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Substrate-induced effects in thermally cycled graphene & electron and thermoelectric transports across 2D material heterostructures
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Substrate-induced effects in thermally cycled graphene & electron and thermoelectric transports across 2D material heterostructures
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i
SUBSTRATE-INDUCED EFFECTS IN THERMALLY CYCLED
GRAPHENE & ELECTRON AND THERMOELECTRIC TRANSPORTS
ACROSS 2D MATERIAL HETEROSTRUCTURES
By
CHEN, CHUN-CHUNG
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
MAY 2015
Copyright 2015 Chen, Chun-Chung
i
Dedication
This thesis is dedicated to my parents and family
for their support
ii
Acknowledgements
I would like to thank my research advisor, Prof. Stephen B. Cronin, for giving me
the opportunity of doing research in his group. I appreciate all his encouragements,
comments and funding to lead me to my achievements in his group.
Thanks to all the members of the Cronin research group, Adam Bushmaker,
Wei-Hsuan Hung, Jesse R. Theiss, Mehmet Aykol, Prathamesh Pavaskar, I-Kai Hsu,
Chia-Chi Chang, Wenbo Hou, Mohammed Amer, Rohan Dhall, Zuwei Liu, Shun-Wen
Chang, Yun-Chiao Huang, Zhen Li, Jing Qiu, Guangtong Zeng, Shermin Arab, Bingya
Hou, Jihan Chen, Nirakar Poudel, and Ioannis Chatzakis. I couldn’t achieve my success
without all the collaboration and discussion with them.
I would also like to thank my friends from other research labs, Haitian Chen,
Ting-Wei Yen for all the research and friendship supports.
Thanks to Dr. Jia Grace Lu, Dr. Chongwu Zhou, Dr. William H. Steier, Dr. and
Dr. Edward Goo for being the committees of my qualification exam.
Thanks to Dr. Kian Kaviani for both financial and research resources supports.
Thanks to Dr. Donghai Zhu for his managements in USC clean-room. Thanks to Shanna
Mitchell, Angelique Miller and Kim Reid for their managements in our research funding.
Lastly, I'd like to thank my parents, my wife, siblings, and all my families.
iii
Table of Contents
Dedication………………………………………………………………………………….i
ii
Acknowledgements………………………………………………………………………..ii
i
List of
Figures……………………………………………………………………………..iii
Abstract…………………………………………………………………………………...
Chapter 1 : Introduction…………………………………………………………………...1
1.1: Electron structure of graphene………………………………………………..2
1.2: Phonon dispersion relations interaction of graphene……………………...….5
1.3: Raman spectroscopy of strain and doping effects in graphene……………….6
1.4: Schottky junction at graphene-silicon interface……………………………..11
1.5: Polymer electrolyte doping in graphene…………………………………….16
1.6: Thermoelectric effects at heterojunction of 2-dimension materials....……...19
Chapter 2: Raman spectroscopy of ripple formation in suspended graphene
2.1: Introduction………………………………………………………...……….24
2.2: Experiment…………………………………………………………….……25
2.3: Conclusion………………………………………...……………………......36
Chapter 3: Raman spectroscopy of substrate-induced effects in thermally cycled
graphene
3.1: Introduction………………………………………………………...……….37
3.2: Experiment…………………………………………………………….……39
3.3: Conclusion………………………………………...……………………......47
Chapter 4: Graphene/silicon Schottky diodes
4.1: Introduction………………………………………………………...……….48
4.2: Experiment…………………………………………………………….……49
4.3: Conclusion………………………………………...……………………......60
Chapter 5: Gate-tunable graphene/silicon Schottky/Ohmic contact
5.1: Introduction………………………………………………………...……….61
5.2: Experiment…………………………………………………………….……63
5.3: Conclusion………………………………………...……………………......70
iv
Chapter 6: Interface thermal conductance across a graphene/hexagonal boron nitride
heterojunction
6.1: Introduction………………………………………………………...……….72
6.2: Experiment…………………………………………………………….……73
6.3: Conclusion………………………………………...……………………......79
Chapter 7: Thermoelectric transport across graphene/hexagonal boron nitride/graphene
heterostructures
7.1: Introduction………………………………………………………...……….81
7.2: Experiment…………………………………………………………….……83
7.3: Conclusion………………………………………...……………………......91
Chapter 8: Future work
Graphene silicon interface future development………………………...……….92
Bibliography……………………………………………………………………………..98
v
List of Figures
Figure 1-1. A top view of the real-space cell of monolayer graphene showing the
inequivalent A and B and the unit vector a
1
and a
2
. (b) The reciprocal space
unit cell showing the first Brillouin zone (BZ) with its high-symmetry points
and lines, such as the T point connecting Γ to ΚΣ connecting Γ to M; and T΄
connecting Κ to M. The two primitive vector, k
x
andk
y
, on the top of the three
hexagons show the reciprocal space coordinate axes………………………..3
Figure 1-2. The band structure of single layer graphene along M ΓKM…………………5
Figure 1-3. Calculated phonon dispersion of graphene, showing the longitudinal (LO)
phonon, in-plane transverse optical (iTO) phonon, out-of-plane transverse
optical (oTO) phonon, and corresponding acoustic phonon, LA, iTA,
oTA…………………………………………………………………………..6
Figure 1-4. Strain-induced phonon softening in graphene. (a, b) Evolution of the spectra
of the 2D Strain-induced phonon softening in graphene. (a, b) Evolution of
the spectra of the 2D (a) and G (b) bands of graphene under strain. The
spectra of the 2D band and the first 2 spectra of the G band are fit by single
Lorentz peaks; the other G band spectra are fit by 2 lorentz peaks of fixed
width 16 cm
-1
(smooth overlapping curves). (c) The variation of the phonon
frequencies of 2D, G
+
and G
-
bands from (a) and (b) as a function of strain.
The solid lines are linear fits………………………………………………….8
Figure 1-5. Raman spectroscopy of the G and 2D lines of charged graphene. (a) and (b)
show two-dimensional maps of the G and 2D lines, respectively, as function
of applied back gate voltages. Both plots are peak height normalized. (c)
Shows the G line peak shift [extracted from (a) as function of the induced
carrier concentration. Dashed lines show theoretical expectations for finite
temperature. (d) Same for the 2D peak shift. The same relative frequency
scale as in (c) is used, indicated by the horizontal scale bars (1 cm
-1
/ phonon)
…………………...…………………………………………………………..10
Figure 1-6. Raman spectra of graphene as a function of gate voltage. (a) Raman spectra
at values of V
TG
between 22.2 V and þ4.0 V. The dots are the experimental
data, the black lines are fitted lorentzians, and the red line corresponds to the
Dirac point. The G peak is on the left and the 2D peak is on the right. (b),
Position of the G peak (Pos(G)); top panel) and its FWHM (FWHM(G);
bottom panel) as a function of electron and hole doping. The solid blue lines
are the predicted non-adiabatic trends from ref. 16. (c) Position of the 2D
peak (Pos(2D)) as a function of doping. The solid line is our adiabatic DFT
vi
calculation……………………………………………………………….......11
Figure 1-7. (a) Energy band diagram of graphene and n-, p-type silicon before contact. (b)
Energy band diagram of graphene-n-type silicon junction…………………12
Figure 1-8. Energy band diagram of graphene-n-type silicon junction under (a) reverse
bias, and (b) forward bias………………………………………………...…13
Figure 1-8. Energy band diagram of graphene-n-type silicon junction under (a) reverse
bias, and (b) forward bias…………………………………………………...14
Figure 1-10. Photovoltaic characterizations of graphene/n-Si solar cells. (a) Energy
diagram of the forward-bias upon illumination. Ф
G
(4.8 ~ 5.0 eV) , Ф
n-Si
(4.24 eV) is the work function of graphene and n-Si respectively. V
0
is the
build-in potential, Ф
b
is the barrier height, χ is the electron affinity of silicon
(4.05 eV). E
g
is the bandgap of silicon (1.12 eV) and E
F
is the energy of the
Fermi level. V
bias
is the applied voltage. The depth of the Fermi level below
the Si conduction band edge (E
C
– E
v
) is ~0.25 eVfor the n-Si used in this
work. (b) Semilogarhythmic-scale dark I-V curves of two graphene/n-Si
cells of different junction areas. The ideality factor (n) and the series
resistance (R
s
) of the 0.1 cm
2
cell extrapolated from the linear regimes in
the insets are 1.67 and 10.5 Ω, respectively. The shunt resistance is up to 45
MΩ which is estimated from reverse bias I-V sweep. (c) Light J-V curves of
the cells illuminated with simulated AM 1.5 Global light. (D) Light-
intensity-dependence short circuit current density (J
sc
), open circuit voltage
(V
oc
), fill factor (FF), and solar energy conversion efficiency (η) plots of a
0.1 cm
2
graphene/ n-Si cell………………………………………………..15
Figure 1-11. Electrochemically top-gated graphene transistor. (a) Schematic diagram of
the experimental setup. The black dotted box between the drain and source
indicates the thin layer of polymer electrolyte (PEO + LiClO
4
), and the blue
stripe between the electrodes represents the graphene sample. Thleft inset
shows the optical image of a single-layer graphene connected between
source and drain gold electrodes. Scale bar: 5 µm. The right inset is a
schematic illustration of polymer electrolyte to gating, with Li
+
(magenta)
and ClO
4
¯
(cyan) ions and the Debye layers near each electrod. (b) I
SD
as a
function of top-gate voltage (V
TG
). The inset shows the I
SD
time
dependence at fixed V
TG.
