Ferroelectric gating of graphene 1

FERROELECTRIC GATING OF GRAPHENE
By
Guangxin Ni
SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
AT
NATIONAL UNIVERSITY OF SINGAPORE
UNIVERSITY ADDRESS
JUNE 2012
c
⃝ Copyright by Guangxin Ni, 2012
NATIONAL UNIVERSITY OF SINGAPORE
DEPARTMENT OF
PHYSICS
The undersigned hereby certify that they have read and
recommend to the Faculty of Science for acceptance a thesis entitled
“Ferroelectric gating of graphene” by Guangxin Ni in partial
fulfillment of the requirements for the degree of Doctor of Philosophy.
Dated: June 2012
External Examiner:
Research Supervisor:
Barbaros
¨
Ozyilmaz
Examing Committee:
ii
NATIONAL UNIVERSITY OF SINGAPORE
Date: June 2012
Author: Guangxin Ni
Title: Ferroelectric gating of graphene

Department: Physics
Degree: Ph.D. Convocation: July Year: 2013
Permission is herewith granted to National University of Singapore to
circulate and to have copied for non-commercial purposes, at its discretion, the
above title upon the request of individuals or institutions.
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IS CLEARLY ACKNOWLEDGED.
iii
To my family.
iv
Table of Contents
Table of Contents v
Acknowledgements viii
Abstract x
1 Introduction 1
1.1 From carbon to graphene . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The electronic field effect in graphene . . . . . . . . . . . . . . . . . . 4
1.3 Large-scale graphene synthesis and its potential applications . . . . . 6
1.4 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Structure of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Background of graphene and ferroelectric 12
2.1 Band structure of graphene . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 Electronic properties of graphene . . . . . . . . . . . . . . . . . . . . 15
2.3 Optical properties of graphene . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Ferroelectric dielectrics and applications . . . . . . . . . . . . . . . . 18
3 Fabrication and experimental setups 25
3.1 Graphene fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.1 Mechanical exfoliated graphene . . . . . . . . . . . . . . . . . 26
3.1.2 Chemical vapor deposition of graphene . . . . . . . . . . . . . 28
3.2 Fabrication of graphene field effect transistor GFET . . . . . . . . . . 30
3.2.1 GFET devices using mechanically exfoliated graphene . . . . . 30
3.2.2 GFET devices made out of chemical vapor deposition graphene 31
3.3 Ferroelectric dielectric preparation and characterization . . . . . . . . 32
3.4 Transport measurements and experimental set-ups . . . . . . . . . . . 35
v
4 Ferroelectric gated graphene field effect transistors (GFeFETs) as
non-volatile memory devices 38
4.1 Introduction and background . . . . . . . . . . . . . . . . . . . . . . 39
4.2 P(VDF-TrFE) gated GFeFET non-volatile memory . . . . . . . . . . 41
4.2.1 Asymmetric bit writing using ferroelectric gating . . . . . . . 42
4.2.2 Symmetric bit writing using ferroelectric gating and back ground
doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2.3 Understanding of ferroelectric gating . . . . . . . . . . . . . . 57
4.3 Summary and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 59
5 Quasi-periodic nanoripples in graphene grown by chemical vapor
deposition and its impact on charge transport 61
5.1 Introduction and background . . . . . . . . . . . . . . . . . . . . . . 62
5.2 Sample fabrications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6 Large-scale CVD graphene at high non-volatile electrostatic doping
using ferroelectric polymer gating 74

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.2 Sample fabrications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.3 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7 Wafer scale graphene ferroelectric hybrid devices for low voltage
electronics 90
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.2 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
8 Ongoing experiments 100
8.1 Non-volatile p-n junctions . . . . . . . . . . . . . . . . . . . . . . . . 100
8.2 Optical transmittance of strained or gated graphene . . . . . . . . . . 106
9 Summary, conclusion and outlook 109
9.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
9.2 Unsolved questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
9.2.1 Can we reach the VHS regime? . . . . . . . . . . . . . . . . . 111
9.2.2 Can we completely remove the quasi-periodic nanoripples? . . 113
vi
9.2.3 Can we achieve less than 100 Ω/✷ sheet resistance in CVD
graphene? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
9.3 Future outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
9.3.1 Gate-tunable graphene-ferroelectric photonics . . . . . . . . . 116
9.3.2 Piezoelectric effect induced electrical nanogenerator . . . . . . 117
9.3.3 Ultrahigh doping of graphene using single crystal ferroelectric
thin film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Bibliography 119
Publications 141
Patents 143
vii
Acknowledgements

