investigation of electric and thermoelectric … · measurement. in addition, we also investigated...
TRANSCRIPT
INVESTIGATION OF ELECTRIC AND
THERMOELECTRIC PROPERTIES OF
GRAPHENE NANORIBBON
ZHANG KAIWEN
(M. Sc, NANJING UNIV)
A THESIS SUBMITTED
FOR THE DEGREE OF MASTER OF SCIENCE
DEPARTMENT OF PHYSICS
NATIONAL UNIVERSITY OF SINGAPORE
(2012)
1
DECLARATION
I hereby declare that this thesis is my original work and it has been
written by me in its entirety. I have duly acknowledged all the sources of
information which have been used in the thesis.
This thesis has also not been submitted for any degree in any university
previously.
2
ACKNOWLEDGEMENTS
I met a lot of friends during my life of study and research in Singapore.
These friends, not only accompanied me to pass through for the five years, but
also helped me when I most needed.
First and foremost, I would like to dedicate my deepest gratefulness to my
supervisor Prof. Li Baowen. He is a rigorous physicist and talented scholar. I am
very proud to be his student. What I have learned from him are not only the
physics, but more importantly, the skill to deal with the real world.
I‟d like to thank my supervisor Dr. Özyilmaz Barbaros who brought me to
the world of graphene and guided me on experiments. He builds a lab with
dedicated instruments and provides us with most convenient experimental
environment.
My sincere thanks to Dr. Zhang Gang and Dr Xu Xiangfan who give me
their patient guidance and meticulous help. They helped me with all the
background acknowledge on physics and taught me all the skills and technology
on experiments.
Thanks to Dr. Daniel. S. Pickard, who gives me a lot of useful advice
when we work together, and Dr Manu Jaiswal for helpful discussion on my
projects. Thanks to my collaborators from HIM lab, Dr.Viswanathan Vignesh,
Miss Wang Yue, Miss Hao Hanfang, and Mr. Fang Chao
3
Thanks to my labmates Dr. Surajit Saha, Dr. Lee Jonghak, Dr.R.S.S.
Mokkapati. Mr. Ho Yuda, Mr. Toh Chee Tat, Mr. Gavin Koon Mr. Jayakumar
Balakrishnan, Dr. Ni Guangxin and his wife, Mr. Alexandre Pachoud, Mr.
Hennrik Anderson. Mr. Ahmet Avsar, Mr. Orhan Kahya, Mr. Wu Jing, Mr.
Huangyuan, Mr. Zhang Shujie, Mr. Ibrahim Nor, Miss Yeo Yuting, Miss Zhao
Yuting, Mr. Tan, Junyou.
I‟d like to thank Dr. Yang Nuo, Dr. Yao Donglai, Dr. Zhang Lifa and his
wife, Dr. Chen Jie and his wife, Dr. Xie Lanfei, Dr. Ma Fusheng, Dr. Shi Lihong,
Dr. Ni Xiaoxi, Mr. Liu Sha and his wife, Miss Zhu Guimei, Mr. Zhang Xun.
Miss Ma Jing, Miss Liu Dan. They are not only my collegers but also close
friends with so many wonderful memories during the life in Singapore.
The financial support from the National University of Singapore is
gratefully acknowledged.
My special thanks to my husband Mr. Zhao Xiangming whose love
completed and enriched my life.
Last but not least, thanks to my parents. Their support and understand
give me all the courage to seek improvement in life. 爸爸，妈妈，谢谢你们。
4
LIST OF PUBLICATIONS
1. K. W. Zhang, X. M. Zhao, X.F. Xu, V. Vignesh, John T.L. Thonge, V.
Venkatesan, Daniel S. Pickard, B. W. Li, B. Özyilmaz, Graphene
Nano-ribbon Transistors Fabricated by Helium Ion Milling, going to submit
to APL, 2012
2. X. F. Xu, Y. Wang, K. W. Zhang, X. M. Zhao, S. Bae, M. Heinrich, C. T.
Bui, R. G. Xie, John T. L. Thong, B. H. Hong, K. P. Loh, B. W. Li and B.
Öezyilmaz, arXiv:1012.2937, Phonon Transport in Suspended Single Layer
Graphene , submitted to nature material
3. K. W. Zhang, X. M. Zhao, X.F. Xu, V. Vignesh, John T.L. Thonge, V.
Venkatesan, Daniel S. Pickard, B. W. Li, B. Özyilmaz, Ultranarrow Graphene
Nanoribbon Fabricated by Helium Ion Milling, (poster)APS March meeting,
USA, 2011
5
TABLE OF CONTENTS
Chapter 1 Introduction .......................................................................... 15
1.1 Graphene: background and literature review .......................... 15
1.1.1 Graphene in carbon family .............................................. 15
1.1.2 Electronic properties of graphene .................................... 17
1.1.3 Band structure in graphene .............................................. 18
1.1.4 Band gap in graphene nanoribbon (GNR) ....................... 19
1.2 Thermoelectrical properties of graphene ................................. 21
1.2.1 Seebeck coefficient and the figure of merit ZT ............... 21
1.2.2 Thermoelectrical properties in graphene ......................... 23
1.3 Objective and scope of this thesis ........................................... 24
Chapter 2 Experimental techniques ...................................................... 26
2.1 Preparation of graphene ........................................................... 26
2.1.1 Micromechanical exfoliation ........................................... 26
2.2 Experimental techniques for graphene patterning and
characterization ........................................................................................ 27
2.2.1 Electron beam lithography .............................................. 27
2.2.2 Reactive Ion etching ........................................................ 30
2.2.3 Helium Ion Microscope ................................................... 31
2.2.4 Raman spectroscopy ........................................................ 32
2.2.5 Atomic force microscopy ................................................ 34
6
2.3 Experimental techniques for electrical studies ........................ 35
2.3.1 Low temperature vacuum system .................................... 35
Chapter 3 Graphene nanoribbon patterned by Helium ion Lithography
……………………………………………………………..37
3.1 Introduction ............................................................................. 37
3.2 Experimental Method .............................................................. 38
3.2.1 Graphene device fabrication ............................................ 39
3.2.2 Helium ion lithography(HIL) .......................................... 40
3.2.3 Raman spectroscopy and electrical measurement ........... 42
3.3 Experimental Result ................................................................ 42
3.3.1 HIM pattering on suspended graphene ............................ 42
3.3.2 HIM pattering on supported graphene for electrical
measurement .................................................................................... 43
3.3.3 Raman spectroscopy characterization ............................. 44
3.3.4 Electrical properties characteristic .................................. 47
3.4 Conclusion ............................................................................... 52
Chapter 4 Thermal Power in Graphene nanoribbon ............................. 54
4.1 Introduction ............................................................................. 54
4.2 Sample preparation .................................................................. 55
4.2.1 Device fabrication ........................................................... 55
4.2.2 Graphene nanoribbon fabrication .................................... 57
7
4.3 Measurement and the Result ................................................... 58
4.3.1 Temperature coefficient of Resistance(TCR) for
thermometers.................................................................................... 58
4.3.2 Thermal power in graphene stripe. .................................. 59
4.3.3 Thermal power in graphene nanoribbon. ........................ 61
4.4 Conclusion ............................................................................... 64
Chapter 5 Conclusion and outlook ....................................................... 66
5.1 Thesis summary ....................................................................... 66
5.2 Future work ............................................................................. 67
8
SUMMARY
Graphene has been discovered in lab for only eight years. Its excellent
properties make the research of this new material very important, not only for
the fundamental physics but also for the application. Even more, the energy
band gap opening in graphene nanoribbon (GNR) makes it a potential
application material in semiconductor field.
In this thesis, we developed a method to fabricate ultra-narrow GNRs
which is called helium ion Lithography (HIL) using helium ion microscope
(HIM). Suspended GNRs with widths down to 5nm and supported GNRs with
widths down to 20nm are patterned by directly modifying graphene strips
through surface sputtering by helium ions.
The temperature dependent conductance measurements on supported
Graphene Field Effect Transistors (GFETs) show an estimated energy gap of
13mev for 60nm wide GNR. Detailed 2D conductance measurements at low
temperature reveal an enhanced characteristic energy scale for the disorder
potential, which can be attributed to the damage on graphene lattice induced by
helium ion bombardment and is further confirmed by Raman spectroscopy
measurement.
In addition, we also investigated the thermoelectric properties of GNR.
GNR on Si/SiO2 substrate was fabricated by plasma etching method because of
its easy and economical manipulation. Seebeck coefficient S of GNR with
9
width of ~70nm and length of 1μm was measured as a function of the back gate
voltage at different ambient temperatures. At low temperatures, the Seebeck
coefficient increases with increasing temperature, which can be explained by
electron-hole puddles localized. However, at high temperatures, the Seebeck
coefficient shows a decreasing with increasing temperature which indicates an
energy gap exists. Compared with the thermoelectric properties in bulk
graphene sheet, the magnitude of S is enhanced. Its optimized value occurred at
150K, which might due to the enhanced quantum confinement effect in GNR.