The dotted line corresponds to the Dirac point
(change neutrality point). (c) I
SD
versus V
SD
at different top-gate voltages.
The black dotted line corresponds to the value of V
DS
at which the data in
Fig 1-11(b) was measured………………………………………………….17
Figure 1-12. Graphene Fermi energy plotted as a function of gate voltage. The gray dash
lines indicate the conduction and valance band energy of silicon………....18
vii
Figure 1-13. Experimental thermal interface conductance (G
i
) versus temperature for a
3.0 nm-thick-FLG/SiO
2
interface reported by Chen et al[22]. FLG/SiO
2
interface reported by Mak et al[23]. HOPG/Ti/Al (filled circles) and
HOPG/Au (open circles) interfaces reported by Schmidt et al[24]. a SLG/Au
interface reported by Cai et al[25]. a Au/Ti/three-layer graphene/SiO
2
stack
reported by Koh et al[26]. and a diamom/Au interface reported by Stoner
and Maris…………………………………………………………………..20
Figure 1-14. Graphene field-effect tunneling transistor. (A) Schematic structure of the
experiment device. In the most basic version of the FET, only graphene
electrode (Gr
B
) is essential, and the outside electrode can be made from a
metal. (B) The corresponding band structure with no gate voltage applied.
(C) The same band structure for a finite gate voltage V
g
and zero V
b
. (D)
Both V
g
and V
b
are finite. The cones illustrate graphene’s Dirac-like
spectrum and, for simplicity, we consider the tunnel barrier for electrons...21
Figure 1-15. Tunneling characteristics for a graphene-hBN device with 6 ± 1 layers of
hBN as the tunnel barrier. (A) I-Vs for different V
g
(in 10-V steps). Because
of finite doping, the minimum tunneling conductivity is achieved at ≈ 3V.
The inset compares the experimental I-V at V
g
= 5 V (red curve) with theory
(dark), which takes into account the linear DOS in the two graphene layers
and assumes no momentum conservation. Further examples of experimental
curves and their fitting can be found in the supporting material. (B) Zero-
bias conductivity as a function of V
g
. The symbols are experimental data,
and the solid curve is the modeling. The curve is slightly shifted with
respect to zero V
g
because of remnant chemical doping. In all the
calculations, they assumed the hole tunneling with m = 0.5 m
0
and Δ ≈ 1.5
eV[30,31] and used d as measured by atomic force microscopy. Both I
and σ are normalized per tunnel area, which was typically 10 to 100 µm
2
for the studied devices. Temperature, 240K………………...……………22
Figure 1-16. Trade-off between electrical conductivity (σ), Seebeck coefficient (S), and
thermal conductivity (κ) that involves increasing the number of free carriers
from insulators to metals…………………………………………………..23
Figure 2-1. (a) Optical microscope image of a graphene single layer suspended over a 3
µm trench. (b) Spatial mapping of the G band Raman shift taken
perpendicular to the trench before and after thermal cycling to 700K….…27
Figure 2-2. Atomic force microscope (a) image and (b) cross-sectional analyses of the
suspended graphene single layer shown in Figure 1 (a) before and (b) before
and after thermal cycling to 700K……………………………………….…29
viii
Figure 2-3. Raman spatial maps taken during (a) heat-up to 650K and (b) cool-down
from 700K…………………………………………………………………..31
Figure 2-4. (a) Difference between the average G band Raman shift of the suspended and
substrate regions and estimated biaxial compression taken during thermal
cycling. (b) Raman upshift between the substrate and suspended regions
plotted as a function of graphene thickness………………………………...33
Figure 3-1. Optical image of single layer graphene (SLG1)…………………………….39
Figure 3-2. (a) G band and (b) 2D band Raman data of single layer graphene taken
during the first thermal cycling………………………………………….….41
Figure 3-3. (a) G band and (b) 2D band Raman data of single layer graphene taken
during the second thermal cycling. ………………………………………...42
Figure 3-4. (a) AFM height profile of suspended triple layer graphene before and after
the thermal cycling. (b) Spatially-mapped Raman spectral data of the triple
layer graphene before and after thermal cycling. (c) Optical microscope
image of the triple layer suspended graphene sample……………………...43
Figure 3-5. (a) Spatially-mapped Raman spectral data and (b) AFM height profile of the
bilayer graphene show in Figure 4 before and after the second thermal
cycling to 700K…………………………………………………………..…43
Figure 3-6. (a) G band and (b) 2D band Raman data of single layer graphene taken
during three thermal cycles to 500K, 600K, and 700K…………………….44
Figure 3-7. Raman intensity ratio of the 2D and G bands taken during the first and
second thermal cycles…………………………………………………...….45
Figure 4-1. (a) Schematic diagram, (b) optical micrograph, and (c) SEM image of a
graphene on n-type silicon Schottky diode…………………………………51
Figure 4-2. Current-voltage characteristics of a graphene on n-Si device with and without
illumination. The inset figure shows current on a log scale……………….52
Figure 4-3. Current-voltage characteristics of a graphene on p-Si Schottky diode with
and without illumination. Inset shows the enlarged dark current-voltage
characteristics…………………………………………………………….…53
Figure 4-4. (a) Optical microscope image of a graphene flake and gold electrode. (b)
Short-circuit photocurrent spatial map. (c) Short-circuit photocurrent along
the X-axis of the short-circuit photocurrent map in (b)…………………….54
ix
Figure 4-5. Current-voltage characteristics measured at T = 100 K, 300 K, and 400 K for
(a) an n-Si device and (b) a p-Si device. The inset figures show current on a
log scale……………………………………………………………………..55
Figure 4-6. Current-voltage characteristics of a graphene on p-Si Schottky diode before
and after vacuum annealing…………………………………………….…..59
Figure 5-1. (a) Optical microscope image of the graphene-on-silicon device before
depositing the electrolyte top gate, and (b) schematic diagram of the device
structure……………………………………………………………………..64
Figure 5-2. I-V
bias
characteristics taken at different gate voltages of (a) graphene-Si (p-
type) and (b) graphene-Si (n-type) devices. The inset figures show the I-V
characteristics at V
G
= 0V………………………………………………...…65
Figure 5-3. Low bias conductance plotted as a function of graphene Fermi energy for (a)
graphene-Si (p-type) and (b) graphene-Si (n-type) devices. The right and left
solid vertical lines represent the conduction and valence bands of silicon, and
the middle dashed line represents the Fermi energy of silicon…………..…66
Figure 5-4. Both experimental and modeling normalized low bias conductance plotted as
a function of graphene Fermi energy for (a) graphene-Si (p-type) and (b)
graphene-Si (n-type) devices. The right and left solid vertical lines represent
the conduction and valence bands of silicon, and the middle dashed line
represents the Fermi energy of silicon…………………………………...…69
Figure 5-5. (a) Graphene-silicon I-V
bias
characteristics taken under illumination at
different gate voltages. (b) Short circuit current (I
sc
) with and without
illumination plotted as a function of graphene Fermi energy………………70
Figure 6-1. (a) Optical imageand (b) schematic diagram of the graphene/h-BN device
and experiment setup……………………………………………………….75
Figure 6-2. Raman frequency shifts of the (a) G and (b) 2D bands of the graphene, and (c)
h-BN optical phonon mode plotted as a function of the electrical heating
power………………………………………………………………………..76
Figure 6-3. Temperature calibration of the Raman frequency shifts of the (a) G and (b)