Over my four-year Ph.D time, I would like to express my deep thanks to my advisor,
Prof. Barbaros
¨
Ozyilmaz. He is both knowledgeable and insightful, and has pointed
me in the right direction many times; I cannot imagine having had a better advisor.
I enjoyed learning from him, and I appreciated his encouragement and support of
new ideas. His sense of what is genuinely of scientific value and his intuition for good
and clean experiments has had a strong impact on me. Last but not least, his great
passion has motivated me during the past four years and will continue to keep me
moving in the future.
I would also like to express my appreciation to Dr. Zheng Yi, from whom I
learnt most of my knowledge of electronic transport measurements and data analysis
skills. His strict attitude on experiments and his flexibility in addressing challenges
influenced me deeply. He gave insightful guidance for my projects and experiments,
and for what i am very grateful.
I would like to thank Prof. Yao Kui, who is an expert in ferroelectric material.
He gave me much insightful guidance about ferroelectrics. I would like to thank Prof.
Christian Kurtsiefer, who is the most knowledgeable person I know on optics and is
capable of building dedicated instruments by himself. He is always very patient with
even my most detailed questions and always gives me very useful guidance and help.
I would like to thank Dr. Chin-Yaw Tan and Dr. Shuting Chen for their help with
the ferroelectric polymer thin films in time of great need. I would like to thank Dr.
TROADEC, Cedric, who helped me with the synthesis of a shield mask to greatly
speed up my research. I would like to thank Dr. Ao-Chen, Hongzhi Yang, Dr. Manu
Jaiswal, Dr. Xiangfan Xu, Minggang Zeng, Lanfei Xie, Jayakumar Balakrishnan,
Xiangming Zhao, Kaiwen Zhang, Cheetat Toh, Dr. Qiaoliang Bao Dr. Chen Yu and
Yufeng Song (from NTU) for their help.
I also wish to thank the following for their guidance and help: Prof. Guoqing Xu,
viii
ix

Prof. Yuanping Feng, Prof. Jiansheng Wang, Prof. Jie Yan and Prof. Lin Yi .
Finally, I would like to thank to my family, my parents and my wife, for their
patience and absolute love.
NUS, Singapore Guangxin
December 28, 2011
Abstract
In this dissertation, we describe experimental investigations of charge transport prop-
erties of both mechanically exfoliated and chemical vapor deposited (CVD) graphene
and its potential applications using functional ferroelectric substrates.
We demonstrated a non-volatile memory device in a graphene field-effect transis-
tor structure using ferroelectric gating. Two distinct bistable resistance states were
maintained by controlling the polarization of the ferroelectric thin film.
Furthermore, this thesis is devoted a better understanding of CVD graphene. We
elucidated a new type of quasi-periodic nanoripple arrays (NRAs) within a single
graphene domain. The impact of these NRAs on charge transport of CVD graphene
was also studied.
Utilizing the hybrid CVD graphene and ferroelectric polymer structure, we demon-
strated a novel type of flexible transparent conductors with low sheet resistance, high
transparency and good mechanical flexibility.
By transferring large-scale CVD graphene to wafer-size ferroelectric inorganic sub-
strates (PZT), an array of low-voltage operation transistors and non-volatile memory
devices were fabricated and investigated.
x
Chapter 1
Introduction
1.1 From carbon to graphene
Carbon is one of the most versatile elements in the universe. It is an element that
is fundamental for life on the planet; it is the building block of virtually all organic
chemistry. It also has the highest sublimation point of all elements at about 3500
◦

