethat the channelmight consist of nonstoichiometric120573-MnO

2

some other polymorphic modifications of manganese diox-ide or lower Mn oxides which might undergo a MIT underthe action of either temperature or electric field Howeverthis question obviously requires additional investigation inparticularmeasurements of119877(119879)dependences and switchingproperties at higher temperatures If this assumed high-temperature MIT would occur in for example nonstoichio-metric 120573-MnO

2 one could expect observation of double-

NDR I-V characteristics in such samples at low temperaturesanalogously to those in V

2O3Cr (Figure 9) where this effect

is due to the MITs [29] with the only difference being thatin the case of MnO

2this curve should be N-S-shaped (unlike

the S-N-shaped one in Figure 9) since in chromium-dopedvanadium sesquioxide the inverse MIT is high-temperatureas opposed to MnO

2which as we discussed above (see

Figure 17) exhibits the inverse MIT at low temperaturesNote however that the discussed high-temperature MIT

in 120573-MnO2minus119910

may be unobservable under the temperature

change in equilibrium conditions but displays itself onlyunder the applied electric field as the S-type electricalswitching effect because the transition temperature is closeto or higher than the temperature of MnO

2decomposition

(723K) Such a nonequilibrium transition occurs at switchingin those materials where the usual temperature-inducedMITwith a well-defined 119879

119905does not take place for example in

CGSs for which the equilibrium transition temperature 1198791199050

is higher than 119879119892 while in a high electric field 119879

119905(119864) lt 119879

1199050

might be lower than 119879119892 where 119879

119892is the temperature of the

glass-crystal transition and119864 is the electric field strength [30]Summarizing we have studied the electrical properties

(conductivity temperature dependence and Hall and Seebeckeffects) of the 120573 phase of manganese dioxide obtained bypyrolysis thermal vacuum evaporation and anodic oxida-tion The change of conductivity mechanisms dependingon temperature in a range of 450ndash25K has been shownand the metal-insulator phase transition at low (lt90K)temperatures has been revealed The specific feature of thistransition described in terms of the Mott mechanism isthat the metal phase exists at low temperatures while athigher temperatures the material is a semiconductor withthe hopping conductivity over the mixed valence states ofmanganese ions

The low-temperature switching effect with an NDR andN-shaped current-voltage characteristic associated with thephase transition in manganese dioxide has been found in theMOM two-terminal devices based on anodicMn oxide filmsOn the contrary the devices based on vacuum-depositedfilms have been found to exhibit an S-NDR at room andhigher temperatures which is suggested to be caused byeither the thermistor effect or a high-temperature MIT innonstoichiometric 120573-MnO

2

It should be emphasized that the low-temperature MITin 120573-MnO

2with 119879

119905= 70ndash80K is the inverse Mott transition

which is akin for instance to the transition in V2O3Cr

at 119879119905= 190ndash385K (for chromium dopant concentration in

the range of 05ndash18 at) [51] We thus assume that farther

16 Advances in Condensed Matter Physics

5 10 150Voltage (V)

0

1

2

3

4

5

6

7

8Cu

rren

t (m

A)

(a)ΔV

th(V

)

0

1

2

3

1 2 3 4 5 6 7 80W (at )

(b)

Figure 19 I-V curve (a) of Au-V2minus119910

W119910O5times 119899H2O-Au sandwich structure with119910= 003 and119881th scattering as a function of tungsten admixture

percentage 119910 (b) [104 105]

investigations of the phase transition in manganese dioxidedescribed in this paper are a rather interesting and topicalscientific problem since manganese dioxide can serve as amodel object for studying such inverse metal-insulator phasetransitions

Finally we note that the results presented in this sectionindicate the possibility of application of manganese oxide asa material for thin film sandwich switching devices Deviceswith NDR (N- and S-shaped I-V characteristics) have poten-tial applications in microelectronics as switches memoryelements and microsensors (these issues will be discussedin more detail below in Section 4) Particularly manganeseoxide microswitches [82] can be utilized for implementationof neuristors built with Mott-transition-based memristors[100]

24 Effect of Doping It is only natural that the systemsexhibiting the NDR effects possess a high applied potential inelectronics [2 4 8 18 100 101] yet the stage of EF is a weaklink of chain in the technology process Note that the formingprocess may be brought about by laser irradiation [102] notby applying of electric field In the case of laser treatment(or ldquolaser formingrdquo unlike the above described electricalforming) the parameters of the structures are characterizedby the absence of the scatter that is the I-V characteristics ofall structures are almost identical [103] One more demerit tobe avoided is the scatter in switching parameters (the value of119881th first of all) and their instability during operation In thissubsection we discuss the issues concerning the switchingparameter stabilization by means of doping

In the work [104] we have studied the switching effectin the MOM structures on the basis of W-doped V

2O5-gel

filmsThese structures require preliminary EF similar to thatin anodic oxide films resulting in formation of a conducting

channel within the initial dielectric xerogel filmThe channelconsists of vanadiumdioxide and switching is associatedwiththe insulator-to-metal transition in VO

2 As was shown in

[104 105] for the pure (undoped) V2O5-gel the switching

parameters vary in a wide range because the phenomenonof EF is statistical in nature (like electrical breakdown) andits statistical character shows itself as a spread in the observedthreshold voltages of the ensuing structures that is actuallyat multiple measurements 119881th = ⟨119881th⟩ plusmn Δ119881th

It has been shown [104] that the statistical spread in valuesof the threshold parameters can be minimized by means ofdoping (Figure 19) Unsophisticated reasoning could accountfor this result for pure V

2O5-gel electroforming leads to

formation of VO2with 119879

119905= 340K and each switching

event requires heating up and cooling down from roomtemperature to 119879

119905 this thermal cycling can modify the

peripheral regions of the channel which leads to the changeof the switching threshold voltage On the other hand forthe samples with a high concentration of W the MIT issuppressed [104] and switching is degenerated Betweenthese two outermost points an optimum should exist Asone can see from Figure 19 this optimal value correspondsto 3 at of W that is for V

097W003

O2the switching

parameters are the most stableThe transition temperature ofV097

W003

O2is lower than that for pure vanadium dioxide

and hence the magnitude of the aforesaid thermal cyclingis decreased which results in an increase of stability of theswitching parameters

Next we have studied the effect of doping on switchingin AOFs on Ti [29] These films were obtained in 5 watersolution of citric acid (C

6H8O7) in volt-static regime at 119881

119886

= 20V The samples were doped with aluminium by meansof adding soluble Al-containing substances to the electrolyte

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

Films vol 97 no 2 pp 129ndash143 1982[46] R Collongues La Non-Stoechiometrie Masson Paris France

1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

9 no 5 pp 391ndash396 2014[67] B Sun W Zhao Y Liu and P Chen ldquoResistive switching effect

of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

1990[70] S Mukherjee S Karmakar H Sakata and B K Chaudhuri

ldquoLow-temperature metallic behavior of amorphous MoO3-

TeO2thin filmsrdquo Journal of Applied Physics vol 97 no 12 Article

ID 123707 2005[71] AMottaghizadeh Q Yu P L Lang A Zimmers andH Aubin

ldquoMetal oxide resistive switching evolution of the density ofstates across the metal-insulator transitionrdquo Physical ReviewLetters vol 112 no 6 Article ID 066803 2014

[72] R Xie C T Bui B Varghese et al ldquoAn electrically tunedsolid-state thermalmemory based onmetal-insulator transitionof single-crystalline VO

2nanobeamsrdquo Advanced Functional

Materials vol 21 no 9 pp 1602ndash1607 2011

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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FluidsJournal of

Atomic and Molecular Physics

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

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Superconductivity

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Physics Research International

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Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

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Soft MatterJournal of

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ThermodynamicsJournal of

Advances in Condensed Matter Physics 15

minus15

minus10

minus5

0

5

10

15Cu

rren

t (m

A)

0500 10 15minus10 minus05minus15

Voltage (V)

(a)

minus2

minus1

0

1

2

Curr

ent (

mA

)

10 2minus2 minus1

Voltage (V)

(b)

Figure 18 (a) I-V characteristic of anodic oxide film on manganese at T = 77K (b) I-V characteristic of vacuum-deposited MnO2at 119879 =

293K

In some cases this process might by modified by high-fieldeffects such as Schottky injection impact ionization Poole-Frenkel effect and Zener or avalanche breakdown Notethat unlike a conventional thermistor with an Arrhenius-like conductivity law manganese oxide exhibits a weaker119877(119879) dependence characteristic of the hopping conductivitymechanism which seems to account for the observed weaktemperature dependence of the threshold voltage

An alternative mechanism for the S-type switching effectmay be connected with a possible high-temperature usual(ie not inverse)MIT in somemanganese oxide As is knownEF (see Section 22) leads to the formation of a filament ofhighly conducting material a switching channel Similarlyto what is observed for Mo oxide (Section 231) and otherTMOs (Sections 21 and 22) we suppose that the compositionof this channel differs from the material of the initial oxidefilm since its conductivity noticeably exceeds that of anunformed structure In view of such a plentiful set of phasesand crystal structures in the Mn-O system one can supposethat the channelmight consist of nonstoichiometric120573-MnO

2

some other polymorphic modifications of manganese diox-ide or lower Mn oxides which might undergo a MIT underthe action of either temperature or electric field Howeverthis question obviously requires additional investigation inparticularmeasurements of119877(119879)dependences and switchingproperties at higher temperatures If this assumed high-temperature MIT would occur in for example nonstoichio-metric 120573-MnO

2 one could expect observation of double-

NDR I-V characteristics in such samples at low temperaturesanalogously to those in V

2O3Cr (Figure 9) where this effect

is due to the MITs [29] with the only difference being thatin the case of MnO

2this curve should be N-S-shaped (unlike

the S-N-shaped one in Figure 9) since in chromium-dopedvanadium sesquioxide the inverse MIT is high-temperatureas opposed to MnO

2which as we discussed above (see

Figure 17) exhibits the inverse MIT at low temperaturesNote however that the discussed high-temperature MIT

in 120573-MnO2minus119910

may be unobservable under the temperature

change in equilibrium conditions but displays itself onlyunder the applied electric field as the S-type electricalswitching effect because the transition temperature is closeto or higher than the temperature of MnO

2decomposition

(723K) Such a nonequilibrium transition occurs at switchingin those materials where the usual temperature-inducedMITwith a well-defined 119879