2D bands of the graphene, and (c) h-BN optical phonon mode plotted as a
function of temperature……………………………………………………..77
Figure 6-4. Temperature of the graphene and h-BN calibrated with Gand 2D bands and
BN optical phonon Raman frequencies during the (a) first and (b) second
electrical heating……………………………………………………………77
Figure 6-5. Temperature difference across the interface of graphene/h-BN calibrated
with 2D, G bands and BN optical phonon Raman frequencies of the (a) first
x
and (b) second electrical heating……………………………………………79
Figure 7-1. (a) Optical image and (b) schematic diagram of the graphene/h-
BN/graphene/Al
2
O
3
heterostructure device and measurement setup……….84
Figure 7-2. In-plane and cross-plane I-V characteristics of the bottom and top graphene
strips of the heterostructure, the inset figure plots the cross-plane I-V
characteristics with the unit of nA…………………………………………..85
Figure 7-3. The 200 and 400 Hz thermoelectric voltages across the
graphene/BN/graphene heterostructure as a function of the applied 100 and
200 Hz AC voltages together with the corresponding DC voltages measured
at top graphene temperature (right axis)………………...………………….85
Figure 7-4. (a) Optical image indicating the locations of Raman spectrum taken near the
heterojunction. (b) Temperature of the graphene at the indicated location
with respect to the applied voltage……………………………………….…86
Figure 7-5. (a) Optical image indicating the locations of Raman spectrum taken near the
heterojunction. Raman 2D band frequencies as functions of the applied
voltage taken at (b) point 1, (c) point 2 for the top graphene, and (d) point 3
for the bottom graphene………………………………………………….....87
Figure 7-6. Temperature coefficient of the Raman 2D band frequency for the top
graphene at (a) point 1, and (b) point 2………………………………….…87
Figure 7-7. (a) The 200, and (b) 400 Hz thermoelectric voltage as a function of the
maximum possible temperature drop (∆T) across the heterostructure……..89
Figure 7-8. Temperature coefficient as a function of the applied power of the graphene/h-
BN/graphene heterostructure……………………………………………….90
Figure 8-1. (a) XPS spectra of the pristine and the N-doped graphene. (b) XPS C 1s
spectrum and (c) XPS N 1s spectrum of the N-doped graphene. The C 1s
peak can be split to three Lorentzian peaks at 284.8, 285.8, and 287.5 eV,
which are labeled by red, green, and blue dashed lines. The N 1s peak can be
split to three Lorentian peaks at 401.7, 400.1, and 398.2 eV, which are
labeled by red, green, and blue dashed lines. (d) Schematic representation of
the N-doped graphene. The blun, red, green, and yellow spheres represent
the C, “graphitic” N, “pyridinic” N, and “pyrrolic” N atoms in the N-doped
graphene, respectively[205]………………………………………………...93
Figure 8-2. Electrical properities of the N-doped graphene. (a) SEM image of an
example of the N-doped graphene device. (b) Bird’s-eye view of a schematic
device configuration. (c) and (d) I
ds
/ I
ds
characteristics at various V
g
for the
xi
pristine graphene and the N-doped graphene FET device, respectively, The
insets are the presumed band structures. (e) Transfer characterictics of the
pristine graphene (V
ds
at -0.5 V) and the N-doped graphene (V
ds
at 0.5 and 1.0
V)[205]……………………………………………………………………....94
Figure 8-3. (a) Schematic diagram of CVD growth of boron-doped graphene on Cu
surface with phenyboronic acid as the carbon and boron sources. The red,
grey, yellow, and green spheres represent boron, caebon, oxygen and
hydrogen atoms, respectively. (b) Optical micrograph of a monolayer boron-
doped graphene transferred onto SiO
2
/Si substrate. The arrow points to blank
SiO
2
/Si substrate. (c) SEM image of the boron-doped graphene film
transferred onto SiO
2
/Si substrate[206]………………………………….…95
Figure 8-3. (d) AFM image of the region pointed by black arrow in panel (b) with a z-
scale of 20 nm. (e) Histogram of thickness distribution from AFM height
images. (f) Contrast enhanced photograph of the B-doped graphene sample
on 4-inch SiO
2
/Si substrate. (g) UV-vis transmittance spectra of the boron-
doped graphene and the reference intrinsic graphene on quartz substrate. The
intrinsic graphene monolayer was CVD grown on copper using methane and
then transferred on the quartz substrate. Inset: the photograph of boron-
doped graphene monolayer on a quartz substrate[206]…………………….96
Figure 8-4. (a) Typical Raman spectra of the boron-doped (red) and intrinsic (black)
graphene transferred on SiO
2
/Si substrate by dry transfer procedure. (b)
Optical micrograph of a boron-doped graphene device. (c) Raman map of D
band intensity the channel region of the boron-doped graphene device shown
in (b). (d) Source-drain current (I
ds
) vs back gate voltage (V
g
) with V
ds
= 0.1
V of the boron-doped (red) and intrinsic (black) graphene device,
respectively[206]…….………………………………...……………………97
xii
xiii
Abstract
This dissertation discusses the Raman spectroscopy of substrate-induced effects
on graphene and electron transport at graphene-silicon interface. In the chapter 2 and 3,
the discussion will be focused on Raman spectroscopy of thermally cycled graphene,
which analysis the substrate-induced effects on graphene during the thermal cycling
process by the Raman datataken before, during, and after the thermal cycling. The
substrate-supported and suspended graphene samples are studied in the experiment, and
demonstrate different Raman signal shifting. Both Raman G and 2D bands of the
graphene show significant upshifts of after the thermal cycling, which indicate the
compression and doping effects on graphene induced from the mismatch of the thermal
expansion coefficients and the trapped charge transferring between graphene and the
supported SiO
2
substrate. Uniform ripples are also observed in suspended graphene, after
the thermal cycling, while similar Raman frequencies shifting in the suspended graphene
are not observed. The electron transports at graphene-silicon interface will be presented
in chapter 4 and 5, which demonstrates the formation of Schottky barrier with energy
barrier height of 0.41 eV on n-type silicon and 0.45 eV on p-type silicon at the room
temperature at graphene-silicon interface due to the energy difference between graphene
Fermi energy and silicon electron affinity. This energy mismatch can be tuned to
eliminate the Schottky barrier and result in Ohmic contact at graphene-silicon interface
by using electrolyte chemical doping, which shifts graphene Fermi energy to match the
conduction or valance bands of silicon. The experimental data proves the reducing of the
Schottky barrier height and the observations of low bias conductance and short circuit
photocurrent at graphene-silicon interface reveal the evolution of the graphene-silicon
xiv
interface and corroborate the Ohmic contact at the interface. Also, a model of electron
transports at graphene-silicon interface is presented, which simulates electron transports
at graphene-silicon interface based on electron distributions, density of states, the
Schottky barrier, and electron tunneling effects in both graphene and silicon to estimate
the low bias conductance variation with respect to the graphene Fermi energy shifting. In
addition to graphene, a heterostructure of graphene with another 2D material stack,
hexagonal boron nitride (h-BN), will be discussed in chapter 6 and 7, including the
investigations of interface thermal conductance and thermoelectric effects at the
graphene/h-BN heterostructures.
