effect of structural defects on the electrical properties ...898103/fulltext01.pdf · 1.1....

Determination of Electrical and Gas sensitivity Properties of

Graphene Sheets 1FA593: Project in Physics and Materials Science

(30 credits)

SYLVESTER WAMBUA MAKUMI

12/07/2015

Supervisor: Prof Klaus Leifer

Co-Supervisors:

Hu Li Ishtiaq Hassan Wani

Examiner: Prof Håkan Rensmo

i

Abstract

The understanding of the properties of graphene on a substrate is essential for the development

of the next generation electronic technology. Of equal importance is the understanding of ways

to modify its properties to suit specific application. Pure graphene has revealed high electrical

conductivity [35] however in the actual fabrication and application of graphene, defects are

unavoidable. We therefore need to understand the effect of defects on the properties of graphene

material and ways of modifying these properties. In this study, the modification of graphene’s

electrical properties using atomic scale structural defects has been studied. The relationship

between defect density and the electrical properties of graphene on SiO2 substrate have been

investigated using the PeakForce TUNA mode of MultiMode 8 AFM. NO2 gas sensing property

of graphene has been investigated using the Keithley 6430 source meter. It has been shown that

atomic scale structural defects lower the electrical conductivity of graphene sheet. For high

defect densities, graphene sheet did not show any conductivity. It has been shown that, the NO2

gas sensing property of graphene is good and can be increased by exposing graphene sheet to UV

light. A response of 12.56% has been achieved in N2 gas condition.

ii

LIST OF CONTENTS

Abstract i

Contents ii

1. NTRODUCTION 1

1.1. Background information 1

1.2. Electronic structure of graphene 2

1.3. Electrical properties of graphene 5

1.4. Gas sensing mechanism of graphene 6

1.5. Other Related Studies 8

1.5.1. Effect of structural defects on the electrical properties of graphene 8

1.5.2. Gas sensing properties of graphene 9

1.6. Atomic Force Microscope (AFM) 9

1.6.1. PeakForce TUNA 11

1.6.1.1. PF TUNA Imaging mode 12

1.6.1.2. I-V Spectroscopy mode 12

1.7. Basic understanding of Raman spectroscopy spectrum 13

2. EXPERIMENT I: ELECTRICAL PROPERTIES MEASUREMENT USING

PEAKFORCE TUNA 14

2.1. Sample Preparation 14

2.2. Raman spectroscopy studies 15

2.3. Experimental Details 17

3. EXPERIMENT III: TESTING THE GAS SENSING PROPERTY OF GRAPHENE 19

3.1. Experimental details 19

4. RESULTS AND DISCUSSION 20

4.1. Electrical properties of Silver contacts 20

4.2. Electrical properties of Graphene 21

4.2.1. Evaluation 27

4.3. Gas sensing properties of graphene 28

4.3.1. Evaluation 30

5. POSSIBLE APPLICATIONS OF RESULTS 31

iii

6. CONCLUSION 32

ACKNOWLEDGEMENT 32

References 33

APPENDIX I 39

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1. INTRODUCTION

1.1. Background information

To advance from the current semiconductor technology level dominated by silicon, there is

need for new materials with better controllable properties than silicon. Graphene has been

found to be a potential material to use in place of silicon. Suspended Graphene sheets exhibit

the highest carrier mobility[1], [2] but for application purpose, graphene need to be supported

by a substrate. Therefore, it is important to understand the properties of graphene sheet on a

substrate.

The graphene’s unique electronic properties and possible ways to modify it have drawn a

large interest. The possibility to modify the electronic property of graphene sheets by

chemical or physical means is a crucial step in the application of graphene in different

electronic devices and to make graphene a competitive material for future electronics. In the

past few years, many researchers have studied ways of modifying the graphene’s

properties[3]–[5].

The use of defects is one of the ways used to manipulate the mechanical and electrical

properties of graphene. Both the nature and amount of defects have a great effect on the

properties of graphene [6]. Defects can be seen as imperfections that can degrade the

electrical and mechanical properties of a material. However, structural defects in graphene

can be very useful in modifying the graphene properties for specific applications. Ion

irradiation using different ions[7]–[12]has been shown to be an effective methods of

introducing controlled amount of structural defect in a graphene material.

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In this study, Ga+ ions have been used to introduce atomic scale structural defects in graphene

sheet on SiO2 substrate. The effect of these defects on the electrical conductivity of graphene

has been studied using the PeakForce TUNA mode of MultiMode 8 AFM.

Studies have shown that graphene may offer an excellent sensing device in its application as

a sensor for different gases [13]–[15], radiation [16],biomolecules, and different chemicals

[17]–[19].Other studies have found reduced graphene oxide to be sensitive to toxic

vapors[20] water vapor[21].However, the gas sensitivity of graphene is not well studied and

there is need for more studies. In this study, the sensitivity property of graphene to NO2 has

been studied.

1.2. Electronic structure of graphene

Graphene is made up of carbon atoms arranged in honeycomb pattern. Carbon is the sixth

element of the periodic table. Its atom has six protons, A neutrons, and six electrons. If A = 6

and 7 result to the stable isotopes 12

C and 13

C, respectively, and A = 8 yield the radioactive

isotope 14

C. The isotope 12

C is the most common in nature. These 12

C take 99% of all carbon

atoms, 13

C and 14

C are only in traces[22]. At atomic ground state, the 6 electrons in a carbon

atom usually in 1s22s

22p

2 configuration, that is two electrons in the inner shell 1s orbital, two

in the 2s orbital and the other two in the 2p orbital. In the presence of other atoms, it is

favorable to excite one electron from the 2s to the third 2p orbital to form a covalent with the

other atoms. � hybridization involves a superposition of the 2s and two 2p orbitals to obtain

the planar � hybridization.

The carbon atoms in graphene condense in a honeycomb lattice due to this � hybridization.

Three valence electrons, in the carbon atom, form covalent C-C bonds in the x-y plane with

three neighboring carbon atoms. These form the �-bonds, which are responsible for the high

mechanical strength of graphene. There is one valence electron per atom which does not take

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part in the covalent �-bond formation. This remaining electron combines with its nearest

neighbors to form the orbital. These orbitals make graphene very conductive. Pure

graphene has one conduction electron per atom.