10
LIST OF FIGURES
Figure 1.1 Graphene is the base for other dimensional graphitic materials:
0D buckyball, 1D carbon nanotube and 3D graphite (taken form
reference3). ........................................................................................... 16
Figure 1.2 The atoms arrangement of graphene22
........................................ 18
Figure 1.3 The band structure of (a) single layer graphene (b) bilayer
graphene33
............................................................................................ 19
Figure 1.4 The diagram of the Seebeck coefficient of a material (Picture
taken from wikipedia) .......................................................................... 21
Figure 1.5 The diagram of thermoelectrical (a) generator and (b) cooler
(Picture taken from wikipedia) ............................................................ 22
Figure 2.1 Exfoliated single layer graphene on 300nm SiO2 substrate ....... 27
Figure 2.2 The process flow of standard E-beam lithography ..................... 28
Figure 2.3 Photograph and schematic of our scanning electron microscope
(Nova NanoSEM 230). ......................................................................... 29
Figure 2.4(a) EBL pattern of alignment mark, 4 marks indicated by the red
circle (b) EBL pattern of Hall bar electrode (c) EBL pattern of two
terminal device (d) EBL pattern of 4 terminal device. ........................ 30
Figure 2.5 The operation diagram of Helium Ion Microscpope. (Picture
taken from wikipedia) .......................................................................... 32
Figure 2.6 The Energy level diagram showing the states involved in
Raman signal. (Picture taken from wikipedia) .................................... 33
Figure 2.7 Typical Raman spectrum of single layer graphene ..................... 34
Figure 2.8 Block diagram of atomic force microscope (Picture taken from
wikipedia) ............................................................................................ 35
Figure 2.9 Picture of low temperature system, the inset shows the details
inside the probe .................................................................................... 36
Figure 3.1 Optical image of supported graphene with electrode defined by
standard E-beam lithography ............................................................... 39
Figure 3.2 Direct exfoliating of graphene on pre-patterned SiO2 substrate.
11
The scale bar is 10 μm ......................................................................... 40
Figure 3.3 Demonstration of Helium ion lithography on supported
graphene stripe. .................................................................................... 41
Figure 3.4(a) HIM-image on suspended GNRs with width of 20nm and
10nm respectively. Scale bar: 500nm (b) HIM-image of a suspended
graphene nanoribbon with varying widths fabricated by helium-ion
milling. Scale bar: 100nm. ................................................................... 43
Figure 3.5 Zoom in AFM image of the 60nm wide nanoribbon. Scale bar:
200nm. ................................................................................................. 44
Figure 3.6 (a) Raman map of integrated 2D-line intensity for helium-ion
milled graphene ribbon. The white dash line emphasizes the cutting
trace (b) Raman map of integrated G-line intensity (c) Raman map of
integrated D-line intensity. ................................................................... 45
Figure 3.7 Raman spectrum for Location A(Loc A)marked by Blue cross
in Fig. 3.6a and Location B(Loc B)marked by black cross in Fig. 3.6a.
The scale bars for all images are 700nm. ............................................. 46
Figure 3.8 The conductance of GNR vs. back-gate for different
temperatures from T = 6.5 K to 400 K ................................................. 48
Figure 3.9 Minimum conductance of GNR with W=60nm and L=250nm at,
Gmin vs. 1/T with fits to NNH (red curve) and VRH (blue curve).
Black dots denote experimental data ................................................... 49
Figure 3.10 Conductance vs. back-gate voltage at different source-drain
bias at T=4.3 K. .................................................................................... 50
Figure 3.112D plot of Conductance of graphene nanoribbon with width of
60nm as a function of Vsd and Vbg at T=4.3 K. .................................... 51
Figure 4.1 Optical image of thermal power device, 1 is heater, 2 and 3 is
thermometers........................................................................................ 57
Figure 4.2 Etching process for graphene nanoribbon. 1) PMMA is spin
coated on top of graphene sheet; 2) etching pattern is exposure to
electron beam in SEM chamber; 3) after development, cross section
picture shows over dose of etching. 4) exposed part of graphene is
etched by O2 plasma............................................................................. 58
Figure 4.3 Seebeck coefficient (S) of graphene with width of 5um and
length of 7um as a function of backgate Vbg at temperature 15k, 50k,
12
100k, 130k,170k, 210k, 250k and290k. ............................................... 60
Figure 4.4 Seebeck Coefficient of graphene stripe at fixed backgate Vbg =
1v( Red triangle) and -50V(blue dot)................................................... 61
Figure 4.5Resistance of GNR as a function of back gate voltage V𝑏𝑔 at
different temperatures 10k, 50k, 195k, 250k, and 300k. Inset is the
optical picture of the device and AFM picture of the GNR. The scale
bar is 500nm ......................................................................................... 62
Figure 4.6 Seebeck coefficient S of GNR (W=70nm, L=1μm) as a function
of back gate Vbg at different temperatures 15k, 50k, 200k, 250k, and
300k...................................................................................................... 63
Figure 4.7 Seebeck Coefficient of graphene stripe at fixed backgate
Vbg~3v( Red triangle) and 40V(blue dot) ............................................ 64
13
LIST OF ABBREVIATIONS
Si Silicon
2D Two Dimensional
SLG Single Layer Graphene
BLG Bilayer Graphene
ExG Exfoliated Graphene
GNR Graphene Nano-ribbon
GFET Graphene Field Effect Transistor
GNR-FET Graphene Nanoribbon Field Effect Transistor
SiO2 Silicon Dioxide
STM Scan Tunneling Microscope
CVD Chemical Vapor Deposition
EBL E-Beam Lithography
SEM Scanning Electron Microscope
PMMA Poly(methyl methacrylate)
NPGS Nanometer Pattern Generation System
Cr Chromium
Au Gold
RIE Reactive Ion Etching
K Kelvin
14
T Tesla
EF Fermi Level
SMU Source Measurement Unit
DOS Density of States
Al Aluminum
HIM Helium Ion Microscope
HIL Helium Ion Lithography
AFM Atomic Force Microscopy
EMF Electromotive Force
15
Chapter 1 Introduction
Graphene, which is only one-atom thick, is now considered to be the
world‟s thinnest material1. This strictly two-dimensional (2D) material was
thought to be not stable and could not exist in nature. Once it was discovered
in the lab, it has attracted tremendous interest and is believed to be a wonderful
material for next generation electronics. This flat monolayer of carbon atoms,
tightly packed into two dimensional honeycomb lattice, is the basic building
block for graphitic materials of all other dimensionalities. The discovery of
graphene opens a new research era for material science and its application.
1.1 Graphene: background and literature review
1.1.1 Graphene in carbon family
As the thinnest known material in the universe, graphene has attracted the
most enthusiasm and attention in the world. This novel material was
experimentally founded by Geim‟s group using mechanically exfoliation
method with scotch tape in 20041, 2
. This truly two dimensional material acts as
the „building block‟ of other carbon family members, shown in Fig 1.13: it can
be wrapped into zero dimensional buckminsterfullerene(C 60); it can also be
rolled up into widely used one dimensional carbon nanotubes, which have
been extensively investigated for device applications in the last two decades4;
the three-dimensional graphite in pencils can also be realized by simply
stacking graphene sheets5.
16
Figure 1.1 Graphene is the base for other dimensional graphitic materials: 0D buckyball,
1D carbon nanotube and 3D graphite (taken form reference3).
All of these carbon materials have been used in many applications much
earlier before graphene emerged, yet many of their electronic and magnetic
properties originate from the properties of graphene. Indeed, graphene has
been theoretically studied to describe other carbon-based materials for around
sixty years before it became a reality6, 7
.
Two dimensional crystals were believed to be thermodynamically
unstable and unable to exist in nature8, 9
, while numerous attempts at obtaining
two dimensional crystals were failed10
. The reason that people believed it only
exists theoretically is that the thermal fluctuation in 2D crystal causes the
lattice dislocations or defects at finite temperature to destabilize the crystal
structure.3, 6, 7, 11
However, half a century later, Geim and his colleague cleaved
the one-atom-thickness layer from bulk graphite by mechanically exfoliation2.
This relatively simple technique involves repeated peeling off
three-dimensional graphite, since graphene layers are only weakly coupled.
17
Taking advantage of the same method, the team has also managed to obtain
free-standing two dimensional crystals of other materials such as single-layer
boron nitride12
. Afterwards, numerous research groups from all around world
investigated this new born material13-18
. The excellent properties making
graphene one of the hottest topics in physics in recent years and a graphene
“gold rush” has started since then.
1.1.2 Electronic properties of graphene
Carbon-based systems show an unlimited number of different structures
with variety of physical properties4, 19
. Among systems with only carbon atoms,
graphene plays an important role since it is the basis for understanding of the
electronic properties in other allotropes. The discovery of both single layer
graphene (SLG) and bilayer graphene (BLG) has revolutionized the physics of
low dimensional systems and led to novel nanoscale device applications2, 20, 21
.
Within the last eight years, it helped create one of the most successful
interdisciplinary research efforts driven by graphene‟s outstanding electronic,
chemical, optical, and mechanical properties.
18
Figure 1.2 The atoms arrangement of graphene22
Graphene is composed of carbon atoms arranged on a honeycomb
structure, and can also be thought of benzene rings stripped out from their
hydrogen atoms23
, which are shown in Fig 1.2. Every carbon atom has three
nearest neighbors with an interatomic distance of 1.42 angstrom. Each atom
has one s and three p orbitals, among which, only the perpendicular p orbital
contributes to conductivity and hybridizes to form valence and conduction
bands. Because the two sublattices give different contributions in the
electronic structure, a pseudo-spin24
is defined for the relative contribution of
the A and B sublattices, which consequently introduces chirality to graphene21,
25.
1.1.3 Band structure in graphene
The primary shape of graphene band structure consists of two conical
valleys that touch each other at the symmetry point in the Brillouin zone, which
19
is called Dirac point. As shown in Fig. 1.3A, the energy spectrum varies linearly
with the magnitude of momentum away from the Dirac point3. From a purely
basic science point of view, the massless, chiral, Dirac-like electronic spectrum
of single layer graphene with two linear energy bands touching each other at a
single point is the fundamental basis for the observation of many exotic
phenomena.
The energy spectrum of bilayer graphene is quite different from single
layer. Although it only adds one additional layer, the entirely quantum
phenomena changed based on the massive nature of bilayer‟s chiral Dirac
fermions26-32
. By broking the sublattice symmetry, the spectrum is made of
four massive Dirac bands (two conduction bands, two valence bands) and has
hyperbolic dispersion relation. In this situation, the band gap opens29
, as
shown in Fig. 1.3B.