C.
These amazing characteristics of carbon are attributed to its unique electronic states
and incredible bonding capabilities. Carbon has four valance electrons, which can
hybridize in many ways. This hybridization may be sp, sp
2
or sp
3
allowing carbon to
form linear chains, planar sheets and tetrahedral structures (Fig. 1.1). Consequently,
carbon has intrigued and inspired physicists, chemists, biologists and recently medical
scientists in their research. This general interest in carbon indicates the arrival of a
new era, which we might call the “carbon age” [1].
Carbon has long been known to exist in three allotropes: diamond, graphite (mul-
tilayered graphene) and amorphous carbon [2]. Depending on how the carbon atoms
are arranged, their properties vary greatly. In the mean time, new carbon family
members continue to emerge. In 1985, the Noble Prize-winning C
60
was discovered,
1
2
which not only created an entirely new branch of carbon chemistry, but also extended
the carbon materials from three-dimension (3-D) to quasi zero-dimension (0-D) [3, 4].
Subsequently, carbon nanotubes (CNT) were discovered using transmission electron
microscopy (TEM) during the examination of carbon samples by S. Iijima in 1991
[5]. A carbon nanotube can be viewed as a graphite sheet (graphene) that is rolled
up into a nanoscale tube. The discovery of CNT opened a rich field in fundamental
science and stimulated the development of CNT in various applications.
The two dimensional form of carbon, named graphene, consists of a sheet of atoms
packed in a honeycomb lattice structure. Graphene was predicted to have peculiar
electronic properties more than 60 years ago [6]. However, it was generally believed

up until recently that such a membrane only an atom thick could not exist due to
thermal fluctuations [7].
In 2004, scientists from Manchester University reported their observation of few-
layer and monolayer graphene. They used a rather simple approach to start a rev-
olution in the field of condensed matter physics and materials science [8]. They
started with three-dimensional graphite and extracted a single sheet (a monolayer of
atoms) through a technique called mechanical exfoliation. They reported that this
single atomic layer of graphite was stable at ambient conditions and that it had a
pronounced electric field effect [9].
Graphene is found to possess many peculiar properties [11]. It is the first truly
2D crystalline material with remarkably high crystal quality and it is representative
of a whole class of 2D materials including single layers of Boron-Nitride (BN) and
Molybdenum-disulphide (MoS
2
) [12]. Its charge carriers exhibit giant intrinsic carrier
mobility (1,000,000 cm
2
/Vs) [13] and can travel micrometers without scattering at low
3
C
C
E
1S
2S
2Px
2Py
2Pz
sp
sp
sp

3
2
C
C H
2 2
Figure 1.1: Different carbon-carbon hybridization and its corresponding representa-
tion materials. The top line shows the sp
3
hybridization and the diamond atomic
structure; the middle line shows the sp
2
hybridization and the corresponding C
60
,
graphite and carbon nanotube atomic structures, respectively; the bottom line shows
the sp hybridization and the C
2
H
2
atomic structure [10].
temperatures. In the lower energy regime, the charge carriers mimic massless Dirac
fermions with a constant Fermi velocity of 10
6
m/s [7]. Thus, electron transport in
graphene is described by the Dirac equation rather than the Schr¨odinger equation.
Consequently, graphene provides an ideal platform for the investigation of relativistic
quantum phenomena in condensed matter physics experiments.
Graphene also exhibits outstanding optical and mechanical properties. Graphene
can effectively absorb 2.3 % incoming light over a wide range of wavelengths from the
visible to the near infrared (IR) [14]. Owing to its covalent carbon-carbon bonding,

graphene is also one of the strongest materials with a remarkably high Young’s mod-
ulus of ∼ 1 TPa [15]. The combination of its high transparency, wideband tunability
and excellent mechanical properties make graphene a very promising candidate for
flexible electronics, optoelectronics and phonotics [16]. Consequently, it is generally
believed that graphene may be one of the most promising and versatile materials ever
4
discovered. It could hold the key to everything from super fast computers to high-
capacity batteries [16]. Consequently, in 2010 the breakthrough in graphene research
was awarded the Nobel Prize in physics.
1.2 The electronic field effect in graphene
The electric field effect, which continuously tunes the Fermi level (E
F
) in the conical
energy band structure of graphene, plays a critical role in studying its extraordinary
electronic properties and its potential applications [16]. Therefore, a graphene field
effect transistor device structure is the most heavily relied upon platform.
A GFET consists of five components: source and drain contacts for the cur-
rent injection and detection, graphene as a current channel sits between those two
contacts, a gate dielectric and a gate contact for charge density modulation. This
remarkably simple and successful design provides new opportunities for basic science
and innovative device applications. Utilizing this approach, many exotic experimen-
tal observations, including integer quantum hall effect [17], Klein tunneling [18], p-n
junctions [19], high frequency graphene transistors, nanoribb ons [20], single molecular
detectors [21] and tunable band gap in bilayer graphene [22], have been recorded.
Currently, there are two extremely important directions for graphene research in
terms of fundamental physics studies, both of which are highly related to graphene’s
electric field effect. One lies in the pursuit of Dirac point physics [23], and the other
aims for the van Hove Singularity (VHS) regime [24, 25].
Near the Dirac point, the low energy excitation spectrum of graphene is expected
to produce novel electronic properties such as charge carrier interaction induced sym-