Graphene can be seen as a semiconductor without a bandgap. As electron traveling through a

semiconductor, it is influenced by the positively and negatively charged nuclei; there is an

internal electric field, the crystal field. When an external electric field is applied, the electrons

are influenced by two fields; the internal electric field and the external field due to the applied

external voltage. Thus, the total force on the electron will be

= �� + ��

The influence of the internal field is very complicated and it is determined by the electronic

properties of the material. These affect the current that flow in the material.

In crystal semiconductors, atoms are arranged periodically. This leads to periodic variation of

the potential energy. Therefore, the energy E as a function of k, E (k) is periodic because the

effective potential is periodic. The periodic zone picture of the E-k diagram is as shown in

figure 1 (a). The reduced zone, that is, the band structure for k values between − � and

� will

be as shown in figure 1 (b). The density of states in a band is very large but the number of

carrier concentration, which is responsible for electrical conductivity is very small. Therefore,

a small portion of the E-k diagram is important in the understanding of electrical conductivity

of a material. Only charge carriers close to the top of the valence band and those close to the

bottom of the conduction band participate in electrical conductivity of the material.

For each value there is a corresponding allowed energy value which is a solution of the

Schrödinger equation. values are discrete but the number is large such that a continuous

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line is drawn. These leads to the E-k diagram shown in figure 1. is the electron wave

vector, E is the energy, and is the Fermi energy.

(a) (b)

Fig. 1. The E-k diagram (a) Periodic zone picture and (b) reduced zone picture for ordinary semiconductor. (c)

The band dispersion near theK̅-point for ideal monolayer graphene and (d) the π-band near the K̅-point for

ideal bilayer graphene. is the electron wave vector.

There is two atoms per cell in a graphene structure. This leads to two ‘conical’ points per

Brillouin zone ( and ’) at which the band crossing occurs. A monolayer graphene shows

energy bands which have a linear dispersion which can be described by the equation =ħ � [23], where is the electron wave vector, it is the propagation vector, � = m/s is

the Fermi velocity, energy, and ħ is the reduced planks constant. This behavior is due to

symmetry considerations [24], [25]. On the other hand, a bilayer graphene show a parabolic

Ef Ef

(d) (c)

E(e

V)

k (A-1)

E (e

V)

k (A-1)

k(Å-1) k (Å-1)

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spectrum as shown in figure 1(d). The two systems form zero-gap semiconductors or a zero-

overlap semimetal. The lower valence �- and upper conduction �∗-bands meet at the �̅- and �′̅̅ ̅-points. These points, �̅ and �′̅̅ ̅, are the Dirac point. Their energy position (� ) is exactly

at the Fermi Level (� ). The conical spectrum in graphene results from the interaction of the

energy bands originating from the sub-lattices A and B. The quantum-mechanical hopping

between the sub lattices A and B give two energy bands whose intersection close to the edges

of the brillouin zone is a conical energy spectrum. Since the involved electrons belong to two

different sub-lattices, an energy gap is not opened. Hence, graphene is seen as a zero-gap

semiconductor or as a zero-overlap semimetal. Hence, graphene show unusual semi metallic

behavior.

1.3. Electrical properties of graphene

Graphene has revealed high electrical conductivity [2], [26]–[28]. Carrier mobility of up to

10,000 cm2/Vs was found for few layer graphene and up to 15,000 cm2/Vs at 300K for

multilayer graphene [28]. Electron in graphene are able to cover micrometer-long distances

without scattering even at room temperature [29]. Multilayer graphene has been found to be

able to sustain very high current densities of about × 7A/cm2 in ambient air [30]. The

estimated charge carrier velocity in graphene is high, about 106 m/s at the Dirac points. As a

result, graphene show electronic properties for a two dimensional gas of charged particles

which is described using relativistic Dirac equation instead of non-relativistic Schrödinger

equation. The charge carriers behave like massless Dirac fermions [31], [32]. In particular,

there is nothing relativistic about electrons moving around carbon atoms, when the electrons

interact with the periodic potential of graphene’s lattice new quasiparticles result. For low

energies E, these quasiparticles are precisely described by the Dirac equation with an

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effective speed of �� = ms-1

.These particles are called massless Dirac fermions and can

be seen as neutrinos with electron charge e or electrons without their rest mass mo[29].

Some semiconductors reveal charge mobility as high as ≈77,000 cm2 V

–1 s

–1 (Indium

antimonide (InSb)); however, these values are only achieved for un-doped bulk

semiconductors. For graphene, mobility remains high even at high charge carrier

concentration ( > cm2) in chemically and in electrically doped graphene [13].

In a defective graphene sheet, Charge transport usually through a combination of tunneling,

hopping, c-axis conduction across nano-holes, and percolation conduction pathways [4].

However, in a defect free graphene, c-axis transport is insignificant and charge transport

occurs through the graphene channel in the ab-plane [33]. c-axis transport is more significant

in a graphene sheet with nano-holes where charge carries diverge at the nano-holes’ walls [4].

If the graphene sheet is highly defective, charge carriers follow percolative conduction

pathways [4].Structural defects scatter charge carriers [3], [6], [34]–[37]. Therefore, the

presence of structural defects lower the electrical conductivity of graphene sheet as it has

been observed in this study.

1.4. Gas sensing mechanism of graphene

The operation principle of graphene gas-sensing device is based on the changes of its

electrical conductivity as a result of interaction of the graphene sheet and the gas molecules.

The gas molecules act as either electron donor or acceptors [13]. The transfer of electrons

from graphene sheet (or gas molecule) to the gas molecules (or graphene sheet) increases the

number of holes (or electrons) in the sheet. This increased charge carrier increase the

electrical conductivity of graphene. Therefore, by monitoring the changes in the conductivity

of graphene we can know the presence of gas molecules in the environment.

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Graphene is an excellent material to use as gas sensing devices because of the following

unique properties. First, it is very conductive; graphene show metallic conductivity thus, low

Johnson noise very low carrier densities[13], and a few extra electrons or holes can cause

significant changes in carrier concentration. This leads to changes in its conductivity.Second,

it is two-dimensional material; hence, a large surface area is exposed to interact with the gas

molecules. This increases the graphene sensitivity to gas molecule.

In this study, the NO2 gas sensing property of graphene has been investigated. Previous

studies have found NO2 molecules to be an electron acceptor which change graphene to p-

type [38], [39]. Electrons move from the graphene sheet to the NO2 molecules. This increases

holes concentration [13], [38], [40] in the graphene sheet. Therefore, absorption of NO2

molecules leads to an increase in the electrical conductivity of graphene.