Figure 1.3 The band structure of (a) single layer graphene (b) bilayer graphene33
1.1.4 Band gap in graphene nanoribbon (GNR)
The band gap opening in bilayer graphene makes it a potential material in
20
semiconductor field27, 34, 35
. In spite of broking A-B symmetry in bi-layer
graphene, quantum confinement induced by cleaving graphene to quasi
one-dimensional GNR36-40
, is considered as another widely used way to create
energy band gap in graphene based devices. Theoretical works using
Zone-folding approximation41
, π-orbitial tight-binding models42, 43
and first
principle calculations44, 45
predict the band gap Eg of a GNR scaling as
Eg = α/W with the GNR width W, where α ranges between 0.2-1.5,
depending on the model and the crystallographic orientation46
. However, these
theoretical estimates can neither explain the experimentally observed energy
gaps of etched nanoribbons of widths beyond 20 nm, which turn out to be
larger than predicted, nor explain the large number of resonances found inside
the gap39, 47, 48
. On the other hand, numerous methods are invented to fabricate
GNR, including plasma etching48, 49
, atomic force microscopy anodic
oxidation50
, scanning tunneling microscopy lithography51
, as well as chemical
methods including chemical derived techniques52-54
and anisotropic etching55
.
However, these processes presently lack control over the width, orientation
and layer number of graphene. Recently, Helium-ion lithography (HIL) shows
powerful ability for patterning GNR because of its high resolution56, 57
.
Suspended GNR with width of 10nm was achieved by this method57
, while
there is lack of study on the GNR‟s properties. In my thesis, GNR fabricated
by HIL will be studied.
21
1.2 Thermoelectrical properties of graphene
1.2.1 Seebeck coefficient and the figure of merit ZT
The energy loss in industry is a great waste. Approximately 90 per cent of
the world‟s power is generated by heat engines that use fossil fuel combustion
as a heat source. The heat engine typically operates at 30-40 per cent efficiency.
As a result, roughly 15 terawatts of heat is lost to the environment58
.
Thermoelectric device could potentially convert part of this low-grade waste
heat to useful electricity.
The thermopower or Seebeck coefficient, represented by S, of a material
measures the magnitude of an induced thermoelectric voltage in response to a
temperature difference across that material as shown in Fig. 1.4.
S = −∆𝑉
∆𝑇
Figure 1.4 The diagram of the Seebeck coefficient of a material (Picture taken from
wikipedia)
At the atomic scale, the applied temperature gradient causes charged
carriers in the material to diffuse from the hot side to the cold side. Based on
22
this mechanism, thermoelectric cooler or generator is built, as shown in Fig. 1.5.
Carriers flow through the n-type element, crosses a metallic interconnect, and
passes into the p-type element. If a power source is provided, the thermoelectric
device acts as a cooler. Electrons in the n-type element move opposite the
direction of current and holes in the p-type element will move in the direction of
current, both removing heat from one side of the device. When a heat source is
provided, the thermoelectric device works as a power generator.
Figure 1.5 The diagram of thermoelectrical (a) generator and (b) cooler (Picture taken
from wikipedia)
For a material to be a good thermoelectric cooler or generator, it must have
a high thermoelectric figure of merit, ZT. The figure of merit is defined by:
ZT = S^2 ∗ σ/к
Where S is the Seebeck coefficient, σ is the electrical conductivity, and к is
the thermal conductivity. It has been challenging to increase ZT>1, since the
parameters of ZT are generally interdependent58-60
. Increasing the
thermoelectric power S for a material also leads to a simultaneous decrease in
23
the electrical conductivity. Also, an increase in the electric conductivity leads to
a comparable increase in the electronic contribution to the thermal conductivity.
Thus, bulk materials have a limited ZT. The highest ZT for bulk material report
to date is about 2.4 in Be2Se361-63
. However, recent studies have suggested that
the value of ZT may become significantly higher by incorporating
nanostructures into bulk materials or use low dimensional structures. The use
of low-dimensional systems for thermoelectric application is mainly due to: a)
enhance the density of states near E , leading to an enhancement of the
Seebeck coefficient; b) decrease of phonon conductivity by increasing the
boundary scattering.
1.2.2 Thermoelectrical properties in graphene
Graphene, which is a 2D material, can provide such quantum confinement
effect for the application on thermoelectric material. Large thermopower has
been discovered experimentally in single layer graphene64
. Unfortunately, due
to the large thermal conductivity in graphene15, 65-67
, figure of merit in
graphene is much smaller than 1, which prevents the graphene from heat
engineering application. On the other hand, Theoretical works have proved
that thermopower can be significantly enhanced in functional graphene
material, such as GNR68-71
, graphane68, 72, 73
(Hydrogenated graphene), due to
band gap opening. Although this enhancement has not been observed in
24
gapped dual gate bilayer graphene due to charge puddles near the CNP74
, the
optimized value occurs at 100 Kevin provides an opportunity for low-T
thermoelectric application. As a result, experiment work is also needed to
investigate the thermoelectric properties in gapped GNR.
1.3 Objective and scope of this thesis
In the first part of this thesis, the main focus is to pattern graphene sheet in
to quasi-one dimensional graphene nanoribbon with the help of helium ion
beam sputtering. Band structure is modified after the ion beam cutting and the
energy gap opens. The effect of helium ion bombardment to graphene is
analyzed. The second part investigates the thermoelectrical properties changes
in graphene nanoribbon compared to graphene sheets.
The thesis is organized as follows: Chapter 2 introduces the methods of
preparing graphene samples and an overview on experimental techniques used
in this thesis. Experimental results are presented in Chapter 3 and Chapter 4. In
chapter 3, we introduce the method of preparing graphene nanoribbon from
graphene sheet both on suspended substrate and supported substrate. We show
that the width of the GNR in this method can be narrowed down to 5nm on
suspended samples and 20nm on supported ones. Electrical properties
characterization of the supported GNR with width of 60nm shows the energy
band gap opening in later part of this chapter. In chapter 4, we study the
thermoelectric properties of graphene based devices. First, we study the
25
thermoelectrical properties in graphene sheet. Then, we investigate the
thermopower in GNR. We find that the enhancement of thermal power may due
to the opening of a band gap in GNR. Moreover, the temperature behavior of
GNR‟s thermopower at low temperature region deviates from that of gapped
semiconductor materials. This could be explained by the electron hole puddles
in GNR. The conclusion and outlook will be presented in chapter 5.
26
Chapter 2 Experimental techniques
2.1 Preparation of graphene
2.1.1 Micromechanical exfoliation
In 2004, graphene was first experimentally discovered by Geim‟s group
using micro-mechanical exfoliation method. This method is simple and
convenient, but it provides high quality and enough sample sizes for academic
research.
The details of the method are as following: A small high quality graphite
piece is selected as the seed. Two clean pieces of scotch tapes are used to stick
the two faces of the graphite piece, and then separated gently. This is called one
step of exfoliation. The initial graphite piece will become two parts sticking on
each tape, in which one part is selected as the seed for next exfoliation. The
exfoliation is repeated until a fairly thin and more or less transparent graphite
piece can be found on one tape. Then this tape is carefully transferred onto a 300
nm SiO2 wafer. After transferring, graphene can be observed on 300nm SiO2
surface under optical microscope.
The exfoliation method relies on two factors: first, the arrangement of
carbon atoms in graphite forms layer structure. Each carbon atom is bonded to
three other atoms inside a layer; however, each layer is only weakly coupled by
Van der Waals force. As a result, graphite is easily been separated into pieces
during exfoliation. Second, graphene has a relatively high optical contrast on
27
300nm SiO2 substrate which makes the location of graphene piece on substrate
become possible, as shown in Fig. 2.1.
Figure 2.1 Exfoliated single layer graphene on 300nm SiO2 substrate
2.2 Experimental techniques for graphene patterning and characterization
2.2.1 Electron beam lithography
Electron beam lithography is a lithography technique that uses a focused
electron beam in a patterned fashion on a resist layer to selectively either
remove or retain exposed area. Among the various lithography techniques, the
EBL enable the fabrication scale down to around 10nm, which is much higher
than photolithography or ion beam lithography. This advantage makes the EBL
the key technique in the nano-fabrication area. EBL is also the main lithography
method used in this thesis.
The details of the EBL process are described as following: First, a thin layer
of resist is spin-coated onto a targeted substrate, which is SiO2 in our case. A
specific designed pattern is generated using the Nanometer Pattern Generation
28
System (NPGS). The pattern can be alignment mark, etch mask, hall bar
electrode or any other specific shape. This pattern is then incorporated into the
SEM by the NPGS software. The area of the resist which is exposed to the beam
with a specific time will become more soluble in the developing process, due to
the reduced molecule weight of the resist. As a result, the design pattern will be
generated on the resist after developing process. The process flow is shown in
Fig. 2.2.
Figure 2.2 The process flow of standard E-beam lithography
In this thesis, the lithography process is performed using the FEI Nova
NanoSEM 230 Scanning Electron Microscope, as shown in Fig. 2.3. 30KV was
selected for the beam voltage to get high resolution. PMMA A4 is selected as
the polymer resist for the EBL. The developer is a mixed solution of MIBK and
IPA with the ratio of 1:1.
29
Figure 2.3 Photograph and schematic of our scanning electron microscope (Nova
NanoSEM 230).
There are three main types of patterns we generated by the EBL. First is the
alignment mark, which serves as a function of alignment for the next step EBL.
The graphene flake recognized under optical microscope and located with
respect to the corner of the wafer. The x and y axis of the graphene flake
determined by this method is not accurate enough to be directly patterned by
SEM. As a result, a more detailed and nanometer scale alignment mark is
exposed and developed first to surely cover the graphene flake, as shown in Fig.