1
Chapter 1
Introduction
Graphene is a two-dimensional material with only one layer of carbon atom. It has
been attracting engineers and scientists’ interests since its first discovery in 2004[1], due
to its superior electron mobility which ranges from 2000 to 30,000 cm
2
V
-1
s
-1
for substrate
supported graphene and can be as high as 230,000 cm
2
V
-1
s
-1
for free standing suspended
graphene[2, 3], unusual stiffness, which is able to sustain up to 10% of strain[4], and high
electric current carrying capacity (< 10
8
A/cm
2
). The carrier type and concentration of
graphene can be modulated simply by applying electric field effects[5]. The low electron
scattering also allows the observation of quantum hall effect on graphene in room
temperature[6]. These superior electrical and mechanical properties of graphene make it
the candidate for the next-generation field effect transistor and transparent conductor
material. Moreover, in contrast to carbon nanotube, graphene has the advantages over
carbon nanotubes of being naturally compatible with thin film processing, enabling large
device areas and high operating powers. Also, graphene is more readily scalable and has
lower contact resistance.In addition to exfoliating graphene from graphite, graphene can
also be synthesized by using chemical vapor deposition (CVD) on Cu, Ni or other metal
substrates. Silicon carbide has also been used as a substrate to synthesize graphene. These
epitaxially synthesized graphene solves the size limitation and increases the application
of graphene[7].
2
1.1 Electron structure of graphene
The single layer graphene is a network of carbon atoms bonded with sp2
hybridizations to form hexagonal lattice structures. The strong covalent bonds bond
carbon atoms with 120
o
angle to form a planar one atom thick carbon sheet, which
determinate the thermal and mechanical properties of graphene,whiletheπ bondsweakly
bond the out of plan electrons and allow electrons to hop between carbon atoms, which
determinate the electron transport properties of graphene.The unit cell of single layer
graphene includes two carbon atoms, A and B, as shown in Figure 1-1, the lattice vector
can be repressed as:
𝑎
!
=
𝑎
2
3𝑥 +𝑦 ,𝑎
!
=
𝑎
2
3𝑥 −𝑦
Where a = 2.46 is lattice parameter, which is derived from the distance of carbon-
carbon atoms, 1.42, of graphite, and the reciprocal lattice vector, b
1
and b
2
, of the first
Brillouin zone in graphene are given by:
𝑏
!
=
2𝜋
𝑎
3
3
𝑘
!
+𝑘
!
,𝑏
!
=
2𝜋
𝑎
− 3
3
𝑘
!
−𝑘
!
𝑘
!
and 𝑘
!
are the directions of the reciprocal vector as shown in Figure 1-1 (b).
The graphene Brillouin zone corners, K and Ḱ with coordinates of (0,
!!
!!
𝑘
!
), and (0, -
!!
!!
𝑘
!
), are called Dirac points, where the bottom ofconduction band touches the top of
valence band, and result in zero energy gap in graphene[8, 9].
3
(a) (b)
The electron structure of single layer graphenecan be calculated by tight binding
approach. According to the tight binding model of single layer graphene, which limits the
interactions between carbon atoms to A-A, A-B, B-A, and B-B, constructed by Partoens
et el, the tight-bindingBloch functions of carbon atom A, and B can be constructed and
expressed as:
𝜓
!
!
𝑟 =
!
!
𝜙
!
𝑟−𝑟
!
exp 𝑖𝑘 ⋅𝑟
!
,
𝜓
!
!
𝑟 =
!
!
𝜙
!
𝑟−𝑟
!
exp 𝑖𝑘 ⋅𝑟
!
.
𝜙
!
and 𝜙
!
are the wave function of carbon atoms A, and B, N is the number of
unit cells, which is 1 for single layer graphene, and the eigenfunction can then be written
as:
Ψ
!
𝑟 = 𝑐
!
𝜓
!
!
𝑟 +𝑐
!
𝜓
!
!
𝑟
The tight-binding Hamiltonian for single layer graphene to be:
ℋ=
𝜓
!
!
|𝐻|𝜓
!
!
𝜓
!
!
|𝐻|𝜓
!
!
𝜓
!
!
|𝐻|𝜓
!
!
𝜓
!
!
|𝐻|𝜓
!
!
Figure 1-1. (a) A top view of the real-space cell of monolayer graphene showing the
inequivalent A and B and the unit vector a
1
and a
2
. (b) The reciprocal space unit cell showing
the first Brillouin zone (BZ) with its high-symmetry points and lines, such as the T point
connecting Γ to ΚΣ connecting Γ to M; and T΄ connecting Κ to M. The two primitive vector,
k
x
andk
y
, on the top of the three hexagons show the reciprocal space coordinate axes[8].
4
Where 𝜓
!
!
|𝐻|𝜓
!
!
, and 𝜓
!
!
|𝐻|𝜓
!
!
equal 0, due to the missing of inter-atom
transferring and the electron transferring between carbon atom A and B, 𝜓
!
!
|𝐻|𝜓
!
!
, and
𝜓
!
!
|𝐻|𝜓
!
!
, can be written as:
𝜓
!
!
𝐻𝜓
!
!
= 𝜙
!
∗
𝑟−𝑟
!
×𝐻 𝑒
!!⋅!
!"
!
!
!!!
𝜙
!
𝑟−𝑟
!
−𝑅
!"
!
𝑑𝑟 = 𝛾
!
!
𝑓 𝑘
Here
𝑅
!"
!
=𝑎
!
!
𝑘
!
, 𝑅
!"
!
=𝑎 −
!
! !
𝑘
!
+
!
!
𝑘
!
, and 𝑅
!"
!
=𝑎 −
!
! !
𝑘
!
−
!
!
𝑘
!
The tight binding Hamiltonian of single layer graphene can be then simplified and
expressed as:
ℋ=
0 𝛾
!
!
𝑓(𝑘)
𝛾
!
!
𝑓
∗
(𝑘) 0
Where 𝑓 𝑘 = 𝑒
!!
!
!
!
+ 2𝑒
!!!
!
!
! !
cos(𝑘
!
!
!
) , and 𝛾
!
!
is the parameter of
energy integral for electron transferring between a carbon atom to it’s nearest neighbor,
which ~ 3.0eV[10].
The band structure of single layer graphene is shown in Figure 1-2, which
indicates the zero energy gap at Dirac points, and the band structure near the Dirac point
can be expressed by a linear dispersion, 𝐸 k =
!
!
𝛾
!
!
𝑎k = ℏv
!
k, where k is the
electron wave vector, and v
!
is the Fermi velocity of graphene(~ 1×10
6
m/s). The linear
dispersion also causes the symmetry trigonal cone’s band structure near the Dirac points
due to the trigonal warping effect.
5
1.2 Phonon dispersion relations interaction of graphene
The unit cell of single layer grapheneis constructed by two carbon atoms as
shown in Figure 1-1, which leads to six phonon branches, including one out-of-plane
(o)optical phonon (O),oneout-of-plane acoustic phonon (A), two in-plane optical (i)
phonons, and two in-plane acoustic phonons. For the out-of-plane phonon mode, the
vibrations of atom are perpendicular to the graphene plane, while the in-plane phonon
mode is the atom vibrating in the direction parallel to the graphene plane. The phonon
modes can also be further classified as longitudinal (L) or transverse (T) modes, which
depend on the atomic vibrating parallel or perpendicular to the direction of carbon-carbon
atoms in the unit cell. Figure 1-3 shows the total six-phonon modes of single layer
graphene, which are out-of-plane optical transverse phonon (oTO), in-plane optical
transverse phonon (iTO), in-plane optical longitudinal phonon (iLO), out-of-plane
acoustic transverse phonon (oTA), in-plane acoustic transverse phonon (iTA), and in-
Figure 1-2. The band structure of single layer graphene along M ΓKM
[10].