The molecular doping strength is determined by the density of states (DOS) and the lowest

unoccupied and the highest occupied molecular orbitals (LUMO & HOMO) of the adsorbate.

The transfer of charge may occur because of the relative position in the DOS of the LUMO

and HOMO of the adsorbate. In case the HOMO is located above the Dirac point of

graphene, charge will be transferred from the adsorbate to graphene[39]. When the LUMO is

below the Dirac point, transfer of charge from graphene to the molecule will take place. The

transfers of charge are, to a small extend, determined by the mixing of the LUMO and

HOMO with graphene orbitals (hybridization). the Dirac point of graphene is above the

LUMO of NO2[39]. This leads to electron transfer from the graphene sheet into the NO2

molecule. Polarization of the NO2 on the graphene surface result to charges leading to gating

effect. This contributes to the increase in electrical conductivity of graphene. In addition,

some NO2 orbitals occur close to the Dirac point. This results to some charge transfer from

the NO2 molecule to graphene through orbital mixing.This transfer of charges increases the

conductivity of graphene as seen in this study.

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1.5. Other Related Studies

1.5.1. Effect of structural defects on the electrical properties of graphene

The electrical properties of defective graphene have been studied both theoretically and

experimentally.Conductivity of graphene can be increased by introducing vacancy defects[3].

They observed that, vacancy defects increase the conductivity of graphene sheets by more

than one order of magnitude. For small vacancy defects density, graphene near the vacancy

defects has metallic properties. However, for higher vacancy defect density, the defects act as

scattering centers, hence conductivity of graphene decrease with increasing defect density.

Intrinsic defects degrade the quality of graphene on SiO2 through complicated mechanism

rather than defect scattering only [41]. In their study, they have found that, the effect of

lattice defects on graphene conductivity become remarkable only when the defect density

exceed ~103/�m

2. They have noted that, the height of graphene on SiO2 substrate is

proportional to its defect densities.

Structural defects in graphene sheets cause intervalley [42] and intervalley scattering [36],

[42] that lower its electrical conductivity. The Fermi Velocity is lower near the defects as a

result of enhanced scattering[42]. Structural defects can also lead to a band-gap in a graphene

electronic structure[42].

In their study, graphene sheets on SiO2were irradiated by Ne+ and He

+ ions. They found that,

lattice defects greatly depress the minimum conductivity, even below / ℎ (the minimum

metallic value) and induce insulating temperature dependence of the conductivity. They have

noted that, defects induced by ion irradiation cause significant intervalley scattering which

results to a conductivity proportional to charge carrier density, with mobility decreasing as

the inverse of the ion dose. Point defects, grain boundaries, disorders, wrinkles, folds, cracks

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and tears scatter charge carriers hence increasing the electrical resistance of graphene sheets

[37], [43].

Thiyagarajan et al. [4] have studied the electrical transport of multilayer graphene (MLG)

after Ar plasma irradiation. They have observed that, the conductivity of MLG reduce with

defect inclusion and MLG is transformed from metallic to semiconductor. Defective MLG

show a metallic-to-semiconductor transition in the resistance as temperature changes.

There is no available study that has employed the PeakForce TUNA technique to study the

electrical properties of defected graphene on SiO2 substrate.

1.5.2. Gas sensing properties of graphene

Studies have shown that graphene may offer an excellent sensing device in its application as

a sensor for different gases [13], [14], [38], [44], [45], [46]. Chen et al. [44] showed that a

pristine graphene is sensitive to gas molecules at concentrations as low as 158 ppq at room

temperature. They have shown that, a continuous UV light illumination during gas detection

is able to make simple two-terminal graphene based sensor sensitive to as low as 158 ppq NO

molecules at room temperature. The ultra-sensitivity was also confirmed by the low-level

detection of NO2, NH3, N2O, O2, SO2, CO2, and H2O. Few layer graphene show good

sensitivity for NO2, NH3, H2O and CO [13]. Wu et al. [46] have use CVD graphene to sense

hydrogen gas in air with concentration between 0.0025 and 1%. NO2 molecules have been

found to be an electron acceptor, which change graphene to p-type [38]. In this study, the

NO2 gas sensing property of graphene has been studied.

1.6. Atomic Force Microscope (AFM)

The AFM involve a sharp probe that is scanned across the surface of a sample. While the tip

is being scanned on the sample surface, the interatomic forces between the surface of the

sample and the tip causes a vertical displacement of the tip and corresponding bending of the

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cantilever. This bending is governed by Hooke’s law, = , where is the force on the tip,

is the spring constant of the cantilever, and is the displacement of the cantilever. The

cantilever can be displaced by direct contact force, van der Waals forces, electric force,

magnetic force, etc. A laser beam is transmitted to the backside of the free end of the

cantilever, which reflects it to form a spot on a position-sensitive photo-detector (PSPD) as

shown in figure 2.

(a) (b)

Fig 2.(a)Schematic diagram of the basic principle of AFM (b) The z position of the probe (black curve), force-

time curve (blue curve) and current-time curve (brown curve) for one cycle in PF TUNA.

If the cantilever moves, the spot also move correspondingly. The detector then converts the

laser spot movement to electric signals, which is then provided to a computer for processing.

The AFM software interpretsthese signals, which give information about the topography of

the sample since the movement of the tip corresponds to the topography of the sample

surface.

The signal generated by the photodetectoris supplied to a feedback circuit andinto the z-

piezo. This is used to control the distance or force between the probe and the sample surface.

The AFM can be operated in different modes depending on the properties of a sample the

user wants to determine. Currents is passed through the tip to probe the electrical

Tip

Photodetector

Cantilever

Sample

Laser beam

http://wiki.eanswers.com/en/Electric_current

http://wiki.eanswers.com/en/Electrical_conductivity

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conductivity or transport properties of the underlying sample. This has been done in this

study using the PeakForceTunneling AFM (PF TUNA)

1.6.1. PeakForce TUNA

Like PeakForce QNM, PF-TUNA mode builds on PeakForce Tapping mode of the AFM.A

probe that is coated with an electrically conductive material is scanned across the surface of

the sample in PeakForce Tapping mode. The user applies a DC bias between the tip and the

sample. The TUNA module senses the current passing through the sample to the AFM tip. In

PeakForceTapping, the maximum force on the tip (peak force) is maintained at a constant

value for each individual cycle. By maintaining a constant tip-sample force, topographic and

current images are generated simultaneously.