2.4a. This alignment mark which can be observed in SEM provides nanometer
scale accuracy for the following EBL process.
The second type of pattern is the etch mask which serves a function of
defining the graphene‟s geometry. The shapes of exfoliated graphene are
usually random, which are not suitable for the electrical measurement. The
unwanted area of the graphene flake is exposed by the EBL process while the
other part is covered with the PMMA resist. Then, the unwanted area is
removed by the reactive ion etching described in the following section while the
30
other part is protected by the resist.
The third type of pattern is the designed metal electrodes, such as hall bar,
two terminal device, four terminal device and thermal power measurement
device, as shown in Fig. 2.4 (b-d). After the designed area is exposed, the wafer
was thermally evaporated with metal contacts, which is chromium and gold in
our case. After evaporation, the whole device is dipped into acetone for a few
hours to remove the left PMMA resist, and to lift-off the unwanted metal on top
of PMMA resist. As a result, a metal electrode is formed for the following
electrical measurement.
Figure 2.4(a) EBL pattern of alignment mark, 4 marks indicated by the red circle.scale
bar:50 μm (b) EBL pattern of Hall bar electrode, scale bar: 20 μm(c) EBL pattern of two
terminal device. Scale bar: 50μm (d) EBL pattern of 4 terminal device. Scale bar:5
0μm
2.2.2 Reactive Ion etching
Reactive ion etching is an etching technique used in many micro
31
fabrication processes. Chemically reactive plasma is generated by an RF source
under low pressure: electromagnetic field generated by the RF source will stripe
the electron of gas atoms and produce positive ions. The electrons striped by the
electromagnetic force will build up a potential drop, which is usually several
hundred volts, across the targeted substrate and the top plate. This potential
difference will drive the positive ions onto the targeted substrate and remove the
material with both chemical reaction and physical bombard.
In our experiment, oxygen is used as the source gas for etching graphene,
since the oxygen ions are easily reacted with carbon atoms. The RF power is
usually selected to be 20W, which will generate an etching speed of around 20
layers per minute.
2.2.3 Helium Ion Microscope
Helium ion microscope is the new member of the microscope family based
on a scanning helium ion beam. It has some unique properties compare with
electron beam and focused ion beam: first, the helium ions have much smaller
de Broglie wavelength (small diffraction effect) than electrons, which leading to
a much higher resolution (around 0.25 nm) than SEM; second, it has a much
lower sputtering effect than the focused ion beam due to the relative light mass
of helium ions. The small diffraction effect combined with high resolution make
it an ideal tool for direct cutting and patterning of ultra-thin materials.
32
In addition to the high spatial resolution, the shallow escape depth (~1nm)
of the He ions excited secondary electrons provide images with good surface
contrast. Furthermore, the electron flood gun removes the charging effect on the
sample, which makes the HIM able to image non-conducting samples.
The operation diagram is shown in Fig. 2.5a. The helium ions are generated
around the sharp tip (around 1 to 3 atoms) and accelerated down a column with
a series of alignment, focus, and scanning elements, that landing on the sample
with a diameter of around 0.75 nm. The numbers of secondary electrons
detected by the ET detector determine the gray scale of each image point.
Figure 2.5 The operation diagram of Helium Ion Microscpope. (Picture taken from
wikipedia)
2.2.4 Raman spectroscopy
Raman spectroscopy is a spectroscopic tool which is usually to detect the
vibrational, rotational or other low frequency modes in different material. It
relies on the inelastic scattering of sample molecules with photons which
33
usually come from the incident laser. The incident photons interact with the
molecule vibrations, phonons and other excitations in the system, which
provide red or blue shift of incident photons‟ frequency, as shown in Fig. 2.6.
The Rayleigh scattering signal, in which the frequency doesn‟t change, is
filtered out by the analyzer, while the rest of the two scattering signals are
collected.
Figure 2.6 The Energy level diagram showing the states involved in Raman signal.
(Picture taken from wikipedia)
Raman spectroscopy is widely used in graphene community to determine
the graphene parameters, such as number of graphene layers, strain in graphene,
graphene quality, as well as graphene temperature. Fig. 2.7 is the typical Raman
signal of a graphene piece lie on top of SiO2 substrate. There are three typical
peaks in the graphene‟s Raman spectrum, the D band, G band and 2D band. The
D band appears due to the lattice defect or molecule absorbers, the G band
indicates the vibrational state of graphene‟s sp2 bonding, while the 2D band
shows the stacking of graphene layers.
34
Figure 2.7 Typical Raman spectrum of single layer graphene.
A lot of experiments were done to study the Raman signal response of
graphene under difference conditions. Ferrari, et al, demonstrated that the G
band intensity and 2D band FWHM will increase while the layer of graphene
increases75
. The difference of the signals is quite obvious that it makes Raman
spectroscopy an ideal method to determine the layer of graphene. Raman
spectrum is also used to study the hydrogenation of graphene and its reverse
effect68
. The emerging of the D band after the hydrogenation of graphene
indicates the attachment of hydrogen atoms on the graphene lattice, while the
decrease of D band intensity shows successfully recover of hydrogenated
graphene back into pristine graphene. Mohiuddin, et al, show that while the
strain in graphene lattice changes, the frequency of G band will shift left or
right76
. Balandin, et al, show that while the temperature of graphene changes,
the frequency of 2D band will change accordingly15
.
2.2.5 Atomic force microscopy
35
Atomic force microscope is a high resolution scanning probe microscopy,
which relies on the interaction between the tip and the surface of the sample.
Piezoelectric parts are used to precisely manipulate the tip in x and y directions
in nano-scale range. A laser combined with a photo detector is used to
determine the z position of the tip as shown in Fig. 2.8. The resolution of AFM
in z direction can reach to orders of fractions of a nanometer.
Figure 2.8 Block diagram of atomic force microscope (Picture taken from wikipedia)
Due to AFM‟s high resolution in z axis, it is mainly used to determine the
thickness and surface morphology of graphene. Moreover, the tapping mode of
AFM provides a nondestructive method compared to other microscope such as
SEM or HIM.
2.3 Experimental techniques for electrical studies
2.3.1 Low temperature vacuum system
36
The electrical measurements in this thesis are mainly conducted in the low
temperature vacuum system from Cryogenic Pte Ltd, as shown in Fig. 2.9. After
the wafer is bonded on the delicated LCC package, the package is loaded into
the probe of the system with wires conducted out to the SMU and lock-in
measurement units. The chamber of the wafer in the probe can be pump to a
vacuum level of 1e-4
mbar. The cooling power of the system comes from the
Pulse Tube with a compressor of 100W. The temperature of the system is
controlled by a Lakeshore 340 temperature controller.
Figure 2.9 Picture of low temperature system, the inset shows the details inside the probe
37
Chapter 3 Graphene nanoribbon patterned by
Helium ion Lithography
3.1 Introduction
Graphene, a two dimensional atomic-thin layer of hexagonally arranged
carbon atoms, is widely considered to be a promising candidate for future
nano-electronics due to its high mobility1, 14, 77
, stability33
and high thermal
conductivity15
. Charge transport of graphene is totally different from
conventional semiconductor materials due to its linear energy dispersion
relation33
. This unique structure is the key for the superior properties of
graphene. However, lacking an energy band gap in graphene‟s band structure
limits its application in semiconductor industry: graphene based field-effect
transistors (FETs) show a limited current on-off ratios due to the absence of
band gap.49
A number of approaches have been proposed to induce a band-gap. A
non-zero band gap can be induced in graphene by breaking the inversion
symmetry of the AB-stack in bi- or trilayer graphene28, 78-80
, but it is very
difficult to control the exact number of layers during fabrication. Alternatively,
quasi-one-dimensional confinement of the carriers in graphene nanoribbons
induces an energy gap in the single-particle spectrum39, 48, 49
. Lithographic
etching is reported as the earliest and most convenient method to produce GNRs
from graphene sheet. However, standard e-beam lithography gives only access
38
to 20 nm and above size range, and only with specialized processing81
. Several
alternative methods have been developed to produce GNRs, including chemical
sonication of exfoliated graphite54
, controlled nano-cutting with metal
particles82
, etching with physical masks (e.g. nanowires)83
, or unzipping of
multi-wall carbon nanotubes53, 84
. However, these processes presently lack
control over the width, orientation and layer number of graphene. Recently, a
high on/off ratio (which can exceed 104 at room temperature) is achieved in
suspended GNRs even with 150nm in width16
, representing a significant
breakthrough in the field of graphene-based electronics. According to the
quantum confinement effect, an even higher on-off ratio could be expected for
narrower GNR. However, most current lithography methods are based on resist
(such as PMMA) patterning, which is not suitable for suspended devices49, 81
.
Recently, Helium-ion lithography (HIL) shows powerful ability for
patterning GNR because of its high resolution and resist-free characteristics56, 57
.
Suspended GNR with width of 10nm was achieved by this method, while there
is lack of study on the GNR‟s properties. In this thesis, we demonstrate the
capability of HIL to fabricate the ultra-narrow suspended and supported
graphene nano-ribbon. And the electronic transport of supported GNR
fabricated by HIM is studied.
3.2 Experimental Method
39
3.2.1 Graphene device fabrication
Supported graphene was exfoliated from natural graphite, and transferred
to 300nm SiO2/Si substrate. Standard E-beam lithography is used to predefine
the graphene stripe and metal contact as shown in Fig. 3.1. The graphene stripes
have around 200nm in width and 1μm in length. The short width and length is
to facilitate the following Helium ion pattering process.
