thermal conductivity and heat capacity of dielectric and ......thermal conductivity of materials...

Patrick E HopkinsProfessor

Mech amp Aero EngMat Sci amp Eng

PhysicsUniversity of Virginia

phopkinsvirginiaedupatrickehopkinscom

Thermal conductivity and heat capacity of dielectric and ferroelectric hafnium

zirconium oxide thin films

Thermal resistance and heat capacity in hafnium zirconium oxide(Hf1ndashxZrxO2) dielectrics and ferroelectric thin films

Ethan A Scott1 Sean W Smith2 M David Henry2 Christina M Rost1 Ashutosh Giri1

John T Gaskins1 Shelby S Fields3 Samantha T Jaszewski3 Jon F Ihlefeld34

and Patrick E Hopkins135a)

1Department of Mechanical and Aerospace Engineering University of Virginia Charlottesville Virginia22904 USA2Sandia National Laboratories Albuquerque New Mexico 87185 USA3Department of Materials Science and Engineering University of Virginia Charlottesville Virginia 22904USA4Department of Electrical and Computer Engineering University of Virginia Charlottesville Virginia 22904USA5Department of Physics University of Virginia Charlottesville Virginia 22904 USA

(Received 15 August 2018 accepted 23 October 2018 published online 7 November 2018)

We report on the thermal resistances of thin films (20 nm) of hafnium zirconium oxide(Hf1ndashxZrxO2) with compositions ranging from 0 x 1 Measurements were made via time-domain thermoreflectance and analyzed to determine the effective thermal resistance of the films inaddition to their associated thermal boundary resistances We find effective thermal resistancesranging from 2879 to 2472 m2 K GW1 for amorphous films which decreased to 1581m2 K GW1 upon crystallization Furthermore we analyze the heat capacity for two compositionsxfrac14 05 and xfrac14 07 of Hf1ndashxZrxO2 and find them to be 218 6 056 and 264 6 053 MJ m3 K1respectively Published by AIP Publishing httpsdoiorg10106315052244

Due to their unique ferroelectric behavior ease of manu-facture and inherent silicon compatibility HfO2-based sys-tems have recently begun to garner attention as potentialcandidates for non-volatile memory negative differentialcapacitance transistors and energy harvesting applicationsamong others1ndash4 Since ferroelectric properties were firstdemonstrated in 20115 various factors have been shown toallow stability of the ferroelectric phase including alloyingwith Zr6 depositing onto a nitride electrode layer such asTaN7 as well as tuning the grain size and film thickness689

The ferroelectric response of HfO2-based films is attributedto the polar crystalline structure inherent to the orthorhombicPca21 phase17 When alloyed with ZrO2 ferroelectricity inHf1ndashxZrxO2 systems can be tuned with a field-induced phasetransition from the tetragonal to orthorhombic phase10

which broadens the horizons for application in energy stor-age devices as well as electronic memory devices andarchitectures1

While ample studies have focused upon the electricaland structural properties of Hf1ndashxZrxO2 systems15ndash11 thereexists a gap in the literature in terms of their thermal proper-ties particularly in thin-film form Even for pure hafnia orzirconia the literature on thermal properties is limited espe-cially with regard to heat capacity12 The preferred methodof fabrication for Hf1ndashxZrxO2 films is atomic layer deposition(ALD)111 and though prior studies have reported measure-ments of the thermal conductivity of ALD grown HfO2

13ndash16

films there have been no studies investigating their thermalproperties when alloyed with ZrO2 Furthermore given thepotential for HfO2-based materials to impact infrared sensingand thermal energy harvesting applications knowledge of

the thermal properties is vital to CMOS integrated devicedevelopment17

In this study we measure the thermal resistance andeffective thermal conductivity of Hf1ndashxZrxO2 films grownbetween TaN and aluminum electrodes for nominal Zr dop-ing concentrations of xfrac14 0 05 07 and 1 As annealingenables crystallization into the ferroelectric phase inHf1ndashxZrxO2 we report on the effective thermal conductivityvalues for both annealed and unannealed films Furthermoreour use of time-domain thermoreflectance (TDTR) for ther-mal metrology allows for determination of the volumetricheat capacity of selected Hf1ndashxZrxO2 films when depositedon thermally insulating substrates Thus we also report onthe measured volumetric heat capacity of films for nominalZr concentrations of xfrac14 05 and xfrac14 07 a thermophysicalparameter that is critical for further development of devicesbased on this material for example devices leveraging pyro-electric effects1718

Samples were fabricated by rf-magnetron sputtering a10 nm thick TaN layer onto (001) silicon substrates Thermalatomic layer deposition (ALD) was then used to deposit20 nm thick films of Hf1ndashxZrxO2 for compositions rangingfrom 0 x 1 The precursors for the HfO2 and ZrO2 cyclesincluded Tetrakis(dimethylamino) hafnium (TDMA Hf) andTetrakis(dimethylamino)zirconium (TDMA Zr) respec-tively at 75 $C with H2O used as the oxidant for both ForHfO2 and ZrO2 the growth per cycle (GPC) was 01086 and00968 nm respectively measured via ellipsometry Tocontrol the composition of the Hf1ndashxZrxO2 films the numberof cycles for each precursor was adjusted relative to theother For example for xfrac14 05 (55 HfZr) 20 ldquosupercyclesrdquoof 5 ZrO25 HfO2 were utilized and for xfrac14 07 (37 HfZr)20 ldquosupercyclesrdquo of 7 ZrO23 HfO2 were utilized Thisa)Electronic mail phopkinsvirginiaedu

0003-69512018113(19)1929015$3000 Published by AIP Publishing113 192901-1

APPLIED PHYSICS LETTERS 113 192901 (2018)





Thermal conductivity of materials - nanoscopic

Heat capacity(energy density of carriers)

Velocity(how fast they move)KEIVAN ESFARJANI GANG CHEN AND HAROLD T STOKES PHYSICAL REVIEW B 84 085204 (2011)

-600

-400

-200

0

200

400

600

800

G K X G L X W L

100

(Gru

neis

en-3

)

Freq

uenc

y (1

cm

)

DOS Kpoints

Band Structure and DOS for Si

ExperimentsIntegrated DOS

Total DOS

FIG 3 (Color online) Phonon band structure of Si using forceconstants up to the fifth neighbor shell Plus signs representexperimental data of Nelin and Nilsson30 Left portion of figure showsthe DOS and right portion of figure shows the rescaled Gruneisenparameters [100 times (γ minus 3)]

simulations can be done within a reasonable time Using theharmonic FCs we can obtain the phonon spectrum As can beseen in Fig 3 the speeds of sound and most of the featuresare reproduced with very good accuracy It is well known thatin order to reproduce the flat feature in the transverse acoustic(TA) modes near the X point one must go well beyond thefifth neighbor For the band structure and the density of states(DOS) the overall agreement is good except for the Gruneisenparameters of the TA branch where our calculations whichonly include cubic force constants up to the first neighbor shelloverestimate γ (XTA) Based on Klemensrsquo formula [Eq (8)]one might anticipate that our model will slightly underestimatethe lifetime of TA modes and thus their contribution in thethermal conductivity

D Phonon lifetimes and mean-free paths

To get an idea of the relative contributions of the matrixelements representing the strength of the three-phonon inter-actions versus the phase space available for these transitionscharacterized by the two-phonon DOS we show in Fig 4 theplots of these quantities We define the contribution of thematrix elements as

F (ω) =sum

kλ

δ(ω minus ωkλ)sum

12

|V (kλ12)|2 (19)

From Fig 4 we can note that optical phonons have a muchlarger weight coming from the matrix element |V (kλ12)|2This explains why they have such a larger relaxation ratecompared to acoustic modes for which the contribution ofmatrix elements is very small The two-phonon DOS isrepresentative of the phase space available for the transitionsand is defined as

DOSplusmn2 (ω) =

sum

12

δ(ω minus ω1 plusmn ω2) (20)

From Fig 4 it can be inferred that one-phonon absorptionor emission (DOS+

2 ) dominates for low-frequency phonons

-02

-01

0

01

02

0 200 400 600 800 1000JD

OS

(arb

itrar

y un

its)

Frequency (1cm)

Joint Density Of States for Si

Square of Matrix elementsω=ω1minusω2ω=ω1+ω2

FIG 4 (Color online) Top line in blue is the DOS associatedwith two-phonon creation or annihilation (DOSminus

2 ) and bottom line ingreen is the DOS associated with one-phonon emission or absorption(DOS+

2 ) The red line is the contribution of the matrix elementsdefined in Eq (19) The peak at 500 cmminus1 is the main reason forsmaller lifetimes of optical modes

(acoustic) while two-phonon absorption or emission (DOSminus2 )

dominates at high frequencies (LA and optical)Next we show in Fig 5 the calculated lifetimes of the three

acoustic and optical modes versus frequency for a regularmesh of k-points in the first Brillouin zone at T = 70 and

10

100

1000

10000

1 2 4 8 16

Lif

etim

e (p

s)

Frequency(THz)

3 103ν2

TA1TA2LA

TO1TO2LO

10

100

1000

10000

Lif

etim

e (p

s)

104ν3

TA1TA2LA

TO1TO2LO

FIG 5 (Color online) Lifetimes of the six branches in Si at 277 Kvs frequency on a logarithmic scale Top plot is for umklapp andbottom plot is for normal processes The quadratic dependence of theacoustic modes can be noticed for normal processes while umklappprocesses seems to scale as 1ω3

085204-8

KEIVAN ESFARJANI GANG CHEN AND HAROLD T STOKES PHYSICAL REVIEW B 84 085204 (2011)

-600

-400

-200

0

200

400

600

800

G K X G L X W L

100

(Gru

neis

en-3

)

Freq

uenc

y (1

cm

)

DOS Kpoints



Total DOS





F (ω) =sum

kλ


12

|V (kλ12)|2 (19)


DOSplusmn2 (ω) =

sum

12




-02

-01

0

01

02

0 200 400 600 800 1000

JDO

S (a

rbitr

ary

units

)

Frequency (1cm)









10

100

1000

10000

1 2 4 8 16

Lif

etim

e (p

s)

Frequency(THz)

3 103ν2

TA1TA2LA

TO1TO2LO

10

100

1000

10000

Lif

etim

e (p

s)

104ν3

TA1TA2LA

TO1TO2LO


085204-8

PRB 84 085204

3976

REV

IEW

wwwadvmatdewwwMaterialsViewscom

copy 2010 WILEY-VCH Verlag GmbH amp Co KGaA Weinheim Adv Mater 2010 22 3970ndash3980wileyonlinelibrarycom

different phonon modes and reduce thermal conductivity A schematic diagram is shown in Figure 5 capturing these var-ious phonon scattering mechanisms along with the electrical transport within a thermoelectric material

Thus in certain cases nanodots clearly play a very signifi cant role in reducing lattice thermal conductivity probably by effec-tively scattering phonons that otherwise would have relatively long mean free paths In many of these cases it has been clearly demonstrated that the reduction in thermal conductivity far exceeds any concomitant reduction in the power factor caused

of Sb [ 73 ] In contrast similar fractions of nanoparticles of Bi or Pb (two elements that have the same atomic mass as the Pb ions in the rock salt lattice) were found to have no such effect [ 73 81 ] ErAsInGaAs is another interesting example to study along these lines since the size distribution of ErAs nanoparticles in the matrix is not a strong function of the growth parameters and they are typically 2ndash4 nm in diameter [Figure 3 c] [ 82 ] The volume fraction of the embedded nanoparticles can be easily changed from 001-6 without introducing defects or disloca-tions Thermal conductivity measurements show a reduction by as much as a factor of 3 compared to the bulk alloy [Figure 4 b]

The question remains as to why the inclu-sion of nanodots can reduce the thermal conductivity below the alloy limit Detailed calculations of phonon transport have been performed for ErAsInGaAs materials although the principles developed through these studies are fairly general and apply for other nanodot material systems as well [ 72 82 ] Atomic scale defects in alloys scatter pho-nons due to differences in mass or due to generation of strain fi elds and the scattering cross-section follows Rayleigh scattering as d 6 λ 4 where d is the nanodot diameter and λ is the phonon wavelength Hence short wavelength phonons are effectively scattered in alloys but the mid-to-long wavelength phonons can propagate without signifi cant scattering and thereby still contribute to heat conduction By inclusion of nanoparticles signifi cant reduction in lattice thermal con-ductivity can be achieved by the additional scattering of mid- and long-wavelength pho-nons by the nanoparticles Calculations show that a wide size distribution of nanoparticles is preferable since it can effectively scatter

Figure 5 Schematic diagram illustrating various phonon scattering mechanisms within a ther-moelectric material along with electronic transport of hot and cold electrons Atomic defects are effective at scattering short wavelength phonons but larger embedded nanoparticles are required to scatter mid- and long-wavelength phonons effectively Grain boundaries can also play an effective role in scattering these longer-wavelength phonons

Nanoparticle

Short wavelength phonon

Midlong wavelength phonon

Atomic defect

Grainboundary

Hot Electron

Cold Electron

Figure 4 Lattice thermal conductivity as a function of temperature for (a) various PbTe-based alloys (x = 01) and nanostructured samples The value of x = 01 was chosen because these samples have the same concentration of added component to PbTe as those in LAST-18 and SALT-20 (b) InGaAs with and without embedded ErAs nanodots It is seen in both cases that the inclusion of nanodots into the microstructure results in a signifi cant reduction to the lattice thermal conductivity In the PbTe system solid solution alloying is effective around room temperature (see black dotted arrow) but not at high temperature Nanostructuring is shown to be effective both at room temperature and at high temperatures (see brown dotted arrows)

0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g

Solid solution alloying

nanostructuring(A)


Mean free pathscattering time(how often energy carriers scatter and lose energy)

Adv Mat 22 3970

Classic example Phonon boundary scattering and reduced k

APL 105 082907

Grain boundaries in BTO FE Domain boundaries in BFO

APL 102 121903

observed even for grain sizes as large as 63 nm As expectedthe epitaxial thin film sample shows a higher thermal con-ductivity than any nano-grained samples but is a factorof two lower than the reported bulk values818 which isattributed mainly to film size effects This coincideswell with data taken by Foley et al7 on SrTiO3 showing asimilar dependence of thermal conductivity with grain sizeand a similar reduction from bulk values of approximately11 W m1 K1 (Ref 28)

The dependence of thermal conductivity on grain sizeshown in Fig 3 illustrates limitation of the phonon meanfree path spectrum by grain boundaries With smallergrains phonons with mean free paths greater than the grainsizes scatter more readily translating into a reduced abilityto conduct thermal energy This is consistent with previousobservations of nano-grained silicon29 and our previous

measurements of grain size dependence on the thermalconductivity of SrTiO37 The strong dependence of thermalconductivity on grain size greater than 40 nm implies pho-nons with mean free paths greater than 40 nm are conduct-ing thermal energy This directly conflicts with the picturethat phonons in these complex oxides (eg BaTiO3 andSrTiO3) have non-spectral (ie gray) mean free paths thatare 2 nm which has been used to analyze phonon trans-port in SrTiO3 previously9 The spectral nature of thermalconductivity in BaTiO3 is illustrated by the model used inthis study shown in the inset of Fig 3 (details of thismodel are described below) We see that with the nano-structured sample the reduction in thermal conductivityarises from a limited contribution of the low frequencylong wavelength phonons At higher frequencies the con-tribution to thermal conductivity is identical to bulkbehavior

Our model is based on semi-classical formalisms of thekinetic theory expression for thermal conductivity to modelthe spectral phonon transport and grain boundary scatteringin our BaTiO3 films We approximate the phonon dispersionby a sine-type relation and only take contributions to thethermal conductivity from the acoustic branches of the pho-non dispersion into account Our model is based on theKinetic Theory expression j frac14 Ck=3 frac14 C2s=3 where j isthe thermal conductivity C is the heat capacity is thesound velocity k is the mean free path and s is the scatteringtime The boundary scattering is taken into account in thetotal scattering time by Matthiessenrsquos rule given by

1

sfrac14 ATx2 exp

B

Tthorn Dx4 thorn

df ilmthorn

dgb(1)

In this expression from left to right we account for thephonon-phonon scattering impurity scattering film thick-ness scattering and grain boundary scattering respectivelyHere T is the sample temperature x is the phonon fre-quency d is the appropriate thickness or grain size and A Band D are fitting parameters associated with the bulk scatter-ing processes These fitting parameters are determined ini-tially by fitting the model to bulk single crystal data18

without the additional grain boundary and interface scatter-ing components and are given as Afrac14 700 1017 s K1Bfrac14 165 K and Dfrac14 1 1035 s3

FIG 2 Plan-view scanning electronmicrographs of polycrystalline BaTiO3

films annealed between (a) 800 ampC and(e) 1000 ampC (f) is a cross-sectionalimage of the 1000 ampC annealed BaTiO3

film

FIG 3 Room temperature thermal conductivity of BaTiO3 as a function ofgrain size along with the measured thermal conductivity of a single crystalfilm For comparison we also show the thermal conductivity of bulk singlecrystal BaTiO3 reported by Mante and Volger18 The dashed line representsour model calculations for BaTiO3 as a function of grain size Also includedis similar data for another common perovskite SrTiO3 from Foley et al7

The inset shows the spectral contribution to thermal conductivity with vary-ing phonon frequency highlighting the impact of nano-structuring to lowfrequency phonons

082907-3 Donovan et al Appl Phys Lett 105 082907 (2014)

This article is copyrighted as indicated in the article Reuse of AIP content is subject to the terms at httpscitationaiporgtermsconditions Downloaded to IP 137545881On Wed 27 Aug 2014 200415





1

sfrac14 ATx2 exp

B

Tthorn Dx4 thorn

df ilmthorn

dgb(1)





film





associated with grain boundaries in silicon strontium tita-nate and yttria-stabilized zirconia (YSZ)