6
plane acoustic longitudinal phonon (iLA). The iTO and iLO modes are Raman active
modes and degenerate near the Brillouin zone center (Γ point), which allow the photon-
induced electron-phonon interaction in graphene[9]
[11].
1.3 Raman spectroscopy of strain and doping effects in graphene
Raman spectroscopy is an optical, noncontact, and damage free tool for
characterizing graphene, it can identify the number of graphene layers, calibrate the strain
or compression, detect the temperature variation, and evaluate the doping level on
graphene. The Raman scattering is a photon scattered inelastically by a crystal and
creating or annihilating a phonon. The first-order Raman effect can be expressed as
𝜔 = 𝜔
!
± Ω, where 𝜔, is the incident photon frequency, 𝜔′ is the scattered photon
frequency, and Ω is the phonon frequency created or destroyed in the scattering process.
Figure 1-3. Calculated phonon dispersion of graphene, showing the longitudinal (LO)
phonon, in-plane transverse optical (iTO) phonon, out-of-plane transverse optical (oTO)
phonon, and corresponding acoustic phonon, LA, iTA, oTA (phonon branches adapted
from [11]).
7
The photon with 𝜔
!
− Ω is called the Stokes, and 𝜔
!
+ Ω is the anti-Stokes. For the
second-order Raman scattering, two phonons are involved in the inelastic scattering
process.There are several bands in the Raman spectroscopy of graphene, as shown in the
Figure 2.Here we focus on the Raman G band and 2D band for the observation of the
temperature, strain and doping effects in graphene. The Raman G and 2D bands,which
appear at 1582 and 2650 cm
-1
, are the first and second order resonance Raman scattering.
Both Raman G and 2D band frequencies are very sensitive to the variation of temperature,
strain, and carrier concentration in graphene, and therefore make the Raman spectroscopy
a great tool of studying the electrical and mechanical properties of graphene.
The strain effects in graphene cause the crystal compressed or stretch out of its
equilibrium. The presence of the strain in graphene will result in the phonon softening
and the opposite for the presence of compression, and therefore, cause the Raman
frequency of graphene downshifting or up-shifting. Moreover, the Raman G band splits
into two G
+
and G
ˉ
bands as the crystal equilibrium of graphene is significantly stretched
by straining, while the 2D band still maintains a single band. The Raman G band
frequency under strain can be expressed as:
𝐴𝜀
!!
+𝐵𝜀
!!
−𝜆 (𝐴−𝐵)𝜀
!"
(𝐴−𝐵)𝜀
!"
𝐵𝜀
!!
+𝐴𝜀
!!
−𝜆
= 0
Where 𝜆 = 𝜔
!
−𝜔
!
!
, 𝜔 and 𝜔
!
are the G band frequencies with and without strain
perturbations,𝐴 and 𝐵 are phonon deformation potential coefficients, and𝜀
!"
is the strain
tensor. Here the strain tensors can be reduced to 𝜀
!!
= 𝜀, 𝜀
!!
= 𝜐𝜀, and 𝜀
!"
= 0.
8
𝜀and𝑥 are the magnitude and direction of the applied strain, and 𝑣= 0.16 is the Poission
ratio, which described the graphene strip under uniaxial stress without constraining its
lateral boundary. Because the G band frequency shift is small, 𝜆 = 𝜔
!
−𝜔
!
!
≈
2𝜔
!
(𝜔−𝜔
!
), and the G
+
and G
ˉ
band frequencies can be expressed as:
𝜔
!
!=𝜔
!
+
𝐵−𝑣𝐴
2𝜔
!
𝜀
𝜔
!
!=𝜔
!
+
𝐴−𝑣𝐵
2𝜔
!
𝜀
According to the experimental observations form Huang et el, shown in Figure 1-
4, the strain coefficients for 2D, G
-
, and G
+
bands are −21±4.2 𝑐𝑚
!!
/%, −12.5±
2.6 𝑐𝑚
!!
/%, and −5.6±1.2 𝑐𝑚
!!
/%, which lead to the potential coefficients 𝐴 and B
Figure 1-4. Strain-induced phonon
softening in graphene. (a, b) Evolution of
the spectra of the 2D (a) and G (b) bands of
graphene under strain. The spectra of the
2D band and the first 2 spectra of the G
band are fit by single Lorentz peaks; the
other G band spectra are fit by 2 lorentz
peaks of fixed width 16 cm
-1
(smooth
overlapping curves). (c) The variation of the
phonon frequencies of 2D, G
+
and G
-
bands
from (a) and (b) as a function of strain. The
solid lines are linear fits[12].
(a)
(b)
(c)
9
to be −4.4±0.8×10
!
𝑐𝑚
!!
and −2.5±0.5×10
!
𝑐𝑚
!!
for the Raman G band
frequency[12].
In addition to the strain, Raman spectroscopy is also a perfect tool for monitoring
carrier concentration in graphene. The change of carrier concentration in graphene will
result in phonon stiffening, and causing frequency up-shifting in both Raman G and 2D
bands, as shown in Figure 1-5, the G and 2D band frequencies show up-shifting for both
n- and p-type doping[13]. However, when the doping is significantly increased, the 2D
band shows phonon stiffening for hole doping and softening for electron doping, while
the G band still shows phonon stiffening for both electron and hole doping.The previous
work reported by Das et el has observed a large 2D band phonon softening and causing
the frequency downshift when the graphene Fermi energy is shifted over 500 meV (n-
doping) from its charge neutrality point,as shown in Figure 1-6[5].
10
Figure 1-5. Raman spectroscopy of the G and 2D lines of charged graphene. (a) and (b) show
two-dimensional maps of the G and 2D lines, respectively, as function of applied back gate
voltages. Both plots are peak height normalized. (c) Shows the G line peak shift [extracted
from (a) as function of the induced carrier concentration. Dashed lines show theoretical
expectations for finite temperature]. (d) Same for the 2D peak shift. The same relative
frequency scale as in (c) is used, indicated by the horizontal scale bars (1 cm
-1
/phonon)[13].
11
1.4 Schottky junction at graphene-silicon interface
Figure 1-7 (a) shows the energy diagram of graphene and silicon. The vacuum
level is the reference level, φ
G
is the graphene work function, which is -4.6 eV, χ is the
Figure 1-6. Raman spectra of graphene as a function of gate voltage. (a) Raman spectra at
values of V
TG
between 22.2 V and þ4.0 V. The dots are the experimental data, the black lines
are fitted lorentzians, and the red line corresponds to the Dirac point. The G peak is on the left
and the 2D peak is on the right. (b), Position of the G peak (Pos(G)); top panel) and its FWHM
(FWHM(G); bottom panel) as a function of electron and hole doping. The solid blue lines are
the predicted non-adiabatic trends from ref. 16. (c) Position of the 2D peak (Pos(2D)) as a
function of doping. The solid line is our adiabatic DFT calculation[5].
12
silicon electron affinity, 4.01 eV. The energy mismatch between graphene and silicon
will result in a Schottky barrier at the interface, Figure 1-7 (b) shows the energy diagram
after graphene is in contact with n-type silicon, where W is the depletion width, φ
GS
is the
Schottky barrier, and V
bi
is the build-in potential barrier at the interface.
The Schottky barrier can be expressed as:
𝜑
!"
= 𝜑
!
− 𝜒
Vacuum level
-4.6 eV
χ
φ
G
E
F
(n-Si)
E
V
: -5.13eV
Graphene
p/n-Si
E
C
: -4.01eV
E
F
(p-Si)
Figure 1-7. (a) Energy band diagram of graphene and n-, p-type silicon before contact. (b)
Energy band diagram of graphene-n-type silicon junction.
(b)
(a)
13
And the build-in potential barrier is:
𝑉
!"
= 𝜑
!"
−𝜑
!
Which indicates that 𝑉
!"
is a function of the carrier concentration in silicon.