metry breaking, new phase transitions, evanescent transport and anomalous phonon
5
softening, etc [26–29]. These exotic physical phenomena are attributed to graphene’s
peculiar lattice structure. At the Dirac point, the electronic density of states van-
ishes, and as one expects the screening disappears. Consequently, the unscreened, long
range coulomb interaction becomes dominant at the Dirac point and leads to strong
renormalization of the Dirac band structure [30]. Many physical characteristics, such
as the Fermi velocity, charge compressibility, spin susceptibility and specific heat can
be strongly affected by electron-electron interactions [31]. Furthermore, when the
Fermi level is shifted away from the Dirac point, the physics near the Dirac point can
still be strongly affected by the interactions of quasiparticles with plasmons [32]. How-
ever, experimentally, it is not easy to reach the Dirac point using normal dielectrics
like SiO
2
due to the existence of electron-hole puddles induced by charged impurities
[33, 34]. Thus, suspending graphene devices or utilizing new dielectrics such as hexag-
onal boron nitride (h-BN), with a single-crystal nature, a lattice matching structure
and an ultra-flat surface morphology would be desirable [35, 36].
In graphene, a saddle point (M points of the Brillouin zone) leads to a divergence
in the density of states (DOS), which is also known as VHS. When E
F
is close to the
VHS regime, it has been predicted that many intriguing phenomena such as charge
density waves, superconductivity or magnetism can be observed due to electronic
instabilities [37]. However, it is impossible to reach the VHS regime using normal
dielectrics. Although electrolyte gating can provide high electrostatic doping up to
4× 10
14
cm
−2

, it is still outside the VHS regime [24, 38]. Thus, novel dielectrics with
ultrahigh κ and atomically flat surface morphology are the key to this goal.
6
1.3 Large-scale graphene synthesis and its poten-
tial applications
Unlike the silicon MOSFET devices, it is hard to expect GFET to work for logic
circuit applications unless a sizable electrical band gap is achieved through addi-
tional processes [39–41]. On the other hand, the gapless nature of graphene does not
prevent its application in many other areas, such as photonics, optoelectronics and
plasmonics [42]. Indeed, some preliminary results have been reported, ranging from
graphene-based solar cells [43], to organic light emitting diodes, touch panels [44],
photodetectors [45], ultrafast transistors [46], and graphene-based THz metamateri-
als [47]. Graphene is also currently being explored for both biological applications
and energy harvesting (Fig. 1.2).
However, it is impossible to use mechanically exfoliated graphene for industrial
applications. Thanks to the technical breakthrough of large-scale graphene synthesis,
wafer-scale graphene films of decent quality have been fabricated by many groups in
the world [48–50]. For the time being, there are mainly three approaches to synthesiz-
ing large-scale graphene, i.e., epitaxial SiC graphene [51], chemical vapor deposition
(CVD) graphene [50] and chemically modified graphene [52]. In the following, we
briefly review these three methods for graphene synthesis before discussing its poten-
tial applications.
Epitaxial SiC graphene is synthesized by the desorption of silicon from SiC single
crystal surfaces at high temperatures, leaving behind multilayer graphene that be-
haves like pristine graphene [53]. As one might expect, such simplicity does not come
without compromise: the strong interaction between graphene and the SiC substrate
7
leaves graphene “intrinsically” electron doped and tends to break the symmetry of the
graphene lattice [54]. Moreover, the high price of SiC poses a challenge to wide-use
commercialization.