We used substrate vicinality to prepare a set of epitaxialBiFeO3 films with varying numbers of domain variants anddomain wall densities Films were prepared using adsorption-controlled reactive molecular-beam epitaxy (MBE) on (001)-oriented non-vicinal (oriented within 605 of (001)) andvicinal 4 miscut along [100] and vicinal 4 miscut along[110] SrTiO3 substrates Synthesis details can be found else-where2425 All films were phase-pure by X-ray diffractionand were of high crystalline quality with omega rockingcurve full width at half maximum values equivalent to theunderlying substrates (typically 001)

Figure 1 presents domain orientation maps of the4-domain (a) and 2-domain (b) variant specimens deducedfrom the PFM images (Fig 1 in supporting information)40 Inalmost every case the domains share the same normal orienta-tion but the domain density and morphology is distinct for thetwo specimens As anticipated there are far more domains aswell as polarization directions apparent for the 4-domainfilm Images from the 1-domain variant samples exhibited nocontrast signifying a uniform single polarization

Focusing on the domain walls the 4-variant case wasfound to exhibit 1990 lm of domain boundary per lm2 offilm area compared with only 1398 lm per lm2 of film forthe 2-variant specimen and no measured domain walls forthe single-variant specimen Local polarization rotationangles along every domain wall can additionally be mappedbased on simple lookup tables which consider the adjacentdomain orientations26 As with our previous work on similarspecimens all domain boundaries exhibited essentiallypurely 71 rotations Domain boundary types can similarlybe determined and visualized including charged (head-to-

head tail-to-tail) and neutral (head-to-tail and tail-to-head)interfaces as shown in Figs 1(c) and 1(d) for 4-domain and2-domain films respectively The ratio of charged to neutraldomain boundaries is 2021 for the 4-domain variant and1051 for the 2-domain variant

With this knowledge of the domain boundary statisticswithin the films we measured the thermal conductance ofthe 30 nm thick BiFeO3 films with TDTR23 Our assumptionsin this analysis are outlined in the supporting informationThe effective thermal conductivities of the BiFeO3 filmsdetermined from our TDTR measurements are shown inFig 2 We observe a clear trend in the effective thermal con-ductivities of the BiFeO3 and the number of domain variantsAn increase in the number of domain variants and subse-quently density of domain walls in the film leads to adecrease in thermal conductivity We ascribe this depend-ency to phonons scattering in the domain boundaries and cre-ating a temperature gradient across the individual domainwalls More domain variants in the BiFeO3 lead to more do-main boundaries as shown in Fig 1 and therefore increasedphonon scattering and lower thermal conductivities We notethat the domain boundaries are coherent unlike grain boun-daries which are typically highly disordered and therebyforce phonon scattering through impurity-like mechanismsCharged domain walls may be important to the thermalresponse but additional experiments are necessary to isolatethis effect We also point out that the thermal conductivitiesof the BiFeO3 films are most likely affected by size effectsdue to the thin film geometry that is phonon scattering atthe film boundaries of the BiFeO3 can cause a reduction inthe thermal conductivity of the films as compared to athicker or ldquobulkrdquo sample27ndash29 However since all samplesare 30 nm the finite size of the sample has the same effect in

FIG 1 Ferroelectric domain orientationmaps for 4-domain (a) and 2-domain (b)specimens with corresponding imagesof domain boundary types and chargingin (c) and (d) revealing the substantialdifference in domain wall density fordistinct polarization variants The200 nm scale bars in (a) and (b) apply toall images for each specimen (columns)

121903-2 Hopkins et al Appl Phys Lett 102 121903 (2013)

Downloaded 28 Mar 2013 to 137541851 This article is copyrighted as indicated in the abstract Reuse of AIP content is subject to the terms at httpaplaiporgaboutrights_and_permissions

all of the films therefore highlighting the domain walleffects on thermal transport in BiFeO3

Since the thermal conductivity of BiFeO3 has not beenreported elsewhere we compare these effective thermal con-ductivities to other material systems to put our reported effec-tive thermal conductivities into perspective We plot thethermal conductivity of bulk SrTiO32030 a prototypical perov-skite and amorphous SiO231 The effective thermal conductiv-ities of the BiFeO3 films show temperature dependenciessimilar to crystalline SrTiO3 (ie a slight maximum due tothe onset of Umklapp scattering) which is expected since theBiFeO3 films are fully crystalline but the values are muchcloser than those of SiO2 especially at elevated temperaturesand in the multi-domain samples

Since the phonon scattering across the domain wallsleads to a temperature drop across the domain boundarieswe can quantify the thermal transport across the domainboundaries with a thermal boundary conductance3233 Thisidea of thermal boundary conductance across domain wallsor ldquointernal interfacesrdquo was first observed in potassium dihy-drogen phosphate (KDP) at liquid helium temperatureswhere phonon transport in the KDP was mostly ballistic andphonon transmission across the domain walls was nearlyentirely specular and elastic1213 To calculate the thermalboundary conductance of the domain walls in the BiFeO3

films we use a series resistor approach utilizing the data pre-sented in Fig 23435 From our domain wall maps we deter-mine dfrac14 715 and 502 nm for the 2- and 4-domain variantsamples respectively We calculate the thermal boundaryconductance for both the 2- and 4-domain variant casesand average the resulting values to give the conductanceacross the coherent domain boundary shown in Fig 3 The

uncertainties in these values are calculated from the standarddeviation about of mean values calculated from the 2- and4-domain variant samples The domain boundary conduct-ance exhibits values that are similar to typical boundary con-ductances between well acoustically matched metals andnon-metals (ie on the order of 100 MW m2 K1 at roomtemperature)36 For comparison we also plot the thermalboundary conductance across grain boundaries in YSZ34 sil-icon37 and SrTiO320 We also include Si grain boundarythermal boundary conductances determined with moleculardynamics (MD) simulations3839 The thermal boundary con-ductances across the YSZ Si and SrTiO3 grain boundariesare consistently higher than the Kapitza conductances acrossthe BiFeO3 domain boundaries even though the grain boun-daries are highly disordered regions while in contrast thedomain walls are completely coherent This indicatesstrongly resistive phonon processes in the domain wallregion To put these values into perspective we plot theequivalent conductances of some thicknesses d of SiO2These conductances are calculated via hSiO2

frac14 jSiO2=d where

d is indicated in Fig 3 The thermal boundary conductanceacross the BiFeO3 domain boundaries are similar to 10 nmof SiO2 again indicating the relatively high thermal resistiv-ity associated with the domain walls

The very low thermal boundary conductance across do-main boundaries is surprising given the coherency of theinterfaces It is possible that this phenomenon is intrinsic toferroelastic domain boundaries as Weilert and coworkersmeasured substantially lower thermal conductivities in poly-domain KDP compared to poled crystals1213 Another possi-ble source of the thermal resistance is the presence ofinhomogeneous strain at the domain walls Interestingly

FIG 2 Effective thermal conductivities of the BiFeO3 films (filled sym-bols) There is a clear dependence of the thermal transport on the number ofdomains which we ascribe to additional temperature drops across the nano-meter thick domain walls caused by phonon scattering in the localized strainfield For comparison we also plot the thermal conductivity of bulk SrTiO3

(open squares Refs 20 and 30) and amorphous SiO2 (solid line Ref 31)

FIG 3 Thermal boundary conductance across the domain walls in theBiFeO3 films For comparison we also plot the calculated thermal boundaryconductance across grain boundaries in YSZ (filled triangles Ref 34) sili-con (filled circles Ref 37) and SrTiO3 (empty triangles Ref 20) We alsoinclude Si grain boundary thermal boundary conductances determined withmolecular dynamics from Refs 38 and 39 The thermal boundary conduc-tances across the YSZ Si and SrTiO3 grain boundaries are consistentlyhigher than the thermal boundary conductances across the BiFeO3 domainboundaries even though the grain boundaries are highly disordered regionswhere the domain walls are completely coherent We also plot the equivalentconductances of some thickness d of SiO2 (solid lines with d indicated in theplot) The thermal boundary conductance across the BiFeO3 domain bounda-ries is similar to the equivalent conductance of 10 nm of SiO2












Spectral phonon transport in alloys

How do defects and interfaces play a role

3976

REV

IEW








Nanoparticle



Atomic defect

Grainboundary

Hot Electron

Cold Electron


0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g


nanostructuring(A)

Adv Mat 22 3970

Short wave point defects

Long wave Boundaries

conductivity increases with thickness we can safely say thatthe reduction is not due to film dislocations Intriguinglythe thermal conductivities of the alloy thin films measuredin this Letter are among the lowest of any of the previousmeasurements on SiGe-based thin-film systems We notethat the only previous data that approach our lowest mea-sured value are those in which the authors admit that themeasured samples have poor crystal quality (black filledsquares in Fig 2) [2]

To quantify this effect we turn to a model originallyproposed by Wang and Mingo [31] in which thermalconductivity is given by

frac14Z c=kBT

0

k4BT3

22v3 ethT yTHORNy4 exp ethyTHORNfrac12exp ethyTHORN 1amp2 dy (1)

where kB is Boltzmannrsquos constant is Planckrsquos constantdivided by 2 T is temperature and y frac14 =kBTis a dimensionless parameter The average velocity v iscalculated by v frac14 frac12eth1 xTHORNv2

Si thorn xv2Geamp1=2 where x is

the Ge concentration and vSi and vGe are the averagespeeds of sound in Si and Ge respectively as calculatedby Wang and Mingo [31] The scattering time for a givenfrequency is related to the individual processes viaMattheissenrsquos rule frac14 eth1

U thorn 1a thorn 1

b THORN1 where U

a and b are the umklapp alloy and boundary scatteringtimes respectively These are given by

U frac14 frac12eth1 xTHORN1USi thorn x1

UGeamp1 (2)

a frac14 frac12xeth1 xTHORNA4amp1 (3)

andb frac14 d=v (4)

where1USiethGeTHORN frac14 BSiethGeTHORN

2 exp ethCSiethGeTHORN=TTHORN (5)

The constants A B andC are taken from Ref [31] and d isthe film thicknessOur model is thus identical to that in Ref [31] except

for the cutoff frequency which we define as c frac14 2v=awith a being the lattice constant of the Si1xGex filmapproximated by Vegardrsquos law a frac14 eth1 xTHORNaSi thorn xaGewhere aSi and aGe are the lattice constants of silicon andgermanium respectively Equation (1) assumes a disper-sionless Debye system This is acceptable for Si1xGexsystems with nondilute alloying compositions since thedispersive phonons scatter strongly with the alloy atomsdue to their high frequencies This assertion is substanti-ated by the reasonable agreement found between thismodel our data and previously reported measurementson thin-film alloys in Refs [2723] as shown in Fig 2To first assess the role of alloy composition Fig 3

shows the measured thermal conductivity versus Geconcentration and the predictions of the thermal conduc-tivity for bulk and thin-film Si1xGex of three differentthicknesses at room temperature using Eq (1) ForSi1xGex with 02lt xlt 08 we found that the thermalconductivity is almost flat and in agreement with ourexperimental results This lack of dependence on the Geconcentration is much more pronounced in thin films than

1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Period or Film Thickness (nm)

T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2

SiGe SL Ref 4SiGe SL Ref 6

Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Total Sample Thickness (nm)

FIG 2 (color online) Thermal conductivity measurements onSi08Ge02 of the thickness series along with previously reportedvalues of different SiGe superlattices alloy-based superlatticesand alloy films at room temperature Closed symbols representsuperlattices open symbols represent Si1xGex films The ther-mal conductivity is plotted versus (a) period or film thicknessand (b) total sample thickness The figure also shows the modelpresented in Eq (1)

00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10

Composition Series Thickness Series

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm

FIG 3 (color online) Predictions of the thermal conductivityas a function of Ge composition for bulk and thin-film Si1xGexof three different thicknesses calculated at room temperatureby using Eq (1) The symbols correspond to experimental dataon the thickness series (down open triangles) and compositionseries (up filled triangles) With decreasing film thicknessalloying induces smaller and smaller changes in the thermalconductivity as size effects begin to dominate

PRL 109 195901 (2012) P HY S I CA L R EV I EW LE T T E R Sweek ending

9 NOVEMBER 2012

195901-3

Phys Rev Lett 109 195901

Thermal conductivity Si1-xGex alloys

3976

REV

IEW








Nanoparticle



Atomic defect

Grainboundary

Hot Electron

Cold Electron


0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g


nanostructuring(A)

Adv Mat 22 3970



frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3







J Appl Phys 121 205104

Spectral phonon transport in ferroelectric solid solutions

How do defects and interfaces play a roleThermal conductivity of PZT thin films

compositions (x) which were calculated as a ratiometricmixture of the room temperature heat capacities of PbZrO3

and PbTiO327

For this study we amplitude-modulate the pump beamwith an 8 MHz sinusoid and monitor the ratio of the in-phaseto an out-of-phase signal of the probe beam with a lock-inamplifier We fit the TDTR model to the data by varying thethermal conductivity of the PZT films and the thermalboundary conductance between the top metal film and thePZT samples While the 1=e thermal penetration depth ofour pump beam at 8 MHz is less than or approximately equalto the PZT film thickness for all the compositions in thisstudy (approximately 135 nm for 0ltx lt 07 increasing toapproximately 180 nm at xfrac14 1) our analysis suggests thatthe TDTR data could be sensitive to thermal transport acrossthe platinized-silicon stack (100 nm Pt40 nm ZnO300 nmSiO2Bulk Si) upon which the PZT films are depositedTherefore the platinized-silicon samples were also charac-terized via TDTR to eliminate the number of unknowns inthe thermal model for the PZT thin films

For performing these calibrations platinized-siliconsamples both with and without the 300 nm SiO2 were fabri-cated for TDTR measurements For these samples a two-layer model of a platinum thin film on either SiO2 or Si wasemployed where the thermal boundary conductance betweenthe layers (h1) was fit to the TDTR data (heat capacity ther-mal conductivity and thickness of the platinum top layer areall known as are the heat capacity and thermal conductivityof SiO2 and Si) This two-layer approach was used in orderto lump the thermal conductivity of the 40 nm ZnO layer inwith the conductances across the PtZnO and ZnOSiO2 orZnOSi interfaces into a single total conductance At 8 MHzthe buried 300 nm SiO2 layer can be considered ldquothermallythickrdquo and it is therefore reasonable to consider it as asemi-infinite bottom layer in the model

In practice the measurements made on the sample with300 nm SiO2 were unable to provide a reliable value for h1

due to the competing sensitivity of the thermal data to theproperties of the SiO2 Alternatively fitting the data for thesample without the SiO2 provided much more accurateresults due to the fact that the sensitivity to h1 is increasedbecause of the two order of magnitude increase in the j ofthe semi-infinite layer (14 W m1 K1 for SiO2 145 W m1

K1 for Si) Fitting this data resulted in a lumped conduc-tance of the 40 nm ZnO film along with its adjacent bound-ary conductances of hZnOfrac14 96 MW m2 K1

For fitting the PZT thin film data a three-layer model isused layer 1 is the aluminum thin film layer 2 is the PZTthin film and layer 3 is SiO2 (semi-infinite) Due to the largeconductances of the platinum and ZnO thin films(hPt frac14 jPt=dPtfrac14 41 W mndash1 K1100 nmfrac14 410 MW m2 K1hZnOfrac14 96 MW m2 K1) compared to the effective conduc-tance of the PZT thin films (hPZT frac14 jPZT=dPZTfrac14 13 W m1

K1300 nmfrac14 433 MW m2 K1) it is reasonable to com-bine hPt and hZnO into a single conductance for use in thethree-layer model between the PZT and SiO2 layers(h2frac14 778 MW m2 K1) via h2 frac14 ethhPt thorn hZnOTHORN1 With h2

thoroughly characterized the thermal conductivity of the

PZT thin films can be extracted from the TDTR data withthe three-layer model to a high degree of confidence

III RESULTS

Figure 3 shows the measured thermal conductivities ofthe PZT thin films as a function of their solid solution com-position fabricated with pyrolysis temperatures of 350 ampC(blue squares) and 400 ampC (red circles) Starting with thePbTiO3 thin film (x frac14 100) we measure a thermal conduc-tivity of 224 W m1 K1 This value is 557 lower thanthe single crystal value of 506 W m1 K1 reported in Ref28 which we attribute to phonon scattering at the film andgrain boundaries in our samples As the molar fraction ofPbZrO3 increases (x decreases) we observe a decrease in thethermal conductivity compared to the PbTiO3 (xfrac14 100)end-member Over the range 080ltx lt 100 the thermalconductivity drops from 224 W m1 K1 to 140 W m1

K1 a reduction of 375 Such a steep reduction in thethermal conductivity of an initially stoichiometrically purematerial system with the addition of an additional specieshas been shown to occur in several systems1516 and is oftenexplained in the context of alloyimpurity phonon scatteringIn this case the fraction of B-sites in the ABO3 perovskitesystem populated with zirconium instead of titanium atomsincreases as x decreases and these zirconium atoms serve asmass-impurity scattering sites for phonons We do notbelieve that this reduction between the xfrac14 10 and xfrac14 080to be due to an increase in phonon scattering caused by phys-ical boundaries because of the fact that the xfrac14 080 sampleis thicker and has larger grains than the xfrac14 10 sample

Across the range for x lt 080 the trend in thermalconductivity remains largely flat with the exception of anapparent discontinuity in the vicinity of the MPB (045 ltx lt054) This discontinuity is present in both of the finer com-position sets that were pyrolyzed at temperatures of 350 ampC

FIG 3 Thermal conductivity (j) of PZT thin films with various solid-solution compositions x fabricated with pyrolysis temperatures of 350 ampC(blue squares) and 400 ampC (red circles) The black dashed vertical linesdenote the locations of the phase boundaries from Fig 1 at 20 ampC The blueand red dashed vertical lines highlight the observed discontinuities in jaround the MPB for the 350 ampC (fine-grained) and 400 ampC (large-grained)pyrolysis sample sets