Figure 3.1 Optical image of supported graphene with electrode defined by standard
E-beam lithography
Suspended graphene sheet was fabricated by direct exfoliation from
graphite on pre-patterned SiO2 substrate, as shown in Fig. 3.2. The diameter of
pre-patterned hole is around 3 μm and the depth is 300nm. After exfoliation,
the device was annealed at 300 degree in Ar/H2 environment for 3 hours in
order to remove the glue residue.
40
Figure 3.2 Direct exfoliating of graphene on pre-patterned SiO2 substrate. The scale bar
is 10 μm
3.2.2 Helium ion lithography(HIL)
Helium ion lithography is carried out using Helium Ion Microscope (Zeiss
Orion system), operated at ~43kV acceleration voltage with a beam current of
0.6pA. The ion-beam control uses a modified Nanometer Pattern Generation
System (NPGS, Nabity). The HIL process is demonstrated as in Fig. 3.3. A
focused ion beam is designed to scan a double U shape on the graphene stripe,
which result in a narrow graphene nanoribbon in the centre. The graphene area
which is exposed to the ion beam is removed by the ion bombard.
41
Figure 3.3 Demonstration of Helium ion lithography on supported graphene stripe.
The fabrication of these GNRs using HIL requires an ultra-clean sample
surface. There are two reasons for this: first, the surface impurities will block
the helium ion beam from cutting the graphene, which will result in inconsistent
edges of GNR while cutting; second, the surface impurities tend to scatter the
helium ions, which will damage the bulk GNR.
To obtain a clean surface in our samples, we perform a three step annealing
process: First, graphene flakes are annealed at 3000C under Argon-Hydrogen
environment (5% H2) to remove exfoliation related glue residues. Subsequent
to metal electrode deposition, the graphene is annealed again at 2500C under
same conditions. In the final step, the sample is mounted on a heating stage
located in the HIM chamber. This allows for in-situ annealing under vacuum
conditions to remove organic contaminants prior to helium-ion patterning.
Simultaneously, with the vacuum annealing, an UV exposure is also used to
42
clean the graphene surface from amorphous-carbon related contaminants.
3.2.3 Raman spectroscopy and electrical measurement
The graphene is characterized by the Raman spectroscopy before and after
cutting. The Raman spectroscopy used in this thesis is WITec CRM200 Raman
system with 532nm excitation laser. The power is blow 0.3mW to avoid damage
to the graphene sheet and the laser spot diameter is around 400nm. The
conductance measurements on our GNR field-effect transistors (GNR-FETs)
were carried out using the standard combination of Keithley 6221 current
source and Keithley 2182A nano-voltmeter. A current-reversal technique is
used to cancel the effects of thermal electromotive force (EMF) in the voltage
test lead connections.
3.3 Experimental Result
3.3.1 HIM pattering on suspended graphene
Fig. 3.4a shows a HIM image of GNRs with width of 10nm and 20nm,
which are suspended on the substrate with pre-etched holes. Fig. 3.4b shows a
suspended GNR, the width of which varies from 5nm, 10nm to 20nm in a
staircase-like pattern (dark area is the cutting trace). This demonstrates that
HIM is able to consistently pattern the suspended graphene sheet into minimum
5nm ribbon.
43
Figure 3.4(a) HIM-image on suspended GNRs with width of 20nm and 10nm
respectively. Scale bar: 500nm (b) HIM-image of a suspended graphene nanoribbon
with varying widths fabricated by helium-ion milling. Scale bar: 100nm.
3.3.2 HIM pattering on supported graphene for electrical measurement
We also fabricate supported GNR devices for the properties study. Fig. 3.5
shows the AFM image of 60nm wide supported GNR. We fabricated dozens
(>30) of supported GNRs device with width ranging from 20nm to 100nm using
above procedure.
44
Figure 3.5 Zoom in AFM image of the 60nm wide nanoribbon. Scale bar: 200nm.
3.3.3 Raman spectroscopy characterization
We first examine the influence of helium-ion sputtering on the graphene
surface by Raman spectroscopy. The 2D Raman maps of intensity of G-band,
second-order Raman band and D-band are plotted in Fig. 3.6 (a-c). Brighter
colour shows higher intensity. In Fig. 3.6a, the white dashed line indicates the
cutting trace and the source (drain) area is marked with S(D). The height of the
D peak in Fig. 3.6c indicates the disorder induced during fabrication.
45
Figure 3.6 (a) Raman map of integrated 2D-line intensity for helium-ion milled
graphene ribbon. The white dash line emphasizes the cutting trace (b) Raman map of
integrated G-line intensity (c) Raman map of integrated D-line intensity.
We select two locations: location A(Loc A) is located in the centre of the
GNR and location B(Loc B) is located adjacent to the GNR. These two
locations are marked in Fig. 3.6a and the respective Raman spectrum (blue and
46
black curves respectively) is shown in Fig. 3.7. Raman spectrum for the
individual curves is normalized to its respective G peak intensity for easy
comparison. The Raman spectrum at Loc A (blue curve) exhibits two new sharp
features appearing at 1356cm-1 (D-band) and 1626cm-1 (D‟-band), as a
consequence of increased disorder. The ID/IG intensity ratio between the
disorder-induced D-band and the characteristic pristine graphene G-band is as
high as 2.1. The FWHM of second-order Raman band at 2705cm-1 broadens to
47cm-1.
Figure 3.7 Raman spectrum for Location A(Loc A)marked by Blue cross in Fig. 3.6a and
Location B(Loc B)marked by black cross in Fig. 3.6a. The scale bars for all images are
700nm.
Far away from the cutting line, which is the location B, the Raman
spectrum shows features similar to pristine graphene. The D peak intensity is
much smaller than the D peak intensity in Location A. This demonstrates that
47
the graphene damage is only located along the cutting line. The further away of
the cutting line, the less the damage.
Yet the result qualitatively showed that there is a higher defect density in
the 0.4 micron spot measured on the ribbon than far away from the ribbon.
However, the ion bombardment and back-scattering effects do introduce
additional disorder. To get further insight into the characteristics in our samples,
charge transport was investigated down to low temperatures in helium-ion
patterned supported GNRs.
3.3.4 Electrical properties characteristic
The electrical transport measurement of GNR was done from 4.2K to 400K
at vacuum condition. Before measurements, the samples are in-situ annealed at
400 K under high vacuum conditions to remove loosely attached ad-atoms and
water absorbents. The GNR with width range from 60nm to 100nm were
measured. We selected a typical device with width of 60nm discussed as
following:
The conductance of a 60 nm patterned GNR-FET is plotted as a function of
back-gate voltage at different temperatures in the inset of Fig. 3.8. The
conductance of GNR shows a bipolar feature similar to pristine graphene. At
the charge neutrality point (Vg ~ 30 V), the conductance reaches minimum at all
the temperature ranges. While the temperature drops, the conductance of GNR
48
drops at all temperature range, which is different from that in pristine single
layer graphene. This phenomenon indicates that the GNR is defective85
. At low
temperatures, the strong insulating behavior around the charge neutrality point
indicates the formation of a transport band gap81
.
Figure 3.8 The conductance of GNR vs. back-gate for different temperatures from T =
6.5 K to 400 K
The plot of minimum conductance as a function of temperature is shown in
Fig. 3.9. At high temperature range, the transport can be described within the
thermal-activation theory,min
~ exp( / 2 )a B
G E k T , where the activation energy
13a
E meV is obtained by a linear fit to the Arrhenius plot. This value of the gap
is somewhat larger than the case for other lithographically formed nanoribbon
with the same width described in literature and can be better compared with the
gaps for ~ 40 nm pristine GNRs, reported previously39, 86
. This indicates the
possibility that the effective ribbon width for our device is smaller than the
geometrical value because of the strongly defected edge of the ribbon.
49
At low temperatures, the conductance deviates from the linear behavior of
thermal activation. Similar to the plasma-etched nanoribbons, the behavior in
this regime is consistent with the variable range hopping (VRH) mechanism,
where 1/ (1 )
min 0~ exp( / )
DG T T
. Here,
0T indicates the characteristic temperature
scale for the localized states, and D is the dimension of the VRH. The best fit to
the data at low temperatures is attained with D=2, indicating a two dimensional
VRH.
Figure 3.9 Minimum conductance of GNR with W=60nm and L=250nm at, Gmin vs. 1/T
with fits to NNH (red curve) and VRH (blue curve). Black dots denote experimental data
We also study the transport gap for the defective nano-ribbon by measuring
the conductance of the GNR at temperature of 4.3 K with varying global gate
and source-drain bias. Fig. 3.10 shows the conductance of GNR on the same
device discussed in the previous section. The conductance of graphene
nanoribbon is suppressed in a large back-gate range near the charge neutrality
50
point at low bias. Using the method as described in references39
, we obtained
the estimate of the back-gate width of conductance suppression, ~ 50bg
V V , by
extrapolating the slope of the smoothed dG/dVg in the on-state regions to zero.
This back-gate conductance gap represents a disorder energy-scale rather than a
transport-gap energy-scale. Although previous experiments suggest that these
two energy scales are linearly dependent for GNRs of varying width39
, the
constant of proportionality represents the level of disorder in the system. In the
present case, the large voltage-span for back-gate suppression reflects the
enhanced disorder potential rather than an increase in the transport gap. This is
consistent with the observations made from Raman spectroscopy that
helium-ion milling of GNRs results in additional damage to the graphene lattice
from the back-scattered Helium ions.
Figure 3.10 Conductance vs. back-gate voltage at different source-drain bias at T=4.3 K.
51
In addition to suppression of conductance at small bias, the 2D conductance
plots also reveal a series of resonances which are characteristic of GNRs. These
peaks indicate the resonant conduction paths through localized states inside the
transport gap, which is in agreement with other experimental works for
disordered GNR86
. At larger source-drain bias, the suppressed region becomes
smaller. At the source-drain bias around 50mV, the conductance of the ribbon is
fully activated.