The self-assembly of soluble graphene sheets demonstrates the possibility of low-
cost synthesis and the fabrication of large-scale conducting flexible films. However,
these chemically modified graphene films show relatively poor electrical conductiv-
ity owing to the poor interlayer junction contact resistance and the structural de-
fects formed during the vigorous exfoliation and reduction processes [52]. Moreover,
its non-uniform thickness characteristic further increases its electrical resistance and
limits its optical transparency. Thus, it is unsuitable for most optoelectronics and
nanoelectronic applications.
The chemical vapor deposition (CVD) method on copper turns out to be one of
the most efficient and economical ways of producing graphene. The advantage of
the CVD method is that the growth rate of graphene is lowered by two orders of
magnitude once the first layer is formed and the catalytic surface largely passivated,
which yields a large-scale single layer of graphene. The drawback to this method is
that the nucleation site density is difficult to control, which makes large-scale CVD
graphene polycrystal instead of single crystal. The optimization of growth conditions
and copper surface morphology is still ongoing.
One of the most promising applications of graphene is its use as a transparent
conductor. Transparent conductors are an integral part of many type of devices,
including displays, smart windows, touch panels, organic light-emitting diodes and
solar cells. It acts as a window for light to pass through to the active material
beneath or as an ohmic contact for carrier transport out of photovoltaic devices. While
8
Graphene flexible displays
Graphene touch panel
Graphene battery
Graphene in OLED
Graphene supercapacitor
Graphene in biological
applications
Graphene photodetectors

Graphene polarizer
Graphene in solar cells
Graphene transistors
a
b
g
d
c
h
f
e
j
i
Figure 1.2: Examples of graphene potential applications ranging from graphene flexi-
ble displays [55], touch panels [44], supercapacitors [56], organic light emitting diodes
[57], graphene batteries, photodetectors [45], light polarizers [58], solar cells [43],
transistors [59]and biological applications [60].
indium tin oxide (ITO) is currently the gold standard for transparent conductors, it
has several limitations. Indium is a diminishing resource, and ITO has complicated
processing procedures and poor mechanical flexibility. Consequently, there is high
demand for novel electrode materials with flexibility, high transparency and excellent
conductivity [42]. Graphene exhibits very promising results along this direction.
Besides transparent conductors, graphene is also promising as a saturable ab-
sorber, a key component in ultrafast laser systems. This is because graphene has
non-linear optical properties, broad wavelength range transmittance, a large absorp-
tion per layer and ultrafast carrier dynamics. The combination of these factors make
graphene an ideal ultra-broadband, fast saturable absorber [61].
Graphene-based transistors have developed rapidly and are now considered as an
option for post-silicon electronics [62]. This is because graphene provides an alter-
native solution to resolve the short-channel effects, which is one common challenge

9
faced by the current FET devices [63]. Although graphene transistors are unlikely
suitable for modern digital logic circuits due to the lack of a band gap, its ultra-fast
carriers make GFET more easily usable for radio-frequency applications. Experimen-
tally, wafer-scale graphene transistors with a cutoff frequency approaching 400 GHz
have been already achieved [64].
The exploration of other potential applications of graphene is still ongoing. As
ultrafast memories, graphene with potentially aggressive scaling ability and ultrafast
reading speed have been achieved by our laboratory group [65, 66]. In photonics, ul-
trafast photodetectors and graphene-based light polarizers have been experimentally
demonstrated [45].
1.4 Motivations
The goal of this dissertation is to study the electrical transport properties of graphene
(both mechanically exfoliated and CVD graphene) on ferroelectric substrates and
its potential applications for non-volatile memory, transparent conductors and novel
types of transistors. Furthermore, we investigate the original limiting factor of CVD
graphene. More specifically:
• As a one atom thick single crystal, graphene’s electronic properties are closely
related to the surrounding environment. Currently, most graphene research is
restricted to normal Si/SiO
2
substrate. Although SiO
2
dielectric can provide ex-
cellent optical contrast to graphene, which was the key in discovering graphene
by micromechanical exfoliation, it has several critical drawbacks, i.e., low dielec-
tric constant (κ = 3.9), high concentration of surface impurity charges, surface
10
optical phonons, and hydrophilic surface properties. Thus, the pursuit of new
dielectrics and substrates with novel functionality is of great importance, not