205104-4 Foley et al J Appl Phys 121 205104 (2017)

BulkThin film

and 400 C to yield different average grain size morpholo-gies (lt100 nm average diameter at 350 C gt 500 nm aver-age diameter at 400 C) Since the discontinuity is present inboth cases the existence of the discontinuity appears to beunrelated to grain size Apart from this region the thermalconductivity is approximately 12 6 02 W m 1 K 1 and canbe attributed to the strong scattering of high-frequency pho-nons via a variety of point defect-scattering mechanismsincluding mass-disorder and strain due to differences inatomic radii Interestingly the thermal conductivity doesnot increase as x decreases over the range 0lt x lt 020approaching pure PbZrO3 at x frac14 0 In most alloy sys-tems1516the trend in thermal conductivity as a function ofthe composition will create a ldquoU-shaperdquo where the thermalconductivities of the constitutive components (x frac14 0 1) areboth much greater than the thermal conductivity over 020lt x lt 080 However the PZT system does not exhibit thisU-shaped symmetry as a function of the composition withthe thermal conductivity of thin film PbZrO3 measuring 44lower than thin film PbTiO3 (125 and 225 W m 1 K 1respectively)

While there are published measurements of the thermalconductivity of bulk ceramic PbZrO3 from 2ndash40 K (Ref 29)and 345ndash530 K (Ref 30) there remains a gap in measuredthermal conductivities from 40ndash345 K (cf Fig 4)Nonetheless the temperature trends in these two publisheddata sets suggests a relatively short phonon mean free pathof a significant portion of heat carrying vibrations within thematerial on the order of some fraction of the unit cell sizeleading to an amorphousglass-like trend in the temperaturedependence of the thermal conductivity This glass-like trendis markedly different from that of bulk PbTiO3 which exhib-its a clear maximum in thermal conductivity around 40 Kand decreases for increasing temperaturemdasha trend typicallyobserved in crystalline materials due to Umklapp scatter-ing31 As a result it is reasonable to postulate that the consid-erable difference in the thermal conductivities of thin filmPbZrO3 and PbTiO3 is driven by the intrinsic properties ofthe materials and not an extrinsic size effect

In order to confirm this postulation bulk samples ofPbZrO3 (x frac14 0) 7030 PZT (x frac14 030) and 3070 PZT(x frac14 070) were fabricated to verify that the observed trendsin the thin film samples extended to the bulk as well Thethermal conductivities of these samples are plotted in theinset of Fig 5 (black diamond) along with the bulk data for

PbTiO3 from Ref 28 (white diamond) and bulk data for sam-ples around (Ref 10 upward triangles) and at (Ref 11downward triangle) the MPB Similar to the thin film datathe thermal conductivity decreases dramatically for x lt 10ultimately asymptoting to a thermal conductivity of157 6 013 W m 1 K 1 for bulk PbZrO3 This value forPbZrO3 compares well with the porosity-corrected valuereported in Ref 30 of 179 W m 1 K 1 measured at a tem-perature of 345 K

IV DISCUSSION

One of the potential causes for the large difference inbulk thermal conductivities between stoichiometrically simi-lar materials such as PbTiO3 and PbZrO3 may be explainedby the nature of their respective ferro-distortions that makethem technologically relevant In the case of PbTiO3 as thecrystal goes from cubic to tetragonal below the Curie tem-perature (approximately 500 C) there is a shift of the TiO6

FIG 4 Fits of Eq (1) to bulk data for(a) PbTiO3

28 and (b) PbZrO32930 to

extract impurity and Umklapp scatter-ing coefficients Solid magenta linesdenote total thermal conductivitywhich is the sum of the contributionfrom the acoustic modes (jAM bluedashed lines) modeled by a sine-typedispersion and the optical models cal-culated using the minimum limit (jMLred dashed lines) using a Debye-typedispersion

FIG 5 Thermal conductivity of PZT thin films plotted with the model fromEq (1) The data and model related to samples pyrolyzed at 350 C aredenoted by blue squares and dashed blue line respectively while the dataand model related to samples pyrolyzed at 400 C are denoted by red circlesand dashed red line respectively Inset Thermal conductivity of bulk PZTwith various solid-solution compositions Black diamonds represent samplesfabricated and measured as part of this work white diamond from Ref 28upward triangles from Ref 10 and downward triangle from Ref 11 Thedashed black line is the model from Eq (1) with film boundary and grainboundary scattering omitted The black arrow highlights the discontinuity inj based on literature values for bulk materials around the MPB


This talk Hafnium zirconium oxide thin films

phase appears at room temperature910 To takeadvantage of these high-temperature phases withhigher dielectric constant which are metastable atroom temperature control over the respective crys-tal structures must be developed To realize a high-dielectric-constant phase at lower temperature oneapproach is elemental doping into HfO2 In 2006Tomida et al reported that the dielectric constant ofHf1ndashxSixO2 was increased when doped with a smallamount of Si after annealing at 800C9 Based onfirst-principles calculations Fischer et al eluci-dated the influence of dopants on the dielectricproperties of HfO2 and ZrO2

10 These results areclosely related to tetragonal phase formation In thisresearch trend the unexpected ferroelectricity ofthin HfO2-based films was first discovered in 2007by Boscke et al at dynamic random-access memory(DRAM) manufacturer Qimonda when the com-pany was also looking for optimized dielectricmaterials for DRAM capacitors and verified bythe Waser group in Aachen The experimentscontinued at NaMLab and Fraunhofer CNT andthe results were first published in 2011 Bosckeet al reported evidence for the formation of ferro-electric crystalline phase in SiO2-doped HfO2 thinfilms deposited by ALD5 The ferroelectric behavioris believed to originate from the noncentrosymmet-ric orthorhombic phase (space group Pca21) whichis not found in the equilibrium phase diagram ofHfO2

4ndash99 Since then numerous experimental andtheoretical studies on ferroelectric HfO2-basedmaterials have been reported

In this paper recent advances in the ferroelectricproperties of HfO2-based films especiallyHf05Zr05O2 (HZO) since 2011 including dopingeffects mechanical stress effects interface effectsand ferroelectric film thickness effects are compre-hensively reviewed411ndash99 These effects are themain factors affecting the ferroelectric propertiesof HZO thin films as shown in Fig 1 Table Ipresents a brief comparison of material propertiesand scalability between conventional PZT and fer-roelectric HfO2 (including HZO) Compared withPZT HZO is compatible with CMOS flow [evenback-end of the line (BEOL) thermal budget] andcan exhibit robust ferroelectricity even below 50 nmthickness

DOPING EFFECTS ON HFO2 FILM

Recently ferroelectricity in thin (10 nm) Hf1ndashxBxO2 films where B = Si Zr Y Al Gd Sr Laetc deposited by ALD has been reported5ndash8 Amongthe reported dopants Zr is the most promising fortwo reasons First the Zr dopant content formaximum ferroelectric polarization can bestable at 50 due to its very similar physicaland chemical properties to those of Hf while otherdopants are stable at much lower doping concen-trations (lt 20 for most dopants)6ndash8 By alternatelydepositing Hf and Zr precursors (at HfZr ratio of

11) through an ALD process homogenous andreproducible HZO thin films with ferroelectricpolarization can be realized more easily in massproduction whereas other ratios (such as 20) aredifficult to achieve homogeneously (as ALD canresult in vertical inhomogeneous doping) Secondferroelectric properties of HZO films can be achievedat relatively low processing temperature becausethe crystallization temperature of ZrO2 is generallylower than that of other high-k dielectrics It hasbeen reported that during deposition of the TiN topelectrode by an ALD process at 400C41 or a CVDprocess at 500C12 ferroelectric polarization can beobtained by crystallization of the as-deposited HZOfilm without further heat treatment However HfO2

films doped with elements other than Zr requirerelatively high-temperature (gt 650C) treatmentmethods to stabilize the orthorhombic phase inorder to obtain ferroelectric polarization6ndash8

Muller et al first reported the observation offerroelectricity in capacitors based on HZO11 Thenthey also investigated the ferroelectric phase tran-sition according to composition covering the entiremixing range of Hf1xZrxO2 (x = 0 to 1) films asshown in Fig 2a b12 The electrical behavior of theHf1xZrxO2 (x = 0 to 1) films was dependent on thecomposition ratio When the Zr[Hf + Zr] composi-tional ratio was 0 linear dielectric property of theTiNHfO2TiN capacitor was observed However asthe Zr[Hf + Zr] compositional ratio was increased

Fig 1 Schematic illustration of factors affecting the ferroelectricproperties of HZO thin film and representative electrical resultsReprinted with permission from Ref 5

Ferroelectric Hf05Zr05O2 Thin Films A Review of Recent Advances 247

JOM 71 246


What are the phonon thermal transport mechanisms dictating the thermal conductivity of HZO thin films

Interplay amongbull Boundary scatteringbull ldquoAlloyrdquo scattering

(Hf and Zr masses)bull Crystalline (FE phase) vs

amorphous effects

Can we measure heat capacity of 20 nm thick HZO film

Top Electrode (Al for TDTR measurements)

Thermal ALD20 nm Hf1-xZrxO2

0 ⋜ x ⋜ 1As deposited or600 C annealed

10 nm TaN

Silicon substrate

Measuring thermal conductivity in thin films TDTR

TDTR Reviews and AnalysesRev Sci Instr 75 5119

Rev Sci Instr 79 114902J Heat Trans 132 081302

Ann Rev Heat Trans 16 159

43FDIBOJDBM ampOHJOFFSJOH

SP Tsunami3 W 80 MHz

90 fs pluse width

Pump

Isolator

EOM

BiBO

Redfilter

Dichroic

Probe

Camera toimagesample

Bluefilter

Lock-inamplifier

Photodiode

Delay line (sim7 ns)

ĶĴłĿĲ 4DIFNBUJD PG 553 TZTUFN BU UIF 6OJWFSTJUZ PG 7JSHJOJB

0 1 2 3 4 5

0

1

2

3

4

5

6

7

8

9

10

Pump-probe time delay (ns)

TDTR data 115 nm AlSi

Thermal model

ĶĴłĿĲ 553 EBUB PO B ON M ĕMN FWBQPSBUFE PO B 4JTVCTUSBUF BMPOH XJUI UIF CFTU ĕU UIFSNBM NPEFM 1SJPS UP M FWBQPSBUJPO13 UIF 4J XBT QSPDFTTFE XJUI BO BDJE FUDI UP SFNPWF UIF NBKPSJUZPG UIF TJMJDPO OBUJWF PYJEF MBZFS ćF UIFSNPQIZTJDBM QSPQFSUJFTEFUFSNJOFE GSPN UIF NPEFM CFTU ĕU BSF ℎ = 3808Nminus2 minus1 GPSUIF UIFSNBM CPVOEBSZ DPOEVDUBODF BDSPTT UIF M4J JOUFSGBDF BOE120581120581 = 112058118Nminus2 minus1 GPS UIF UIFSNBM DPOEVDUJWJUZ PG UIF 4J TVCTUSBUF

UIFSNBM EJČVTJPO UISPVHI UIF M ĕMN PDDVST13 XIJDI UZQJDBMMZPDDVST PO B UJNF TDBMF PG o QT lt13 gt SPN QTUP TFWFSBM OBOPTFDPOET13 UIF 553 TJHOBM JT SFMBUFE UP UIFUIFSNBM CPVOEBSZ DPOEVDUBODF BDSPTT UIF M4J JOUFSGBDFBOE UIF UIFSNBM FČVTJWJUZ PS UIFSNBM EJČVTJWJUZ JOUP UIF 4J13EFQFOEJOH PO UIF NPEVMBUJPO GSFRVFODZ PG UIF QVNQ ltgtPS QVSQPTFT PG NFBTVSJOH UIF UIFSNBM CPVOEBSZ DPOEVDUBODF CFUXFFO UXP TPMJET13 UIF 553 EBUB CFUXFFO sim QTUP B GFX OBOPTFDPOET DPOUBJOT UIF QFSUJOFOU JOGPSNBUJPO

5P RVBOUJGZ UIF UIFSNBM CPVOEBSZ DPOEVDUBODF GSPNUIF 553 EBUB13 BO BDDVSBUF UIFSNBM NPEFM UIBU SFMBUFTUIF NFBTVSFE MPDLJO PVUQVU UP UIF UIFSNBM FYDJUBUJPO BOEQSPQBHBUJPO JO UIF TUSVDUVSFT PG JOUFSFTU NVTU CF VTFE PSNPTU 553 FYQFSJNFOUT13 UIF VTF PG (BVTTJBO QVNQ BOEQSPCF TIBQFT BMPOH XJUI B NFUBM USBOTEVDFS UIBU JT UIJDLFSUIBO UIF PQUJDBM QFOFUSBUJPO EFQUIT GBDJMJUBUFT UIF TPMVUJPOUP UIF DZMJOESJDBM IFBU FRVBUJPO JO B NVMUJMBZFS TUSVDUVSF BNFUBM ĕMN UIBU JT simo ON TIPVME TVďDF lt13 13 gtćF TQFDJĕDT PG UIF UIFSNBM NPEFM UP QSFEJDU UIF UFNQFSBUVSFDIBOHF PO UIF TVSGBDF PG UIF NFUBM USBOTEVDFS IBWF CFFO

PVUMJOFE JO TFWFSBM XPSLT QSFWJPVTMZ lto13 13 gt U JTJNQPSUBOU UP OPUF UIBU EVF UP UIF MBTFS QVMTF BDDVNVMBUJPOJO UIF TBNQMF GSPN B 5J 4BQQIJSF PTDJMMBUPS13 UIF UFNQFSBUVSFSJTF PO UIF TBNQMF TVSGBDF DPOTJTUT PG UXP QBSUT B SFBMDPNQPOFOU UIBU SFQSFTFOUT UIF UFNQFSBUVSF SJTF EVF UP UIFFYDJUBUJPO PG B TJOHMF QVMTF BOE TVCTFRVFOU UIFSNBM EJČVTJPOGSPN UIF TVSGBDF PG UIF NFUBM JOUP UIF VOEFSMZJOH NBUFSJBMBOE BDSPTT UIF NBUFSJBM JOUFSGBDFT UIJT SFBM SFTQPOTF JTEJSFDUMZ SFMBUFE UP UIF UJNF EPNBJO SFTQPOTF PG UIF TVSGBDFUFNQFSBUVSF GPMMPXJOH UIF PQUJDBM QVNQ QVMTF BOE BOJNBHJOBSZ DPNQPOFOU UIBU SFQSFTFOUT UIF UFNQFSBUVSF SJTFGSPN UIF QVMTF BDDVNVMBUJPO UIJT JNBHJOBSZ SFTQPOTF JT QSFEPNJOBOUMZ DPOUSPMMFE CZ UIF DIBOHF JO TVSGBDF UFNQFSBUVSFTVCKFDUFE UP UIF QFSJPEJD IFBU TPVSDF BU GSFRVFODZ 119891119891 PUIUIF SFBM BOE JNBHJOBSZ DPNQPOFOUT PG UIF IFBUJOH FWFOU BUUIF TBNQMF TVSGBDF DPOUBJO JOGPSNBUJPO BCPVU UIF UIFSNBMQSPQFSUJFT PG UIF TBNQMF BOE DBO CF VTFE UP BOBMZ[F 553EBUB GPS SPCVTU EBUB BOBMZTJT ćF UFNQFSBUVSF SJTF QSFEJDUFEGSPN UIF UIFSNBM NPEFM JT SFMBUFE UP UIF NFBTVSFE PVUQVU PGUIF MPDLJO BNQMJĕFS EVSJOH 553 FYQFSJNFOUT WJB

119881119881JO = Re 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891

119881119881PVU = Im 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891

XIFSF 119881119881JO JT UIF JOQIBTF DPNQPOFOU PG UIF MPDLJO USBOTGFSGVODUJPO BOE SFMBUFE UP UIF SFBM DPNQPOFOU PG UIF UFNQFSBUVSF SJTF BOE119881119881PVU JT UIF PVUPGQIBTF DPNQPOFOU PG UIF MPDLJO USBOTGFS GVODUJPO BOE SFMBUFE UP UIF JNBHJOBSZ DPNQPOFOUPG UIF UFNQFSBUVSF SJTF 119885119885119885119891119891119891 11989111989111988513 XIJDI JT UIF MPDLJO USBOTGFSGVODUJPO13 JT B GVODUJPO PG QVNQNPEVMBUJPO GSFRVFODZ1311989111989113 BOETVSGBDF UFNQFSBUVSF SJTF13 11989111989113 BOE JT HJWFO CZ

119885119885 10076491007649119891119891119891 11989111989110076651007665 = 120585120585infin10055761005576

119872119872=minusinfin119891119891 10076491007649119891119891 119891 119891119891MBTFS10076651007665 exp 10077131007713120484120484119872119872119891119891MBTFS12059112059110077291007729 119891