Where 𝑉
!"
is the energy barrier for electron to transport from silicon to graphene,
if a positive voltage is applied to the silicon with respect to the graphene, reverse bias, V
R
,
the barrier height, from silicon to graphene, will increase, as shown in Figure 1.8 (a). If a
positive voltage is applied the graphene side with respect to silicon, forward bias, V
a
, the
barrier height will reduce, and therefore, electrons can flow from silicon to graphene, as
indicated in Figure 1.8 (b). The energy mismatch at the graphene/silicon interface results
in the Schottky barrier, and rectifying I-V characterization when a bias voltage is applied
to it[14].
Figure 1-9 shows the I-V characteristics of graphite in contact with n-type silicon, n-type
GaAs, and n-type 4H-SiC. Rectifying I-V behaviors indicate the formation of the
Figure 1-8. Energy band diagram of graphene-n-type silicon junction under (a) reverse bias,
and (b) forward bias.
(a) (b)
14
Schottky barrier in between graphite and other semiconductor substrates. The zero bias
Schottky barrier heights extracted from the I-V characteristics are 0.4, 0.6, and 1.15
eV[15].
In addition to the rectifying I-V characteristics, the transparency of graphene
allows light absorption in the underlying silicon substrates. Li et.al, have also reported the
graphene-silicon junction, which is used as solar cells, where graphene serves as a
transparent electrode, and the depletion region in the silicon substrates generate
photocurrent when the device is illuminated with a light source. Figure 1-10 is their
experiment results, showing the energy diagram of an illuminated graphene/n-Si solar
Figure 1-9. Plots of the room-temperature current density J with respect to applied bias V on
(a) n-type Si/graphite (red squares), (b) n-type GaAs/graphite (blue circles), and (c) n-type 4H-
SiC/graphite junctions (black triangles). Inset: J-V plots on semilogharithmic axes[15].
15
cell with forward-bias applied, and the I-V characteristics with and without light
illuminations, which indicate an open-circuit voltage (V
OC
) of 0.48 V, short-circuit
current density (J
SC
) of 6.5 mA/cm, a fill-factor (FF) of 56%, and overall solar energy
conversion efficiency (η) of 1.65% for the graphene/n-Si devices[16].
Figure 1-10. Photovoltaic characterizations of graphene/n-Si solar cells. (a) Energy diagram of
the forward-bias upon illumination. Ф
G
(4.8 ~ 5.0 eV) , Ф
n-Si
(4.24 eV) is the work function of
graphene and n-Si respectively. V
0
is the build-in potential, Ф
b
is the barrier height, χ is the
electron affinity of silicon (4.05 eV). E
g
is the bandgap of silicon (1.12 eV) and E
F
is the
energy of the Fermi level. V
bias
is the applied voltage. The depth of the Fermi level below the
Si conduction band edge (E
C
– E
v
) is ~0.25 eVfor the n-Si used in this work. (b)
Semilogarhythmic-scale dark I-V curves of two graphene/n-Si cells of different junction areas.
The ideality factor (n) and the series resistance (R
s
) of the 0.1 cm
2
cell extrapolated from the
linear regimes in the insets are 1.67 and 10.5 Ω, respectively. The shunt resistance is up to 45
MΩ which is estimated from reverse bias I-V sweep. (c) Light J-V curves of the cells
illuminated with simulated AM 1.5 Global light. (D) Light-intensity-dependence short circuit
current density (J
sc
), open circuit voltage (V
oc
), fill factor (FF), and solar energy conversion
efficiency (η) plots of a 0.1 cm
2
graphene/ n-Si cell[16].
16
1.5 Polymer electrolyte doping in graphene
The energy mismatch results in Schotty barrier at graphene/silicon interface,
which implies that the barrier could be eliminated if the graphene Fermi energy can be
shifted to match the conduction or valance bands of silicon, and directly Ohmic contact
would be achieved at the interface. These would require ~ 0.6 eV energy shifting in
graphene Fermi energy as indicated in Figure 1.7 (a). Das et, al, have reported shifting
graphene Fermi energy for more than 0.7 eV from its charge neutrality point by using
polymer electrolyte doping, in their work, they monitor the Raman frequencies of
graphene while applying polymer electrolyte doping to it. Figure 1-11(a) shows their
experiment setup and polymer electrolyte doping in graphene, and 1-11 (b), (c) show the
source-drain current (I
SD
) at different applied gate voltages. Their observations of the
Raman frequencies of graphene with polymer electrolyte doping have been shown in
Figure 1-6, which demonstrates the shifting of the Raman G and 2D band frequencies and
the changing of full width half maximum (FWHM) of Raman G band with respect to the
applied gate voltages, a maximum Fermi energy of 800 meV and nearly 4×10
13
cm
-2
electron concentration are reported in their work, which suggests that polymer electrolyte
doping is able to shift graphene Fermi energy to match the conduction or valance bands
of silicon to eliminated the Schorrky barrier at graphene/silicon interface and create
Ohmic contact at the interface.
The main factors that the polymer electrolyte doping can shift graphene Fermi
energy for more than ± 0.6 eV from its charge neutrality point is the high capacitance of
the polymer electrolyte, and the low density of state in graphene[5].
17
According to Das et al., the relation between the top gate voltage and the
Figure 1-11. Electrochemically top-gated graphene transistor. (a) Schematic diagram of the
experimental setup. The black dotted box between the drain and source indicates the thin layer
of polymer electrolyte (PEO + LiClO
4
), and the blue stripe between the electrodes represents
the graphene sample. Thleft inset shows the optical image of a single-layer graphene connected
between source and drain gold electrodes. Scale bar: 5 µm. The right inset is a schematic
illustration of polymer electrolyte to gating, with Li
+
(magenta) and ClO
4
¯
(cyan) ions and the
Debye layers near each electrod. (b) I
SD
as a function of top-gate voltage (V
TG
). The inset
shows the I
SD
time dependence at fixed V
TG.
The dotted line corresponds to the Dirac point
(change neutrality point). (c) I
SD
versus V
SD
at different top-gate voltages. The black dotted line
corresponds to the value of V
DS
at which the data in Fig 1-11(b) was measured[5].
18
(1)
(2)
graphene Fermi energy can be expressed as:
𝑉
!"
=
𝐸
!
𝑒
+𝜑
where 𝐸
!
=ℏ|𝑣
!
| 𝜋𝑛 , 𝜑= 𝑛𝑒/𝐶
!"
, and n is the graphene carrier concentration, (in
units of cm
-2
). Equation 1 can then be written as:
𝑉
!"
=
ℏ|!
!
| !"
!
+
!"
!
!"
Using 𝐶
!"
= 2.2×10
!!
F cm
!!
, and a graphene Fermi velocity of 𝑣
!
= 1.1×10
!
ms
!!
,
Equation 2 can be written as:
𝑉
!"
= 1.28×10
!!
𝑛+7.27×10
!!"
𝑛
From this equation, the graphene Fermi energy and the applied gate voltage can be
established, and plotted in Figure 1-12
Figure 1-12 indicates that the Fermi energy of graphene can be shifted over 0.85 eV from
its charge neutrality point by the polymer electrolyte doping, which is more it is needed
to eliminate the Schottky barrier at graphene/silicon interface.
-4 -3 -2 -1 0 1 2 3 4
-0.9
-0.6
-0.3
0.0
0.3
0.6
0.9
Fermi Energy (eV)
Gate Voltage (V)
E
C
(Si)
E
V
(Si)
Figure 1-12. Graphene Fermi energy plotted as a function of gate voltage. The gray dash
lines indicate the conduction and valance band energy of silicon.