119905does not take place for example in

CGSs for which the equilibrium transition temperature 1198791199050

is higher than 119879119892 while in a high electric field 119879

119905(119864) lt 119879

1199050

might be lower than 119879119892 where 119879

119892is the temperature of the

glass-crystal transition and119864 is the electric field strength [30]Summarizing we have studied the electrical properties

(conductivity temperature dependence and Hall and Seebeckeffects) of the 120573 phase of manganese dioxide obtained bypyrolysis thermal vacuum evaporation and anodic oxida-tion The change of conductivity mechanisms dependingon temperature in a range of 450ndash25K has been shownand the metal-insulator phase transition at low (lt90K)temperatures has been revealed The specific feature of thistransition described in terms of the Mott mechanism isthat the metal phase exists at low temperatures while athigher temperatures the material is a semiconductor withthe hopping conductivity over the mixed valence states ofmanganese ions

The low-temperature switching effect with an NDR andN-shaped current-voltage characteristic associated with thephase transition in manganese dioxide has been found in theMOM two-terminal devices based on anodicMn oxide filmsOn the contrary the devices based on vacuum-depositedfilms have been found to exhibit an S-NDR at room andhigher temperatures which is suggested to be caused byeither the thermistor effect or a high-temperature MIT innonstoichiometric 120573-MnO

2

It should be emphasized that the low-temperature MITin 120573-MnO

2with 119879

119905= 70ndash80K is the inverse Mott transition

which is akin for instance to the transition in V2O3Cr

at 119879119905= 190ndash385K (for chromium dopant concentration in

the range of 05ndash18 at) [51] We thus assume that farther

16 Advances in Condensed Matter Physics

5 10 150Voltage (V)

0

1

2

3

4

5

6

7

8Cu

rren

t (m

A)

(a)ΔV

th(V

)

0

1

2

3

1 2 3 4 5 6 7 80W (at )

(b)

Figure 19 I-V curve (a) of Au-V2minus119910

W119910O5times 119899H2O-Au sandwich structure with119910= 003 and119881th scattering as a function of tungsten admixture

percentage 119910 (b) [104 105]

investigations of the phase transition in manganese dioxidedescribed in this paper are a rather interesting and topicalscientific problem since manganese dioxide can serve as amodel object for studying such inverse metal-insulator phasetransitions

Finally we note that the results presented in this sectionindicate the possibility of application of manganese oxide asa material for thin film sandwich switching devices Deviceswith NDR (N- and S-shaped I-V characteristics) have poten-tial applications in microelectronics as switches memoryelements and microsensors (these issues will be discussedin more detail below in Section 4) Particularly manganeseoxide microswitches [82] can be utilized for implementationof neuristors built with Mott-transition-based memristors[100]

24 Effect of Doping It is only natural that the systemsexhibiting the NDR effects possess a high applied potential inelectronics [2 4 8 18 100 101] yet the stage of EF is a weaklink of chain in the technology process Note that the formingprocess may be brought about by laser irradiation [102] notby applying of electric field In the case of laser treatment(or ldquolaser formingrdquo unlike the above described electricalforming) the parameters of the structures are characterizedby the absence of the scatter that is the I-V characteristics ofall structures are almost identical [103] One more demerit tobe avoided is the scatter in switching parameters (the value of119881th first of all) and their instability during operation In thissubsection we discuss the issues concerning the switchingparameter stabilization by means of doping

In the work [104] we have studied the switching effectin the MOM structures on the basis of W-doped V

2O5-gel

filmsThese structures require preliminary EF similar to thatin anodic oxide films resulting in formation of a conducting

channel within the initial dielectric xerogel filmThe channelconsists of vanadiumdioxide and switching is associatedwiththe insulator-to-metal transition in VO

2 As was shown in

[104 105] for the pure (undoped) V2O5-gel the switching

parameters vary in a wide range because the phenomenonof EF is statistical in nature (like electrical breakdown) andits statistical character shows itself as a spread in the observedthreshold voltages of the ensuing structures that is actuallyat multiple measurements 119881th = ⟨119881th⟩ plusmn Δ119881th

It has been shown [104] that the statistical spread in valuesof the threshold parameters can be minimized by means ofdoping (Figure 19) Unsophisticated reasoning could accountfor this result for pure V

2O5-gel electroforming leads to

formation of VO2with 119879

119905= 340K and each switching

event requires heating up and cooling down from roomtemperature to 119879

119905 this thermal cycling can modify the

peripheral regions of the channel which leads to the changeof the switching threshold voltage On the other hand forthe samples with a high concentration of W the MIT issuppressed [104] and switching is degenerated Betweenthese two outermost points an optimum should exist Asone can see from Figure 19 this optimal value correspondsto 3 at of W that is for V

097W003

O2the switching

parameters are the most stableThe transition temperature ofV097

W003

O2is lower than that for pure vanadium dioxide

and hence the magnitude of the aforesaid thermal cyclingis decreased which results in an increase of stability of theswitching parameters

Next we have studied the effect of doping on switchingin AOFs on Ti [29] These films were obtained in 5 watersolution of citric acid (C

6H8O7) in volt-static regime at 119881

119886

= 20V The samples were doped with aluminium by meansof adding soluble Al-containing substances to the electrolyte

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

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1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

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of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

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ldquoLow-temperature metallic behavior of amorphous MoO3-

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wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

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2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

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2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

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[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

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[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

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[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

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PhotonicsJournal of

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Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

16 Advances in Condensed Matter Physics

5 10 150Voltage (V)

0

1

2

3

4

5

6

7

8Cu

rren

t (m

A)

(a)ΔV

th(V

)

0

1

2

3

1 2 3 4 5 6 7 80W (at )

(b)

Figure 19 I-V curve (a) of Au-V2minus119910

W119910O5times 119899H2O-Au sandwich structure with119910= 003 and119881th scattering as a function of tungsten admixture

percentage 119910 (b) [104 105]

investigations of the phase transition in manganese dioxidedescribed in this paper are a rather interesting and topicalscientific problem since manganese dioxide can serve as amodel object for studying such inverse metal-insulator phasetransitions

Finally we note that the results presented in this sectionindicate the possibility of application of manganese oxide asa material for thin film sandwich switching devices Deviceswith NDR (N- and S-shaped I-V characteristics) have poten-tial applications in microelectronics as switches memoryelements and microsensors (these issues will be discussedin more detail below in Section 4) Particularly manganeseoxide microswitches [82] can be utilized for implementationof neuristors built with Mott-transition-based memristors[100]

24 Effect of Doping It is only natural that the systemsexhibiting the NDR effects possess a high applied potential inelectronics [2 4 8 18 100 101] yet the stage of EF is a weaklink of chain in the technology process Note that the formingprocess may be brought about by laser irradiation [102] notby applying of electric field In the case of laser treatment(or ldquolaser formingrdquo unlike the above described electricalforming) the parameters of the structures are characterizedby the absence of the scatter that is the I-V characteristics ofall structures are almost identical [103] One more demerit tobe avoided is the scatter in switching parameters (the value of119881th first of all) and their instability during operation In thissubsection we discuss the issues concerning the switchingparameter stabilization by means of doping

In the work [104] we have studied the switching effectin the MOM structures on the basis of W-doped V

2O5-gel

filmsThese structures require preliminary EF similar to thatin anodic oxide films resulting in formation of a conducting

channel within the initial dielectric xerogel filmThe channelconsists of vanadiumdioxide and switching is associatedwiththe insulator-to-metal transition in VO

2 As was shown in

[104 105] for the pure (undoped) V2O5-gel the switching

parameters vary in a wide range because the phenomenonof EF is statistical in nature (like electrical breakdown) andits statistical character shows itself as a spread in the observedthreshold voltages of the ensuing structures that is actuallyat multiple measurements 119881th = ⟨119881th⟩ plusmn Δ119881th

It has been shown [104] that the statistical spread in valuesof the threshold parameters can be minimized by means ofdoping (Figure 19) Unsophisticated reasoning could accountfor this result for pure V

2O5-gel electroforming leads to

formation of VO2with 119879

119905= 340K and each switching

event requires heating up and cooling down from roomtemperature to 119879

119905 this thermal cycling can modify the

peripheral regions of the channel which leads to the changeof the switching threshold voltage On the other hand forthe samples with a high concentration of W the MIT issuppressed [104] and switching is degenerated Betweenthese two outermost points an optimum should exist Asone can see from Figure 19 this optimal value correspondsto 3 at of W that is for V

097W003

O2the switching

parameters are the most stableThe transition temperature ofV097

W003

O2is lower than that for pure vanadium dioxide

and hence the magnitude of the aforesaid thermal cyclingis decreased which results in an increase of stability of theswitching parameters

Next we have studied the effect of doping on switchingin AOFs on Ti [29] These films were obtained in 5 watersolution of citric acid (C

6H8O7) in volt-static regime at 119881

119886

= 20V The samples were doped with aluminium by meansof adding soluble Al-containing substances to the electrolyte

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

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1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

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of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

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ldquoLow-temperature metallic behavior of amorphous MoO3-

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Materials vol 21 no 9 pp 1602ndash1607 2011

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[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

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wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

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2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

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[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

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AerodynamicsJournal of

Volume 2014

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PhotonicsJournal of

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Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

Advances in Condensed Matter Physics 17

minus6

minus4

minus2

0

2

4

6

8

Curr

ent (

mA

)

minus20 minus15 minus5minus10 5 10 15 200Voltage (V)

Figure 20 I-V characteristic of Al-doped TiOx [29]

For the insertion of Al3+ ions into the AOF the process ofdoping was carried out at cathodic polarization

For the samples doped with Al we encountered theeffect of stabilization of the switching characteristics Thepoint is that usually the I-V curves might spontaneouslyslightly change their parameters with time during operationand moreover after several thousand switching cycles theS-shaped I-V curve completely degrades and switching nolonger occurs The above described behaviour is typical ofthe pure nondoped samples while for the structures basedonAOFTiO

2Al the behaviour is radically different For these

samples threshold voltage is of the order of 10V (Figure 20)and current-voltage characteristics demonstrate stability andlong-term reproducible operation (up to 1010 cycles withouta noticeable change in the threshold parameters) It can beassumed that the stabilization of the switching parameters iscaused by a change in the energy-band structure of titaniumdioxide as a result of doping it with aluminium [29 106]