XIFSF 120585120585 JT B DPOTUBOU SFMBUFE UP UIF FMFDUSPOJDT13 UIFSNPSFĘFDUBODF DPFďDJFOU13 MBTFS QPXFST13 BOE GSFRVFODZ PG UIF MBTFSTPVSDF13 119891119891MBTFS13 BOE 120591120591 JT UIF QVNQQSPCF EFMBZ UJNF Z OBUVSFPG 13 QVMTF BDDVNVMBUJPO JT UBLFO JOUP BDDPVOU 4PMWJOH GPS WBSJPVT QVNQQSPCF EFMBZ UJNFT13 12059112059113 ZJFMET UIF PVUQVU PGUIF MPDLJO BNQMJĕFS UIBU JT SFMBUFE UP UIF NFBTVSFE EBUBUISPVHI UIF WBSJPVT UIFSNBM QSPQFSUJFT PG UIF TZTUFN 5PBOBMZ[F UIF EBUB13 UIF OFHBUJWF SBUJP PG119881119881JO UP119881119881PVU119885minus119881119881JO119881119881PVU119885ZJFMET B RVBOUJUZ UIBU JT EJSFDUMZ SFMBUFE UP UIF SFBM UFNQFSBUVSFSJTF PO UIF TVSGBDF PG UIF TBNQMF BOE JOWFSTFMZ SFMBUFE UPUIF JNBHJOBSZ UFNQFSBUVSF SJTF PO UIF TVSGBDF PG UIF TBNQMF6TJOH UIJT SBUJP JTNVDINPSF SPCVTU UIBOVTJOH FJUIFS119881119881JO BOE119881119881PVU BMPOF TJODF JU NJOJNJ[FT FSSPS EVF UP QSPCF CFBN ESJęBOE EFQIBTJOH13 EFDSFBTFT UIF OPJTF EVF UP UIF FMFDUSPOJDT13 BOEFMJNJOBUFT UIF OFFE UP TDBMF UIF NPEFM UP UIF FYQFSJNFOUBMEBUB PS OFFE UP LOPX UIF UIFSNPSFĘFDUBODF DPFďDJFOU PGUIF NFUBM USBOTEVDFS lt13 gt O JHVSF 13 TIPX UIF CFTUĕU PG UIF NPEFM UP UIF 553 EBUB BMPOH XJUI UIF WBMVFT PGM4J ℎ BOE UIF 4J 120581120581 UIBU BDIJFWF UIJT CFTU ĕU PęFO VTF BO4J TVCTUSBUF BT B DBMJCSBUJPO PG 553 UP FOTVSF PVS FYQFSJNFOUBM NFBTVSFNFOU DBO BDDVSBUFMZ SFQSPEVDF UIF UIFSNBMDPOEVDUJWJUZ PG TJOHMF DSZTUBMMJOF TJMJDPO BU SPPN UFNQFSBUVSF lt13 gt OPUF13 TVCTUBOUJBMMZ CFMPX SPPN UFNQFSBUVSF13

broad we derive all equations using a modulated heatsource noting that the solution is equivalent to that of anunmodulated source when x0frac14 0 Thus given the sameabsorbed average power of aA the fully extinguished sinu-soidally modulated source terms for pulsed and CW sourcesrespectively can be expressed as

GpulsedethtTHORN frac14 aE etheix0t thorn 1THORNX1

nfrac141detht n=fsTHORN (8)

GCWethtTHORN frac14 aA etheix0t thorn 1THORN (9)

These power functions are displayed in the inset to Fig 1(a)Given the radial symmetry and the periodic nature of thetime varying heat source Eq (2) is conveniently solved inHankel and frequency space Taking the Hankel and Fouriertransforms the heat diffusion equation and boundary condi-tion after simplification become

2 ~T~

zeth THORN

z2frac14 q2 ~T

~zeth THORN (10)

q2 frac14 jrk2 thorn iCvxjz

(11)

~Q~

top frac141

2pexp k2r2

0

8

~G xeth THORN (12)

where k denotes the Hankel transform variable and x denotesthe frequency space variable The notation used here consis-tent with a previous work26 is such that for a function

Yethz r tTHORN ~Y amp ~Yethz rxTHORN denotes the Fourier transform of Y

while ~Y~amp ~Y

~ethz kxTHORN denotes the Hankel transform of ~Y For

notational clarity we drop the k and x dependence of trans-formed functions The solution to this ordinary differentialequation in z after applying boundary conditions and noting

that the heat flux component in depth is ~Q~

zeth THORN frac14 jz

~T~

z is

given in matrix form as

~T~

zeth THORN~Q~

zeth THORN

2

64

3

75 frac14 cosh qzeth THORN 1

qjzsinh qzeth THORN

qjzsinh qzeth THORN cosh qzeth THORN

2

4

3

5~T~

top

~Q~

top

2

64

3

75

(13)

This solution is generalized to layered systems by noting that

Eq (13) is valid for any layer in which ~T~

top and ~Q~

top for that

layer are known While the heat flux is prescribed at layer 1rsquossurface the temperature at this surface is unknown To obtainthis quantity we invoke a semi-infinite boundary condition atthe back side of the final layer of some system having n layers(refer to Fig 1(a)) such that the following condition holds

limz1

~Qn~ethzTHORN frac14 0 (14)

Applying this condition to the nth layer allows the determi-

nation of ~T~

topn and ~Q~

topn defined to be the temperature and

heat flux component in depth at the surface of layer n ie at

z frac14Pnndash1

jfrac141 dj These quantities can then be related to the bot-tom temperature and heat flux of the (n ndash 1)th layer throughthe thermal boundary conductance (TBC) h (nndash1)n mathe-matically represented in matrix notation by

~T~

botn1

~Q~

botn1

2

64

3

75 frac141 1

h n1eth THORN=n

0 1

2

4

3

5~T~

topn

~Q~

topn

2

64

3

75 (15)

so that the bottom temperature and heat flux of the (n ndash 1)thlayer are known allowing for the solution to the temperatureand heat flux at the top of this layer as well This process canbe repeated for an arbitrary number of layers until ultimatelythe temperature at the top of layer 1 is determined This matrixapproach1427ndash29 can then be generalized so that the tempera-ture and heat flux within the nth layer can be determined from

~T~

n zeth THORN

~Qn~

zeth THORN

2

64

3

75 frac14cosh qnzneth THORN 1

qnjznsinh qnzneth THORN

qnjznsinh qnzneth THORN cosh qnzneth THORN

2

64

3

75

Yjfrac141

jfrac14n1n2

MjNj

~T~

top

~Q~

top

2

64

3

75 frac14~A~

~B~

~C~

~D~

2

64

3

75~T~

top

~Q~

top

2

64

3

75

(16)

FIG 1 Sample schematic for (a) the layered structure for the insulatedboundary condition discussed in Section II A and (b) the transparent sub-stratemetal filmliquid example supporting the bidirectional heat flux condi-tion discussed in Section II B All parameters used are listed within theirrespective layers to include in-plane and out-of-plane thermal conductivity(jr and jz) volumetric heat capacity (Cv) and thickness (d) Note that thefinal layers do not include d to emphasize that they are semi-infinite withrespect to the thermal length scales of laser heating The inset to (a) showsthe time-dependent functions governing the laser heat source for both pulsed(repetition rate of 80 MHz) and CW cases with modulation at 10 MHz

175107-3 J L Braun and P E Hopkins J Appl Phys 121 175107 (2017)

2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Characteristic

impulses

andresp

onsesfor(a)TDTR(b)FDTRan

d(c)SSTR

techniquesIn

TDTRthemag

nitude

ofthethermorefl

ectance

ismon

itored

asafunctionof

pump-probedelay

time

whilein

FDTR

thephaselagbetweenthepump

andprobeismon

itored

asafunctionof

frequen

cyIn

SSTRtemperature

chan

gesaremon

itored

forgivenchan

gesin

heatflux

Noticetheincrease

inthermal

pen

etration

dep

thresultingfrom

thelower

mod

ulation

frequen

cies

employedin

SSTR

temperaturechan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

experim

entsthe

timede

laybetweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

temperaturechan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshiftin

thermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becom

eslow

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

periods

ofthemod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarrerent

pump

pow

ers

thus

indu

cing

aFou

rier-likerespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebeamsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pen

etration

depths

(iethede

pth

ben

eath

thesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pen

ding

onthemod

ulation

freque

ncy

Furthergiventhepu

mpan

dprob

espot

sizes

canbefocu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with

micrometer-resolution

andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpertine

ntleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

reportedin

theliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

temperature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

temperatureof

thematerial(iethether-

morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftemperaturechan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mber

densityof

thecarriers

excitedby

theop

ticalperturbation

Thu

sthetotalph

o-torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompon

ents59

R

=R

TT+

R

N

N

(1)

Thermal conductivity of HZO thin films












13ndash16







In addition to thermal resistance heat capacity is also ofinterest for thin Hf1ndashxZrxO2 systems For nominal composi-tions of xfrac14 05 and xfrac14 07 a second set of samples werefabricated and annealed in the same manner as previouslydescribed on top of a 400 nm layer of SiO2 on silicon inorder to increase sensitivity to the volumetric heat capacityof the Hf1ndashxZrxO2 layer (sensitivity analysis in the supple-mentary material) To a first approximation the thermalpenetration depth d can be estimated as d frac14

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffij=ethpCvf THORN

p

where j is the layer thermal conductivity Cv is the volumet-ric heat capacity and f is the modulation frequency of thepump2728 Setting j frac14 135 W m$ 1 K$ 1 and Cv frac14 165MJ m$ 3 K$ 1 the thermal penetration depth in SiO2 can beestimated as 228 nm for a pump modulation frequency f of5 MHz More rigorous formalisms provide higher degrees ofaccuracy for the actual thermal penetration depth29ndash31 how-ever given that the thickness of the SiO2 films is 400 nm andall modulation frequencies were above 5 MHz it is safe toassume that the thermal penetration depth is contained withinthe SiO2 layer As such we utilize a four-layer model for

sensitivity calculations and when fitting for volumetric heatcapacity the four layers consist of an 80 nm aluminum trans-ducer layer followed by the 20 nm Hf1ndashxZrxO2 films fol-lowed by 10 nm of TaN on a SiO2 substrate

For the four-layer model we verify the aluminum thick-ness through profilometry and picosecond ultrasonics32ndash35

(80 6 5 nm) calculate the thermal conductivity via theWiedemann-Franz law from four-point probe resistivitymeasurements (110 W m$ 1 K$ 1) and assume a literaturevalue of 243 MJ m$ 3 K$ 1 for the volumetric heat capacity atroom temperature3637 For the SiO2 substrate we apply athermal conductivity of 135 W m$ 1 K$ 1 and assume a litera-ture value of 165 MJ m$ 3 K$ 1 for the volumetric heat capac-ity of intrinsic silicon at 300 K38 For the TaN layer wesputter a 10 nm layer of TaN on top of SiO2 and verify thick-ness through profilometry (10 6 1 nm) We measure theeffective thermal conductivity in the same manner previ-ously discussed which is found to be 148 6 021W m$ 1 K$ 1 For reference Bozorg-Grayeli et al havereported values of 30 and 34 W m$ 1 K$ 1 as the intrinsicthermal conductivity of TaN films of 50 and 100 nm respec-tively25 We note that our measured effective thermal resis-tance of the TaN layer also includes the interfacial resistancebetween the aluminum transducer and the TaN layerhowever we proceed under the assumption that the resis-tance attributed to the TaN layer is the dominant resistanceFor the lattice heat capacity of TaN we apply a literaturevalue of 294 MJ m$ 3 K$ 139 Given that the effective thermalconductivities of the Hf1ndashxZrxO2 films were determined fromTDTR analyses of the AlHf1ndashxZrxO2TaNSi samples theonly unknown of these AlHf1ndashxZrxO2TaNSiO2 samples isthe volumetric heat capacity of the Hf1ndashxZrxO2 film Todecrease the uncertainty in our reported values of heat capac-ity of the Hf1ndashxZrxO2 film we analyze TDTR sensitivity cal-culations4041 In summary we find an increase in sensitivityto the heat capacity of the Hf1ndashxZrxO2 layer when there is anSiO2 layer and also by analyzing the data from the in-phasesignal Therefore we analyze the in-phase signal for samplesof Hf1ndashxZrxO2 concentrations of xfrac14 05 and xfrac14 07 fittingonly for the heat capacity of that layer To enhance accuracyfurther we analyze data for pump frequencies of 582 84and 122 MHz Further details of the sensitivity analysis canbe found within the supplementary material

A few observable trends in the effective thermal con-ductivity and thermal resistance of the Hf1ndashxZrxO2 filmsemerge from Fig 2 First it is of note that the effectivethermal conductivity is in most cases significantly higherwhen subjected to a 30 s anneal at 600 C We attribute thisincrease to an increase in crystallinity of the film whichwas verified through GIXRD A second more subtle resultfor the annealed samples shown in Fig 2 is a slightdecrease in the mean effective thermal conductivity foralloys of HfO2 and ZrO2 While all effective thermal con-ductivity values are within error no definitive claims canbe made regarding trends in the data however it can beobserved that the nominal effective thermal conductivityranges from 58 to 257 higher for pure HfO2 or ZrO2

compared to alloys of the two Similar results have beenshown in a number of other alloyed material systems owingto alloy scattering of phonons47ndash50 There are no signs of

FIG 2 (a) The effective thermal resistance of the Hf1ndashxZrxO2 films as afunction of ZrO2 concentration x (b) recasts this resistance as an effectivethermal conductivity jEff which is the product of the film thickness and theinverse of its associated thermal resistance In both panels the unannealedsamples are represented by solid blue squares whereas the annealed samplesare represented by open red circles

192901-3 Scott et al Appl Phys Lett 113 192901 (2018)

APL Materials 6 058302

bull Increase in k due to crystallizationbull Most likely boundary scattering limitedbull Values similar to other ALD grown films

058302-3 Scott et al APL Mater 6 058302 (2018)

TABLE I Summary of thermal properties for the ALD high-k dielectrics investigated in this study along with relevant sampledetails is the intrinsic thermal conductivity of the high-k dielectric film and TBR is the total interfacial resistance acrossboth interfaces of the film Note NM = not measurable (too thin) For these films we assume the nominal thickness valuewith 5 uncertainty

Film (W m 1 K 1) TBR (m2 K GW 1) Density (g cm 3) Nominal thickness (nm) Thickness (XRR) (nm)

Al2O3 150 plusmn 009 692 plusmn 050 333 plusmn 006

1 NM3 NM5 46710 939

HfO2 100 plusmn 006 903 plusmn 066 1033 plusmn 036

1 NM3 3115 50710 974

TiO2 252 plusmn 007 801 plusmn 071 41 plusmn 0141 NM3 NM10 1011

deviation in the measurement of the thickness of the aluminum transducer and thickness of the ALDfilm By applying a series resistor model that treats the total resistance as a summation of the filmand interfacial resistances47 the intrinsic film thermal conductivity and total interfacial resistance arethen deconvolved from the effective thermal conductivity with the following expression

eff =i

1 +iRtot

d

(1)

where i is the intrinsic thermal conductivity of the film Rtot is the total interfacial resistance (iethe total TBR across both the Alfilm and filmSi interfaces) and d is the film thickness A non-linearleast squares model fit was applied to the experimental data with i and Rtot as the fitting parametersfor each film The intrinsic thermal conductivities and thermal boundary resistances for the filmsdetermined via Eq (1) are listed in Table I The corresponding uncertainties are obtained by fittingfor these parameters at the experimental upper and lower bounds for Eff

We find good agreement between the model and experimentally measured values for effectivethermal conductivity The resultant intrinsic thermal conductivities of the Al2O3 films are within therange of previous measurements of amorphous ALD-grown Al2O38ndash11 While several reports on thethermal conductivity of HfO2 thin films exist in the literature (for a review see Ref 8) they rangein deposition technique and crystallinity We are only aware of one previous work on the thermal

FIG 1 Measured effective thermal conductivities of TiO2 (triangles) Al2O3 (circles) and HfO2 (squares) films ranging from1 to 10 nm A series thermal resistor model [Eq (1)] is applied to the data for which the intrinsic thermal conductivity andtotal thermal boundary resistance are the fitting parameters The best fits are shown as the lines in the plot













13ndash16









p











frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3

PZT J Appl Phys 121 205104


and PbTiO327










III RESULTS






SiGe Phys Rev Lett 109 195901

Heat capacity of HZO thin films












13ndash16







this trend for the unannealed samples As the unannealedsamples are amorphous and because the measured effectivethermal conductivities of the pure hafnia and zirconiafilms are nearly identical compositions of the two wouldyield a negligible change in thermal conductivity We re-emphasize however that these observations are based uponthe nominal values of the measurements and overall trendswithin the two different datasets (as-deposited andannealed) cannot be concluded with high certainty due tothe relatively large uncertainties in these effective thermalconductivities However our results do conclusively showthat annealing the Hf1ndashxZrxO2 films increases the thermalconductivity which we attribute to crystallization of theas-deposited amorphous film

For the results of the heat capacity measurements inTable I we note that with their associated uncertainties themeasurements are within error of previously reportedmeasurements for the heat capacity of pure hafnia or purezirconia For Hf058Zr042O2 we report a volumetric heatcapacity of 218 6 056 MJ m3 K1 which is slightly lowerthan prior measurements of pure HfO2 and 264 6 053 forHf036Zr064O2 Of the existing measurements for the room-temperature heat capacity measurements of HfO2 all are ofthe monoclinic phase1242ndash44 Because compositions ofx 05 for Hf1ndashxZrxO2 have been shown to also includetetragonal and orthorhombic crystalline phases111 it couldserve to explain why we measure a slightly lower heat capac-ity We also note relatively large error bars in our measure-ment of approximately 30 for the two measurementsWhile all the fits for the heat capacity have a low meansquare error [as can be seen in Fig 3(a)] we gain furtherinsight into the accuracy of the TDTR data fit for heat capac-ity by generating a contour in Fig 3(b) which illustratesuncertainty in the interplay between the effective thermalconductivity and heat capacity of a Hf1ndashxZrxO2 film Weutilize a similar uncertainty contour calculation as has beenpreviously outlined in the literature51ndash54 which calculatesthe sum of the standard deviation between the fitted thermalmodel and the measured data according to the followingequation52

r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)

where Xmi and Xdi represent the in-phase values from thethermal model and the measured TDTR data respectively attime delay i and n is the total number of time delays in aparticular TDTR scan The best fit of the thermal model tothe TDTR data provides the lowest value of r which we

denote as rmin Therefore a contour with a constant value of2rmin would correspond to a 95 confidence interval forcombinations of thermal conductivity and heat capacitywhich produce a standard deviation less than or equal to2rmin As an example we use Eq (1) to calculate a r contourplot for a Hf036Zr064O2 sample measured with TDTR at amodulation frequency of 84 MHz [shown in Fig 3(b)] Thebest fit to the data in this example provides a rmin of505$ 105 and therefore a 95 confidence interval can begenerated by outlining a contour of r values equal to11$ 104 Therefore for a given thermal conductivity of1 W m1 K1 heat capacity values ranging from 21 to25 MJ m3 K1 could be obtained within a 95 confidenceinterval As the thermal conductivity of the Hf1ndashxZrxO2 layeris not the only parameter with uncertainty in the thermalmodel we utilize propagation of error to take into accountuncertainty in the thickness of all films in the stack (AlHf1ndashxZrxO2 and TaN) as well as uncertainty in theHf1ndashxZrxO2 and TaN effective thermal conductivity to obtainthe error displayed in Table I