Figure 3.11 2D plot of Conductance of graphene nanoribbon with width of 60nm as a
function of Vsd and Vbg at T=4.3 K.
A more detailed 2D map of conductance as a function of global gate and
source-drain bias is plot as shown in Fig. 3.11. We obtained the energy scale
sde V of ~ 50 meV for this device. This value of the energy scale in the bias
direction is surprisingly close to the value of intrinsic band-gap of a 60 nm GNR
52
due to quantum confinement (Eg ~ 60 meV), following theoretical estimates
that also include electron-electron interactions87, 88
. However, this must be
interpreted in light of the strong disorder potential seen from the back-gate
dependence. In plasma-etched GNRs, the transport-gap obtained from the 2D
conductance plots can be related to the energy of the smallest charged-puddle
along the length of the GNR86
. The charging energy of this island is typically
governed by the width of the GNR. In case of helium-ion milled GNRs, the
additional lattice damage produces new localized states near the neutrality point
of the energy spectrum. The formation of these mid-gap states is already known
for the case of bulk graphene due to lattice damage or attachment of ad-atoms68,
89. Therefore, an accurate description of the transport-gap for our system needs
a more detailed analysis to account for this additional disorder within the
charged graphene islands.
3.4 Conclusion
In summary, we successfully fabricated suspended and supported graphene
nanoribbons using helium ion lithography. Suspended GNRs were patterned to
widths down to 5nm, while the smallest width for supported GNR was 20 nm.
In addition, supported GNR-FETs with width of 60nm were fabricated and
characterized for transport properties. The disordered energy-scale is strongly
enhanced in our system as suggested by the large back-gate voltage-span of
53
conductance suppression. This behaviour can be explained by the large disorder
induced by the back-scattering of helium ions, which is further confirmed by
Raman mapping.
54
Chapter 4 Thermal Power in Graphene nanoribbon
4.1 Introduction
Thermoelectric properties (TEP) of graphene have been investigated both
theoretically69, 72, 90-93
and experimentally64, 74, 94, 95
. Kim et al.64
discussed
temperature and carrier density dependence of the thermal power in graphene
experimentally in 2009 and found that the linearity of thermopower in
temperatures at fixed doping level can be explained by Mott relation fitting96
.
This suggests a diffusive thermopower in graphene. The maximum value of
thermopower or Seebeck coefficient is around 80μv/K , appeared near the
central neutrality point. Near zero carrier concentration, the observed result of S
explicitly departures from the formula ∝ 1/√𝑛 given by Boltzmann theory
with 𝑛 as the number density of the charge carriers. Hwang et al. have
proposed the electron-hole-puddle model to explain the experimental observed
transport at very low doping. By this model, local carrier density is finite and
total transport coefficients are given by the averages of the semi classical
Boltzmann results in the puddles.
In addition, TEP of high mobility graphene also been experimentally
investigated by Wu et al..94
The Failure of the Mott relation could indicate
importance of the electron-electron interaction in high mobility samples near
CNP.
Different from single layer, the energy band gap opens in a bilayer
55
graphene would lead to an enhancement in thermopower. This has been
predicted theoretically97
. Experiment work has done by Chen et al.98
on a dual
gated bilayer graphene and showed that, inside the gap regime, temperature
linearity will be broken and the optimized value of S achieves at around 100K.
The phenomena in bilayer graphene from band gap opening could occur in
gaped GNR or functional graphene device with the same reason. Theoretical
work predicts a significant enhancement of Seebeck coefficient in
ultra-narrower GNR69, 71
and graphane72
.
The decrease of thermal conductivity and increase of thermoelectrical
power factor make graphene a possible candidate for energy engineering. In our
work, we measured the TEP in graphene nanoribbons. Our samples were
prepared using electron beam lithography combined with plasma etching. The
enhancement of the magnitude of Seebeck coefficient with width of 80nm
compared to two-dimensional graphene stripe indicated that the gap opening in
this particular GNR device do affected the thermal power signal. Moreover, the
change of thermopower as a function of temperature is nonlinearity.
4.2 Sample preparation
4.2.1 Device fabrication
Graphene was mechanically exfoliated and transferred to the SiO2 substrate
as described in chapter 2. Heater and thermometers are defined with standard
56
electron beam lithography (see in chapter 2), followed by Cr/Au(5/35nm)
evaporation and lift off in hot acetone. Fig4.1a displays an optical image of a
graphene thermopower device. For thermal power measurement, at least three
electrodes, two thermometers and one heater, are needed. Electrode 1 is the
heater, and Electrode 2 and 3 are two thermometers. Each of these two
thermometers is connected to 4 wires, so that their resistance can be measured
accurately by 4-probe measurement. Depending on the size of the graphene
flakes, the distance of the thermometers can vary from 2 μm to7 μm, while the
heater is fabricated as close as possible to electrode 2 to generate a temperature
gradient efficiently. The distance usually varies from 700 nm to 1 μm in our
devices. In order to get a uniform thermal distribution perpendicular to the
channel (or along the thermometer electrodes), the length of the heater is
designed larger than the thermometers. Oxygen plasma etching is used to isolate
the graphene flake electrically from the heater. After wire bonding, the device is
loaded in to the chamber of Vacuum system for measurement.
57
Figure 4.1 Optical image of thermal power device, 1 is heater, 2 and 3 is thermometers.
4.2.2 Graphene nanoribbon fabrication
After device fabricating, graphene sheet needs to be further etched to
quasi-one dimensional graphene nanoribbon. We use the plasma etching
method for fabrication GNR in this experiment. This method was considered as
simplest and most economical method and was widely used for fabricating
GNR. The process is described in Fig 4.2. First, a layer of PMMA A5 was
spin-coated on top of graphene sheet. The thickness of the PMMA layer is
around 400nm and quite uniform which make sure of the stable etching result.
Etching pattern is edited and designed by NPGS and Design CAD. The pattern
is later exposed under SEM with critical dose of electron beam (see in Fig 4.2.2).
A little bit over dose will help to get narrower graphene nanoribbon. After
developed (Fig 4.2.3), the sample was transferred into the chamber of Reactive
Ion Etching (RIE), and the unprotected part was etched by O2 plasma.
58
Figure 4.2 Etching process for graphene nanoribbon. 1) PMMA is spin coated on top of
graphene sheet; 2) etching pattern is exposure to electron beam in SEM chamber; 3)
after development, cross section picture shows over dose of etching. 4) exposed part of
graphene is etched by O2 plasma.
4.3 Measurement and the Result
4.3.1 Temperature coefficient of Resistance(TCR) for thermometers
Before the thermopower measurement, the Temperature coefficient of
Resistance (TCR) for the two thermometers is calculated. The TCR is the
relative change of the resistance R of thermometer when the temperature is
changed by 1 Kelvin
R(T) = R(T0)(1 + α∆T)
Where T0 is the reference temperature and ΔT is the difference between T
and T0. Finally, α is the linear temperature coefficient. With this fixed α, we can
calculated the temperature changes when resistance changes, vice versa.
After loading the sample in to Vacuum system, the resistances of the two
59
thermometers are measured with temperature slowly decreasing from 300K to
4K. The curve slot at fixed temperature point is used as α. This figure will be
recorded for calculating the temperature gradient later in thermopower
measurement.
4.3.2 Thermal power in graphene stripe.
We first study the thermal power in two-dimensional graphene sheet. The
optical picture of the device is shown in Fig 4.1. An ac current is applied to
heater 1 to generate a temperature gradient cross the graphene( or along the two
thermometers 2 and 3). Potential difference is then generated because that the
carriers keep moving from the hot side to the cold side. ∆V is measured across
the electrode 2 and 3. With the same applied ac current on the heater, we also
measure the resistance changes of the two thermometers. Combined with the
TCR, temperature difference is calculated. Thus, Seebeck coefficient can be
obtained by the equation: S = ∆V/∆T.
In Fig 4.4, thermopower of graphene stripe with width of 5 μm and length
of 7 μm is measured as a function of V𝑏𝑔 from 15K to 300K. The sign of the S,
which indicates the sign of the majority charge carriers, changes from positive
to negative when across the CNP. Away from CNP, the magnitude of Seebeck
coefficient is slightly decreased with increasing carrier density which is
manipulated by the back gate voltage Vbg. According to the Boltzmann
60
formulation64
, the Seebeck efficient can be considered as the entropy transport
per unit charge97
. This can provide us as a qualitative understanding of the
behavior of graphene thermopower‟s temperature dependence. While the
Fermi level is far away from the Dirac point, the electrons are highly
degenerate and only portions of T/EF transport with entropy. As a result, the
Seebeck coefficient is proportional to the temperature at high carrier densities.
However, close to the charge neutrality point, both electrons and holes exist in
graphene due to the charge inhomogeneity in graphene surface. Contribution
of Seebeck effect from both electrons and holes will cancel each other and the
absolute |S| will decrease as the carrier density decrease. Since the
electron-hole puddle99
exists in almost all the graphene devices near the charge
neutrality, the non-degenerate limit is hard to achieve. In our experiment, the
maximum S at 300K is around 53μv/K .
Figure 4.3 Seebeck coefficient (S) of graphene with width of 5 μm and length of 7 μm
61
as a function of backgate Vbg at temperature 15K, 50K, 100K, 130K,170K, 210K, 250K
and290K.
When ambient temperature decreased, the magnitude of TEP also
decreased. Linearity relationship was found in two-dimension graphene, Fig 4.4
shows that, at a fixed V𝑏𝑔 , the magnitude of S changes linearly with
temperature both near the CNP as well as away from CNP. This can be
explained by famous Mott‟s relation96
which is mathematically derived from
Boltzmann‟s transport equations under the relaxation time or scattering rate
approximation.