only for fundamental studies, but also for potential applications.
• Ferroelectrics are unique in having both ultrahigh dielectric constants up to
a few thousand and a nonlinear, hysteretic dielectric response to an electric
field. The ultrahigh κ makes ferroelectrics promising substrates for studying
the charge scattering mechanism in graphene, which could be a crucial step in
realizing ultrahigh mobility on substrates. Equally important, the ultrahigh κ
may allow ultrahigh electrostatic doping in graphene with charge carrier density
exceeding electrolyte gating and with gate tunability at cryogenic temperatures.
From an application point of view, the hysteretic ferroelectric gating provides a
novel functionality of non-volatile graphene-ferroelectric field effect transistors,
which could be crucial for many kinds of applications such as non-volatile mem-
ory, transparent conductors, and ultrafast lasers with low-power consumption
and high efficiency.
• The technical breakthrough in synthesizing large-scale CVD graphene represents
a milestone for graphene’s wide-range applications. Currently, grain boundaries
are generally believed to be the main scattering source in CVD graphene and
much effort has focused on increasing the grain size of such polycrystalline
graphene to 100 µm and beyond. However, the quality of micrometer CVD
graphene devices is still generally lower than that of mechanical exfoliated
graphene. This indicates that there are still other unknown aspects of this
new two-dimensional polycrystalline material and further exploration of CVD
graphene is required.
11
1.5 Structure of this thesis
This thesis is devoted to experimentally investigating the electronic transport proper-
ties of single layer graphene and its potential applications with ferroelectric substrates.
The thesis is divided into three sections. The first section, from chapter 1 to chap-
ter 3, introduces background information of the thesis. Chapter 1 gives an overview
of graphene research. Chapter 2 presents the theoretical background of graphene and
ferroelectric material involved in this thesis. Chapter 3 demonstrates experimental

techniques and apparatuses that are used in the research.
The second section, from chapter 4 to chapter 7, is devoted to the investigation
of ferroelectrically gated single layer graphene. Chapter 4 mainly focuses on the fer-
roelectric polymer (P(VDF-TrFE)) gated exfoliated graphene field effect transistor
for non-volatile memory applications. Chapter 5 investigates quasi-periodic nanorip-
ples in large-scale Cu-CVD graphene. Chapter 6 devotes on the study of large-scale
CVD graphene and P(VDF-TrFE) hybrid structure as it relates to graphene-based
transparent conductors. Chapter 7 focuses on the electrical transport studies of CVD
graphene on ferroelectric inorganic Pb(Zr
0.3
T i
0.7
)O
3
(PZT) substrates.
The third section includes chapter 8 and chapter 9. Chapter 8 summarizes exper-
iments which have not been completed. Chapter 9 is devoted to the summary of this
thesis and on outlook for future. Experiments results presented from Chapter 4 to
Chapter 7 have been published.
Chapter 2
Background of graphene and
ferroelectric
2.1 Band structure of graphene
The exotic electronic properties of graphene are directly correlated with its band
structure. In this section, a brief discussion of the energy bands is carried out within
the tight binding approximation.
Figure 2.1 shows the graphene honeycomb lattice structure. In one unit cell, there
are two carbon atoms one from each sub-lattice A and B. Each sub-lattice can be
regarded as being responsible for one branch of the energy dispersion (Fig. 2.2). The
inability to transform one type of dispersion into another makes them independent

of each other. The inequivalence of sub-lattice A and B is the origin of the chiral
nature of graphene and the valley degeneracy. Each carbon atom has four atomic
orbitals involved in bonding with the other carbon atoms in the graphene plane. The
2s, 2p
x
and 2p
y
orbitals hybridize to form three sp
2
orbitals. This strong covalently
bonded σ bonds are responsible for the robust mechanical properties of graphene.
The remaining 2p
z
orbital yields the π bands which are perpendicular to the planar
12
13
Μ
Γ
Κ
Κ’
b
γ
a
1
a2
γ
γ
1
2
3

b2
b1
a
b
Figure 2.1: (a) Lattice structure of graphene, made out of two interpenetrating trian-
gular lattices (as represented by the white and black points). (b) The dotted regime
in the upper hexagonal lattice structure shows the corresponding Brillouin zone.
structure. The π bands are much closer to the Fermi surface than the σ bands,
thus determining the transport properties of graphene. Hence, the subsequent tight-
binding approach only includes the impact of π bands.
Using the tight-binding approach, the energy bands of graphene have the form of
E(k
x
,k
y
)=±γ
√
1 + 4cos(
3aky
2
)cos(
√
3akx
2
) + 4cos
2
(
√
3akx
2