In summary we report on the effective thermal resis-tance of thin films of Hf1ndashxZrxO2 for compositions rangingfrom 0 x 1 in addition to the heat capacity of twodifferent film compositions Ultimately we find theeffective conductivity of the films to be the highest forpure concentrations (in this case hafnia and zirconia) andslightly decreased for alloys of the two Furthermore wenote an increased thermal conductivity when films aresubjected to a 30 s anneal at 600 ampC which is attributed tothe formation of the monoclinic crystalline phase for filmsconsisting primarily of hafnia and tetragonalorthorhombiccrystalline phases for samples alloyed with zirconia Giventhe limited nature of literature regarding the thermody-namic properties of hafnia-zirconia systems and thepromise that Hf1ndashxZrxO2 has demonstrated as a ferroelec-tric material characterization of its thermal properties in

TABLE I Room temperature volumetric heat capacities for Hf1ndashxZrxO2 Forreference specific heat values are also provided for xfrac14 0 and xfrac14 1 and are

displayed as volumetric capacities assuming the materials are fully dense

Hf1ndashxZrxO2 (x) Cv (MJ m3 K1) References

0 263ndash277 12 and 42ndash44

05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46

FIG 3 (a) Representative TDTR data which have been fit for the heatcapacity of the Hf036Zr064O2 film at frequencies of 582 84 and122 MHz The open symbols display measured data and the solid lines rep-resent their associated fits (b) A contour plot which displays the standarddeviation r between the thermal model and measured TDTR data for theHf036Zr064O2 sample at a modulation frequency of 84 MHz The blackdashed contour provides a boundary outlining a 95 confidence intervaldefined as 2rmin for a given thermal conductivity




r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Cha

racteristicim

pulses

andresp


d(c)SS

TR

techniqu

esIn

TDTRthemag

nitude

ofthethermorefl

ectanc

eismon

itored

asafunc

tion

ofpu

mp-prob

ede

laytime

while

inFDTR

theph

aselagbetweenthepu

mp

andprob

eismon

itored

asafunc

tion

offreque

ncy

InSS

TRtem

peraturechan

gesaremon

itored

forgivenchan

gesin

heat

flux

Noticetheincrease

inthermal

pen

etration

depthresultingfrom

thelower

mod

ulationfreque

nciesem

ployed

inSS

TR

tempe

rature

chan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

expe

rimentsthe

timede

laybe

tweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

tempe

rature

chan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshift

inthermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becomes

low

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

period

sof

themod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarre

rent

pump

powers

thus

indu

cing

aFo

urier-lik

erespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebe

amsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pene

trationde

pths

(iethede

pth

bene

aththesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pend

ingon

themod

ulation

freque

ncy

Furthe

rgiventhepu

mpan

dprob

espot

sizes

canbe

focu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpe

rtinentleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

repo

rted

intheliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

tempe

rature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

tempe

rature

ofthematerial(ie

thether-

morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftempe

rature

chan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mbe

rde

nsityof

thecarriers

excitedby

theop

ticalp

erturbation

Thu

sthetotalp

ho-

torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompo

nents59 R

=R T

T+

R NN

(1)

Modulate at different frequencies f to change

sensitivity to C and k

1f

Thermal conductivity of ferroelectric HZO shows strong influence from boundary scattering for 20 nm films












13ndash16









p











r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46



As-deposited ndash amorphousAnnealed ndash Monoclinic or mixed tetragonalorthorhombicHfO2 ndash Monoclinic ZrO2 - tetragonal

process yielded films with a nominal thickness of 20 nmwith a variance of 0068ndash172 nm depending on the compo-sition Actual film compositions are Hf058Zr042O2 for the55 HfZr film and Hf036Zr064O2 for the 37 HfZr film asdetermined by x-ray photoelectron spectroscopy on identi-cally prepared samples11 To facilitate the thermal propertyanalysis control samples were also fabricated without aHf1ndashxZrxO2 layer on both Si and SiO2 substrates For furtherdetails of fabrication processes we direct readers to a priorstudy11

Following fabrication a subset of the samples were sub-jected to a 30 s anneal at 600 C using a rapid thermalannealer in a nitrogen atmosphere To analyze crystallinitygrazing incidence x-ray diffraction (GIXRD) was performedfor samples of each composition An x angle of 2 wasutilized and measurements were taken over a range of26ndash33 of 2h We find that in the unannealed state the filmsare amorphous in agreement with prior findings for unan-nealed films6 As shown in Fig 1 after annealingHf1ndashxZrxO2 films crystallize into either monoclinic or mixedtetragonalorthorhombic phases depending upon the concen-tration of zirconia For films containing primarily hafnia the111 and 111 reflections of the monoclinic phase are readilyapparent at 284 and 316 in 2h respectively561119 Forfilms with zirconia concentrations greater than or equal to50 the intensity of the monoclinic phase reflections isreduced and 011 and 111 reflections associated with amixture of the orthorhombictetragonal phase are intensifiedwhich occur at approximately 304 in 2h11119 Film phasefractions were quantified via the ratios of the integrated peakintensities20 for the monoclinic and tetragonalorthorhombicphases Intensities of the pure HfO2 (monoclinic) and ZrO2

(tetragonal) reflections and atomic scattering factordifferences with composition were used in normalization toaccount for structural and compositional dependences ofpeak intensity respectively Volumetric phase fractions of008 monoclinic and 092 tetragonalorthorhombic werecalculated for the 37 HfZr film and 059 monoclinic and

041 tetragonalorthorhombic were calculated for the 55HfZr film

To verify ferroelectric responses in the Hf1ndashxZrxO2

films polarization electric field responses were measured fornominal compositions of x frac14 05 and x frac14 07 and contrastedagainst pure hafnia To make these measurements contactswere fabricated on the surface of the Hf1ndashxZrxO2 films a10 nm electrode layer of TaN was sputtered onto the surfacefollowed by a 70 nm layer of platinum which wasrf-magnetron sputtered through a shadow mask in order tocreate square contacts with side lengths of approximately635 lm separated by 2 mm in a two dimensional array Areactive ion etch was then used to etch the TaN layer inbetween the platinum contacts leaving isolated electrodesatop the exposed Hf1ndashxZrxO2 layer Polarization-fieldmeasurements were collected with voltage biases rangingfrom 61 to 66 V as displayed in Figs 1(b)ndash1(d) For allas-deposited Hf1ndashxZrxO2 films we measure a linear dielectricresponse (not shown) For the annealed HfO2 sample asshown in Fig 1(b) the same linear response can be seen Forannealed samples of Hf058Zr042O2 and Hf036Zr064O2hysteresis is displayed in the polarization-field responseconfirming ferroelectric behavior in the films811

Following an alcohol clean (five minute sonications inisopropanol acetone and methanol respectively) the sam-ples were then coated with an 80 nm aluminum layer viaelectron beam evaporation to prepare them for thermal prop-erty measurements via time-domain thermoreflectance(TDTR)21 We utilize a repetition rate of 80 MHz and a cen-tral wavelength of 800 nm (bandwidth of 105 nm) and spotsizes of 18 and 11 lm in diameter for the pump and probebeams respectively The thermal properties of the sampleswere measured by fitting the ratio of the in-phase to out-of-phase lock-in signals to a thermal model the particulars ofwhich have been thoroughly detailed in the literature21ndash24

Due to the thinness of the Hf1ndashxZrxO2 and TaN layerswe do not directly fit for the intrinsic thermal conductivity ofthe Hf1ndashxZrxO2 layer since we cannot explicitly separate thethermal conductivity of the layer from the interfaces using asingle measurement on a single sample1326 Rather we treatthe two layers as an effective resistive interface between thealuminum transducer and the silicon substrate As suchwhen modeling the TDTR data we treat each sample as atwo layer system and fit for the effective thermal boundaryconductance In order to quantify the thermal resistance asso-ciated with the Hf1ndashxZrxO2 layer (REff) we take the inverseof the measured thermal boundary conductance and subtractthe thermal resistances measured from the sample without anHf1ndashxZrxO2 layer (complete calculations are detailed in thesupplementary material) The error in the measurement isattributed to measurement repeatability uncertainty inaluminum thickness and uncertainty in the interfacial resis-tance between aluminum and TaN which has been takenfrom the literature25 For the effective film thermal conduc-tivity jEff we take the product of the film thickness and theinverse of the thermal resistance An additional source ofuncertainty is introduced here for film thickness variation inthe ALD Hf1ndashxZrxO2 films The results for REff and jEff aredisplayed in Figs 2(a) and 2(b) respectively

FIG 1 (a) GIXRD measurements of annealed samples for various composi-tions of Hf1ndashxZrxO2 (b)ndash(d) The polarization field responses for theannealed Hf1ndashxZrxO2 films with nominal concentrations of x frac14 0 05 and07 respectively The black innermost curves display polarization fieldresponses for an applied voltage of 1 V the lighter shades moving outwarddisplay voltage increases in 1 V increments ending with an applied voltageof 6 V (light orange) for the outermost curve













13ndash16














-600

-400

-200

0

200

400

600

800

G K X G L X W L

100

(Gru

neis

en-3

)

Freq

uenc

y (1

cm

)

DOS Kpoints



Total DOS





F (ω) =sum

kλ


12

|V (kλ12)|2 (19)


DOSplusmn2 (ω) =

sum

12




-02

-01

0

01

02

0 200 400 600 800 1000JD

OS

(arb

itrar

y un

its)

Frequency (1cm)









10

100

1000

10000

1 2 4 8 16

Lif

etim

e (p

s)

Frequency(THz)

3 103ν2

TA1TA2LA

TO1TO2LO

10

100

1000

10000

Lif

etim

e (p

s)

104ν3

TA1TA2LA

TO1TO2LO


085204-8


-600

-400

-200

0

200

400

600

800

G K X G L X W L

100

(Gru

neis

en-3

)

Freq

uenc

y (1

cm

)

DOS Kpoints



Total DOS





F (ω) =sum

kλ


12

|V (kλ12)|2 (19)


DOSplusmn2 (ω) =

sum

12




-02

-01

0

01

02

0 200 400 600 800 1000

JDO

S (a

rbitr

ary

units

)

Frequency (1cm)









10

100

1000

10000

1 2 4 8 16

Lif

etim

e (p

s)

Frequency(THz)

3 103ν2

TA1TA2LA

TO1TO2LO

10

100

1000

10000

Lif

etim

e (p

s)

104ν3

TA1TA2LA

TO1TO2LO


085204-8

PRB 84 085204

3976

REV

IEW








Nanoparticle



Atomic defect

Grainboundary

Hot Electron

Cold Electron


0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g


nanostructuring(A)



Adv Mat 22 3970


APL 105 082907


APL 102 121903





1

sfrac14 ATx2 exp

B

Tthorn Dx4 thorn

df ilmthorn

dgb(1)





film









1

sfrac14 ATx2 exp

B

Tthorn Dx4 thorn

df ilmthorn

dgb(1)





film






































3976

REV

IEW








Nanoparticle



Atomic defect

Grainboundary

Hot Electron

Cold Electron


0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g


nanostructuring(A)

Adv Mat 22 3970





frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



3976

REV

IEW








Nanoparticle



Atomic defect

Grainboundary

Hot Electron

Cold Electron


0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g


nanostructuring(A)

Adv Mat 22 3970



frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3











and PbTiO327










III RESULTS






BulkThin film





IV DISCUSSION



















JOM 71 246





amorphous effects





10 nm TaN

Silicon substrate







90 fs pluse width

Pump

Isolator

EOM

BiBO

Redfilter

Dichroic

Probe


Bluefilter

Lock-inamplifier

Photodiode



0 1 2 3 4 5

0

1

2

3

4

5

6

7

8

9

10



Thermal model





119881119881JO = Re 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891

119881119881PVU = Im 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891


119885119885 10076491007649119891119891119891 11989111989110076651007665 = 120585120585infin10055761005576








2 ~T~

zeth THORN

z2frac14 q2 ~T

~zeth THORN (10)


(11)

~Q~

top frac141

2pexp k2r2

0

8

~G xeth THORN (12)



while ~Y~amp ~Y





~T~

z is


~T~

zeth THORN~Q~

zeth THORN

2

64

3


qjzsinh qzeth THORN


2

4

3

5~T~

top

~Q~

top

2

64

3

75

(13)



top and ~Q~

top for that


limz1



nation of ~T~

topn and ~Q~



z frac14Pnndash1


~T~

botn1

~Q~

botn1

2

64

3

75 frac141 1

h n1eth THORN=n

0 1

2

4

3

5~T~

topn

~Q~

topn

2

64

3

75 (15)


~T~

n zeth THORN

~Qn~

zeth THORN

2

64

3




2

64

3

75

Yjfrac141

jfrac14n1n2

MjNj

~T~

top

~Q~

top

2

64

3

75 frac14~A~

~B~

~C~

~D~

2

64

3

75~T~

top

~Q~

top

2

64

3

75

(16)



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Characteristic

impulses

andresp


d(c)SSTR

techniquesIn

TDTRthemag

nitude

ofthethermorefl

ectance

ismon

itored

asafunctionof

pump-probedelay

time

whilein

FDTR


andprobeismon

itored

asafunctionof

frequen

cyIn

SSTRtemperature

chan

gesaremon

itored

forgivenchan

gesin

heatflux

Noticetheincrease

inthermal

pen

etration

dep

thresultingfrom

thelower

mod

ulation

frequen

cies

employedin

SSTR

temperaturechan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

experim

entsthe

timede

laybetweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

temperaturechan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshiftin

thermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becom

eslow

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

periods

ofthemod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarrerent

pump

pow

ers

thus

indu

cing

aFou

rier-likerespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebeamsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pen

etration

depths

(iethede

pth

ben

eath

thesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pen

ding

onthemod

ulation

freque

ncy

Furthergiventhepu

mpan

dprob

espot

sizes

canbefocu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpertine

ntleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

reportedin

theliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

temperature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

temperatureof


morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftemperaturechan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mber

densityof

thecarriers

excitedby

theop

ticalperturbation

Thu

sthetotalph

o-torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompon

ents59

R

=R

TT+

R

N

N

(1)













13ndash16









p















1 NM3 NM5 46710 939


1 NM3 3115 50710 974



eff =i

1 +iRtot

d

(1)
















13ndash16









p











frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



and PbTiO327










III RESULTS



















13ndash16









r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46





r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Cha

racteristicim

pulses

andresp


d(c)SS

TR

techniqu

esIn

TDTRthemag

nitude

ofthethermorefl

ectanc

eismon

itored

asafunc

tion

ofpu

mp-prob

ede

laytime

while

inFDTR

theph

aselagbetweenthepu

mp

andprob

eismon

itored

asafunc

tion

offreque

ncy

InSS

TRtem

peraturechan

gesaremon

itored

forgivenchan

gesin

heat

flux

Noticetheincrease

inthermal

pen

etration

depthresultingfrom

thelower

mod

ulationfreque

nciesem

ployed

inSS

TR

tempe

rature

chan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

expe

rimentsthe

timede

laybe

tweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

tempe

rature

chan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshift

inthermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becomes

low

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

period

sof

themod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarre

rent

pump

powers

thus

indu

cing

aFo

urier-lik

erespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebe

amsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pene

trationde

pths

(iethede

pth

bene

aththesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pend

ingon

themod

ulation

freque

ncy

Furthe

rgiventhepu

mpan

dprob

espot

sizes

canbe

focu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpe

rtinentleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

repo

rted

intheliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

tempe

rature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

tempe

rature

ofthematerial(ie

thether-

morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftempe

rature

chan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mbe

rde

nsityof

thecarriers

excitedby

theop

ticalp

erturbation

Thu

sthetotalp

ho-

torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompo

nents59 R

=R T

T+

R NN

(1)



1f













13ndash16









p











r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46

















-600

-400

-200

0

200

400

600

800

G K X G L X W L

100

(Gru

neis

en-3

)

Freq

uenc

y (1

cm

)

DOS Kpoints



Total DOS





F (ω) =sum

kλ


12

|V (kλ12)|2 (19)


DOSplusmn2 (ω) =

sum

12




-02

-01

0

01

02

0 200 400 600 800 1000JD

OS

(arb

itrar

y un

its)

Frequency (1cm)









10

100

1000

10000

1 2 4 8 16

Lif

etim

e (p

s)

Frequency(THz)

3 103ν2

TA1TA2LA

TO1TO2LO

10

100

1000

10000

Lif

etim

e (p

s)

104ν3

TA1TA2LA

TO1TO2LO


085204-8


-600

-400

-200

0

200

400

600

800

G K X G L X W L

100

(Gru

neis

en-3

)

Freq

uenc

y (1

cm

)

DOS Kpoints



Total DOS





F (ω) =sum

kλ


12

|V (kλ12)|2 (19)


DOSplusmn2 (ω) =

sum

12




-02

-01

0

01

02

0 200 400 600 800 1000

JDO

S (a

rbitr

ary

units

)

Frequency (1cm)









10

100

1000

10000

1 2 4 8 16

Lif

etim

e (p

s)

Frequency(THz)

3 103ν2

TA1TA2LA

TO1TO2LO

10

100

1000

10000

Lif

etim

e (p

s)