19
1.6 Thermoelectric effects at heterojunction of 2-dimension materials
Hexagonal boron nitride (h-BN) has been reported as a good substrate for
graphene devices due to its atomically smooth surface, relatively free of dangling bonds
and trapped charges comparing with SiO
2
substrates, moreover, its lattice constant is
similar to graphene. These properties reduce the local doping, and roughness for the
graphene on h-BN device, and enhance the electron transport performance. Dean et al.,
have reported an electron mobility of 60,000 cm
2
V
-1
S
-1
for graphene on h-BN device,
which is three times larger than the graphene device on SiO
2
substrates[17]. For graphene
on h-BN device, a large cross-plane electric field exists across a thin 2D stack and can
result in localized heating, and heat dissipation from 2D devices has been found to be
limited by vertical heat transfer, which implies that the thermal interface conductance
would be a critical factor for heat dissipation of this kind of devices[18-20]. The thermal
interface conductance (G
th
) can be expressed as G
th
= Q/(A×ΔT), where A is the contact
area, Q = I
2
R is the electrical heating power, and ΔT is the temperature gradient between
two materials[21]. Figure 1-13 shows the experimental thermal interface conductance for
the interfaces of single layer graphene (SLG), flew-layer graphene (FLG) and various
substrates at different temperature, which indicates the thermal interface conductance of
10
7
-10
8
Wm
-2
K
-1
at graphene/SiO
2
, graphene/Ti/Au, and graphene/Au interfaces[22-28].
The experimental thermal interface conductance will be discussed in the later chapter.
20
In addition to serve as a good substrate, an interesting electron transport behavior
at graphene/h-BN/graphene is also observed and reported by Britnell et al., Figure 1-14
shows the schematic diagrams of graphene/h-BN/graphene field-effect tunneling
transistor in their work. The insulating h-BN layer serves as a tunneling barrier, and the
tunneling current can be controlled by the applied gate and bias voltages
[29].
Figure 1-13. Experimental thermal interface conductance (G
i
) versus temperature for a
3.0 nm-thick-FLG/SiO
2
interface reported by Chen et al[22]. FLG/SiO
2
interface reported
by Mak et al[23]. HOPG/Ti/Al (filled circles) and HOPG/Au (open circles) interfaces
reported by Schmidt et al[24]. a SLG/Au interface reported by Cai et al[25]. a Au/Ti/three-
layer graphene/SiO
2
stack reported by Koh et al[26]. and a diamom/Au interface reported
by Stoner and Maris[27].
21
Figure 1-15 shows the I-V characteristics of electron transports at graphene/h-
BN/graphene heterostructures, nonlinear I-V curves indicate the electron tunneling
through the heterojunction, and tunneling barriers can be modulated by applying electric
field-effects. Figure 1-15 (B) plots the zero-bias conductivity as a function of applied gate
voltage (V
g
), which shows that the lowest conductivity is achieved at V
g
≈ 3V
[29-31].
Figure 1-14. Graphene field-effect tunneling transistor. (A) Schematic structure of the
experiment device. In the most basic version of the FET, only graphene electrode (Gr
B
) is
essential, and the outside electrode can be made from a metal. (B) The corresponding band
structure with no gate voltage applied. (C) The same band structure for a finite gate voltage
V
g
and zero V
b
. (D) Both V
g
and V
b
are finite. The cones illustrate graphene’s Dirac-like
spectrum and, for simplicity, we consider the tunnel barrier for electrons.
22
In addition to electron tunneling in these Graphene/h-BN/graphene
heterostructures, the graphene/h-BN junction demonstrates relatively low interface
thermal conductance, making it a good candidate for thermal energy conservation devices.
This observation could extend the application of graphene-based heterojunction devices
to thermal energy conversion. Figure 1-16 is the trade-off between electrical conductivity
(σ), Seebeck coefficient (S), and thermal conductivity (κ), which implies the high
Seebeck coefficient in graphene/h-BN/graphene heterostructure devices[32]. An
Figure 1-15. Tunneling characteristics for a graphene-hBN device with 6 ± 1 layers of
hBN as the tunnel barrier. (A) I-Vs for different V
g
(in 10-V steps). Because of finite
doping, the minimum tunneling conductivity is achieved at ≈ 3V. The inset compares the
experimental I-V at V
g
= 5 V (red curve) with theory (dark), which takes into account the
linear DOS in the two graphene layers and assumes no momentum conservation. Further
examples of experimental curves and their fitting can be found in the supporting material.
(B) Zero-bias conductivity as a function of V
g
. The symbols are experimental data, and the
solid curve is the modeling. The curve is slightly shifted with respect to zero V
g
because of
remnant chemical doping. In all the calculations, they assumed the hole tunneling with m =
0.5 m
0
and Δ ≈ 1.5 eV[30,31] and used d as measured by atomic force microscopy. Both I
and σ are normalized per tunnel area, which was typically 10 to 100 µm
2
for the studied
devices. Temperature, 240K[29].
23
experimental study of thermoelectric transport across /h-BN/graphene heterostructure
will be presented in chapter 7.
Figure 1-16. Trade-off between electrical conductivity (σ), Seebeck coefficient (S), and
thermal conductivity (κ) that involves increasing the number of free carriers from insulators
to metals[32].
24
Chapter 2
Raman Spectroscopy of Ripple Formation in Suspended
Graphene
Introduction
Using Raman spectroscopy, we measure the optical phonon energies of suspended
graphene before, during, and after thermal cycling between 300 and 700K. After
cycling, we observe large upshifts (~25cm
-1
) of the G band frequency in the graphene
on the substrate region due to compression induced by the thermal contraction of the
underlying substrate, while the G band in the suspended region remains unchanged.
From these large upshifts, we estimate the compression in the substrate region to be
~0.4%. The large mismatch in compression between the substrate and suspended
regions causes a rippling of the suspended graphene, which compensates for the
change in lattice constant due to the compression. The amplitude (A) and wavelength
(λ) of the ripples, as measured by AFM, correspond to an effective change in length
Δl/l that is consistent with the compression values determined from the Raman data.
The mechanical instability of graphene is one of its most interesting
properties[33-35]. Ripple formation in suspended and on-substrate graphene have been
demonstrated both experimentally[36-38] and theoretically[39-41], though with much
variation in character and orientation. Furthermore, these ripples have been shown to
create midgap states and charge inhomogeneity in the graphene[42, 43]. Therefore, a
method of producing well-ordered graphene ripples will help provide a deeper
understanding of these structures and their electrical, magnetic, and mechanical
properties. Recently, Bao, et al. developed a method for forming well-ordered ripples in a
25
controllable fashion by the thermal cycling of suspended graphene[44]. The period and
amplitude of these ripples were satisfactorily accounted for by a classical elasticity theory
model, which correlated well with the thickness of the suspended graphene.
Raman spectroscopy provides a very precise measure of the vibrational energies
of carbon nanotubes and graphene, which respond very sensitively to changes in strain
and compression. As such, Raman spectroscopy provides a good tool for characterizing
the strain and compression in these nanoscale systems[45, 46]. Cronin et al. were able to
observe changes in the Raman spectra of carbon nanotubes for strains as small as ε =
0.l%[47, 48]. Huang et al. measured the Raman spectra of graphene under uniaxial
strains of a few percent[12]. They observed downshifts in the G and 2D bands of
= ∂ ∂ ε ω /
G
-12.5cm
-1
/% and = ∂ ∂ ε ω /
2D
-21cm
-1
/%, respectively. Similarly, Mohiuddin
et al., studied graphene under uniaxial and biaxial strain both experimentally and
theoretically[49]. They reported values of the strain-induced downshifts of the G band of
= ∂ ∂ ε ω /
G
-30cm
-1
/% and = ∂ ∂ ε ω /
G
-58cm
-1
/% for uniaxial and biaxial strain,
respectively. This biaxial strain coefficient is consistent with recent measurements under
hydrostatic pressure[50].
Experiment
Here, we present the first Raman spectroscopy measurements of periodic ripple
formation in suspended graphene before and after thermal cycling. These ripples arise
from the compression induced in graphene due to the difference in thermal expansion
coefficients between graphene and the underlying silicon substrate. This compression is
26
quantified by measuring the change in the G band Raman frequency, while the amplitude
and wavelength of the ripples are measured by atomic force microscopy (AFM).