A complete cycle involves a single approach and a single retract. In figure 2 (b) The top line

(black) is the Z-position of the probe/tip as a function of time, as it goes through one

period/cycle. As the tip approach and retract, the AFM senses the forces and current flowing

through the sample surface. This is given as force curves and current curves as shown in

figure 2 (b). The middle line (blue) shows the force measured by the probe during approach

and withdraws of the tip. The lower curve (brown) represents the detected current on the

sample surface for one cycle. For a frequency of 2 kHz, the time from A to E is 0.5ms. From

the current-time curve, the PF-TUNA algorithm extracts three measurements: Peak current,

TUNA/Cycle-average current, and Contact average current. The peak current is the current

detected when the AFM tip exerts maximum force on the sample surface (peak force): when

the z-scanner is at its lowest point (at point C in figure 2(b)). TUNA current is the average

current detected in one full tapping cycle (approach and retract), from point A to point E in

figure 2 (b). Contact current is the average current measured when the AFM tip is in contact

with the sample surface I.e. the current measured from point B to point D in figure 2 (b).

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TUNA current involves the current measured when the AFM tip is far away from the sample

and that measured while it is in contact with the sample surface. The AFM software extracts

this currents at every pixel and maps them into different current images, i.e. TUNA current,

Contact current, and Peak current images which are available through different AFM

channels.

1.6.1.1. PF TUNA imaging mode

In PF TUNA imaging mode, the current maps are presented at the same time with the

topography image and mechanical properties maps (Young’s modulus, adhesion force,

deformation and dissipation). The observed current can be used to give the local conductivity,

or electrical integrity of the sample. Offline analysis function (NanoScope Analysis) can be

used to calculate statistics of the electrical properties of different regions, to take cross

sections through the images showing the spatial distribution of the properties, and /or the

correlation among the topographic, mechanical, and electrical properties of the sample.

1.6.1.2. I-V Spectroscopy mode

Local I-V spectra can be measured in the PeakForce TUNA. To extract the I-V curves, first,

the imaging scan is discarded then the tip held in a fixed location and the sample bias is

ramped up and down either once or continuously. The feedback is turned to contact mode

where a constant deflection of the cantilever is maintained while ramping takes place. The

current passing across the sample is plotted against the applied DC bias. The AFM software

is able to record the average of multiple spectra or a single spectrum. The "point & shoot" can

also be used to extract the I-V curves. It is possible to manually select the specific sample

area

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of interest using this feature.In this study, both PF TUNA imaging mode and I-V

spectroscopy mode have been used to investigate the electrical properties of graphene sheets.

1.7. Basic understanding of Raman spectroscopy spectrum

Raman spectroscopy has been shown to be a very powerful technique to investigate the

disorder[47]–[50]and number of layers in a graphene sheet [51].

The Raman signals of a graphene sheet consists of a D peak (at 1350cm-1

), G peak (at 1584

cm-1

) and a 2D peak (at 2700cm-1

).The G and 2D peaks give information about the number of

layers [49], [51]–[55]. The increase in the number of graphene layers leads to an increase in

intensity of G band[54] and shifts the 2D peak towards higher energies[55]as illustrated in the

spectra in Figure 3.These spectra allow us to study the properties of graphene. The D peak

shows the presence of lattice defects [53], [56] which may include physical damage [48], [49]

or sp3 hybridization due to adatoms on the graphene surface [57].

Fig 3.The Raman spectra of one to four layers on SiO2/Si substrate. Retrieved from ref [51].

For low defect density IG does not change but ID and ID’ increase with defect density. The

intensity of the D peak reach a maximum at a certain defect density then it starts decreasing.

The intensity of the D’ peak remain constant and the peak merge with the G peak at high

defect densities [50]. The intensity ratio of the D and G peaks (ID/IG) gives information about

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the concentration of covalent defect sites [50], [58] in the graphene sheet[50]. In this study,

Raman spectroscopy has been used to determine the number of graphene layers and the

changes in structural defect density.

2. EXPERIMENT I:ELECTRICAL PROPERTIES MEASUREMENT USING

PEAKFORCE TUNA

2.1. Sample Preparation

To investigate the effect of nanoscale structural defects on the electrical properties of

graphene, thirteen (13) areas of graphene/SiO2 sample were irradiated with controlled

amounts of Gallium ion using the FIB. Each area was exposed to different amount of ion

dose to introduce deferent defect densities in these areas. The amount of ion dosage is

presentedin Table 1. Ion irradiation has been shown to be one of the best ways to introduce

controlled amounts of structural defects in graphene sheets [7], [59], [60].

In the ion irradiation process, energy is transferred[60] from the incident Ga+ ion to the

graphene sheet by interaction with electrons in the graphene layer and by direct collisions

with its carbon atoms. This interaction result to different types of defects[61] in the graphene

structure like the Stone-Wales (SW) defects, Multiple Vacancies, Single Vacancies (SV),

nano holes, foreign adatoms, carbon adatoms, etc. For ion irradiated graphene, vacancy

defects usually the majority defects [61]. Few Frenkel pairs (FP) and stone-wales defects may

also be present. Single layer graphene is influenced more by ion irradiation than bilayer and

multi-layer graphene[7]; for the same ion dose, single layer graphene show higher defect

density than bilayer and multilayer graphene. In this study, a single layer graphene has been

used. Therefore, high defect densities are expected to be present after ion irradiation. The

STM images (not shown in this report) of Ga+ ion irradiated graphene show vacancy defects

and nano-holes were created in the sheet after high ion dose exposure.

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Sample Number Ion dose(ion/cm2

)

0 0.000 x 1000

1 1.044 x 1011

2 5.219 x 1011

3 1.044 x 1012

4 2.088 x 1012

5 3.131 x 1012

6 4.175 x 1012

7 6.263 x 1012

8 1.044 x 1013

9 1.566 x 1013

10 2.609 x 1013

11 5.219 x 1013

12 1.044 x 1014

13 5.219 x 1014

Table 1.Area number and the corresponding ion dose(ion/cm2)

When low energy (few keV) ions are used to irradiate graphene sheets on SiO2, the projection

range of the implanted ions in the SiO2 is small (few nanometers). This affects the defect

release in graphene sheet [7]. In this study high energy Ga+ ions were used. It is expected

that the projection range is large i.e. the ions travel deeper below the SiO2 layer, the SiO2

substrate is almost unaffected by this implantation. This was proven in a previous studies on

the mechanical properties of ion irradiated SiO2[62]; it was observed that ion irradiation does

not affect the mechanical property of the SiO2 substrate.