104ν3

TA1TA2LA

TO1TO2LO


085204-8

PRB 84 085204

3976

REV

IEW








Nanoparticle



Atomic defect

Grainboundary

Hot Electron

Cold Electron


0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g


nanostructuring(A)



Adv Mat 22 3970


APL 105 082907


APL 102 121903





1

sfrac14 ATx2 exp

B

Tthorn Dx4 thorn

df ilmthorn

dgb(1)





film









1

sfrac14 ATx2 exp

B

Tthorn Dx4 thorn

df ilmthorn

dgb(1)





film






































3976

REV

IEW








Nanoparticle



Atomic defect

Grainboundary

Hot Electron

Cold Electron


0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g


nanostructuring(A)

Adv Mat 22 3970





frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



3976

REV

IEW








Nanoparticle



Atomic defect

Grainboundary

Hot Electron

Cold Electron


0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g


nanostructuring(A)

Adv Mat 22 3970



frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3











and PbTiO327










III RESULTS






BulkThin film





IV DISCUSSION



















JOM 71 246





amorphous effects





10 nm TaN

Silicon substrate







90 fs pluse width

Pump

Isolator

EOM

BiBO

Redfilter

Dichroic

Probe


Bluefilter

Lock-inamplifier

Photodiode



0 1 2 3 4 5

0

1

2

3

4

5

6

7

8

9

10



Thermal model





119881119881JO = Re 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891

119881119881PVU = Im 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891


119885119885 10076491007649119891119891119891 11989111989110076651007665 = 120585120585infin10055761005576








2 ~T~

zeth THORN

z2frac14 q2 ~T

~zeth THORN (10)


(11)

~Q~

top frac141

2pexp k2r2

0

8

~G xeth THORN (12)



while ~Y~amp ~Y





~T~

z is


~T~

zeth THORN~Q~

zeth THORN

2

64

3


qjzsinh qzeth THORN


2

4

3

5~T~

top

~Q~

top

2

64

3

75

(13)



top and ~Q~

top for that


limz1



nation of ~T~

topn and ~Q~



z frac14Pnndash1


~T~

botn1

~Q~

botn1

2

64

3

75 frac141 1

h n1eth THORN=n

0 1

2

4

3

5~T~

topn

~Q~

topn

2

64

3

75 (15)


~T~

n zeth THORN

~Qn~

zeth THORN

2

64

3




2

64

3

75

Yjfrac141

jfrac14n1n2

MjNj

~T~

top

~Q~

top

2

64

3

75 frac14~A~

~B~

~C~

~D~

2

64

3

75~T~

top

~Q~

top

2

64

3

75

(16)



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Characteristic

impulses

andresp


d(c)SSTR

techniquesIn

TDTRthemag

nitude

ofthethermorefl

ectance

ismon

itored

asafunctionof

pump-probedelay

time

whilein

FDTR


andprobeismon

itored

asafunctionof

frequen

cyIn

SSTRtemperature

chan

gesaremon

itored

forgivenchan

gesin

heatflux

Noticetheincrease

inthermal

pen

etration

dep

thresultingfrom

thelower

mod

ulation

frequen

cies

employedin

SSTR

temperaturechan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

experim

entsthe

timede

laybetweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

temperaturechan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshiftin

thermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becom

eslow

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

periods

ofthemod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarrerent

pump

pow

ers

thus

indu

cing

aFou

rier-likerespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebeamsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pen

etration

depths

(iethede

pth

ben

eath

thesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pen

ding

onthemod

ulation

freque

ncy

Furthergiventhepu

mpan

dprob

espot

sizes

canbefocu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpertine

ntleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

reportedin

theliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

temperature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

temperatureof


morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftemperaturechan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mber

densityof

thecarriers

excitedby

theop

ticalperturbation

Thu

sthetotalph

o-torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompon

ents59

R

=R

TT+

R

N

N

(1)













13ndash16









p















1 NM3 NM5 46710 939


1 NM3 3115 50710 974



eff =i

1 +iRtot

d

(1)
















13ndash16









p











frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



and PbTiO327










III RESULTS



















13ndash16









r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46





r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Cha

racteristicim

pulses

andresp


d(c)SS

TR

techniqu

esIn

TDTRthemag

nitude

ofthethermorefl

ectanc

eismon

itored

asafunc

tion

ofpu

mp-prob

ede

laytime

while

inFDTR

theph

aselagbetweenthepu

mp

andprob

eismon

itored

asafunc

tion

offreque

ncy

InSS

TRtem

peraturechan

gesaremon

itored

forgivenchan

gesin

heat

flux

Noticetheincrease

inthermal

pen

etration

depthresultingfrom

thelower

mod

ulationfreque

nciesem

ployed

inSS

TR

tempe

rature

chan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

expe

rimentsthe

timede

laybe

tweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

tempe

rature

chan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshift

inthermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becomes

low

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

period

sof

themod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarre

rent

pump

powers

thus

indu

cing

aFo

urier-lik

erespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebe

amsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pene

trationde

pths

(iethede

pth

bene

aththesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pend

ingon

themod

ulation

freque

ncy

Furthe

rgiventhepu

mpan

dprob

espot

sizes

canbe

focu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpe

rtinentleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

repo

rted

intheliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

tempe

rature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

tempe

rature

ofthematerial(ie

thether-

morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftempe

rature

chan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mbe

rde

nsityof

thecarriers

excitedby

theop

ticalp

erturbation

Thu

sthetotalp

ho-

torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompo

nents59 R

=R T

T+

R NN

(1)



1f













13ndash16









p











r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46














3976

REV

IEW








Nanoparticle



Atomic defect

Grainboundary

Hot Electron

Cold Electron


0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g


nanostructuring(A)



Adv Mat 22 3970


APL 105 082907


APL 102 121903





1

sfrac14 ATx2 exp

B

Tthorn Dx4 thorn

df ilmthorn

dgb(1)





film









1

sfrac14 ATx2 exp

B

Tthorn Dx4 thorn

df ilmthorn

dgb(1)





film






































3976

REV

IEW








Nanoparticle



Atomic defect

Grainboundary

Hot Electron

Cold Electron


0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g


nanostructuring(A)

Adv Mat 22 3970





frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



3976

REV

IEW








Nanoparticle



Atomic defect

Grainboundary

Hot Electron

Cold Electron


0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g


nanostructuring(A)

Adv Mat 22 3970



frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3











and PbTiO327










III RESULTS






BulkThin film





IV DISCUSSION



















JOM 71 246





amorphous effects





10 nm TaN

Silicon substrate







90 fs pluse width

Pump

Isolator

EOM

BiBO

Redfilter

Dichroic

Probe


Bluefilter

Lock-inamplifier

Photodiode



0 1 2 3 4 5

0

1

2

3

4

5

6

7

8

9

10



Thermal model





119881119881JO = Re 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891

119881119881PVU = Im 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891


119885119885 10076491007649119891119891119891 11989111989110076651007665 = 120585120585infin10055761005576








2 ~T~

zeth THORN

z2frac14 q2 ~T

~zeth THORN (10)


(11)

~Q~

top frac141

2pexp k2r2

0

8

~G xeth THORN (12)



while ~Y~amp ~Y





~T~

z is


~T~

zeth THORN~Q~

zeth THORN

2

64

3


qjzsinh qzeth THORN


2

4

3

5~T~

top

~Q~

top

2

64

3

75

(13)



top and ~Q~

top for that


limz1



nation of ~T~

topn and ~Q~



z frac14Pnndash1


~T~

botn1

~Q~

botn1

2

64

3

75 frac141 1

h n1eth THORN=n

0 1

2

4

3

5~T~

topn

~Q~

topn

2

64

3

75 (15)


~T~

n zeth THORN

~Qn~

zeth THORN

2

64

3




2

64

3

75

Yjfrac141

jfrac14n1n2

MjNj

~T~

top

~Q~

top

2

64

3

75 frac14~A~

~B~

~C~

~D~

2

64

3

75~T~

top

~Q~

top

2

64

3

75

(16)



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Characteristic

impulses

andresp


d(c)SSTR

techniquesIn

TDTRthemag

nitude

ofthethermorefl

ectance

ismon

itored

asafunctionof

pump-probedelay

time

whilein

FDTR


andprobeismon

itored

asafunctionof

frequen

cyIn

SSTRtemperature

chan

gesaremon

itored

forgivenchan

gesin

heatflux

Noticetheincrease

inthermal

pen

etration

dep

thresultingfrom

thelower

mod

ulation

frequen

cies

employedin

SSTR

temperaturechan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

experim

entsthe

timede

laybetweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

temperaturechan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshiftin

thermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becom

eslow

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

periods

ofthemod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarrerent

pump

pow

ers

thus

indu

cing

aFou

rier-likerespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebeamsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pen

etration

depths

(iethede

pth

ben

eath

thesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pen

ding

onthemod

ulation

freque

ncy

Furthergiventhepu

mpan

dprob

espot

sizes

canbefocu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpertine

ntleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

reportedin

theliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

temperature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

temperatureof


morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftemperaturechan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mber

densityof

thecarriers

excitedby

theop

ticalperturbation

Thu

sthetotalph

o-torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompon

ents59

R

=R

TT+

R

N

N

(1)













13ndash16









p















1 NM3 NM5 46710 939


1 NM3 3115 50710 974



eff =i

1 +iRtot

d

(1)
















13ndash16









p











frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



and PbTiO327










III RESULTS



















13ndash16









r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46





r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Cha

racteristicim

pulses

andresp


d(c)SS

TR

techniqu

esIn

TDTRthemag

nitude

ofthethermorefl

ectanc

eismon

itored

asafunc

tion

ofpu

mp-prob

ede

laytime

while

inFDTR

theph

aselagbetweenthepu

mp

andprob

eismon

itored

asafunc

tion

offreque

ncy

InSS

TRtem

peraturechan

gesaremon

itored

forgivenchan

gesin

heat

flux

Noticetheincrease

inthermal

pen

etration

depthresultingfrom

thelower

mod

ulationfreque

nciesem

ployed

inSS

TR

tempe

rature

chan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

expe

rimentsthe

timede

laybe

tweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

tempe

rature

chan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshift

inthermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becomes

low

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

period

sof

themod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarre

rent

pump

powers

thus

indu

cing

aFo

urier-lik

erespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebe

amsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pene

trationde

pths

(iethede

pth

bene

aththesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pend

ingon

themod

ulation

freque

ncy

Furthe

rgiventhepu

mpan

dprob

espot

sizes

canbe

focu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpe

rtinentleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

repo

rted

intheliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

tempe

rature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

tempe

rature

ofthematerial(ie

thether-

morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftempe

rature

chan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mbe

rde

nsityof

thecarriers

excitedby

theop

ticalp

erturbation

Thu

sthetotalp

ho-

torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompo

nents59 R

=R T

T+

R NN

(1)



1f













13ndash16









p











r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46















APL 105 082907


APL 102 121903





1

sfrac14 ATx2 exp

B

Tthorn Dx4 thorn

df ilmthorn

dgb(1)





film









1

sfrac14 ATx2 exp

B

Tthorn Dx4 thorn

df ilmthorn

dgb(1)





film






































3976

REV

IEW








Nanoparticle



Atomic defect

Grainboundary

Hot Electron

Cold Electron


0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g


nanostructuring(A)

Adv Mat 22 3970





frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



3976

REV

IEW








Nanoparticle



Atomic defect

Grainboundary

Hot Electron

Cold Electron


0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g


nanostructuring(A)

Adv Mat 22 3970



frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3











and PbTiO327










III RESULTS






BulkThin film





IV DISCUSSION



















JOM 71 246





amorphous effects





10 nm TaN

Silicon substrate







90 fs pluse width

Pump

Isolator

EOM

BiBO

Redfilter

Dichroic

Probe


Bluefilter

Lock-inamplifier

Photodiode



0 1 2 3 4 5

0

1

2

3

4

5

6

7

8

9

10



Thermal model





119881119881JO = Re 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891

119881119881PVU = Im 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891


119885119885 10076491007649119891119891119891 11989111989110076651007665 = 120585120585infin10055761005576








2 ~T~

zeth THORN

z2frac14 q2 ~T

~zeth THORN (10)


(11)

~Q~

top frac141

2pexp k2r2

0

8

~G xeth THORN (12)



while ~Y~amp ~Y





~T~

z is


~T~

zeth THORN~Q~

zeth THORN

2

64

3


qjzsinh qzeth THORN


2

4

3

5~T~

top

~Q~

top

2

64

3

75

(13)



top and ~Q~

top for that


limz1



nation of ~T~

topn and ~Q~



z frac14Pnndash1


~T~

botn1

~Q~

botn1

2

64

3

75 frac141 1

h n1eth THORN=n

0 1

2

4

3

5~T~

topn

~Q~

topn

2

64

3

75 (15)


~T~

n zeth THORN

~Qn~

zeth THORN

2

64

3




2

64

3

75

Yjfrac141

jfrac14n1n2

MjNj

~T~

top

~Q~

top

2

64

3

75 frac14~A~

~B~

~C~

~D~

2

64

3

75~T~

top

~Q~

top

2

64

3

75

(16)



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Characteristic

impulses

andresp


d(c)SSTR

techniquesIn

TDTRthemag

nitude

ofthethermorefl

ectance

ismon

itored

asafunctionof

pump-probedelay

time

whilein

FDTR


andprobeismon

itored

asafunctionof

frequen

cyIn

SSTRtemperature

chan

gesaremon

itored

forgivenchan

gesin

heatflux

Noticetheincrease

inthermal

pen

etration

dep

thresultingfrom

thelower

mod

ulation

frequen

cies

employedin

SSTR

temperaturechan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

experim

entsthe

timede

laybetweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

temperaturechan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshiftin

thermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becom

eslow

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

periods

ofthemod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarrerent

pump

pow

ers

thus

indu

cing

aFou

rier-likerespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebeamsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pen

etration

depths

(iethede

pth

ben

eath

thesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pen

ding

onthemod

ulation

freque

ncy

Furthergiventhepu

mpan

dprob

espot

sizes

canbefocu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpertine

ntleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

reportedin

theliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

temperature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

temperatureof


morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftemperaturechan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mber

densityof

thecarriers

excitedby

theop

ticalperturbation

Thu

sthetotalph

o-torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompon

ents59

R

=R

TT+

R

N

N

(1)













13ndash16









p















1 NM3 NM5 46710 939


1 NM3 3115 50710 974



eff =i

1 +iRtot

d

(1)
















13ndash16









p











frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



and PbTiO327










III RESULTS



















13ndash16









r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46





r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Cha

racteristicim

pulses

andresp


d(c)SS

TR

techniqu

esIn

TDTRthemag

nitude

ofthethermorefl

ectanc

eismon

itored

asafunc

tion

ofpu

mp-prob

ede

laytime

while

inFDTR

theph

aselagbetweenthepu

mp

andprob

eismon

itored

asafunc

tion

offreque

ncy

InSS

TRtem

peraturechan

gesaremon

itored

forgivenchan

gesin

heat

flux

Noticetheincrease

inthermal

pen

etration

depthresultingfrom

thelower

mod

ulationfreque

nciesem

ployed

inSS

TR

tempe

rature

chan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

expe

rimentsthe

timede

laybe

tweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

tempe

rature

chan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshift

inthermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becomes

low

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

period

sof

themod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarre

rent

pump

powers

thus

indu

cing

aFo

urier-lik

erespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebe

amsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pene

trationde

pths

(iethede

pth

bene

aththesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pend

ingon

themod

ulation

freque

ncy

Furthe

rgiventhepu

mpan

dprob

espot

sizes

canbe

focu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpe

rtinentleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

repo

rted

intheliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

tempe

rature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

tempe

rature

ofthematerial(ie

thether-

morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftempe

rature

chan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mbe

rde

nsityof

thecarriers

excitedby

theop

ticalp

erturbation

Thu

sthetotalp

ho-

torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompo

nents59 R

=R T

T+

R NN

(1)



1f













13ndash16









p











r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46
















3976

REV

IEW








Nanoparticle



Atomic defect

Grainboundary

Hot Electron

Cold Electron


0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g


nanostructuring(A)

Adv Mat 22 3970





frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



3976

REV

IEW








Nanoparticle



Atomic defect

Grainboundary

Hot Electron

Cold Electron


0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g


nanostructuring(A)

Adv Mat 22 3970



frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3











and PbTiO327










III RESULTS






BulkThin film





IV DISCUSSION



















JOM 71 246





amorphous effects





10 nm TaN

Silicon substrate







90 fs pluse width

Pump

Isolator

EOM

BiBO

Redfilter

Dichroic

Probe


Bluefilter

Lock-inamplifier

Photodiode



0 1 2 3 4 5

0

1

2

3

4

5

6

7

8

9

10



Thermal model





119881119881JO = Re 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891

119881119881PVU = Im 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891


119885119885 10076491007649119891119891119891 11989111989110076651007665 = 120585120585infin10055761005576








2 ~T~

zeth THORN

z2frac14 q2 ~T

~zeth THORN (10)


(11)

~Q~

top frac141

2pexp k2r2

0

8

~G xeth THORN (12)



while ~Y~amp ~Y





~T~

z is


~T~

zeth THORN~Q~

zeth THORN

2

64

3


qjzsinh qzeth THORN


2

4

3

5~T~

top

~Q~

top

2

64

3

75

(13)



top and ~Q~

top for that


limz1



nation of ~T~

topn and ~Q~



z frac14Pnndash1


~T~

botn1

~Q~

botn1

2

64

3

75 frac141 1

h n1eth THORN=n

0 1

2

4

3

5~T~

topn

~Q~

topn

2

64

3

75 (15)