Figure 4.4 Seebeck Coefficient of graphene stripe at fixed backgate Vbg at 1v( Red
triangle) and -50V(blue dot)
4.3.3 Thermal power in graphene nanoribbon.
Inset of Fig 4.5 is the optical picture of the GNR device and the AFM
62
picture showing the details of graphene nanoribbon. The width and length of the
GNR is 70nm and 1μm respectively. The resistance of the sample is measured
by standard lock-in method. Around the Dirac point, the resistance of the GNR
shows insulating behavior at low temperatures as shown in Fig. 4.5, which is
consistent with the electrical transport studies of GNR prepared by the same
method. A fitting of the resistance as a function of gate voltage V𝑏𝑔 gives a
mobility of 10505 cm2/vs at room temperature.
Figure 4.5 Resistance of GNR as a function of back gate voltage V𝑏𝑔 at different
temperatures 10K, 50K, 195K, 250K, and 300K. Inset is the optical picture of the device
and AFM picture of the GNR. The scale bar is 500nm
Seebeck coefficient was measured using the same method as bulk graphene.
Fig. 4.7 shows the Seebeck coefficient as a function of gate voltage from 15K to
300K. The sign of the signal changes from positive to negative when across the
CNP, which is the same as bulk graphene. However, there are two major
63
changes of GNR thermal power signal compared with bulk one.
Figure 4.6 Seebeck coefficient S of GNR (W=70nm, L=1μm) as a function of back gate
Vbg at different temperatures 15K, 50K, 200K, 250K, and 300K.
First, the maximum thermal power at each temperature has a large increase
compared to the bulk graphene case. At room temperature, the maximum value
of Seebeck coefficient is 143 μV/K, while the maximum value reaches around
225μV/K at 150K. The opening of a small band gap in GNR might account for
such enhancement.
Second, the maximum thermal power for a specific temperature shows
non-monotonic temperature dependence. As shown in Fig. 4.8, the maximum
thermal power is plotted vs temperatures from 15K to 300K. At low
temperatures, the thermal power increases with temperature increasing, while at
64
high temperature, the thermal power shows opposite trend. This anomalous
trend is likely to originate from the electron-hole puddle in GNR. As is
demonstrated by F. Molitor, et al86, 100
, in graphene nano-ribbon fabricated by
the plasma etching method, electron-holes puddles dominate the electron
transport at low charge carries densities. For high temperature, the thermal
power follows almost 1/T dependence of degenerate semiconductors. While at
low temperature, the carriers are delocalized in puddles, the overall
thermopower greatly decreased due to the cancellation from electron and holes.
The lower the temperature, the localization is expected to be stronger, thus the
smaller the thermopower.
Figure 4.7 Seebeck Coefficient of graphene stripe at fixed backgate Vbg~3V( Red
triangle) and 40V(blue dot)
4.4 Conclusion
65
In this chapter, we study the thermoelectric properties in GNR. Graphene
was prepared by mechanical exfoliated method and etched to GNR by plasma
etching. Seebeck coefficient in GNR with width of 70nm and length of 1μm
was measured as a function of back gate with temperature range from 15K to
300K. An enhancement of thermal power is observed in GNR due to the
opening of energy band gap. The maximum value of thermal power is 225μv/K
and appears at 150K instead of room temperature, which also been found in
dual gated bilayer graphene, indicating an opportunity of low-T thermoelectric
material application. The optimization of thermal power in GNR predicts it
could be a potential material in energy engineering.
66
Chapter 5 Conclusion and outlook
5.1 Thesis summary
Due to its extraordinary mobility and thermal conductivity, graphene has
become one of the candidate materials for the next generation computer
technology. However, the fact that graphene lacks of a band gap in its band
structure limits its further application in semiconductor industry. Graphene
nanoribbon pattering provides a promising method of introducing band gap in
graphene‟s band structure.
This thesis studied the electrical and thermoelectrical properties in
graphene nanoribbon. We fabricated graphene nanoribbons with width ranging
from 5nm to 100nm both for suspended or supported graphene. The suppression
of G near the charge neutrality point suggests the opening of an energy gap,
which makes graphene nanoribbon a potential material in semiconductor field.
In the first part, we introduced the development of the helium ion
lithography method on mechanically exfoliated graphene using helium ion
microscope. Using this method, we successfully fabricated graphene
nanoribbons on suspended and supported substrate. Suspended GNRs were
patterned to widths down to 5nm, while the smallest width for supported GNR
was 20 nm. In addition, supported GNR-FETs with width of 60nm and length of
250nm were fabricated and characterized for electron transport properties. The
disordered energy-scale is strongly enhanced in our system as indicated by the
67
large back-gate voltage-span of conductance suppression. This behavior can be
explained by the large disorder induced by the back-scattering of helium ions,
which is further confirmed by Raman mapping.
In the second part, thermal power of graphene nanoribbon with width of
70nm and length of 1μm has been measured. Graphene nanoribbon was
fabricated using simple and economical plasma etching method to avoid large
disorder. The maximum thermopower signal is around 143μv/K at room
temperature. The enhanced signal may because of the opening of energy band
gap in quasi- one dimensional GNR. Thermopower is further optimized at low
temperature and the maximum value appeared at 150K in our experiment. The
enhancement of thermopower in GNR together with the decreased thermal
conductivity makes GNR as a potential material for energy engineering.
5.2 Future work
Helium ion lithography is a powerful tool to fabricate ultra-narrow
graphene nanoribbon. However, we cannot avoid the damage to graphene due to
the back-scattering of ions. Further work should focus on the fabrication of
suspended GNR-FETs. On one hand, back-scattering of helium ion can be
significantly reduced in the absence of the substrate, which could result in a
defect-free GNR. On the other hand, suspended GNR which exclude the
influence of substrate could in principle reach the intrinsic properties of
68
graphene nano-ribbon, which is useful for fundamental studies in ultra-narrow
GNRs and quantum dot structures.
Moreover, the combination of Helium Ion microscope and NPGS software
enable fabrication of arbitrary shape of graphene structures. Future works could
focus on fabricating triangle shape of graphene flake for thermal rectification
effect study, or graphene super-lattice for two-dimensional phononic crystal
study. All these studies rely on the high-resolution and high controllability of
HIL.
Furthermore, the enhanced thermal power in graphene nanoribbon proved
graphene a potential thermoelectrical material. However, the band gap in
graphene nanoribbon with width of 70nm is not sufficient. Future works can
focuse on investigating GNR device with narrower width. HIL method may
help to fabricate narrower GNR in this case.
69
REFERENCE
1
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V.
Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004). 2
K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S.
V. Morozov, and A. K. Geim, Proceedings of the National Academy of
Sciences of the United States of America 102, 10451 (2005). 3
A. K. Geim and K. S. Novoselov, Nat Mater 6, 183 (2007). 4
M. S. Dresselhaus, A. Jorio, M. Hofmann, G. Dresselhaus, and R. Saito,
Nano Lett. 10, 751 (2010). 5
H. Petroski, The Pencil: A History Of Design and Circumstance
(1989). 6
L. D. Landau, Phys. Z. Sowjetunion 11, 26 (1937). 7
R. E. Peierls, Ann. I. H. Poincare 5, 177 (1935). 8
J. W. McClure, Phys. Rev. 104, 666 (1956). 9
P. R. Wallace, Phys. Rev. 71, 622 (1947). 10
J. C. S. a. P.R.Weiss, Phys. Rev. 109, 272 (1958). 11
S. Stankovich, D. A. Dikin, G. H. B. Dommett, K. M. Kohlhaas, E. J.
Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, Nature
442, 282 (2006). 12
C. R. Dean, et al., Nat Nano 5, 722 (2010). 13
K. S. Novoselov, et al., Science 315, 1379 (2007). 14
Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Nature 438, 201 (2005). 15
A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao,
and C. N. Lau, Nano Lett. 8, 902 (2008). 16
L. Ming-Wei, L. Cheng, Z. Yiyang, Y. Hyeun Joong, C. Mark
Ming-Cheng, A. A. Luis, K. Nicholas, W. Noppi, and Z. Zhixian,
Nanotechnology 22, 265201 (2011). 17
C. M. Jaworski, J. Yang, S. Mack, D. D. Awschalom, J. P. Heremans,
and R. C. Myers, Nat Mater 9, 898. 18
K. Uchida, et al., Nat Mater 9, 894. 19
H. Suzuura and T. Ando, Phys. Rev. B 65, 235412 (2002). 20
K. S. Kim, et al., Nature 457, 706 (2009). 21
M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, Nat Phys 2, 620
(2006). 22
A. K. G. a. H.Macdonald, Pgtsucs Todat 10, 35 (2007). 23
M.Wilson, Physcas Today 59, 21 (2006). 24
M.I.Katsnelson, Materials Today 10, 20 (2007). 25
F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988). 26
L. M. Zhang, Z. Q. Li, D. N. Basov, M. M. Fogler, Z. Hao, and M. C.
70
Martin, Phys. Rev. B 78, 235408 (2008). 27
E. V. Castro, K. S. Novoselov, S. V. Morozov, N. M. R. Peres, J. M. B. L.
dos Santos, J. Nilsson, F. Guinea, A. K. Geim, and A. H. C. Neto, Phys.
Rev. Lett. 99, 216802 (2007). 28
T. Ohta, A. Bostwick, T. Seyller, K. Horn, and E. Rotenberg, Science
313, 951 (2006). 29
R. Hassan and C. K. Edwin, Journal of Physics: Condensed Matter 21,
102202 (2009). 30
S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C.