), (1)
where γ = 3.0 eV is the nearest neighbor hopping energy and a = 1.42
˚
A is the
nearest neighbor distance [67]. The plus sign applies to the upper π band while the
minus sign applies to the lower π
∗
band. Figure 2.2a shows the calculated full band
structure of graphene under the assumption that the next nearest neighbor hopping
energy γ
′
=0.2γ is negligible [6]. What makes this band structure so peculiar is that
the valance band and conduction band touch each other at discrete points (Dirac
points), which correspond to the corners of the first Brillouin zone. This creates a
zero-gap semiconductor with linear dispersion near the Dirac points.
14
a
b
3 2 1 1 2 3
5
5
E
k
Figure 2.2: (a) The tight-binding calculated full band structure of graphene. (b)
Zoom-in of the energy bands close to one of the Dirac points.
Near the Dirac points, the charge carriers mimic relativistic particles, propagating
through the honeycomb lattice with zero effective mass and consequently can be
described by the Dirac-like Hamiltonian:
H = v
F

(
0 k
x
∓ ik
y
k
x
± ik
y
0
) = v
F
⃗σ ·
⃗
k (2)
where v
F
is the Fermi velocity, k is the quasi-particle momentum and σ is the
Pauli matrix. The corresponding eigenvectors of such Hamiltonian can be written as
| k > =
1
√
2
e
i
⃗
k·⃗r
(
∓ie
−iθ

k
/2
e
iθ
k
/2
) (3)
The linear dispersion relationship of the quasi-particles can be obtained by substi-
tuting equation 3 in equation 2, as ε = v
F
⃗
k, which has the same form as a photon.
This indicates that quasi-particles in graphene are massless and moving with a ve-
locity of v
F
≈ 1 × 10
8
cm/s. The important consequence of Dirac fermions is that
15
the low-energy physics in graphene is governed by the spectrum close to the K and
K’ points. Many of the new and exciting properties of graphene stem from this fact.
Dirac fermions behave in unusual ways compared to ordinary electrons when subject
to a magnetic field or confining potentials, leading to the observation of an anomalous
quantum Hall effect or the phenomena of Zitterbewegung and Klein tunneling [68].
2.2 Electronic properties of graphene
By transferring graphene (exfoliated, CVD, etc) onto a substrate such as an oxidized
silicon wafer (Si/SiO
2
), the charge carrier density can be tuned from holes to electrons
across the charge neutrality point by applying an external electric field. The gate

voltage induces a surface charge density n = ϵ
0
ϵV
BG
/te, where ϵ is the permittivity
of SiO
2
, e is the electron charge and t is the thickness of the SiO
2
layer. The charge
density shifts with the Fermi level position (E
F
) in the band structure, as shown in
Figure 2.3a. The resistivity increases rapidly as the charge decreases, finally reaching
its maximum value at the Dirac point. From this curve one can extract the field-
effect mobility µ =
1
αe
(
dρ
dV
)
−1
, where α = 7.2 × 10
12
cm
−2
for our field-effect devices
with a 300 nm SiO
2

layer and
dρ
dV
is the derivative of resistivity. Alternatively, one
can also deduce the carrier mobility from the conductivity plot (Fig. 2.3b), where
the minimum conductivity is defined as σ
min
. Note that the carrier mobility is only
meaningful away from the Dirac point.
Near the Dirac point, the conductivity of graphene does not go to zero in the
limit of vanishing density of states but instead exhibits values close to the conduc-
tivity quantum 4e
2
/h. This is is due to the presence of charge scatterers attributed
to the thermally generated carriers and electrostatic charge inhomogeneity puddles