~T~

n zeth THORN

~Qn~

zeth THORN

2

64

3




2

64

3

75

Yjfrac141

jfrac14n1n2

MjNj

~T~

top

~Q~

top

2

64

3

75 frac14~A~

~B~

~C~

~D~

2

64

3

75~T~

top

~Q~

top

2

64

3

75

(16)



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Characteristic

impulses

andresp


d(c)SSTR

techniquesIn

TDTRthemag

nitude

ofthethermorefl

ectance

ismon

itored

asafunctionof

pump-probedelay

time

whilein

FDTR


andprobeismon

itored

asafunctionof

frequen

cyIn

SSTRtemperature

chan

gesaremon

itored

forgivenchan

gesin

heatflux

Noticetheincrease

inthermal

pen

etration

dep

thresultingfrom

thelower

mod

ulation

frequen

cies

employedin

SSTR

temperaturechan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

experim

entsthe

timede

laybetweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

temperaturechan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshiftin

thermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becom

eslow

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

periods

ofthemod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarrerent

pump

pow

ers

thus

indu

cing

aFou

rier-likerespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebeamsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pen

etration

depths

(iethede

pth

ben

eath

thesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pen

ding

onthemod

ulation

freque

ncy

Furthergiventhepu

mpan

dprob

espot

sizes

canbefocu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpertine

ntleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

reportedin

theliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

temperature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

temperatureof


morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftemperaturechan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mber

densityof

thecarriers

excitedby

theop

ticalperturbation

Thu

sthetotalph

o-torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompon

ents59

R

=R

TT+

R

N

N

(1)













13ndash16









p















1 NM3 NM5 46710 939


1 NM3 3115 50710 974



eff =i

1 +iRtot

d

(1)
















13ndash16









p











frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



and PbTiO327










III RESULTS



















13ndash16









r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46





r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Cha

racteristicim

pulses

andresp


d(c)SS

TR

techniqu

esIn

TDTRthemag

nitude

ofthethermorefl

ectanc

eismon

itored

asafunc

tion

ofpu

mp-prob

ede

laytime

while

inFDTR

theph

aselagbetweenthepu

mp

andprob

eismon

itored

asafunc

tion

offreque

ncy

InSS

TRtem

peraturechan

gesaremon

itored

forgivenchan

gesin

heat

flux

Noticetheincrease

inthermal

pen

etration

depthresultingfrom

thelower

mod

ulationfreque

nciesem

ployed

inSS

TR

tempe

rature

chan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

expe

rimentsthe

timede

laybe

tweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

tempe

rature

chan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshift

inthermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becomes

low

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

period

sof

themod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarre

rent

pump

powers

thus

indu

cing

aFo

urier-lik

erespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebe

amsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pene

trationde

pths

(iethede

pth

bene

aththesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pend

ingon

themod

ulation

freque

ncy

Furthe

rgiventhepu

mpan

dprob

espot

sizes

canbe

focu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpe

rtinentleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

repo

rted

intheliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

tempe

rature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

tempe

rature

ofthematerial(ie

thether-

morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftempe

rature

chan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mbe

rde

nsityof

thecarriers

excitedby

theop

ticalp

erturbation

Thu

sthetotalp

ho-

torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompo

nents59 R

=R T

T+

R NN

(1)



1f













13ndash16









p











r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46














3976

REV

IEW








Nanoparticle



Atomic defect

Grainboundary

Hot Electron

Cold Electron


0 200 400 600 800

60

30

0

Temperature K

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddot K

30 ErAsInGaAs

6 ErAsInGaAs

InGaAs

03 ErAsInGaAs

(B)

300 400 500 600 700

25

20

15

10

05

Temperature K

(PbTe)098(PbS)008

PbTe1-xSex

Pb1-xSn

xTe

LAST-18SALT-20

Latti

ce th

erm

al c

ondu

ctiv

ity W

mmiddotK

PbTe

Nan

o-st

ruct

urin

g


nanostructuring(A)

Adv Mat 22 3970



frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3











and PbTiO327










III RESULTS






BulkThin film





IV DISCUSSION



















JOM 71 246





amorphous effects





10 nm TaN

Silicon substrate







90 fs pluse width

Pump

Isolator

EOM

BiBO

Redfilter

Dichroic

Probe


Bluefilter

Lock-inamplifier

Photodiode



0 1 2 3 4 5

0

1

2

3

4

5

6

7

8

9

10



Thermal model





119881119881JO = Re 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891

119881119881PVU = Im 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891


119885119885 10076491007649119891119891119891 11989111989110076651007665 = 120585120585infin10055761005576








2 ~T~

zeth THORN

z2frac14 q2 ~T

~zeth THORN (10)


(11)

~Q~

top frac141

2pexp k2r2

0

8

~G xeth THORN (12)



while ~Y~amp ~Y





~T~

z is


~T~

zeth THORN~Q~

zeth THORN

2

64

3


qjzsinh qzeth THORN


2

4

3

5~T~

top

~Q~

top

2

64

3

75

(13)



top and ~Q~

top for that


limz1



nation of ~T~

topn and ~Q~



z frac14Pnndash1


~T~

botn1

~Q~

botn1

2

64

3

75 frac141 1

h n1eth THORN=n

0 1

2

4

3

5~T~

topn

~Q~

topn

2

64

3

75 (15)


~T~

n zeth THORN

~Qn~

zeth THORN

2

64

3




2

64

3

75

Yjfrac141

jfrac14n1n2

MjNj

~T~

top

~Q~

top

2

64

3

75 frac14~A~

~B~

~C~

~D~

2

64

3

75~T~

top

~Q~

top

2

64

3

75

(16)



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Characteristic

impulses

andresp


d(c)SSTR

techniquesIn

TDTRthemag

nitude

ofthethermorefl

ectance

ismon

itored

asafunctionof

pump-probedelay

time

whilein

FDTR


andprobeismon

itored

asafunctionof

frequen

cyIn

SSTRtemperature

chan

gesaremon

itored

forgivenchan

gesin

heatflux

Noticetheincrease

inthermal

pen

etration

dep

thresultingfrom

thelower

mod

ulation

frequen

cies

employedin

SSTR

temperaturechan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

experim

entsthe

timede

laybetweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

temperaturechan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshiftin

thermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becom

eslow

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

periods

ofthemod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarrerent

pump

pow

ers

thus

indu

cing

aFou

rier-likerespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebeamsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pen

etration

depths

(iethede

pth

ben

eath

thesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pen

ding

onthemod

ulation

freque

ncy

Furthergiventhepu

mpan

dprob

espot

sizes

canbefocu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpertine

ntleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

reportedin

theliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

temperature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

temperatureof


morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftemperaturechan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mber

densityof

thecarriers

excitedby

theop

ticalperturbation

Thu

sthetotalph

o-torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompon

ents59

R

=R

TT+

R

N

N

(1)













13ndash16









p















1 NM3 NM5 46710 939


1 NM3 3115 50710 974



eff =i

1 +iRtot

d

(1)
















13ndash16









p











frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



and PbTiO327










III RESULTS



















13ndash16









r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46





r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Cha

racteristicim

pulses

andresp


d(c)SS

TR

techniqu

esIn

TDTRthemag

nitude

ofthethermorefl

ectanc

eismon

itored

asafunc

tion

ofpu

mp-prob

ede

laytime

while

inFDTR

theph

aselagbetweenthepu

mp

andprob

eismon

itored

asafunc

tion

offreque

ncy

InSS

TRtem

peraturechan

gesaremon

itored

forgivenchan

gesin

heat

flux

Noticetheincrease

inthermal

pen

etration

depthresultingfrom

thelower

mod

ulationfreque

nciesem

ployed

inSS

TR

tempe

rature

chan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

expe

rimentsthe

timede

laybe

tweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

tempe

rature

chan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshift

inthermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becomes

low

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

period

sof

themod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarre

rent

pump

powers

thus

indu

cing

aFo

urier-lik

erespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebe

amsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pene

trationde

pths

(iethede

pth

bene

aththesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pend

ingon

themod

ulation

freque

ncy

Furthe

rgiventhepu

mpan

dprob

espot

sizes

canbe

focu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpe

rtinentleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

repo

rted

intheliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

tempe

rature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

tempe

rature

ofthematerial(ie

thether-

morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftempe

rature

chan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mbe

rde

nsityof

thecarriers

excitedby

theop

ticalp

erturbation

Thu

sthetotalp

ho-

torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompo

nents59 R

=R T

T+

R NN

(1)



1f













13ndash16









p











r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46


















and PbTiO327










III RESULTS






BulkThin film





IV DISCUSSION



















JOM 71 246





amorphous effects





10 nm TaN

Silicon substrate







90 fs pluse width

Pump

Isolator

EOM

BiBO

Redfilter

Dichroic

Probe


Bluefilter

Lock-inamplifier

Photodiode



0 1 2 3 4 5

0

1

2

3

4

5

6

7

8

9

10



Thermal model





119881119881JO = Re 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891

119881119881PVU = Im 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891


119885119885 10076491007649119891119891119891 11989111989110076651007665 = 120585120585infin10055761005576








2 ~T~

zeth THORN

z2frac14 q2 ~T

~zeth THORN (10)


(11)

~Q~

top frac141

2pexp k2r2

0

8

~G xeth THORN (12)



while ~Y~amp ~Y





~T~

z is


~T~

zeth THORN~Q~

zeth THORN

2

64

3


qjzsinh qzeth THORN


2

4

3

5~T~

top

~Q~

top

2

64

3

75

(13)



top and ~Q~

top for that


limz1



nation of ~T~

topn and ~Q~



z frac14Pnndash1


~T~

botn1

~Q~

botn1

2

64

3

75 frac141 1

h n1eth THORN=n

0 1

2

4

3

5~T~

topn

~Q~

topn

2

64

3

75 (15)


~T~

n zeth THORN

~Qn~

zeth THORN

2

64

3




2

64

3

75

Yjfrac141

jfrac14n1n2

MjNj

~T~

top

~Q~

top

2

64

3

75 frac14~A~

~B~

~C~

~D~

2

64

3

75~T~

top

~Q~

top

2

64

3

75

(16)



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Characteristic

impulses

andresp


d(c)SSTR

techniquesIn

TDTRthemag

nitude

ofthethermorefl

ectance

ismon

itored

asafunctionof

pump-probedelay

time

whilein

FDTR


andprobeismon

itored

asafunctionof

frequen

cyIn

SSTRtemperature

chan

gesaremon

itored

forgivenchan

gesin

heatflux

Noticetheincrease

inthermal

pen

etration

dep

thresultingfrom

thelower

mod

ulation

frequen

cies

employedin

SSTR

temperaturechan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

experim

entsthe

timede

laybetweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

temperaturechan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshiftin

thermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becom

eslow

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

periods

ofthemod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarrerent

pump

pow

ers

thus

indu

cing

aFou

rier-likerespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebeamsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pen

etration

depths

(iethede

pth

ben

eath

thesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pen

ding

onthemod

ulation

freque

ncy

Furthergiventhepu

mpan

dprob

espot

sizes

canbefocu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpertine

ntleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

reportedin

theliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

temperature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

temperatureof


morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftemperaturechan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mber

densityof

thecarriers

excitedby

theop

ticalperturbation

Thu

sthetotalph

o-torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompon

ents59

R

=R

TT+

R

N

N

(1)













13ndash16









p















1 NM3 NM5 46710 939


1 NM3 3115 50710 974



eff =i

1 +iRtot

d

(1)
















13ndash16









p











frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



and PbTiO327










III RESULTS



















13ndash16









r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46





r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Cha

racteristicim

pulses

andresp


d(c)SS

TR

techniqu

esIn

TDTRthemag

nitude

ofthethermorefl

ectanc

eismon

itored

asafunc

tion

ofpu

mp-prob

ede

laytime

while

inFDTR

theph

aselagbetweenthepu

mp

andprob

eismon

itored

asafunc

tion

offreque

ncy

InSS

TRtem

peraturechan

gesaremon

itored

forgivenchan

gesin

heat

flux

Noticetheincrease

inthermal

pen

etration

depthresultingfrom

thelower

mod

ulationfreque

nciesem

ployed

inSS

TR

tempe

rature

chan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

expe

rimentsthe

timede

laybe

tweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

tempe

rature

chan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshift

inthermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becomes

low

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

period

sof

themod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarre

rent

pump

powers

thus

indu

cing

aFo

urier-lik

erespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebe

amsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pene

trationde

pths

(iethede

pth

bene

aththesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pend

ingon

themod

ulation

freque

ncy

Furthe

rgiventhepu

mpan

dprob

espot

sizes

canbe

focu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpe

rtinentleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

repo

rted

intheliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

tempe

rature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

tempe

rature

ofthematerial(ie

thether-

morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftempe

rature

chan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mbe

rde

nsityof

thecarriers

excitedby

theop

ticalp

erturbation

Thu

sthetotalp

ho-

torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompo

nents59 R

=R T

T+

R NN

(1)



1f













13ndash16









p











r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46


























JOM 71 246





amorphous effects





10 nm TaN

Silicon substrate







90 fs pluse width

Pump

Isolator

EOM

BiBO

Redfilter

Dichroic

Probe


Bluefilter

Lock-inamplifier

Photodiode



0 1 2 3 4 5

0

1

2

3

4

5

6

7

8

9

10



Thermal model





119881119881JO = Re 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891

119881119881PVU = Im 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891


119885119885 10076491007649119891119891119891 11989111989110076651007665 = 120585120585infin10055761005576








2 ~T~

zeth THORN

z2frac14 q2 ~T

~zeth THORN (10)


(11)

~Q~

top frac141

2pexp k2r2

0

8

~G xeth THORN (12)



while ~Y~amp ~Y





~T~

z is


~T~

zeth THORN~Q~

zeth THORN

2

64

3


qjzsinh qzeth THORN


2

4

3

5~T~

top

~Q~

top

2

64

3

75

(13)



top and ~Q~

top for that


limz1



nation of ~T~

topn and ~Q~



z frac14Pnndash1


~T~

botn1

~Q~

botn1

2

64

3

75 frac141 1

h n1eth THORN=n

0 1

2

4

3

5~T~

topn

~Q~

topn

2

64

3

75 (15)


~T~

n zeth THORN

~Qn~

zeth THORN

2

64

3




2

64

3

75

Yjfrac141

jfrac14n1n2

MjNj

~T~

top

~Q~

top

2

64

3

75 frac14~A~

~B~

~C~

~D~

2

64

3

75~T~

top

~Q~

top

2

64

3

75

(16)



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Characteristic

impulses

andresp


d(c)SSTR

techniquesIn

TDTRthemag

nitude

ofthethermorefl

ectance

ismon

itored

asafunctionof

pump-probedelay

time

whilein

FDTR


andprobeismon

itored

asafunctionof

frequen

cyIn

SSTRtemperature

chan

gesaremon

itored

forgivenchan

gesin

heatflux

Noticetheincrease

inthermal

pen

etration

dep

thresultingfrom

thelower

mod

ulation

frequen

cies

employedin

SSTR

temperaturechan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

experim

entsthe

timede

laybetweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

temperaturechan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshiftin

thermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becom

eslow

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

periods

ofthemod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarrerent

pump

pow

ers

thus

indu

cing

aFou

rier-likerespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebeamsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pen

etration

depths

(iethede

pth

ben

eath

thesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pen

ding

onthemod

ulation

freque

ncy

Furthergiventhepu

mpan

dprob

espot

sizes

canbefocu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpertine

ntleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

reportedin

theliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

temperature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

temperatureof


morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftemperaturechan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mber

densityof

thecarriers

excitedby

theop

ticalperturbation

Thu

sthetotalph

o-torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompon

ents59

R

=R

TT+

R

N

N

(1)













13ndash16









p















1 NM3 NM5 46710 939


1 NM3 3115 50710 974



eff =i

1 +iRtot

d

(1)
















13ndash16









p











frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



and PbTiO327










III RESULTS



















13ndash16









r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46





r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Cha

racteristicim

pulses

andresp


d(c)SS

TR

techniqu

esIn

TDTRthemag

nitude

ofthethermorefl

ectanc

eismon

itored

asafunc

tion

ofpu

mp-prob

ede

laytime

while

inFDTR

theph

aselagbetweenthepu

mp

andprob

eismon

itored

asafunc

tion

offreque

ncy

InSS

TRtem

peraturechan

gesaremon

itored

forgivenchan

gesin

heat

flux

Noticetheincrease

inthermal

pen

etration

depthresultingfrom

thelower

mod

ulationfreque

nciesem

ployed

inSS

TR

tempe

rature

chan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

expe

rimentsthe

timede

laybe

tweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

tempe

rature

chan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshift

inthermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becomes

low

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

period

sof

themod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarre

rent

pump

powers

thus

indu

cing

aFo

urier-lik

erespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebe

amsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pene

trationde

pths

(iethede

pth

bene

aththesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pend

ingon

themod

ulation

freque

ncy

Furthe

rgiventhepu

mpan

dprob

espot

sizes

canbe

focu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpe

rtinentleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

repo

rted

intheliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

tempe

rature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

tempe

rature

ofthematerial(ie

thether-

morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftempe

rature

chan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mbe

rde

nsityof

thecarriers

excitedby

theop

ticalp

erturbation

Thu

sthetotalp

ho-

torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompo

nents59 R

=R T

T+

R NN

(1)



1f













13ndash16









p











r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46


















amorphous effects





10 nm TaN

Silicon substrate







90 fs pluse width

Pump

Isolator

EOM

BiBO

Redfilter

Dichroic

Probe


Bluefilter

Lock-inamplifier

Photodiode



0 1 2 3 4 5

0

1

2

3

4

5

6

7

8

9

10



Thermal model





119881119881JO = Re 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891

119881119881PVU = Im 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891


119885119885 10076491007649119891119891119891 11989111989110076651007665 = 120585120585infin10055761005576