2.2. Raman spectroscopy studies

The Raman spectroscopy has been used to study the nature of the sample before and after ion

irradiation. The Raman spectrum and an AFM image of un-defected graphene/SiO2 is shown

in figure 4. It was observed that, for the graphene sample used in this study, the intensity ratio

of 2D peak (2700 cm-1

) and G peak (1550 cm-1

) is three. This confirms that the graphene is a

single layer (see section 1.7 above). The D peak for graphene sample before irradiation was

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found to be very small as shown in figure 4(a). That shows that the level of defects is very

low.

(a) (b)

Fig 4. (a) Raman spectrum for un-defected graphene (before Ga+ ion irradiation) (b) AFM

Height image of graphene sheets before irradiation. Extracted from [62]

The AFM image in Figure 4 (b) showsgrain boundaries and foreign nanoparticles in the

sample surface. These defects are expected to affect the conductivity of the graphene sheet, as

we shall see later in this study.

Fig 5.Plot of ID/IG as a function of ion dosage in RT-graphene (black) and Cryo-graphene

(red). Extracted from [62]

G

D

D

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In Raman, the intensity ratio of D peak and G peak indicates the defect level. Normally this

can be well explained by the structure change in graphene lattice (See section 1.7). Figure 5

shows the relation of the intensity ratio of D peak and G peak in Raman spectroscopy as a

function of the applied ion dosage. When the defects increase, the ratio of ID/IG will also

increase until a peak, this is the typical transfer of graphene from single crystal to

polycrystalline. Then the ratio will drop, indicating the transfer from polycrystalline to

amorphous carbon [7]. In figure 5, both samples show this typical curve above, but Cryo-

graphene indicates a significant left-shift compared with RT-graphene, which means that at a

certain ion dosage, Cryo-graphene has higher defects density than RT-graphene. It is good to

note that in this study only graphene sample prepared in room temperature has been

investigated.

2.3. Experimental Details

The defected sample was then placed on a steel sample holder using a carbon tape. Silver

paste was applied on two sides (shown in figure 6) of the sample. These would connect the

graphene sheet to the steel sample holder for current to flow through the AFM stage, the

sample and to the AFM tip. AFM Peak Force TUNA was then used to map the current in the

samples when a DC sample bias of 2V, 3V, and 9V was applied. The current present in the

silver paste connecting graphene sheet to the steel sample holder was measured at a DC

sample bias of 2V. TUNA, contact, and peak current imageswere takenfor all the defected

areas of the graphene sheet in ambient conditions. The probe used in this experiment was

SCM-PIT with spring constant of 1-5N/m. The tip was coated with conductive platinum-

Iridium which has an electrical resistivity of ≈ �Ω. [63]. To estimate the amount of

current that can flow through the tip we assume a cylindrical shape of length = and

radius � = . From ohms law,

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= � ��2 [1]

Where is the voltage, � is current, and the resistivity. Substituting the values, we get a

current of 17.6mA. This shows that the tip is good for this study. The silver paste used is

large in dimensions and so it is expected that it have low electrical resistance as seen in this

study.

(a) (b)

Fig 6.Schematic diagram showing the set up in this experiment.(a) Top view of the graphene sample. (b) a cross

section of the set up. Silver paste has been applied on two points to connect the graphene layer to the steel

sample holder.

To understand the conductivity of the sample, I-V curves were taken for randomly chosen

points of the silver paste and un-defected graphene using the I-V Spectroscopy mode of the

AFM.

While scanning in PF TUNA, the cantilever oscillates at a rate of about 2kHz.This means

each single oscillation take 0.5ms. The AFM measures the current through the sample when

the tip is in contact with the sample (contact and peak current) and when not in contact(see

section 1.6.1 for more details on the currents mapped).

of 39

Gas out Gas in

SiO2/Si

Graphen

e

Gold

SourceType equation here.Drain

3. EXPERIMENT II: TESTING THE GAS SENSING PROPERTY OF GRAPHENE

3.1. Experimental details

In this experiment, the gas sensing properties of graphene sheet was investigated. The

sample was first cleaned using ethanol and ultraviolet (UV)/ozone cleaning. Then it was

placed inside the gas-sensingchamber, which is mounted inside APS-4 Probe station. The gas

chamber had a total volume of 153.86 ml. It has a gas inlet and gas outlet. Both inlet and

outlet have same cross sectional area of 0.785mm2.Before gas sensing experiment, sample

was exposed to UV light.

(a)

(b) (c)

Fig. 7 (a) schematic diagram of the gas sensing set up. (b) The optical image and also the current-voltage curve

of the graphene device used.

The two gold (Au) electrodes were touched with needles/probes to form the source and drain.

A schematic diagram of the setup is shown in figure 7(a). The graphene device and its I-V

curve are also shown in figure 7(b) and (c). From the I-V curve we see that the graphene

sheet is Ohmic. The container was then closed tightly and N2 gas supplied to the container at

Au

of 39

a flow rate of 10ml/s. The I-t measurements were taken in this N2 condition at room

temperature by applying a voltage of 0.5V. Current through the graphene sheet was recorded

for about 30 minutes then the N2 gas supply was stopped and NO2 gas, diluted in N2 gas,

supply started. This mixture of N2 and NO2 gas (85% and 15% respectively and its

concentration was 15ppm) was supplied at a flow rate of 40ml/s. The I-t measurements were

taken for a voltage of 0.5V. The gas detection of graphene was studied by monitoring the

current change upon exposure of the graphene sheet to the gas [64] using the Keithley 6430

source meter.

4. RESULTS AND DISCUSSION

4.1. Electrical properties of Silver contacts

The electrical conductivity of the silver contacts(see Figure 6) was studiedto establish the

current available to the graphene sheet. For the silver paste, current as high as 1.2nA was

measured for a DC sample bias of 2V.It has been observed that, high current was measured

on the steep parts of the samples but on the flat areas, measured current was almost zero (see

the figure in appendix I ). This can be understood by analyzing the tip-sample interaction

mechanism. Figure 8 illustrates a AFM tip as it is scanned along the sample surface.