3 Switching Mechanism

The mechanism of threshold switching has for a long timebeen a matter of especial concern and the principal issue iswhether the mechanism is primarily thermal or electronicThere have also been several works treating the switchingeffect as a metal-insulator transition occurring in electricfield (see eg [30] and references therein) Applicationof an electric field to a Mott insulator taking also intoaccount the current flow (since we consider the switchingeffect not a stationary field effect) will result in both thethermal generation of additional carriers due to the Jouleheat and the field-induced generation The latter is due tothe autoionization caused by the Coulomb barrier loweringa phenomenon analogous to the Poole-Frenkel (P-F) effectWhen the total concentration of free carriers reaches thevalue of 119899 = 119899

119888 the transition into the metal state (ie

switching of the structure into the ON state) occurs In amaterial with the temperature-induced MIT this switching(in a relatively low field) occurs just due to the heating ofthe switching channel up to 119879 = 119879

119905according to the critical

temperature model (3) The above mentioned value of 119899119888is

determined by the Mott criterion

119886119867119899119888

13asymp 025 (5)

where 119886119867= 120576ℏ2119898lowast1198902 is the effective Bohr radius 120576 is the static

dielectric permittivity and 119898lowast is the effective mass of charge

carriersIn the paper [30] it has been reported on the switching

mechanism in vanadium dioxide This mechanism is shownto be based on the electronically induced Mott insulator-to-metal transition occurring in conditions of the nonequi-librium carrier density excess in the applied electric fieldThe model takes into account the dependence of the carrierdensity on electric field (see (6) below) as well as thedependence of the critical electric field 119864

119888on carrier density

(7) with fitting parameter 120574For switching in VO

2 the main mechanism for the field-

induced carrier density increase is the P-F effect

119899 = 1198730exp(minus

119882 minus 120573radic119864

119896119879

) (6)

where 1198730is a constant independent of the field and only

slightly dependent on temperature 119882 is the conductivityactivation energy and 120573 = (1198903120587120576120576

119900)12 is the P-F constant

Next the dependence of 119864119888on electron density has been

supposed to be

119864119888= 1198640(1 minus

119899

119899119888

)

120574

(7)

with 119899119888being the Mott critical electron density

While the former of the two postulates (6) has afterwardsbeen repeatedly confirmed (see eg [107ndash113]) the latter israther an ambiguous assumption introduced to adjust theexperimental data on the 119899

119898values with the theory (119899

119898

is the maximum electron density in the switching channelat 119864 = 119864th where 119864th is the switching threshold voltage[30]) Actually (7) has been somehow vindicated from theviewpoint of the scaling hypothesis inherent in a phasetransition metal-insulator transition included [114]

We remind the reader that the dependence expressedby (7) was introduced in [30 114] in order that the 119899

119898(119879)

behaviour might be comprehended The data on the 119899119898

temperature dependence (Figure 21 curve 1) were obtainedon the assumption of a temperature-independent carriermobility 120583 and the problem of 119899

119898reduction at lower tem-

peratures was a stumbling-block since for theMott transitionthe value of 119899

119888should be a constant Note that at 119879 gt 200K

119899119898

asymp 3 sdot 1018 cmminus3 = 119899

119888for VO

2[30]

Now in the light of some recent data on the 120583(119879)

dependence of vanadium dioxide [115ndash117] the problemoutlined above could be revisited It has been shown [115] thatthe conductivity of VO

2can be written as

120590 sim

1

11987932

exp(minus

119864119886

119896119861119879

+

119896119861119879

120576

) (8)

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

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1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

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Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

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switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

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03MoO3rdquo Solid State Communications

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2CCNT

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Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

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2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

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[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

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1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

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3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

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[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

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2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

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24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

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[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

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[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

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2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

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GravityJournal of

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AstrophysicsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

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PhotonicsJournal of

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Biophysics

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ThermodynamicsJournal of

18 Advances in Condensed Matter PhysicsEl

ectro

n de

nsity

(1017

001

01

1

10

100

50

Curve 2Curve 1

100 150 200 250 3000Temperature (K)

cmminus3)

Figure 21 Maximum electron density in the switching channelas a function of ambient temperature in fact 119899

119898depends on the

threshold electric field 119864th and the latter in turn depends on 1198790

The calculations aremade for the cases of 120583= const (curve 1) and 120583 sim

119879119898

minus1 exp(119896119861119879119898120576) (curve 2)Here119879

119898( = 1198790) is the temperature in the

channel centre calculated on the basis of mathematical simulating[30]

where 119864119886is the conductivity activation energy and 120576 is a

constant of the small polaron hopping conduction theorywhich takes into account the influence of thermal latticevibrations onto the resonance integral [118] This behaviourof 120590(119879) has first been shown to be valid for VO

2single

crystals [115] and then for vanadium dioxide switchingchannels [116] and thin films [117] as well It is pertinentto note here that similar results have also been obtainedfor some other vanadium oxides exhibiting metal-insulatortransitions namely for V

2O3[119] V

4O7[120] V

3O5[121]

and V6O11[122]

In (8) the first term in the exponent is responsible for theband conduction whereas the second one characterizes thetemperature dependence of the hopping mobility Thereforethe data on 119899

119898(119879) (Figure 21 curve 1) should be corrected by

means of division by a factor corresponding to the mobilitytemperature dependence 120583(119879) sim (1119879) exp(119896

119861119879120576) note that

the preexponential factor for mobility is proportional to Tminus1unlike that for conductivity in (8) where it is proportional toTminus32 [118] These corrected values of 119899

119898 for 119896

119861120576 = 035 Kminus1

[115] are presented by curve 2 in Figure 21 One can see thatwithin an order of magnitude these values correspond to theMott critical concentration (dotted line in Figure 21)

In conclusion we emphasize that the present amendmentdoes not call into question the results presented in [30] butmerely refines upon them In particular it does not abolishthe hypothesis concerning the scaling of 119864

119888which has been

put forward in [30 114] but parameter 120574 can change forexample it can decrease down to almost zero Thus like inthe work [30] we can state that the switching mechanismis based on the electronically induced Mott metal-insulator

transition taking into consideration the dependence of thecarrier density on electric field (6) and the parametricaldependence of the critical field on current density (7)

A more detailed analysis of the results would have beenpossible on the basis of experimental data on the vanadiumdioxide mobility temperature dependence In the recentstudies [123 124] the values of 120583 sim 01ndash02 cm2 Vminus1sminus1 (atroom temperature) have been obtained which is really closeto an estimate 120583 = 05 cm2Vminus1sminus1 used for calculations in[30] However the measurements in these works have beenperformed in a limited temperature range (in the vicinity ofthe transition) where the mobility only slightly depends ontemperature [123 124]

In recent literature much attention is paid to the problemof relative contributions of thermal and electronic effects inswitching mainly in connection with the development of aldquoMott-transition FETrdquo [125] Particularly the author of [126]compares FETs based on strongly correlated TMOs and thoseon SiThe devices on the basis of SmNiO

3 VO2 and LaAlO

3-

SrTiO3are examined As for the vanadium dioxide it is

stated with the reference to the work [127] that ldquoin VO2

the transition is in large part caused by micrometer-scaleheating by the applied electric fieldrdquo It should be stressedhowever that thermal effects do take place at switching (notat the field effect) [30] and it has always been known thatthe voltage-induced MIT in macroscopic VO

2crystals and

planar micron-size film structures occurs due to the Jouleheating effect [128 129] Note that a ldquomicrometer-scalerdquo sizeis surely macroscopic with respect to nanoscale dimensionsTherefore the results of [127] do not contradict the ideaof the field-controlled MIT in VO

2 In summary one can

arrive at a conclusion that the switching mechanism involvesa combination of both thermal and electronic effects andtheir relative contributions depend on device dimensionsand ambient temperature [30 113 130] For example at arelatively high temperature close to 119879

119905 the mechanism is

merely thermal and switching is described by the criticaltemperature model (3) On the other hand in some cases(nanoscale dimensions and low temperatures) switchingmight be completely electronically induced This conclusionis supported by experiments on electric field-stimulatedMotttransition in VO

2[125 131ndash133] Also separating electric field

and thermal effects in vanadium oxide nanobeams has beenrecently demonstrated in [134]

In addition valuable information about the contributionsof electronic and thermal effects in switching might beobtained when investigating the switching delay time [131]For example electrical switching dynamics of VO

2in the RF

range has been studied in the works [135 136] Particularlytwo distinguishable time scales for electrical switching havebeen observed [135] one in accordance with Joule heatingand one much faster which may suggest contribution of theelectronic Mott MIT-based effects

Finally we note that electronically induced switchingassociated with the MIT has been reported for a number ofother materials (not only for VO

2) for example in a family

of Mott insulators AM4X8(A = Ga Ge M = V Nb Ta X = S

Se) [137 138] SmNiO3[139] 120573-PbxV2O5 [140] and H-doped

NbO2[141]

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

Films vol 97 no 2 pp 129ndash143 1982[46] R Collongues La Non-Stoechiometrie Masson Paris France

1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

9 no 5 pp 391ndash396 2014[67] B Sun W Zhao Y Liu and P Chen ldquoResistive switching effect

of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

1990[70] S Mukherjee S Karmakar H Sakata and B K Chaudhuri

ldquoLow-temperature metallic behavior of amorphous MoO3-

TeO2thin filmsrdquo Journal of Applied Physics vol 97 no 12 Article

ID 123707 2005[71] AMottaghizadeh Q Yu P L Lang A Zimmers andH Aubin

ldquoMetal oxide resistive switching evolution of the density ofstates across the metal-insulator transitionrdquo Physical ReviewLetters vol 112 no 6 Article ID 066803 2014

[72] R Xie C T Bui B Varghese et al ldquoAn electrically tunedsolid-state thermalmemory based onmetal-insulator transitionof single-crystalline VO

2nanobeamsrdquo Advanced Functional

Materials vol 21 no 9 pp 1602ndash1607 2011

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

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FluidsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

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AstronomyAdvances in

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Superconductivity

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Physics Research International

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Solid State PhysicsJournal of

 Computational  Methods in Physics

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Soft MatterJournal of

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PhotonicsJournal of

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ThermodynamicsJournal of

Advances in Condensed Matter Physics 19

C S-diode

V0

RL

(a)

V

I

V0RL

V0VthV998400

(b)