2 ~T~

zeth THORN

z2frac14 q2 ~T

~zeth THORN (10)


(11)

~Q~

top frac141

2pexp k2r2

0

8

~G xeth THORN (12)



while ~Y~amp ~Y





~T~

z is


~T~

zeth THORN~Q~

zeth THORN

2

64

3


qjzsinh qzeth THORN


2

4

3

5~T~

top

~Q~

top

2

64

3

75

(13)



top and ~Q~

top for that


limz1



nation of ~T~

topn and ~Q~



z frac14Pnndash1


~T~

botn1

~Q~

botn1

2

64

3

75 frac141 1

h n1eth THORN=n

0 1

2

4

3

5~T~

topn

~Q~

topn

2

64

3

75 (15)


~T~

n zeth THORN

~Qn~

zeth THORN

2

64

3




2

64

3

75

Yjfrac141

jfrac14n1n2

MjNj

~T~

top

~Q~

top

2

64

3

75 frac14~A~

~B~

~C~

~D~

2

64

3

75~T~

top

~Q~

top

2

64

3

75

(16)



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Characteristic

impulses

andresp


d(c)SSTR

techniquesIn

TDTRthemag

nitude

ofthethermorefl

ectance

ismon

itored

asafunctionof

pump-probedelay

time

whilein

FDTR


andprobeismon

itored

asafunctionof

frequen

cyIn

SSTRtemperature

chan

gesaremon

itored

forgivenchan

gesin

heatflux

Noticetheincrease

inthermal

pen

etration

dep

thresultingfrom

thelower

mod

ulation

frequen

cies

employedin

SSTR

temperaturechan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

experim

entsthe

timede

laybetweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

temperaturechan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshiftin

thermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becom

eslow

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

periods

ofthemod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarrerent

pump

pow

ers

thus

indu

cing

aFou

rier-likerespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebeamsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pen

etration

depths

(iethede

pth

ben

eath

thesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pen

ding

onthemod

ulation

freque

ncy

Furthergiventhepu

mpan

dprob

espot

sizes

canbefocu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpertine

ntleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

reportedin

theliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

temperature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

temperatureof


morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftemperaturechan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mber

densityof

thecarriers

excitedby

theop

ticalperturbation

Thu

sthetotalph

o-torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompon

ents59

R

=R

TT+

R

N

N

(1)













13ndash16









p















1 NM3 NM5 46710 939


1 NM3 3115 50710 974



eff =i

1 +iRtot

d

(1)
















13ndash16









p











frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



and PbTiO327










III RESULTS



















13ndash16









r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46





r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Cha

racteristicim

pulses

andresp


d(c)SS

TR

techniqu

esIn

TDTRthemag

nitude

ofthethermorefl

ectanc

eismon

itored

asafunc

tion

ofpu

mp-prob

ede

laytime

while

inFDTR

theph

aselagbetweenthepu

mp

andprob

eismon

itored

asafunc

tion

offreque

ncy

InSS

TRtem

peraturechan

gesaremon

itored

forgivenchan

gesin

heat

flux

Noticetheincrease

inthermal

pen

etration

depthresultingfrom

thelower

mod

ulationfreque

nciesem

ployed

inSS

TR

tempe

rature

chan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

expe

rimentsthe

timede

laybe

tweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

tempe

rature

chan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshift

inthermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becomes

low

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

period

sof

themod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarre

rent

pump

powers

thus

indu

cing

aFo

urier-lik

erespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebe

amsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pene

trationde

pths

(iethede

pth

bene

aththesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pend

ingon

themod

ulation

freque

ncy

Furthe

rgiventhepu

mpan

dprob

espot

sizes

canbe

focu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpe

rtinentleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

repo

rted

intheliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

tempe

rature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

tempe

rature

ofthematerial(ie

thether-

morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftempe

rature

chan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mbe

rde

nsityof

thecarriers

excitedby

theop

ticalp

erturbation

Thu

sthetotalp

ho-

torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompo

nents59 R

=R T

T+

R NN

(1)



1f













13ndash16









p











r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46




















90 fs pluse width

Pump

Isolator

EOM

BiBO

Redfilter

Dichroic

Probe


Bluefilter

Lock-inamplifier

Photodiode



0 1 2 3 4 5

0

1

2

3

4

5

6

7

8

9

10



Thermal model





119881119881JO = Re 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891

119881119881PVU = Im 10077131007713119885119885 10076491007649119891119891119891 1198911198911007665100766510077291007729 119891


119885119885 10076491007649119891119891119891 11989111989110076651007665 = 120585120585infin10055761005576








2 ~T~

zeth THORN

z2frac14 q2 ~T

~zeth THORN (10)


(11)

~Q~

top frac141

2pexp k2r2

0

8

~G xeth THORN (12)



while ~Y~amp ~Y





~T~

z is


~T~

zeth THORN~Q~

zeth THORN

2

64

3


qjzsinh qzeth THORN


2

4

3

5~T~

top

~Q~

top

2

64

3

75

(13)



top and ~Q~

top for that


limz1



nation of ~T~

topn and ~Q~



z frac14Pnndash1


~T~

botn1

~Q~

botn1

2

64

3

75 frac141 1

h n1eth THORN=n

0 1

2

4

3

5~T~

topn

~Q~

topn

2

64

3

75 (15)


~T~

n zeth THORN

~Qn~

zeth THORN

2

64

3




2

64

3

75

Yjfrac141

jfrac14n1n2

MjNj

~T~

top

~Q~

top

2

64

3

75 frac14~A~

~B~

~C~

~D~

2

64

3

75~T~

top

~Q~

top

2

64

3

75

(16)



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Characteristic

impulses

andresp


d(c)SSTR

techniquesIn

TDTRthemag

nitude

ofthethermorefl

ectance

ismon

itored

asafunctionof

pump-probedelay

time

whilein

FDTR


andprobeismon

itored

asafunctionof

frequen

cyIn

SSTRtemperature

chan

gesaremon

itored

forgivenchan

gesin

heatflux

Noticetheincrease

inthermal

pen

etration

dep

thresultingfrom

thelower

mod

ulation

frequen

cies

employedin

SSTR

temperaturechan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

experim

entsthe

timede

laybetweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

temperaturechan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshiftin

thermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becom

eslow

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

periods

ofthemod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarrerent

pump

pow

ers

thus

indu

cing

aFou

rier-likerespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebeamsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pen

etration

depths

(iethede

pth

ben

eath

thesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pen

ding

onthemod

ulation

freque

ncy

Furthergiventhepu

mpan

dprob

espot

sizes

canbefocu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpertine

ntleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

reportedin

theliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

temperature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

temperatureof


morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftemperaturechan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mber

densityof

thecarriers

excitedby

theop

ticalperturbation

Thu

sthetotalph

o-torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompon

ents59

R

=R

TT+

R

N

N

(1)













13ndash16









p















1 NM3 NM5 46710 939


1 NM3 3115 50710 974



eff =i

1 +iRtot

d

(1)
















13ndash16









p











frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



and PbTiO327










III RESULTS



















13ndash16









r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46





r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Cha

racteristicim

pulses

andresp


d(c)SS

TR

techniqu

esIn

TDTRthemag

nitude

ofthethermorefl

ectanc

eismon

itored

asafunc

tion

ofpu

mp-prob

ede

laytime

while

inFDTR

theph

aselagbetweenthepu

mp

andprob

eismon

itored

asafunc

tion

offreque

ncy

InSS

TRtem

peraturechan

gesaremon

itored

forgivenchan

gesin

heat

flux

Noticetheincrease

inthermal

pen

etration

depthresultingfrom

thelower

mod

ulationfreque

nciesem

ployed

inSS

TR

tempe

rature

chan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

expe

rimentsthe

timede

laybe

tweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

tempe

rature

chan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshift

inthermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becomes

low

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

period

sof

themod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarre

rent

pump

powers

thus

indu

cing

aFo

urier-lik

erespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebe

amsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pene

trationde

pths

(iethede

pth

bene

aththesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pend

ingon

themod

ulation

freque

ncy

Furthe

rgiventhepu

mpan

dprob

espot

sizes

canbe

focu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpe

rtinentleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

repo

rted

intheliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

tempe

rature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

tempe

rature

ofthematerial(ie

thether-

morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftempe

rature

chan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mbe

rde

nsityof

thecarriers

excitedby

theop

ticalp

erturbation

Thu

sthetotalp

ho-

torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompo

nents59 R

=R T

T+

R NN

(1)



1f













13ndash16









p











r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46


























13ndash16









p















1 NM3 NM5 46710 939


1 NM3 3115 50710 974



eff =i

1 +iRtot

d

(1)
















13ndash16









p











frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



and PbTiO327










III RESULTS



















13ndash16









r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46





r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Cha

racteristicim

pulses

andresp


d(c)SS

TR

techniqu

esIn

TDTRthemag

nitude

ofthethermorefl

ectanc

eismon

itored

asafunc

tion

ofpu

mp-prob

ede

laytime

while

inFDTR

theph

aselagbetweenthepu

mp

andprob

eismon

itored

asafunc

tion

offreque

ncy

InSS

TRtem

peraturechan

gesaremon

itored

forgivenchan

gesin

heat

flux

Noticetheincrease

inthermal

pen

etration

depthresultingfrom

thelower

mod

ulationfreque

nciesem

ployed

inSS

TR

tempe

rature

chan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

expe

rimentsthe

timede

laybe

tweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

tempe

rature

chan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshift

inthermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becomes

low

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

period

sof

themod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarre

rent

pump

powers

thus

indu

cing

aFo

urier-lik

erespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebe

amsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pene

trationde

pths

(iethede

pth

bene

aththesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pend

ingon

themod

ulation

freque

ncy

Furthe

rgiventhepu

mpan

dprob

espot

sizes

canbe

focu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpe

rtinentleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

repo

rted

intheliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

tempe

rature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

tempe

rature

ofthematerial(ie

thether-

morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftempe

rature

chan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mbe

rde

nsityof

thecarriers

excitedby

theop

ticalp

erturbation

Thu

sthetotalp

ho-

torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompo

nents59 R

=R T

T+

R NN

(1)



1f













13ndash16









p











r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46


























13ndash16









p











frac14Z c=kBT

0

k4BT3





U thorn 1a thorn 1

b THORN1 where U



UGeamp1 (2)


andb frac14 d=v (4)






1 10 100 1000 100001

10

1 10 100 1000 100001

10

(b)

(a)

The

rmal

Con

duct

ivity

(Wm

-1K

-1)


T = 300K

SiGe SL Ref 2

Si085

Ge015

Ref 2


Si05

Ge05

Ref 6

SiSi071

Ge029

SL Ref 7

Si084

Ge016

Si074

Ge026

SL Ref 7

Si09

Ge01

Ref 7

SiSi071

Ge029

SL Ref 8

Si04

Ge06

Ref 23

Si08

Ge02

(This Work)

Si08

Ge02

Model Eq (1)

T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)



00 02 04 06 08 100

1

2

3

4

5

6

7

8

9

10


T = 300K

The

rmal

Con

duct

ivity

(Wm

-1K

-1)

Ge Composition

Bulk

500 nm

100 nm

300 nm



9 NOVEMBER 2012

195901-3



and PbTiO327










III RESULTS



















13ndash16









r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46





r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Cha

racteristicim

pulses

andresp


d(c)SS

TR

techniqu

esIn

TDTRthemag

nitude

ofthethermorefl

ectanc

eismon

itored

asafunc

tion

ofpu

mp-prob

ede

laytime

while

inFDTR

theph

aselagbetweenthepu

mp

andprob

eismon

itored

asafunc

tion

offreque

ncy

InSS

TRtem

peraturechan

gesaremon

itored

forgivenchan

gesin

heat

flux

Noticetheincrease

inthermal

pen

etration

depthresultingfrom

thelower

mod

ulationfreque

nciesem

ployed

inSS

TR

tempe

rature

chan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

expe

rimentsthe

timede

laybe

tweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

tempe

rature

chan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshift

inthermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becomes

low

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

period

sof

themod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarre

rent

pump

powers

thus

indu

cing

aFo

urier-lik

erespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebe

amsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pene

trationde

pths

(iethede

pth

bene

aththesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pend

ingon

themod

ulation

freque

ncy

Furthe

rgiventhepu

mpan

dprob

espot

sizes

canbe

focu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpe

rtinentleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

repo

rted

intheliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

tempe

rature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

tempe

rature

ofthematerial(ie

thether-

morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftempe

rature

chan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mbe

rde

nsityof

thecarriers

excitedby

theop

ticalp

erturbation

Thu

sthetotalp

ho-

torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompo

nents59 R

=R T

T+

R NN

(1)



1f













13ndash16









p











r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46


























13ndash16









r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46





r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46



2

(a) T

DTR

(b) F

DTR

(c) S

STR

FIG

1

Cha

racteristicim

pulses

andresp


d(c)SS

TR

techniqu

esIn

TDTRthemag

nitude

ofthethermorefl

ectanc

eismon

itored

asafunc

tion

ofpu

mp-prob

ede

laytime

while

inFDTR

theph

aselagbetweenthepu

mp

andprob

eismon

itored

asafunc

tion

offreque

ncy

InSS

TRtem

peraturechan

gesaremon

itored

forgivenchan

gesin

heat

flux

Noticetheincrease

inthermal

pen

etration

depthresultingfrom

thelower

mod

ulationfreque

nciesem

ployed

inSS

TR

tempe

rature

chan

geon

thesurfaceas

func

tion

ofeither

for

inthecase

ofshortpu

lsed

-based

expe

rimentsthe

timede

laybe

tweenthepu

mpan

dprob

epu

lsesW

here

TDTR

utilizesshortpu

lses

(typ

ically

sub-picosecond

)to

mon

itor

thethermorefl

ectanc

ede

cayas

afunc

tion

oftimeafterpu

mppu

lsehe

atingalon

gwiththeph

aseshift

indu

cedfrom

themod

ulated

tempe

rature

chan

geat

f

FDTR

can

utilize

avariety

ofpu

lsed

orcw

-lasersto

mon

itor

theph

aseshift

inthermorefl

ectanc

esign

alsas

afunc

tion

offA

new

techniqu

eha

srecently

emerged

calle

dldquoS

tead

yStateThe

rmorefl

ectanc

erdquo(SST

R)that

operates

like

FDTR

only

inthe

low

freque

ncy

limit

Whe

nf

becomes

low

enou

ghthematerialof

interest

will

reach

steady

state

cond

itions

during

onan

docrarr

period

sof

themod

ulationevent

DuringthistimeSS

TR

mon

itorsthethermorefl

ectanc

eof

thesurfaceat

dicrarre

rent

pump

powers

thus

indu

cing

aFo

urier-lik

erespon

sein

the

materialan

docrarr

ering

analternative

metho

dto

measure

the

thermal

cond

uctivity

ofmaterials

using

opticalpu

mp-prob

emetrologies

The

characteristic

impu

lses

and

respon

sesforeach

ofthesetechniqu

esis

presentedin

Fig1

Wereview

therecent

advanc

esin

SSTR

inSe

ctionIV

Inad

dition

totheirno

n-contactim

plem

entation

an

addition

alad

vantag

eof

TDTRFDTR

and

SSTR

toman

yothe

rthermom

etry

platform

sistherelatively

small

volumean

dne

arsurfaceregion

inwhich

they

measure

Byfocu

sing

thepu

mpan

dprob

ebe

amsan

dusingprop

erlaserwavelen

gths

toen

sure

nano

scaleop

ticalp

enetration

depthsthethermal

pene

trationde

pths

(iethede

pth

bene

aththesurfacein

which

thesetechniqu

esmeasure

thethermal

prop

erties)can

belim

ited

tothefocu

sed

spot

sizeor

much

lessde

pend

ingon

themod

ulation

freque

ncy

Furthe

rgiventhepu

mpan

dprob

espot

sizes

canbe

focu

sedto

leng

thscales

ontheorde

rof

microm-

eters

thermorefl

ectanc

etechniqu

esallow

forspatially

-resolved

surfacemeasurements

ofthermal

prop

erties

with


andtheab

ility

tocreate

thermal

prop

erties

arealldquom

apsrdquo

Wereview

theprevious

ad-

vanc

esof

TDTRan

dFDTRthermal

prop

erty

ldquomap

ping

rdquoin

SectionIII

andreview

allpe

rtinentleng

thscales

ofTDTRFDTR

andSS

TR

inSe

ctionII

Inthemajorityof

theTDTRFDTR

andSS

TR

mea-

surements

repo

rted

intheliterature

thethermal

prop

-erties

ofthesampleof

interest

arecoated

with

athin

metal

film

tran

sduc

erwhich

acts

asareferenc

ether-

mal

massin

which

thechan

gein

refle

ctivityis

directly

related

tothe

chan

gein

tempe

rature

How

everthe

chan

gein

refle

ctivityof

anymaterialis

relatedto

both

thechan

gein

tempe

rature

ofthematerial(ie

thether-

morefl

ectanc

ewhich

isultimatelyof

interest

forthemea-

surements

oftempe

rature

chan

gesan

dthermal

prop

er-

ties)an

dthechan

gein

thenu

mbe

rde

nsityof

thecarriers

excitedby

theop

ticalp

erturbation

Thu

sthetotalp

ho-

torefle

ctan

cesign

alchan

gethat

ismeasuredin

TDTR

FDTR

orSS

TR

can

beexpressed

asthesum

ofthese

twocompo

nents59 R

=R T

T+

R NN

(1)



1f













13ndash16









p











r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46


























13ndash16









p











r frac14 1

n

Xn

ifrac141

Xmi Xdi

Xdi

2

(1)








05 218 6 056 This study

07 264 6 053 This study

1 256ndash260 42 43 45 and 46














thermal conductivity and heat capacity of dielectric and ......thermal conductivity of materials...

Documents