(a) (b)

Fig. 8. (a) Schematic diagram of the AFM tip as it is scanned over a sample with slopes. (b) Show multiple PF

TUNA I-t curves.

AFM tip

Sample

of 39

As the tip is scanned over a flat sample surface, only its sharp end interacts with the sample.

Very small current or even zero current was detected in that case. However, when the tip is

scanned over the slopes in the sample surface, the interaction involves the sides of the tip and

the sample surface, i.e. the tip touch the sample surface by its sides as shown in figure 8. This

has the effect of increasing the contact area between the sample surface and the AFM tip

hence higher current is expected to flow. This confirmed that the sharp part of the tip was not

as conductive as its sides. As a result of this effect, the graphene samples revealed low

currents on the flat surfaces and relatively higher currents on the grain boundaries. This led to

low average current for the entire scanned areas. The problem was observed even after

changing the probe to a new one. However, for comparison purpose the results obtained in

this study is reliable assuming the topography is uniform for all the areas.

The current present in the graphene sheet and the measured resistance is greatly affected by

the electrical properties of silver contacts. A resistance as low as . × − V/pA

( . × + Ω) was measured for silver paste contacting graphene sheet to the steel

sample holder.This resistance is expected to contribute to the resistance measured on the

graphene sheet.

4.2. Electrical properties of Graphene

The electrical property of graphene on SiO2 substrate has been investigated in this study

using the PeakForce TUNA mode of the AFM. The I-V curves obtained using the I-V

spectroscopy mode (see section 1.6.1.2) for un-defected graphene sheet on SiO2substrate

(Figure 9) show linear behavior indicating lack of significant Schottky barriers at the tip-

graphene interface. This observation is consistent with previous studies[65]; Studies have

shown that, graphene form Ohmic contacts with metals[65].From the I-V curves, the

resistance of the samples has been estimated (figure 9).

of 39

From the relation,

� = � =

the resistivity of samples can be determined. Where is the length of the material travelled

by current, is the resistivity, is the width, and the thickness of the sheet. In the PF

TUNA experiment set up, the length L and width W are not well defined, thus making it

difficult to calculate the resistivity of the graphene sheet in this study.

dX/dY = 5.3535e-005 V/pA dX/dY = 5.2713e-004 V/pA dX/dY = 9.6606e-004 V/pA

Fig 9. I-V curves for different possition of the un-defected Graphene Sheet.The blue and red curves show the

approach and retract curves.

The graphene sample used in this study showed a lower electrical conductivity than expected.

This could have been due to a number of factors. First, as we have seen above(section 4.1),

the interaction of the sample surface and the AFM tip may have contributed to the lower

measured current in this study. Second, the graphene-metal contact resistance contribute to

the total resistance of graphene based devices [66], [67]. This may be due to reflection of

charge carrier at the interface and/or contaminations by impurities. The contact resistance

between graphene and silver and that between graphene and the AFM tip can affect the

amount of current measured by the AFM. Third, the electrical continuity in graphene sheet is

greatly influenced by the presence of cracks, and grain boundaries[68]. These defects cause

electrical discontinuity hence lower the electrical conductivity of the graphene sheet in this

study by increasing its electrical resistance. Electrical discontinuity makes some areas of the

graphene sheet show a lower current than expected as seen in this study.

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(a)

(b)

(c)

(d)

Fig. 10. PF TUNA contact curent images and their cross section graphs for a DC sample bias of 3V for

graphene samples (a) area 4, (b) area 7, (c) area 12, and (d) Area 13. Electrical conductivity decrease with

increase in structural defect density.

of 39

13.0 13.3 13.5 13.8 14.0 14.3 14.5 14.8

0.00.0

0.3

0.50.5

0.8

1.01.0

1.3

1.51.5

1.8

2.02.0

TUNA Current

Contact Current

Peak Current

Cu

rre

nt(

pA

)

log(ion dose)

Nevertheless, the results obtained in this study was good in comparing the electrical

properties of graphene sheets with different defect density; since a single graphene sheet has

been used, it is expected that these factors, described above, are constant for all the areas. The

PeakForce TUNA images show a very good correlation between the sample topography and

current measurement.

Using the PeakForce TUNA imaging mode (described in section 1.6.1.1), TUNA, Contact,

and peak current measurements for all the areas have been taken and compared in figure 11

and 12. DC sample bias of 2V, 3V, and 9V have been used in this study. Figure 10 show the

contact current for different areas with different defect densities for an applied DC sample

bias of 3V. It is seen that the contact current decrease with increasing defect density.

However, higher current is detected on the grain boundaries than the other areas of graphene

sheet.

For an applied DC sample bias of 9V, a graph of current versus logarithm of ion dose

revealed that current decreased with defect density. However, the results were only possible

for areas 13 to 9, there after there was no current detected. It was speculated that the current

Graph 11. Graph of average current Vs area number for graphene samples using a DC sample bias of 9V.

of 39

became too high and the probe coating melted or the tip coating could have been worn out

after several mappings.

Figures 11 and 12 give graphs of average current (taken over the whole current images)

against log (ion dose). It was found that, the conductivity of graphene sheets decreases with

increase in defect density. Conductivity throughout the sheet was not uniform; some areas

showed a lower conductivity than expected. This may be due to electrical discontinuity

caused by cracks and grain boundaries [68] observed in the graphene sheets. No current was

detected on area 13, which is highly defected(exposed to ion dose of 5.219 x 1014

ions/cm2).

Figure 10 (d) shows that the current in area 13 remain zero after a DC sample bias is applied.

This shows that structural defects are able to transform graphene sheet from a good electrical

conductor to a non-conductor. Previous studies have found that structural defects change

graphene from metallic to insulator [69]. This effect has been observed in this study.

(a) (b)

Fig 12. (a) Graph of average Current against log(ion dose) for a DC sample bias of 3V (b) Graph of Current(pA)

against log(ion dose) for a DC sample bias of 2V

These results are in agreement with previous studies [4], [36], [37], [41], [43]. The presence

of structural defect are anticipated to greatly influence the electronic properties of graphene

material such as the charge carrier mobility and hence its electrical conductance. Atomic

0.0 12.0 12.5 13.0 13.5 14.0 14.5

0

1

2

3

4

5

6

7

8

9

10

11

12

TUNA current

Contact current

Peak current

Curr

ent(

pA

)

log(ion dose)0.0 12.0 12.5 13.0 13.5 14.0 14.5

-1

0

1

2

3

4

5

6

TUNA Current

Contact Current

Peak Current

Cu

rre

nt(

pA

)

log(ion dose)

of 39

scale structural defects scatter the charge carriers[3], [6], [35]–[37] hence increase the

electrical conductivity of the material.