V

t

Vth

V998400

Tr

(c)

Figure 22 Relaxation oscillations (a) electrical circuit (b) schematic I-V curve and load line and (c) output signal oscillogram

4 Potential Applications of Switching inTransition Metal Oxides

Devices with negative differential resistance (S- or N-shapedI-V characteristics) have potential applications in electronicsas switches memory elements and microsensors [142] Onemore recently emerging field of application is connected withneurochips and neural networks on the basis of memris-tors [125] including those made of TMO-based switchingelements Particularly a NbO

2-based switching device is

considered in [100] in this regardIn a scheme with an S-NDR device at a high enough dc

bias (1198810) relaxation oscillations are observed if the load line

intersects with the I-V curve at a unique point in the negativeresistance region (Figure 22) [142] The frequency of thisoscillation (119891

119903= 1119879

119903) depends on the threshold parameters

and consequently it depends on external parameters forexample on temperature and pressure Sensors with thefrequency output have a number of evident advantages highsensitivity and stability convenience of processing of a signalcapability of remote measurements and low noise suscepti-bilityThe119891

119903(119879)-output temperature sensor based onVO

2has

been first proposed in [143] and then developed in [144]Electrical self-oscillations across out-of-plane threshold

switches based on VO2have also been recently studied

in the article [145] The authors of this work note thatbeside integration as inverters and oscillators in high-speed circuits a prospective potential application may bethe parallel production of periodic signals in large scaleintegrated circuits analogous to the action potentials inneural architectures Note that in the work [100] a MIT-based switching devise has been proposed to be used asa quasistatic neuristor synapse model On the other handdynamic oscillation-basedmodels are also widely explored inthe field of neuromorphic simulation [146ndash149] Particularlyin the works [148 149] the authors present the realization ofcoupled and scalable relaxation oscillators utilizing the MITin metal-insulator-metal transition in VO

2and demonstrate

the potential use of such a system in pattern recognition asone possible computational model based on a non-Booleanneuromorphic computing paradigm Further simulation ofcomputing with networks of synchronous oscillators basedon MIT-devices has been recently presented in [150] Notethat thermally induced oscillations [151 152] resistance noise[153] negative capacitance [154] and some other possibleconcomitant phenomena should apparently be taken intoaccount when constructing neuromorphic circuits on thebasis of switching devices with a MIT-induced NDR

The development of the ideas expressed in [100] goeson the way of both analysis of the various schemes [155]and mathematical models [156] for constructing such aldquomemristor-based neuristorrdquo as well as offering a varietyof materials (mainly TMOs) to create a memristor In viewof the above-said the following research area seems to bepromising namely investigate the possibility of applying theswitching effect in structures based on VO

2(and possibly

other TMOs) to simulate the function of the neuristorsynapse Some of these materials and devices for adaptiveoxide electronics have been recently reviewed in [157] Addi-tional capabilities are provided by a combination of memoryand MIT-induced switching in one device on the basis ofvanadium dioxide [158] see Figure 23 It should be noted thatbipolar memory switching in disordered vanadium oxide hasearlier been reported in the work [159]

To implement these ideas one can use a memristivedevice based on niobium oxide NbO

2[100] As was discussed

above in Section 2 Mott insulators such as NbO2have

long been known to exhibit current-controlled NDR Thisphenomenon is caused by a reversible metal-insulator phasetransition However due to relatively high transition temper-ature (1070K [24]) niobium dioxide consumes a significantamount of energy which evolved as heat Therefore it is notyet possible to arrange a plurality of available neuristors withhigh density on a single chip Vanadium dioxide on the otherhand with the MIT temperature of only 340K seems to bea more attractive material for this application Among other

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

[1] S R Ovshinsky ldquoReversible electrical switching phenomena indisordered structuresrdquo Physical Review Letters vol 21 no 20pp 1450ndash1453 1968

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

Films vol 97 no 2 pp 129ndash143 1982[46] R Collongues La Non-Stoechiometrie Masson Paris France

1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

9 no 5 pp 391ndash396 2014[67] B Sun W Zhao Y Liu and P Chen ldquoResistive switching effect

of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

1990[70] S Mukherjee S Karmakar H Sakata and B K Chaudhuri

ldquoLow-temperature metallic behavior of amorphous MoO3-

TeO2thin filmsrdquo Journal of Applied Physics vol 97 no 12 Article

ID 123707 2005[71] AMottaghizadeh Q Yu P L Lang A Zimmers andH Aubin

ldquoMetal oxide resistive switching evolution of the density ofstates across the metal-insulator transitionrdquo Physical ReviewLetters vol 112 no 6 Article ID 066803 2014

[72] R Xie C T Bui B Varghese et al ldquoAn electrically tunedsolid-state thermalmemory based onmetal-insulator transitionof single-crystalline VO

2nanobeamsrdquo Advanced Functional

Materials vol 21 no 9 pp 1602ndash1607 2011

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

20 Advances in Condensed Matter Physics

00

III

II I

III

3 60 9minus9minus12 minus3minus6

V (V)

V (V)

10minus15

10minus13

10minus11

10minus9

10minus7

10minus5

10minus3

I (A

)

minus24minus48minus72minus96minus120

times10minus4

00

10

20

30

I (A

)

ΔRs

Figure 23 I-V characteristic of VO2on p-Si after final electroform-

ing demonstrating both MIT-induced threshold (I II) and ion-diffusion-based memory (III) switching (inset the same curve atnegative polarity in linear coordinates)

materials for neuromorphic memristive circuits and adaptivesystems one can mention also for example LixCoO2 [160]MoOxMoS

2 and WOxWS

2heterostructures [161] and

some other binary and complex TMOs [157] In conclusionwe would like to mention also a recent work discussinggeneral aspects of neuromorphic networks based on metal-oxide memristors [162] On the other hand dynamicaloscillator-based networks are reviewed in [163]

Other possible applications of the switching effect inVO2include for example microwave switching devices [135

136 164] thermally and optically biased memristive switches[165] electrolyte gated THz photonic devices [166] and thin-film varistors [167] (see also some examples in reviews [125157 168 169]) In addition switching structures particularlythose based on Nb and Ti oxides can be used as accesselements (selective devices) in high density cross-point typeReRAMs [170 171]

5 Conclusion

Nonlinear electric conduction in strongly correlated elec-tron systems exhibiting metal-insulator phase transitions ischaracterized by negative differential resistivity [2 172] Thetheoretical difficulties in the study ofNDRare connectedwiththe fact that the system is far from equilibrium owing to thedissipation caused by the finite current and nonperturbativeanalysis is necessary if the NDR is associated with thethreshold property such as the metal-insulator transition[172]

In this review we have confined our attention mostly toS-type threshold switching (S-NDR) in oxides of transitionmetals Electrical instabilities with voltage-controlled (N-type) NDR and various memory effects have also beenreported by many researchers both in oxides and in othermaterials However ldquopurerdquo threshold switching with an S-shaped 119868(119881) curve aside from chalcogenide semiconductorsis characteristic of a number of transition metal oxides Thisis closely linked to the electronic structure of the transition

metals A set of valence states associated with the existenceof unfilled 119889-shells in these atoms leads to formation ofseveral oxide phases with different properties [23 25 26 173]ranging frommetallic to insulatingThis accounts for the easeof chemical transformations during electroforming On theother hand it is specifically the behaviour of 119889-electrons inthe compounds of transitionmetals that is responsible for theunique properties of these materials causing strong electron-electron and electron-phonon correlations which play animportant role in the mechanism of MITs

The results presented in Sections 2 and 3 of this reviewindicate that current instabilities with the S- or N-NDRexhibit several common features In particular for each of theinvestigated materials there is a certain fixed temperature 119879

0

above which switching disappears At 119879 lt 1198790 the threshold

voltage decreases as the temperature rises tending to zeroat 119879 rarr 119879

0 Comparison of these temperatures with the

temperatures of MIT for some compounds (eg 119879119905= 340K

for VO2 etc) shows that the switching effect is associated

with the insulator-to-metal transition in an electric field Thechannels consisting of these lower oxides are formed ininitial films during preliminary electroforming

Note that formation of Ti lower oxides (Ti119899O2119899minus1

Magneliphases) during EF has also been reported in a number ofworks on memory switching in titanium oxide systems [174175]The same is true for the Ta-O systemwhere TaOx subox-ides have been reported [49 176] Moreover TaO

2exhibiting

a Peierls MIT has been recently reported to exist [177]Since electronic devices that exhibit NDR are useful in

electric circuits the understanding of NDR is also importantfrom the viewpoint of industrial applications [172] As wehave shown in Section 4 above vanadium dioxide appearsto be the most convenient material for various applicationsdue to the fact that its 119879

119905is close to room temperature

Basically the roster of materials exhibitingMITs with sharplydiscontinuous switching of electrical conductivity close toroom temperature remains rather sparse [140] Apart fromVO2 useful devices in this sense might turn out to be

those based on manganese and molybdenum oxides (seeSection 23) as well as 120573-PbxV2O5 (119909 asymp 033) [140] andhydrogen-treated NbO

2with reduced 119879

119905[141]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the RF Ministry of Educationand Science as a base part of state Program no 2014154 inthe scientific field Project no 1426 and State Program no37572014K

References

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Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

Films vol 97 no 2 pp 129ndash143 1982[46] R Collongues La Non-Stoechiometrie Masson Paris France

1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

9 no 5 pp 391ndash396 2014[67] B Sun W Zhao Y Liu and P Chen ldquoResistive switching effect

of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

1990[70] S Mukherjee S Karmakar H Sakata and B K Chaudhuri

ldquoLow-temperature metallic behavior of amorphous MoO3-

TeO2thin filmsrdquo Journal of Applied Physics vol 97 no 12 Article

ID 123707 2005[71] AMottaghizadeh Q Yu P L Lang A Zimmers andH Aubin

ldquoMetal oxide resistive switching evolution of the density ofstates across the metal-insulator transitionrdquo Physical ReviewLetters vol 112 no 6 Article ID 066803 2014

[72] R Xie C T Bui B Varghese et al ldquoAn electrically tunedsolid-state thermalmemory based onmetal-insulator transitionof single-crystalline VO

2nanobeamsrdquo Advanced Functional

Materials vol 21 no 9 pp 1602ndash1607 2011

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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FluidsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

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Superconductivity

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Physics Research International