Elias, J. A. Jaszczak, and A. K. Geim, Phys. Rev. Lett. 100, 016602
(2008). 31
E. A. Henriksen, Z. Jiang, L. C. Tung, M. E. Schwartz, M. Takita, Y. J.
Wang, P. Kim, and H. L. Stormer, Phys. Rev. Lett. 100, 087403 (2008). 32
K. R. Knox, S. Wang, A. Morgante, D. Cvetko, A. Locatelli, T. O.
Mentes, M. A. Niño, P. Kim, and R. M. Osgood, Jr., Phys. Rev. B 78,
201408 (2008). 33
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson,
I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Nature 438, 197
(2005). 34
I. Meric, M. Y. Han, A. F. Young, B. Ozyilmaz, P. Kim, and K. L.
Shepard, Nat Nano 3, 654 (2008). 35
F. Xia, D. B. Farmer, Y.-m. Lin, and P. Avouris, Nano Lett. 10, 715. 36
K. Wakabayashi, M. Fujita, H. Ajiki, and M. Sigrist, Phys. Rev. B 59,
8271 (1999). 37
K. Nakada, M. Fujita, G. Dresselhaus, and M. S. Dresselhaus, Phys. Rev.
B 54, 17954 (1996). 38
S. Adam, S. Cho, M. S. Fuhrer, and S. Das Sarma, Phys. Rev. Lett. 101,
046404 (2008). 39
M. Y. Han, J. C. Brant, and P. Kim, Phys. Rev. Lett. 104, 056801. 40
D. Huang, G. Gumbs, and O. Roslyak, Phys. Rev. B 83, 115405. 41
D. Gunlycke, D. A. Areshkin, J. Li, J. W. Mintmire, and C. T. White,
Nano Lett. 7, 3608 (2007). 42
V. M. Pereira, A. H. Castro Neto, and N. M. R. Peres, Phys. Rev. B 80,
045401 (2009). 43
D. Gunlycke, D. A. Areshkin, and C. T. White, Appl. Phys. Lett. 90,
142104 (2007). 44
J. Fernández-Rossier, J. J. Palacios, and L. Brey, Phys. Rev. B 75,
205441 (2007). 45
E. R. Mucciolo, A. H. Castro Neto, and C. H. Lewenkopf, Phys. Rev. B
79, 075407 (2009). 46
Y.-M. Lin, V. Perebeinos, Z. Chen, and P. Avouris, Phys. Rev. B 78,
161409 (2008).
71
47 Z. Chen, Y.-M. Lin, M. J. Rooks, and P. Avouris, Physica E:
Low-dimensional Systems and Nanostructures 40, 228 (2007). 48
C. Stampfer, uuml, J. ttinger, Hellm, S. ller, F. Molitor, K. Ensslin, and T.
Ihn, Phys. Rev. Lett. 102, 056403 (2009). 49
M. Y. Han, B. Oezyilmaz, Y. Zhang, and P. Kim, Phys. Rev. Lett. 98,
206805 (2007). 50
S. Masubuchi, M. Ono, K. Yoshida, K. Hirakawa, and T. Machida, Appl.
Phys. Lett. 94, 082107 (2009). 51
L. Tapaszto, G. Dobrik, P. Lambin, and L. P. Biro, Nat Nano 3, 397
(2008). 52
L. Jiao, X. Wang, G. Diankov, H. Wang, and H. Dai, Nat Nano 5, 321. 53
L. Jiao, L. Zhang, X. Wang, G. Diankov, and H. Dai, Nature 458, 877
(2009). 54
X. Li, X. Wang, L. Zhang, S. Lee, and H. Dai, Science 319, 1229 (2008). 55
L. C. Campos, V. R. Manfrinato, J. D. Sanchez-Yamagishi, J. Kong, and
P. Jarillo-Herrero, Nano Lett. 9, 2600 (2009). 56
D. C. Bell, M. C. Lemme, L. A. Stern, J. R. Williams, and C. M. Marcus,
Nanotechnology 20, 455301 (2009). 57
M. C. Lemme, D. C. Bell, J. R. Williams, L. A. Stern, B. W. H. Baugher,
P. Jarillo-Herrero, and C. M. Marcus, ACS Nano 3, 2674 (2009). 58
A. I. Hochbaum, R. Chen, R. D. Delgado, W. Liang, E. C. Garnett, M.
Najarian, A. Majumdar, and P. Yang, Nature 451, 163 (2008). 59
K. F. Hsu, S. Loo, F. Guo, W. Chen, J. S. Dyck, C. Uher, T. Hogan, E. K.
Polychroniadis, and M. G. Kanatzidis, Science 303, 818 (2004). 60
T. C. Harman, P. J. Taylor, M. P. Walsh, and B. E. LaForge, Science 297,
2229 (2002). 61
O. Yamashita, S. Tomiyoshi, and K. Makita, Journal of Applied Physics
93, 368 (2003). 62
I. Bejenari and V. Kantser, Phys. Rev. B 78, 115322 (2008). 63
B. Poudel, et al., Science 320, 634 (2008). 64
Y. M. Zuev, W. Chang, and P. Kim, Phys. Rev. Lett. 102, 096807 (2009). 65
K. Saito, J. Nakamura, and A. Natori, Phys. Rev. B 76, 115409 (2007). 66
S. Chen, Q. Wu, C. Mishra, J. Kang, H. Zhang, K. Cho, W. Cai, A. A.
Balandin, and R. S. Ruoff, Nat Mater 11, 203 (2012). 67
S. Chen, et al., ACS Nano 5, 321 (2010). 68
D. C. Elias, et al., Science 323, 610 (2009). 69
Y. Ouyang and J. Guo, Appl. Phys. Lett. 94, 263107 (2009). 70
H. Karamitaheri, N. Neophytou, M. Pourfath, R. Faez, and H. Kosina,
Journal of Applied Physics 111, 054501 (2012). 71
H. Zheng, H. J. Liu, X. J. Tan, H. Y. Lv, L. Pan, J. Shi, and X. F. Tang,
Appl. Phys. Lett. 100, 093104 (2012). 72
X. Ni, G. Liang, J.-S. Wang, and B. Li, Appl. Phys. Lett. 95, 192114
72
(2009). 73
J. O. Sofo, A. S. Chaudhari, and G. D. Barber, Phys. Rev. B 75, 153401
(2007). 74
C.-R. Wang, W.-S. Lu, L. Hao, W.-L. Lee, T.-K. Lee, F. Lin, I. C. Cheng,
and J.-Z. Chen, Phys. Rev. Lett. 107, 186602 (2011). 75
A. C. Ferrari, et al., Phys. Rev. Lett. 97, 187401 (2006). 76
T. M. G. Mohiuddin, et al., Phys. Rev. B 79, 205433 (2009). 77
K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P.
Kim, and H. L. Stormer, Solid State Commun. 146, 351 (2008). 78
J. B. Oostinga, H. B. Heersche, X. Liu, A. F. Morpurgo, and L. M. K.
Vandersypen, Nat Mater 7, 151 (2008). 79
C. H. Lui, Z. Li, K. F. Mak, E. Cappelluti, and T. F. Heinz, Nat Phys 7,
944 (2011). 80
W. Bao, et al., Nat Phys 7, 948 (2011). 81
F. Molitor, A. Jacobsen, C. Stampfer, uuml, J. ttinger, T. Ihn, and K.
Ensslin, Phys. Rev. B 79, 075426 (2009). 82
X. Jia, et al., Science 323, 1701 (2009). 83
J. Bai, X. Duan, and Y. Huang, Nano Lett. 9, 2083 (2009). 84
S. R. Dhakate, N. Chauhan, S. Sharma, and R. B. Mathur, Carbon 49,
4170 (2011). 85
E. H. Hwang and S. Das Sarma, Phys. Rev. B 77, 115449 (2008). 86
F. Molitor and et al., Semiconductor Science and Technology 25,
034002. 87
L. Yang, C.-H. Park, Y.-W. Son, M. L. Cohen, and S. G. Louie, Phys.
Rev. Lett. 99, 186801 (2007). 88
ShimizuT, HaruyamaJ, D. C. Marcano, D. V. Kosinkin, J. M. Tour,
HiroseK, and SuenagaK, Nat Nano 6, 45 (2011). 89
M. I. Katsnelson, F. Guinea, and A. K. Geim, Phys. Rev. B 79, 195426
(2009). 90
L. D. Hicks and M. S. Dresselhaus, Phys. Rev. B 47, 12727 (1993). 91
C.-N. Pan, Z.-X. Xie, L.-M. Tang, and K.-Q. Chen, Appl. Phys. Lett.
101, 103115 (2012). 92
Z.-X. Xie, L.-M. Tang, C.-N. Pan, K.-M. Li, K.-Q. Chen, and W. Duan,
Appl. Phys. Lett. 100, 073105 (2012). 93
X.-Z. Yan, Y. Romiah, and C. S. Ting, Phys. Rev. B 80, 165423 (2009). 94
X. Wu, Y. Hu, M. Ruan, N. K. Madiomanana, C. Berger, and W. A. de
Heer, Appl. Phys. Lett. 99, 133102 (2011). 95
N. Xiao, et al., ACS Nano 5, 2749 (2011). 96
M. C. a. N. F. Mott, Phys. Rev. 181, 1336 (1969). 97
E. H. Hwang, E. Rossi, and S. Das Sarma, Phys. Rev. B 80, 235415
(2009). 98
L. Hao and T. K. Lee, Phys. Rev. B 81, 165445 (2010).
73
99 K. I. Bolotin, K. J. Sikes, J. Hone, H. L. Stormer, and P. Kim, Phys. Rev.
Lett. 101, 096802 (2008). 100
J. Martin, N. Akerman, G. Ulbricht, T. Lohmann, J. H. Smet, K. von
Klitzing, and A. Yacoby, Nat Phys 4, 144 (2008).