(a) (b)

(c) (d)

Fig.13.Graphs of current against log(ion dose) (a) grain boundary current for a DC bias of 2V (b) grain

boundary current for a DC bias of 3V (c) Pristine graphene current for a DC bias of 2V (d) pristine graphene

current for a DC bias of 3V.

From figure 13, it is clear that, grain boundaries show higher electrical conductivity than the

pristine graphene. It has been observed that the grain boundary current decrease with increase

in defect density as shown in figure 13 (a) and (b). This shows that the grain boundaries are

affected by ion irradiation. The current measured on the surface of the pristine graphene was

relatively small. This may be because of the effects of the factors described in section 4.1

above. The interaction of AFM tip and the sample surface may influence the current

0.0 12.0 12.5 13.0 13.5 14.0 14.5

0

25

50

75

100

125

150

175

200

225

250 TUNA Current

Contact Current

Peak Current

Cu

rre

nt(

pA

)

log(ion dose)

0.0 12.0 12.5 13.0 13.5 14.0 14.5

0

25

50

75

100

125

150

175

200

225

250

275

300

TUNA Current

Contact Current

Peak Current

Cu

rre

nt(

pA

)

log(ion dose)

0.0 12.0 12.5 13.0 13.5 14.0 14.5

-10

-8

-5

-3

0

3

5

8

10

TUNA Current

Contact Current

Peak Current

Curr

ent(

pA

)

log(ion dose)

0.0 12.0 12.5 13.0 13.5 14.0 14.5

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

TUNA Current

Contact Current

Peak Current

Cu

rre

nt(

pA

)

log(ion dose)

of 39

measured. These changes occur due to changes in the contact area caused by the topography

of the surfaces (see section 4.1 for details).

It has been observed from graphs 13 (c) and (d) that graphene sheet (free of grain boundary)

with low defect density has a higher electrical conductivity compared with that with higher

defect densities. This shows that structural defects increase the electrical resistance of

graphene sheet.

4.2.1. Evaluation

The PF TUNA mode of the AFM has been shown in this study to be a very powerful

technique in comparing the conductivity of different samples. Its capability to study the

electrical properties of highly conductive and hard samples has been tested in this study. The

challenge sets in when the current to be measured is high, the tip conductive coating could

melt and make it nonconductive. In addition, scanning the tip along a hard surface lead to

wearing out of the tip conductive coating and makes the tip nonconductive. This was a major

problem in this study; it was observed that the sharp part of the tip was less conductive (see

section 4.1).

However, it was possible to compare the electrical properties of different areas with different

defect density and also to get the I-V curves for graphene/SiO2. The I-t curves (Figure 8 (b))

were found to be in good shape. This show that the AFM was operating normally.The PF

TUNA has been shown to be a very effective method in mapping the electrical properties of a

material. From the height, mechanical properties, and current images, it is possible to analyze

the current properties of different areas of the sample and to compare the conductivity with

the topography of the samples. The relationship between structural defect density and the

electrical properties of graphene obtained in this study agree with previous studies [4], [36],

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[37], [41], [43].Therefore, the PeakForce TUNA technique used in this study is good and

reliable in comparingthe electrical properties of different materials.

4.3. Gas sensing properties of graphene

The NO2 gas sensing property of graphene has been investigated in N2 gas at room

temperature. Before the experiment, graphene sample was first cleaned using ethanol and

ultraviolet (UV)/ozone cleaningthen exposed to UV light. A reductionin the baseline

conductivity was observedafter exposure to UV light as shown in Figure 13 (b). Before

exposing graphene to UV light, graphene’s sensitivity to NO2 was insignificant. However,

after the exposure to UV light, it showed a good sensitivity to NO2 gas molecules. Figure

13(a) shows the response after exposure to NO2 gas molecules. It has been observed that,

after NO2 gas supply was started, the conductivity of graphene sheet remained fairly constant

for about 45 seconds. Within this time, it is expected that, the gas-sensing chamber be filled

by N2 gas that was then driven out and NO2 gas concentration increased from zero to a higher

concentration. After the 45 seconds, a rapid increase in current was observed. The current

increased at a rate of about 9.081nA/s. Figure 13 (c) illustrate a linear fit of the rapid change

in current after graphene was exposed to NO2 gas. Six minutes after the start of NO2 gas

supply, a gradual decrease in the rate of change of current was observed that follow

Boltzmann relation. This decrease may be due to some gas molecules leaving the graphene

surface while other molecules are being absorbed into the surface i.e. the rate at which the gas

molecules are leaving the graphene surface increase with time. A response of 12.56% has

been achieved upon exposure to NO2 gas for 46 minutes. The response time(the time taken

for the current to have a rise equal to three times the noise level) was found to be 275s (4.58

minutes).

of 39

1700 1720 1740 1760 1780 1800 1820 1840

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

Cu

rre

nt(

A)

Time(s)

A

(a)

(b) (c)

(d) (e)

Fig 13(a)The I-t curve for NO2gas sensing response of graphene sheet. (b) Change in conductivity of graphene

after it was exposed to UV light. The baseline conductivity dropped after graphene sheet was exposed to UV

light (c) linear fit of the rapid change in current after graphene was exposed to NO2 gas (occurred 45s after NO2

gas supply was started). (d) Gradual decrease in the rate of change of current (occurred 260s(6minutes) after

NO2 gas supply/exposure start).(e) I-t curve showing exponential decay of current after NO2 gas supply was

stopped and N2 gas supply started.