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Solid State PhysicsJournal of

 Computational  Methods in Physics

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

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PhotonicsJournal of

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Journal of

Biophysics

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ThermodynamicsJournal of

Advances in Condensed Matter Physics 21

[2] E Scholl Nonequilibrium Phase Transitions in SemiconductorsSelf-Organization Induced by Generation and RecombinationProcesses Springer Berlin Germany 1987

[3] B T Kolomiets ldquoVitreous semiconductorsrdquo Physica StatusSolidi (B) vol 7 no 2 pp 359ndash372 1964

[4] A Pergament G Stefanovich A Velichko V PutrolainenT Kundozerova and T Stefanovich ldquoNovel hypostasis of oldmaterials in oxide electronics metal oxides for resistive randomaccess memory applicationsrdquo Journal of Characterization andDevelopment of Novel Materials vol 4 no 2 pp 83ndash110 2011

[5] G W Burr M J Breitwisch M Franceschini et al ldquoPhasechange memory technologyrdquo Journal of Vacuum Science andTechnology B vol 28 no 2 pp 223ndash262 2010

[6] G Dearnaley A M Stoneham and D V Morgan ldquoElectricalphenomena in amorphous oxide filmsrdquo Reports on Progress inPhysics vol 33 no 3 pp 1129ndash1191 1970

[7] K L Chopra ldquoAvalanche-induced negative resistance in thinoxide filmsrdquo Journal of Applied Physics vol 36 no 1 pp 184ndash187 1965

[8] D P Oxley ldquoElectroforming switching and memory effects inoxide thin filmsrdquoElectroComponent Science andTechnology vol3 no 4 pp 217ndash224 1977

[9] Y Zhu and M Li ldquoBipolar resistive switching characteristicof epitaxial NiO thin film on Nb-doped SrTiO

3substraterdquo

Advances in Condensed Matter Physics vol 2012 Article ID364376 8 pages 2012

[10] M-J Lee S I Kim C B Lee et al ldquoLow-temperature-grown transition metal oxide based storage materials and oxidetransistors for high-density non-volatile memoryrdquo AdvancedFunctional Materials vol 19 no 10 pp 1587ndash1593 2009

[11] B Lalevic N Fuschillo and W Slusark Jr ldquoSwitching in Nb-Nb2O5-Nb devices with doped Nb

2O5amorphous filmsrdquo IEEE

Transactions on Electron Devices vol ED-22 no 10 pp 965ndash967 1975

[12] G C Vezzoli ldquoRecovery curve for threshold-switching NbO2rdquo

Journal of Applied Physics vol 50 no 10 pp 6390ndash6395 1979[13] S H Shin T Halpern and P M Raccah ldquoHigh-speed high-

current field switching of NbO2rdquo Journal of Applied Physics vol

48 no 7 article 3150 pp 3150ndash3153 1977[14] G C Vezzoli P J Walsh and M A Shoga ldquoInterpretation of

recent transient on-state data in thin chalcogenide glass andNbO2threshold switching materialrdquo Philosophical Magazine B

vol 63 no 3 pp 739ndash755 1991[15] G Taylor and B Lalevic ldquoRF relaxation oscillations in polycrys-

talline TiO2thin filmsrdquo Solid State Electronics vol 19 no 8 pp

669ndash674 1976[16] B P Zakharchenya V P Malinenko G B Stefanovich M Y

Terman and F A Chudnovskii ldquoSwitching in MOM structuresbased on vanadium dioxiderdquo Soviet Technical Physics Lettersvol 11 pp 108ndash111 1985

[17] R CMorris J E Christopher and R V Coleman ldquoConductionphenomena in thin layers of iron oxiderdquo Physical Review vol184 no 2 pp 565ndash573 1969

[18] A E Owen P G Le Comber J Hajto M J Rose and A JSnell ldquoSwitching in amorphous devicesrdquo International Journalof Electronics vol 73 no 5 pp 897ndash906 1992

[19] A K Ray and C A Hogarth ldquoA critical review of theobserved electrical properties ofMIM devices showing VCNRrdquoInternational Journal of Electronics vol 57 no 1 pp 1ndash78 1984

[20] D V Morgan M J Howes R D Pollard and D G P WatersldquoElectroforming and dielectric breakdown in thin aluminiumoxide filmsrdquoThin Solid Films vol 15 no 1 pp 123ndash131 1973

[21] S Hirose H Niimi K Kageyama A Ando H Ieki andT Omata ldquoImpact of the electrical forming process on theresistance switching behaviors in lanthanum-doped strontiumtitanate ceramic chip devicesrdquo Japanese Journal of AppliedPhysics vol 52 no 4 Article ID 045802 2013

[22] A L Pergament G B Stefanovich A A Velichko and S DKhanin ldquoElectronic switching and metal-insulator transitionsin compounds of transition metalsrdquo in Condensed Matter at theLeading Edge pp 1ndash67 Nova Science Publishers 2006

[23] P A Cox Transition Metal Oxides An Introduction to TheirElectronic Structure and Properties Clarendon Press OxfordUK 1992

[24] N F Mott Metal-Insulator Transition Taylor amp Francis Lon-don UK 2nd edition 1990

[25] S V Kalinin and N A Spaldin ldquoFunctional ion defects intransition metal oxidesrdquo Science vol 341 no 6148 pp 858ndash8592013

[26] S-W Cheong ldquoTransition metal oxides the exciting world oforbitalsrdquo Nature Materials vol 6 no 12 pp 927ndash928 2007

[27] A L Pergament G B Stefanovich and F A ChudnovskiildquoMetal-semiconductor phase transition and switching effect inoxides of transitionmetalsrdquo Physics of the Solid State vol 36 no10 pp 1590ndash1597 1994

[28] F A Chudnovskii L L Odynets A L Pergament and GB Stefanovich ldquoElectroforming and switching in oxides oftransition metals the role of metal-insulator transition in theswitchingmechanismrdquo Journal of Solid State Chemistry vol 122no 1 pp 95ndash99 1996

[29] V P Malinenko A L Pergament O V Spirin and V INikulshin ldquoThreshold and memory switching in oxides ofmolybdenum niobium tungsten and titaniumrdquo Journal onSelected Topics in Nano Electronics and Computing vol 2 no2 pp 45ndash49 2014

[30] A L Pergament P P Boriskov AAVelichko andNAKuldinldquoSwitching effect and the metal-insulator transition in electricfieldrdquo Journal of Physics and Chemistry of Solids vol 71 no 6pp 874ndash879 2010

[31] A L Pergament V P Malinenko O I Tulubaeva and LA Aleshina ldquoElectroforming and switching effects in yttriumoxiderdquo Physica Status Solidi A vol 201 no 7 pp 1543ndash15502004

[32] C J DellrsquoOka D L Pulfrey and L Young ldquoAnodic oxide filmsrdquoin Physics of Thin Films M H Francombe and R W HoffmanEds vol 6 pp 1ndash79 Academic Press New York NY USA 1971

[33] G B Stefanovich A L Pergament A A Velichko and L AStefanovich ldquoAnodic oxidation of vanadium and properties ofvanadiumoxide filmsrdquo Journal of Physics CondensedMatter vol16 no 23 pp 4013ndash4024 2004

[34] DG LoveringMolten Salt Technology Springer NewYorkNYUSA 1982

[35] G V Samsonov The Oxide Handbook IFIPlenum New YorkNY USA 1982

[36] K Goto ldquoOn the mechanism of phase transitions of UO225

rdquoSolid State Communications vol 6 no 9 pp 653ndash655 1968

[37] F A Chudnovskii ldquoMetal-semiconductor phase transition invanadium oxides and technical applicationsrdquo Soviet PhysicsmdashTechnical Physics vol 20 no 8 pp 999ndash1012 1976

[38] JDuchene ldquoDirect infraredmeasurements of filament transienttemperature during switching in vanadium oxide film devicesrdquoJournal of Solid State Chemistry vol 12 no 3-4 pp 303ndash3061975

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

Films vol 97 no 2 pp 129ndash143 1982[46] R Collongues La Non-Stoechiometrie Masson Paris France

1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

9 no 5 pp 391ndash396 2014[67] B Sun W Zhao Y Liu and P Chen ldquoResistive switching effect

of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

1990[70] S Mukherjee S Karmakar H Sakata and B K Chaudhuri

ldquoLow-temperature metallic behavior of amorphous MoO3-

TeO2thin filmsrdquo Journal of Applied Physics vol 97 no 12 Article

ID 123707 2005[71] AMottaghizadeh Q Yu P L Lang A Zimmers andH Aubin

ldquoMetal oxide resistive switching evolution of the density ofstates across the metal-insulator transitionrdquo Physical ReviewLetters vol 112 no 6 Article ID 066803 2014

[72] R Xie C T Bui B Varghese et al ldquoAn electrically tunedsolid-state thermalmemory based onmetal-insulator transitionof single-crystalline VO

2nanobeamsrdquo Advanced Functional

Materials vol 21 no 9 pp 1602ndash1607 2011

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

22 Advances in Condensed Matter Physics

[39] A Mansingh and R Singh ldquoThe mechanism of electricalthreshold switching in VO

2crystalsrdquo Journal of Physics C Solid

State Physics vol 13 no 31 pp 5725ndash5733 1980[40] V N Andreev N E Timoschenko I M Chernenko and F A

Chudnovskii ldquoMechanism of formation of switching vanadate-phosphate glassesrdquo Journal of Technical Physics vol 51 no 8 pp1685ndash1689 1981

[41] J K Higgins B K Temple and J E Lewis ldquoElectrical prop-erties of vanadate-glass threshold switchesrdquo Journal of Non-Crystalline Solids vol 23 no 2 pp 187ndash215 1977

[42] J G Zhang and P C Eklund ldquoThe switching mechanism inV2O5gel filmsrdquo Journal of Applied Physics vol 64 no 2 pp

729ndash733 1988[43] J Bullot O Gallias M Gauthier and J Livage ldquoThreshold

switching in V2O5layers deposited from gelsrdquo Physica Status

Solidi (A) vol 71 no 1 pp K1ndashK4 1982[44] A I Ivon V R Kolbunov and I M Chernenko ldquoVoltage-

current characteristics of vanadium dioxide based ceramicsrdquoJournal of the European Ceramic Society vol 23 no 12 pp 2113ndash2118 2003