NO2

N2

N2

4000 6000 8000 10000 12000

0.0000270

0.0000275

0.0000280

0.0000285

0.0000290

0.0000295

0.0000300

0.0000305

Data: Data1_A

Model: ExpDec1

Equation: y = A1*exp(-x/t1) + y0

Weighting:

y No weighting

Chi^2/DoF = 1.9691E-14

R^2 = 0.96215

y0 0.00003 ±2.388E-9

A1 0.00002 ±2.4503E-7

t1 1732.623 ±7.12133Cu

rre

nt (A

)

Time(s)

A

ExpDec1 fit of Data1_A

1500 2000 2500 3000 3500 4000

0.0000275

0.0000280

0.0000285

0.0000290

0.0000295

0.0000300

0.0000305

0.0000310

0.0000315

Data: Data4_A

Model: Boltzmann

Equation:

y = A2 + (A1-A2)/(1 + exp((x-x0)/dx))

Weighting:

y No weighting

Chi^2/DoF = 1.6938E-14

R^2 = 0.96976

A1 0.00002 ±3.446E-6

A2 0.00003 ±1.3804E-8

x0 295.09027 ±228.61916

dx 708.73677 ±24.75321

Cu

rre

nt (A

)

Time(s)

A

Boltzmann fit of Data4_A

1000 1050 1100 1150 1200 1250 1300 1350 1400

0.0000250

0.0000255

0.0000260

0.0000265

0.0000270

0.0000275

0.0000280

Y =1.55919E-5+9.081E-9 X

Cu

rre

nt (A

)

Time(s)

A

Polynomial Fit of Data1_A

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

24

25

26

27

28

29

30

31

32

Cu

rre

nt (u

A)

Time(s)

A

of 39

The rise time (time taken for the current to rise to 90% of the maximum value) was found to

be 1850s (30.8 minutes). A recovery of 10.2% has been achieved in N2 gas condition. When a

graphene sheet is exposed to NO2 gas, electrons move from the graphene sheet to the gas

molecules, thus creating more holes; NO2 molecules act as electron acceptors[70]. This make

graphene sheet more electrically conductive, hence the current measured increase. Initially, it

is expected that, there are more NO2 gas molecules being absorbed into graphene surface than

the number of the gas molecules leaving the surface. This may lead to the rapid change in the

conductivity of graphene due to the high concentration of holes created in the graphene sheet

as a result of electron transfer from graphene to NO2 gas molecules. After some time of gas

supply, the system attains equilibrium and the rise stops.A saturation point (constant current)

is expected at which supply of more NO2 does not lead to a significant change in graphene’s

conductivity. The equilibrium may be because the rate at which gas molecules are leaving the

surface becomes equal to the rate at which gas molecules are being absorbed into the surface.

In this study, the saturation did not come out clearly. After NO2 gas supply was stopped and

N2 gas supply started the current decreased exponentially as shown in figure 13 (e)but could

not drop to the initial baseline current. This may be due to adsorbed gas molecules on the

surface.

4.3.1. Evaluation

The setup used in this experiment has been shown to be an effective way of testing the gas

sensing property of graphene. It is easy to control the conditions inside the container and

prevent contaminants. This setup can be developed to make a graphene based gas sensor. It

has been observed that, graphene’s electrical conductivity increase upon exposure to NO2 gas

molecules. The results obtained in this study are comparable to previous results[13], [38],

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[46], [70]; NO2 molecules increase the electrical conductivity of graphene sheet. Graphene

sheet is therefore a good material for use in NO2 gas sensors.

Chen et al. [44] found that, the conductance of graphene increase by about 1% when its

exposed to 40 ppt of NO2 for 5 min. They have estimated a detection limit (DL) of 2.06ppt.

Other researchers have achieved a DL as low as 5 ppm [14], [71] and even 1ppb [13]

detection of NO2 molecules by graphene. Compared with these results, the sensitivity

reported in this study is good. Though the detection limit has not been tested in this study, it

has been shown that graphene sheet can detect NO2 gas molecules at concentrations of

15ppm.

5. POSSIBLE APPLICATIONS OF RESULTS

Studies on graphene material have advanced speedily from fundamental physics theory to

application stage [72]–[80]. Graphene has been found to be a suitable material in designing

efficient, flexible and light electronics [72], flexible displays [79], batteries and

electrochemical capacitors [76], etc. There is need for electronic devices with lower power

consumption and of higher performance. These applications of graphene greatly rely on,

among others, the electrical conductivity of graphene. It is therefore important to understand

the electrical conductivity of graphene with structural defects since defects are unavoidable.

As shown in this study, electrical conductivity of graphene sheet decrease with increase in

defect density. If high electrical conductivity is needed, one must ensure the graphene

material used has minimum structural defects density possible. The finding in this study can

be used to engineer the electrical conductivity of graphene for specific applications.

Graphene can be used as a NO2 gas molecule sensor. It has been shown in this study that,

graphene has a good sensitivity to NO2 gas molecules. This result can be applied to design

of 39

NO2 gas molecule sensors. Although more study is needed to establish how the responses due

to different types of gas molecules can be distinguished.

6. CONCLUSION

In this study, the electrical conductivity of Ga+ ion irradiated single-layer graphene sheet on

SiO2 substrate were studied using the PeakForce TUNA mode of the AFM. It has been shown

that, the electrical conductivity of graphene sheet decrease with increasing density of atomic

scale structural defects. Grain boundaries show higher electrical conductivity than the pristine

graphene sheet. The PeakForce TUNA has been shown to be a very powerful technique in

comparing the electrical conductivities of different samples. The results obtained in this study

offer useful information on the properties of graphene that can be used to engineer the

properties of graphene to suit specific applications; it gives an insight on the electrical

conductivity of defective graphene and its grain boundaries.

Finally, it has been shown that graphene has a good sensitivity to NO2 gas molecules. Its gas

sensitivity can be increased significantly by exposing it to UV light as it has been shown in

this study. A response of 12.56%was achieved after 46 minutes of exposure to NO2 gas

molecules at 15ppm. This shows that graphene is a good material to use as a NO2 molecules’

sensor.

ACKNOWLEDGEMENT

I greatly appreciate the work of my supervisor, Prof Klaus Leifer, my co-supervisors Hu Li

and Ishtiaq H. Wani, my examiner, Prof Håkan Rensmo and the whole ELMIN group. I thank

my sponsor Erasmus Mundu organization for their support.

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APPENDIX I:

PeakForce TUNA images of silver contact

(a)

(b)

(c)

(d)

Figure 15.AFM PeakForce TUNA images of silver on graphene layer for a DC sample bias of 2V. (a) and (d)

is the height image and its cross section graph. (b) and (e) is the TUNA current image and its cross section

graph. (c) and (g) show the contact current image and its cross section graph. (f) and (h) are the peak current

image and its cross section graph. High current values were measured on the slopes of the sample topography.

effect of structural defects on the electrical properties ...898103/fulltext01.pdf · 1.1....

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