[45] R L Remke R M Walser and R W Bene ldquoThe effect ofinterfaces on electronic switching in VO

2thin filmsrdquoThin Solid

Films vol 97 no 2 pp 129ndash143 1982[46] R Collongues La Non-Stoechiometrie Masson Paris France

1971[47] P Kofstad Nonstoichiometry Diffusion and Electrical Conduc-

tivity in Binary Metal Oxides Wiley-Interscience New YorkNY USA 1972

[48] D R Islamov V A Gritsenko C H Cheng and A Chin ldquoPer-colation conductivity in hafnium sub-oxidesrdquo Applied PhysicsLetters vol 105 no 26 Article ID 262903 2014

[49] W Kulisch D Gilliland G Ceccone et al ldquoTantalum pen-toxide as a material for biosensors deposition properties andapplicationsrdquo in Nanostructured Materials for Advanced Tech-nological Applications J P Reithmaier P Petkov W Kulischand C Popov Eds NATO Science for Peace and SecuritySeries B Physics and Biophysics pp 509ndash524 Springer Sci-ence+Business Media Dordrecht The Netherlands 2009

[50] K D Tsendin E A Lebedev and A B Shmelrsquokin ldquoInstabili-ties with S- and N-shaped current-voltage characteristics andphase transitions in chalcogenide vitreous semiconductors andpolymersrdquo Physics of the Solid State vol 47 no 3 pp 439ndash4452005

[51] A Pergament and G Stefanovich ldquoInsulator-to-metal transi-tion in vanadium sesquioxide does the Mott criterion work inthis caserdquo Phase Transitions vol 85 no 3 pp 185ndash194 2012

[52] J S Brockman L Gao B Hughes et al ldquoSubnanosecondincubation times for electric-field-induced metallization of acorrelated electron oxiderdquo Nature Nanotechnology vol 9 no 6pp 453ndash458 2014

[53] A L Pergament V PMalinenko L AAleshina E L Kazakovaand N A Kuldin ldquoElectrical switching in thin film structuresbased onmolybdenum oxidesrdquo Journal of Experimental Physicsvol 2014 Article ID 951297 6 pages 2014

[54] A L Pergament V P Malinenko L A Aleshina and VV Kolchigin ldquoMetal-insulator phase transition and electricalswitching in manganese dioxiderdquo Physics of the Solid State vol54 no 12 pp 2486ndash2490 2012

[55] L Mai F Yang Y Zhao et al ldquoMolybdenum oxide nanowiressynthesis and propertiesrdquo Materials Today vol 14 no 7-8 pp346ndash353 2011

[56] M C Rao K Ravindranadh A Kasturi and M S ShekhawatldquoStructural stoichiometry and phase transitions of MoO

3thin

films for solid state microbatteriesrdquo Research Journal of RecentSciences vol 2 no 4 pp 67ndash73 2013

[57] R L Smith and G S Rohrer ldquoScanning probe microscopyof cleaved molybdates 120572-MoO

3(010) Mo

18O52(100)

Mo8O23(010) and 120578-Mo

4O11(100)rdquo Journal of Solid State

Chemistry vol 124 no 1 pp 104ndash115 1996[58] D O Scanlon G W Watson D J Payne G R Atkinson R G

Egdell and D S L Law ldquoTheoretical and experimental studyof the electronic structures of MoO

3and MoO

2rdquo Journal of

Physical Chemistry C vol 114 no 10 pp 4636ndash4645 2010[59] M Arita H Kaji T Fujii and Y Takahashi ldquoResistance

switching properties of molybdenum oxide filmsrdquo Thin SolidFilms vol 520 no 14 pp 4762ndash4767 2012

[60] M Hasan ldquoAmaterials approach to resistive switchingmemoryoxidesrdquo Journal of Semiconductor Technology and Science vol 8no 1 pp 66ndash79 2008

[61] A I Gavrilyuk and N A Sekushin Electrochromism andPhotochromism in Oxides of Tungsten andMolybdenum NaukaLeningrad Russia 1990 (Russian)

[62] H Fujishita M Sato S M Shapiro and S Hoshino ldquoInelasticneutron scattering of the low-dimensional conductors (TaSe

4)2I

and Mo8O23rdquo Physica B+C vol 143 no 1ndash3 pp 201ndash203 1986

[63] T Sato T Dobashi H Komatsu T Takahashi and M KoyanoldquoElectronic structure of 120578-Mo

4O11

studied by high-resolutionangle-resolved photoemission spectroscopyrdquo Journal of ElectronSpectroscopy and Related Phenomena vol 144ndash147 pp 549ndash5522005

[64] Y Motome and N Furukawa ldquoOrbital degeneracy and Motttransition in Mo pyrochlore oxidesrdquo Journal of Physics Confer-ence Series vol 320 Article ID 012060 2011

[65] AMaeda T Furuyama and S Tanaka ldquoThreshold-field behav-ior and switching in K

03MoO3rdquo Solid State Communications

vol 55 no 11 pp 951ndash955 1985[66] Y-C Lin D O Dumcenco Y-S Huang and K Suenaga

ldquoAtomic mechanism of the semiconducting-to-metallic phasetransition in single-layered MoS

2rdquo Nature Nanotechnology vol

9 no 5 pp 391ndash396 2014[67] B Sun W Zhao Y Liu and P Chen ldquoResistive switching effect

of AgMoS2FTO devicerdquo Functional Materials Letters vol 8

no 1 Article ID 1550010 4 pages 2015[68] R Rousseau E Canadell P Alemany D H Galvan and

R Hoffmann ldquoOrigin of the metal-to-insulator transition inH033

MoO3rdquo Inorganic Chemistry vol 36 no 21 pp 4627ndash4632

1997[69] E Canadell and M-H Whangbo ldquoBand electronic structure

study of the structural modulation in the Magneli phaseMo8O23rdquo Inorganic Chemistry vol 29 no 12 pp 2256ndash2260

1990[70] S Mukherjee S Karmakar H Sakata and B K Chaudhuri

ldquoLow-temperature metallic behavior of amorphous MoO3-

TeO2thin filmsrdquo Journal of Applied Physics vol 97 no 12 Article

ID 123707 2005[71] AMottaghizadeh Q Yu P L Lang A Zimmers andH Aubin

ldquoMetal oxide resistive switching evolution of the density ofstates across the metal-insulator transitionrdquo Physical ReviewLetters vol 112 no 6 Article ID 066803 2014

[72] R Xie C T Bui B Varghese et al ldquoAn electrically tunedsolid-state thermalmemory based onmetal-insulator transitionof single-crystalline VO

2nanobeamsrdquo Advanced Functional

Materials vol 21 no 9 pp 1602ndash1607 2011

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

Advances in Condensed Matter Physics 23

[73] M R Arora and R Kelly ldquoThe structure and stoichiometryof anodic films on V Nb Ta Mo and Wrdquo Journal of MaterialsScience vol 12 no 8 pp 1673ndash1684 1977

[74] C M Daly and R G Keil ldquoOn the anodic oxidation ofmolybdenumrdquo Journal of the Electrochemical Society vol 122no 3 pp 350ndash353 1975

[75] A L Pergament and G B Stefanovich ldquoPhase compositionof anodic oxide films on transition metals a thermodynamicapproachrdquoThin Solid Films vol 322 no 1-2 pp 33ndash36 1998

[76] R Swanepoel ldquoDetermination of the thickness and opticalconstants of amorphous siliconrdquo Journal of Physics E ScientificInstruments vol 16 no 12 pp 1214ndash1221 1983

[77] W-H Ryu J-H Yoon andH-S Kwon ldquoMorphological controlof highly aligned manganese dioxide nanostructure formed byelectrodepositionrdquoMaterials Letters vol 79 pp 184ndash187 2012

[78] A L Gusev T N Kondyrina V V Kursheva et al ldquoPerspectiveson application of flexible electrochromic panels in housingand communal services facilities and vehiclesrdquo InternationalScientific Journal for Alternative Energy and Ecology vol 10 no78 pp 122ndash137 2009

[79] S Walia S Balendhran P Yi et al ldquoMnO2-based thermopower

wave sources with exceptionally large output voltagesrdquo Journalof Physical Chemistry C vol 117 no 18 pp 9137ndash9142 2013

[80] H Wang C Peng J Zheng F Peng and H Yu ldquoDesign syn-thesis and the electrochemical performance of MnO

2CCNT

as supercapacitor materialrdquoMaterials Research Bulletin vol 48no 9 pp 3389ndash3393 2013

[81] M K Yang J-W Park T K Ko and J-K Lee ldquoResistiveswitching characteristics of TiNMnO

2Pt memory devicesrdquo

Physica Status SolidimdashRapid Research Letters vol 4 no 8-9 pp233ndash235 2010

[82] R Ramesham T Daud A Moopenn A P Thakoor andS K Khanna ldquoManganese oxide microswitch for electronicmemory based on neural networksrdquo Journal of Vacuum Scienceamp Technology B vol 7 no 3 pp 450ndash454 1989

[83] D B Rogers R D Shannon A W Sleight and J L GillsonldquoCrystal chemistry of metal dioxides with rutile-related struc-turesrdquo Inorganic Chemistry vol 8 no 4 pp 841ndash850 1969

[84] P H Klose ldquoElectrical properties of manganese dioxide andmanganese sesquioxiderdquo Journal of The Electrochemical Societyvol 117 no 7 pp 854ndash859 1970

[85] E L Nagaev Physics of Magnetic Semiconductors NaukaMoscow Russia 1979 (Russian)

[86] C-C Hu and T-W Tsou ldquoIdeal capacitive behavior of hydrousmanganese oxide prepared by anodic depositionrdquo Electrochem-istry Communications vol 4 no 2 pp 105ndash109 2002

[87] X-M Shen and A Clearfield ldquoPhase transitions and ionexchange behavior of electrolytically preparedmanganese diox-iderdquo Journal of Solid State Chemistry vol 64 no 3 pp 270ndash2821986

[88] HYKang andCC Liang ldquoThe anodic oxidation ofmanganeseoxides in alkaline electrolytesrdquo Journal of The ElectrochemicalSociety vol 115 no 1 pp 6ndash10 1968

[89] Y M Hu M Y Zhu Y Li H M Jin and Z Z ZhuldquoMagnetic-field-assisted hydrothermal growth of manganesedioxide nanostructures and their phase transformationrdquoMate-rials Science Forum vol 688 pp 148ndash152 2011

[90] C N R Rao and B Raveau Transition Metal Oxides StructureProperties and Synthesis of Ceramics Oxides Wiley-VCH NewYork NY USA 1998

[91] M Regulski R Przeniosło I Sosnowska and J-U HoffmannldquoShort and long range magnetic ordering in 120573-MnO

2mdasha tem-

perature studyrdquo Journal of the Physical Society of Japan vol 73no 12 pp 3444ndash3447 2004

[92] V P Malinenko L A Aleshina S V Loginova and N DTikhonov ldquoPhase transition in pyrolytic manganese dioxiderdquoin Proceedings of the 10th International Conference on Physics ofDielectrics p 39 Herzen State Pedagogical University of RussiaSt Petersburg Russia 2004

[93] L A Aleshina and S V Loginova ldquoTotal profiling of an X-ray pattern of pyrolytic manganese dioxiderdquo Russian PhysicsJournal vol 46 no 5 pp 500ndash503 2003

[94] AWestBasic Solid State ChemistryWiley NewYorkNYUSA1984

[95] L Sheng D Y Xing D N Sheng and C S Ting ldquoMetal-insulator transition in the mixed-valence manganitesrdquo PhysicalReview B vol 56 no 12 pp R7053ndashR7056 1997

[96] A E Sovestnov B T Melekh V V Fedorov and E V FominldquoX-ray emission studies of evolution of the electron and spinstructures ofMn inmixedmanganites Ln

1minus119909Sr119909MnO

3(Ln = La

Sm andCe)rdquoPhysics of the Solid State vol 54 pp 778ndash781 2012[97] E S Borovic V V Eremenko and A S Milner Lectures on

Magnetism Fizmatlit Moscow Russia 2005 (Russian)[98] E L Nagaev ldquoMott transitions in heavily doped magnetic

semiconductorsrdquo Physics of the Solid State vol 40 no 3 pp396ndash400 1998

[99] I V Borisenko M A Karpov and G A Ovsyannikov ldquoMetal-insulator transition in epitaxial films of LaMnO

3manganites

grown by magnetron sputteringrdquo Technical Physics Letters vol39 no 12 pp 1027ndash1030 2013

[100] M D Pickett G Medeiros-Ribeiro and R S Williams ldquoA scal-able neuristor built with Mott memristorsrdquo Nature Materialsvol 12 no 2 pp 114ndash117 2013

[101] S M Sze and K K Ng Physics of Semiconductor Devices Wiley2006

[102] F A Chudnovskii A L Pergament D A Schaefer and GB Stefanovich ldquoEffect of laser irradiation on the properties oftransition metal oxidesrdquo Journal of Solid State Chemistry vol118 no 2 pp 417ndash418 1995

[103] F A Chudnovskii D O Kikalov A L Pergament and G BStefanovich ldquoElectrical transport properties and switching invanadium anodic oxides effect of laser irradiationrdquo PhysicaStatus Solidi A vol 172 no 2 pp 391ndash395 1999

[104] A L Pergament A A Velichko O Y Berezina E L KazakovaN A Kuldin and D V Artyukhin ldquoInfluence of doping onthe properties of vanadium oxide gel filmsrdquo Journal of PhysicsCondensed Matter vol 20 no 42 Article ID 422204 2008

[105] O Y Berezina A A Velichko L A Lugovskaya A L Perga-ment and G B Stefanovich ldquoMetal-semiconductor transitionin nonstoichiometric vanadium dioxide filmsrdquo Inorganic Mate-rials vol 43 no 5 pp 505ndash511 2007

[106] X Wang Y Song L L Tao et al ldquoOrigin of ferromagnetismin aluminum-doped TiO

2thin films theory and experimentsrdquo

Applied Physics Letters vol 105 no 26 Article ID 262402 2014[107] Z Yang S Hart C Ko A Yacoby and S Ramanathan ldquoStudies

on electric triggering of the metal-insulator transition in VO2

thin films between 77K and 300Krdquo Journal of Applied Physicsvol 110 no 3 Article ID 033725 2011

[108] A Axelevitch B Gorenstein and G Golan ldquoInvestigationof the electrical transport mechanism in VOx thin filmsrdquoMicroelectronics Reliability vol 51 no 12 pp 2119ndash2123 2011

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

24 Advances in Condensed Matter Physics

[109] G Beydaghyan V Basque and P V Ashrit ldquoHigh contrastthermochromic switching in vanadium dioxide (VO

2) thin

films deposited on indium tin oxide substratesrdquo Thin SolidFilms vol 522 pp 204ndash207 2012

[110] M Liu H Y Hwang H Tao et al ldquoTerahertz-field-inducedinsulator-to-metal transition in vanadium dioxide metamate-rialrdquo Nature vol 487 no 7407 pp 345ndash348 2012

[111] D-H Qiu Q-Y Wen Q-H Yang Z Chen Y-L Jing andH-W Zhang ldquoElectrically-driven metal-insulator transition ofvanadium dioxide thin films in a metal-oxide-insulator-metaldevice structurerdquoMaterials Science in Semiconductor Processingvol 27 no 1 pp 140ndash144 2014

[112] G Golan A Axelevitch B Sigalov and B Gorenstein ldquoInves-tigation of phase transition mechanism in vanadium oxide thinfilmsrdquo Journal of Optoelectronics and AdvancedMaterials vol 6no 1 pp 189ndash195 2004

[113] S Rathi J-H Park I-Y Lee J M Baik K S Yi and G-H Kim ldquoUnravelling the switching mechanisms in electricfield induced insulator-metal transitions in VO

2nanobeamsrdquo

Journal of Physics D Applied Physics vol 47 no 29 Article ID295101 2014

[114] P P Boriskov A L Pergament A A Velichko G BStefanovich and N A Kuldin ldquoMetal-insulator transitionin electric field a viewpoint from the switching effectrdquohttparxivorgabscond-mat0603132

[115] V N Andreev and V A Klimov ldquoElectrical conductivity ofthe semiconducting phase in vanadium dioxide single crystalsrdquoPhysics of the Solid State vol 49 no 12 pp 2251ndash2255 2007

[116] A Pergament P Boriskov N Kuldin and A Velichko ldquoElec-trical conductivity of vanadium dioxide switching channelrdquoPhysica Status Solidi B vol 247 no 9 pp 2213ndash2217 2010

[117] A Pergament G Stefanovich O Berezina and D KirienkoldquoElectrical conductivity of tungsten doped vanadium dioxideobtained by the sol-gel techniquerdquoThin Solid Films vol 531 pp572ndash576 2013

[118] V V Bryksin ldquoSmall-polaron theory with allowance for theinfluence of lattice vibrations on the resonance integralrdquo Journalof Experimental and Theoretical Physics vol 73 no 5 pp 861ndash866 1991

[119] VNAndreev F A Chudnovskiy JMHonig andPAMetcalfldquoElectrical conductivity in the antiferromagnetic insulatingphase of V

2O3rdquo Physical Review B vol 70 no 23 Article ID

235124 2004[120] V N Andreev and V A Klimov ldquoSpecific features of electrical

conductivity of V3O5single crystalsrdquo Physics of the Solid State

vol 53 no 12 pp 2424ndash2430 2011[121] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V4O7single crystalsrdquo Physics of the

Solid State vol 51 no 11 pp 2235ndash2240 2009[122] V N Andreev and V A Klimov ldquoSpecific features of the

electrical conductivity of V6O11rdquo Physics of the Solid State vol

55 no 9 pp 1829ndash1834 2013[123] D Ruzmetov D Heiman B B Claflin V Narayanamurti and

S Ramanathan ldquoHall carrier density and magnetoresistancemeasurements in thin-film vanadium dioxide across the metal-insulator transitionrdquo Physical Review B vol 79 no 15 ArticleID 153107 2009

[124] D Fu K Liu T Tao et al ldquoComprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO

2thin

filmsrdquo Journal of Applied Physics vol 113 no 4 Article ID043707 2013

[125] A Pergament G Stefanovich and A Velichko ldquoOxide elec-tronics and vanadium dioxide perspective a reviewrdquo Journal onSelected Topics in Nano Electronics and Computing vol 1 no 1pp 24ndash43 2013

[126] E S Reich ldquoMetal oxide chips show promiserdquo Nature vol 494no 7439 p 17 2013

[127] A Zimmers L Aigouy M Mortier et al ldquoRole of thermalheating on the voltage induced insulator-metal transition inVO2rdquo Physical Review Letters vol 110 no 5 Article ID 056601

2013[128] B S Mun J Yoon S-K Mo et al ldquoRole of joule heating

effect and bulk-surface phases in voltage-drivenmetal-insulatortransition in VO

2crystalrdquo Applied Physics Letters vol 103 no

6 Article ID 061902 2013[129] S Kumar M D Pickett J P Strachan G Gibson Y Nishi and

R SWilliams ldquoLocal temperature redistribution and structuraltransition during joule-heating-driven conductance switchinginVO

2rdquoAdvancedMaterials vol 25 no 42 pp 6128ndash6132 2013

[130] J Yoon G Lee C Park B S Mun and H Ju ldquoInvestigation oflength-dependent characteristics of the voltage-induced metalinsulator transition inVO

2filmdevicesrdquoApplied Physics Letters

vol 105 no 8 Article ID 083503 2014[131] G Stefanovich A Pergament and D Stefanovich ldquoElectrical

switching and Mott transition in VO2rdquo Journal of Physics

Condensed Matter vol 12 no 41 pp 8837ndash8845 2000[132] M Nakano K Shibuya D Okuyama et al ldquoCollective bulk

carrier delocalization driven by electrostatic surface chargeaccumulationrdquo Nature vol 487 no 7408 pp 459ndash462 2012

[133] T Nan M Liu W Ren Z-G Ye and N X Sun ldquoVoltagecontrol of metal-insulator transition and non-volatile ferroelas-tic switching of resistance in VOxPMN-PT heterostructuresrdquoScientific Reports vol 4 article 5931 7 pages 2014

[134] A A Stabile S K Singh T Wu L Whittaker S Banerjeeand G Sambandamurthy ldquoSeparating electric field and thermaleffects across the metal-insulator transition in vanadium oxidenanobeamsrdquo Applied Physics Letters vol 107 no 1 Article ID013503 2015

[135] S D Ha Y Zhou C J Fisher S Ramanathan and J P Tread-way ldquoElectrical switching dynamics and broadband microwavecharacteristics of VO

2radio frequency devicesrdquo Journal of

Applied Physics vol 113 no 18 Article ID 184501 2013[136] F Dumas-Bouchiat C Champeaux A Catherinot A Crun-

teanu and P Blondy ldquoRf-microwave switches based onreversible semiconductor-metal transition of VO

2thin films

synthesized by pulsed-laser depositionrdquoApplied Physics Lettersvol 91 no 22 Article ID 223505 2007

[137] P Stoliar M Rozenberg E Janod B Corraze J Tranchant andL Cario ldquoNonthermal and purely electronic resistive switchingin a Mott memoryrdquo Physical Review B vol 90 no 4 Article ID045146 2014

[138] P Stoliar L Cario E Janod et al ldquoUniversal electric-field-driven resistive transition in narrow-gap Mott insulatorsrdquoAdvanced Materials vol 25 no 23 pp 3222ndash3226 2013

[139] N Shukla T Joshi S Dasgupta P Borisov D Lederman andS Datta ldquoElectrically induced insulator to metal transition inepitaxial SmNiO

3thin filmsrdquo Applied Physics Letters vol 105

no 1 Article ID 012108 2014[140] P M Marley A A Stabile C P Kwan et al ldquoCharge dispro-

portionation and voltage-induced metal-insulator transitionsevidenced in 120573-Pb

119909V2O5nanowiresrdquo Advanced Functional

Materials vol 23 no 2 pp 153ndash160 2013

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

Advances in Condensed Matter Physics 25

[141] M Kang S Yu and J Son ldquoVoltage-induced insulator-to-metaltransition of hydrogen-treated NbO

2thin filmsrdquo Journal of

Physics D Applied Physics vol 48 no 9 Article ID 095301 2015[142] A L Pergament E L Kazakova andG B Stefanovich ldquoOptical

and electrical properties of vanadium pentoxide xerogel filmsmodification in electric field and the role of ion transportrdquoJournal of Physics D Applied Physics vol 35 no 17 pp 2187ndash2197 2002

[143] A L Pergament G B Stefanovich and F A ChudnovskiildquoSemiconductor-metal phase transition and switching in vana-dium dioxide in a high electric fieldrdquo Technical Physics Lettersvol 19 no 10 pp 663ndash665 1993

[144] B-J Kim G Seo Y W Lee S Choi and H-T Kim ldquoLinearcharacteristics of a metalinsulator transition voltage and oscil-lation frequency in VO

2devicesrdquo IEEE Electron Device Letters

vol 31 no 11 pp 1314ndash1316 2010[145] A Beaumont J Leroy J-C Orlianges and A Crunteanu

ldquoCurrent-induced electrical self-oscillations across out-of-plane threshold switches based on VO

2layers integrated in

crossbars geometryrdquo Journal of Applied Physics vol 115 ArticleID 154502 2014

[146] A Belatreche L Maguire M McGinnity L McDaid and AGhani ldquoComputing with biologically inspired neural oscilla-tors application to colour image segmentationrdquo Advances inArtificial Intelligence vol 2010 Article ID 405073 21 pages2010

[147] P Strumillo and M Strzelecki ldquoApplication of coupled neuraloscillators for image texture segmentation andmodeling of bio-logical rhythmsrdquo International Journal of Applied Mathematicsand Computer Science vol 16 no 4 pp 513ndash523 2006

[148] S Datta N Shukla M Cotter A Parihar and A Raychowd-hury ldquoNeuro inspired computing with coupled relaxationoscillatorsrdquo in Proceedings of the 51st Annual Design AutomationConference (DAC rsquo14) pp 1ndash6 ACM San Francisco Calif USAJune 2014

[149] A Parihar N Shukla S Datta and A Raychowdhury ldquoExploit-ing synchronization properties of correlated electron devices ina non-boolean computing fabric for template matchingrdquo IEEEJournal on Emerging and Selected Topics in Circuits and Systemsvol 4 no 4 pp 450ndash459 2014

[150] A Parihar N Shukla S Datta and A Raychowdhury ldquoSyn-chronization of pairwise-coupled identical relaxation oscilla-tors based on metal-insulator phase transition devices a modelstudyrdquo Journal of Applied Physics vol 117 no 5 Article ID054902 2015

[151] YWang J Chai SWang et al ldquoElectrical oscillation in PtVO2

bilayer stripsrdquo Journal of Applied Physics vol 117 no 6 ArticleID 064502 2015

[152] S A Dyakov J Dai M Yan and M Qiu ldquoThermal self-oscillations in radiative heat exchangerdquo Applied Physics Lettersvol 106 no 6 Article ID 064103 2015

[153] Z Topalian S-Y Li G A Niklasson C G Granqvist and LB Kish ldquoResistance noise at the metal-insulator transition inthermochromic VO

2filmsrdquo Journal of Applied Physics vol 117

no 2 Article ID 025303 2015[154] X He J Xu X Xu et al ldquoNegative capacitance switching via

VO2band gap engineering driven by electric fieldrdquo Applied

Physics Letters vol 106 no 9 Article ID 093106 2015[155] Y Liu T P Chen Z Liu et al ldquoSelf-learning ability realizedwith

a resistive switching device based on a Ni-rich nickel oxide thinfilmrdquo Applied Physics A vol 105 no 4 pp 855ndash860 2011

[156] SWen Z Zeng andTHuang ldquoExponential stability analysis ofmemristor-based recurrent neural networks with time-varyingdelaysrdquo Neurocomputing vol 97 pp 233ndash240 2012

[157] S D Ha and S Ramanathan ldquoAdaptive oxide electronics areviewrdquo Journal of Applied Physics vol 110 no 7 Article ID071101 2011

[158] A Velichko A Pergament V Putrolaynen O Berezinaand G Stefanovich ldquoEffect of memory electrical switchingin metalvanadium oxidesilicon structures with VO

2films

obtained by the sol-gel methodrdquo Materials Science in Semicon-ductor Processing vol 29 pp 315ndash320 2015

[159] F J Wong T S Sriram B R Smith and S Ramanathan ldquoBipo-lar resistive switching in room temperature grown disorderedvanadium oxide thin-film devicesrdquo Solid-State Electronics vol87 pp 21ndash26 2013

[160] V H Mai A Moradpour P A Senzier et al ldquoMemristive andneuromorphic behavior in a Li

119909CoO2nanobatteryrdquo Scientific

Reports vol 5 article 7761 2015[161] A A Bessonov M N Kirikova D I Petukhov M Allen T

Ryhanen and M J A Bailey ldquoLayered memristive and mem-capacitive switches for printable electronicsrdquo Nature Materialsvol 14 pp 199ndash204 2015

[162] M Prezioso F Merrikh-Bayat B D Hoskins G C AdamK K Likharev and D B Strukov ldquoTraining and operationof an integrated neuromorphic network based on metal-oxidememristorsrdquo Nature vol 521 no 7550 pp 61ndash64 2015

[163] D E Nikonov G Csaba W Porod et al ldquoCoupled-oscillatorassociative memory arrayoperationrdquo httparxivorgabs13046125

[164] SDHa Y ZhouA EDuwel DWWhite and S Ramanathanldquoquick switch strongly correlated electronic phase transitionsystems for cutting-edge microwave devicesrdquo IEEE MicrowaveMagazine vol 15 no 6 pp 32ndash44 2014

[165] G Seo B-J Kim H-T Kim and Y W Lee ldquoThermally- oroptically-biased memristive switching in two-terminal VO

2

devicesrdquo Current Applied Physics vol 14 no 9 pp 1251ndash12562014

[166] M D Goldflam M K Liu B C Chapler et al ldquoVoltageswitching of a VO

2memory metasurface using ionic gelrdquo

Applied Physics Letters vol 105 no 4 Article ID 041117 2014[167] B-J Kim YW Lee S Choi S J Yun andH-T Kim ldquoVO

2thin-

film varistor based onmetal-insulator transitionrdquo IEEE ElectronDevice Letters vol 31 no 1 pp 14ndash16 2010

[168] Z Yang C Ko and S Ramanathan ldquoOxide electronics utilizingultrafast metal-insulator transitionsrdquo Annual Review of Materi-als Research vol 41 pp 337ndash367 2011

[169] Y Zhou and S Ramanathan ldquoCorrelated electronmaterials andfield effect transistors for logic a reviewrdquo Critical Reviews inSolid State and Materials Sciences vol 38 no 4 pp 286ndash3172013

[170] S Kim J Park J Woo et al ldquoThreshold-switching charac-teristics of a nanothin-NbO

2-layer-based PtNbO

2Pt stack

for use in cross-point-type resistive memoriesrdquoMicroelectronicEngineering vol 107 pp 33ndash36 2013

[171] D Lee J Park J Park et al ldquoStructurally engineered stackableand scalable 3D titanium-oxide switching devices for high-density nanoscale memoryrdquo Advanced Materials vol 27 no 1pp 59ndash64 2014

[172] S Nakamura ldquoNegative differential resistivity from hologra-phyrdquo Progress ofTheoretical Physics vol 124 no 6 pp 1105ndash11142010

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

26 Advances in Condensed Matter Physics

[173] E Dagotto ldquoComplexity in strongly correlated electronic sys-temsrdquo Science vol 309 no 5732 pp 257ndash262 2005

[174] D-H Kwon K M Kim J H Jang et al ldquoAtomic structure ofconducting nanofilaments in TiO

2resistive switchingmemoryrdquo

Nature Nanotechnology vol 5 no 2 pp 148ndash153 2010[175] J J Yang J P Strachan F Miao et al ldquoMetalTiO2 interfaces

for memristive switchesrdquo Applied Physics A vol 102 no 4 pp785ndash789 2011

[176] K M Kim S R Lee S Kim M Chang and C S HwangldquoSelf-limited switching in Ta

2O5TaO119909memristors exhibiting

uniformmultilevel changes in resistancerdquo Advanced FunctionalMaterials vol 10 pp 1527ndash1534 2015

[177] L Zhu J Zhou Z Guo and Z Sun ldquoRealization of a reversibleswitching in TaO

2polymorphs via Peierls distortion for resis-

tance random access memoryrdquo Applied Physics Letters vol 106Article ID 091903 2015

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of