Graphene membranes, ranging from single layers (0.35nm) to multiple layers
(2nm) in thickness, and 0.5 to 20µm in width, are deposited suspended across pre-defined
trenches on Si/SiO
2
substrates using mechanical exfoliation[1]. Spatially resolved micro-
Raman spectra are collected in a Renishaw inVia micro-Raman spectrometer, while the
temperature is varied in a Linkam THMS temperature-controlled stage. In this work, a
532nm 5W Spectra Physics solid state laser is collimated and focused through a Leica
DMLM microscope and used to irradiate these samples with a 100X objective lens with
NA=0.9, working distance=0.3mm, and spot size=0.5µm. All measurements were
performed in air under standard atmospheric conditions.
Figure 2-1a shows an optical microscope image of a graphene single layer
suspended over a 3mm trench. Spatial mappings of the G band Raman shift taken before
and after thermal cycling to 700K are shown in Figure 2-1b at the locations indicated by
the dashed line in Figure 2-1a. Before thermal cycling, a slight upshift in the Raman
frequency can be seen in the trench region. This indicates either a small compression in
the suspended region or, more likely, a small strain in the substrate region. After thermal
cycling, however, a large upshift of Δω
G
=25cm
-1
is observed in the substrate region,
while the trench region remains unchanged, indicating the presence of significant
compression in the single layer graphene on the substrate. Such compression arises from
the differential thermal expansion between graphene and the substrate, in particular, from
the negative thermal expansion of graphene[12].
27
single layer
graphene
3µm trench
laser scan
direction
(a)
0 2 4 6 8 10 12 14 16
1575
1580
1585
1590
1595
1600
1605
Raman Shift (cm
-1
)
Distance (µm)
trench
before
after
(b)
Figure 2-1. (a) Optical microscope image of a graphene single layer suspended over a 3mm
trench. (b) Spatial mapping of the G band Raman shift taken perpendicular to the trench
before and after thermal cycling to 700K.
28
The biaxial compression of the graphene on the substrate is manifested differently
for the suspended portion of the graphene. Because the bending energy of the thin
membrane is much smaller than the potential energy induced by changing bond lengths,
the compressive strain in the suspended graphene is relieved by the formation of ripples,
as shown in Figure 2-2. In the ideal case where the ripples can be approximated as a
sinusoid with amplitude (A) and wavelength (λ), the effective contraction of the graphene
is given by:
dx
x
A dl l
∫ ∫
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
−
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
+ = = Δ 1
2
cos
2
1
2
λ
π
λ
π
( )
4 2
) / ( / λ λ π ε A O A
l
l
+ =
Δ
= ,
where we have used a Taylor series expansion to obtain the final form. Figure 2-2 shows
an AFM topography image and cross-section analyses of the suspended graphene before
and after thermal cycling. Before heating, the graphene appears flat. However, after
thermal cycling, ripples can be seen. In order to accurately analyze these real ripple
patterns, which deviate significantly from the sinusoidal idealization, we evaluate the
actual change in length Dl/l using the AFM software (DI, Nanoscope) to be 0.40%, which
is in good agreement with the compression value determined from the Raman upshifts
shown in Figure 2-1, as described below. From the AFM cross-section data, we
determine the average amplitude and wavelength of these ripples to be 5.2nm and
0.26mm, respectively.
29
bilayer
single layer
trench
(a)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
10
15
20
25
30
35
40
Height (nm)
Distance (µm)
(b)
Figure 2-2. Atomic force microscope (a) image and (b) cross-sectional analyses of the
suspended graphene single layer shown in Figure 1 (a) before and (b) before and after thermal
cycling to 700K.
30
Spatially mapped Raman spectra were taken after every 100K increment during
heat-up and cool-down, and are shown in Figure 2-3. According to the observations of
Bao et al. during the thermal cycling, the suspended graphene samples became taut at
temperatures higher than 600K due to the thermal expansion of the underlying substrate
and the thermal contraction of the graphene[44]. Subsequent cooling from 700 to 300K
creates compression and ripples in the graphene samples. In our Raman measurements,
the G band Raman frequency of the suspended graphene in the trench region was roughly
equal to that measured in the substrate region during heat-up (Fig. 2-3a). During cool-
down, however, the Raman frequencies of the suspended and substrate regions begin to
deviate significantly due to the compression induced by the thermal contraction of the
silicon substrate and the thermal expansion of the graphene (Fig. 2-3b). After thermal
cycling, the Raman upshift observed in the substrate region relative to the suspended
region was w
sub
-w
sus
=22.7cm
-1
. The first principles calculations of Mohiuddin et al.
predict downshifts of = ∂ ∂ ε ω /
G
-58cm
-1
/% for biaxial strain[49]. Assuming this
coefficient for both tension and compression[50], we estimate a compression of 0.39%
from the 22.7cm
-1
upshift observed in our work after thermal cycling. This value of
compression agrees well with the value obtained from AFM. We note these frequency
shifts are much larger than could be explained by the temperature dependence of the
Raman peaks alone, which follow /K cm 016 . 0
-1
− ≈
∂
∂
ε
ω
T
according to Ref. [51].
31
0 2 4 6 8 10 12 14 16
1573
1574
1575
1576
1577
1578
1579
1580
1581
Raman Shift(cm
-1
)
Distance (µm)
300K
400k
500k
650K
300K
650K
(a)
0 2 4 6 8 10 12 14 16
1570
1575
1580
1585
1590
1595
1600
1605
Raman Shift (cm
-1
)
Distance (µm)
700K
300K
500K
400K
600K
(b)
Figure 2-3. Raman spatial maps taken during (a) heat-up to 650K and (b) cool-down from
700K.
32
700 600 500 400 300
0
5
10
15
20
25
ω
sub
-ω
sus
(cm
-1
)
T (K)
-0.1
0.0
0.1
0.2
0.3
0.4
heat-up
cool-down
(a)
Estimated Compression (%)
As mentioned above, the relatively small variations in the Raman frequency along
the length of the graphene before and during heat-up indicate some slight strain induced
during mechanical exfoliation or by the thermal expansion of the trench. Figure 2-4a
shows the difference in the average Raman frequency between the substrate and
suspended regions (ω
sub
-ω
sus
), plotted as a function of temperature as the sample is
thermally cycled between 300 and 700K. The data is found to follow a linear dependence
on temperature. The biaxial compression estimated from Mohiuddin’s work is also shown
in the figure on the right axis.
33
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
0
5
10
15
20
25
ω
sub
− ω
sus
(cm
-1
)
Thickness (nm)
(b)
Spatially mapped Raman spectra and AFM data were taken before, during, and
after thermal cycling on a total of four suspended graphene samples. Table I summarizes
these results. Samples 1 and 2 showed Raman upshifts of Δω
G
=22.7cm
-1
and 10.4cm
-1
and estimated compressions of 0.39% and 0.18%, respectively, based on the theoretical
predictions of Mohuiddin et al.[49]. These results are consistent with the effective
compressions obtained from the AFM data, 0.4% and 0.25%, respectively. Sample 3
shows results for a graphene trilayer that exhibits a somewhat smaller Raman upshift and
compression after thermal cycling. Unfortunately, no AFM data could be obtained from
this sample after thermal cycling. Sample 4 shows data from a multi-layered sample of
Figure 2-4. (a) Difference between the average G band Raman shift of the suspended and
substrate regions and estimated biaxial compression taken during thermal cycling. (b) Raman
upshift between the substrate and suspended regions plotted as a function of graphene
thickness.
34
graphene, which exhibits a significantly lower value of Raman-estimated and AFM-
estimated compression. Figure 4b shows a plot of the relative upshift of the G band after
thermal cycling (ω
sub
-ω
sus
) plotted as a function of the graphene thickness. A clear trend
can be seen in the sample thickness dependence of the Raman upshift, which is consistent
with the observations of Proctor et al. under hydrostatic pressure[50]. This plot clearly
shows that the graphene thickness plays a significant role in the compression created by
thermal cycling, such that thinner graphene samples experience more compression than
thicker graphene samples.
The thermal expansion coefficient (TEC) of graphene can be estimated from our
measurements. Carbon nanostructure materials are known to exhibit an anomalous
(negative) thermal expansion coefficient[52-54]. Here, we observe a compression of 0.4%
over a 400K (1 × 10
-5
/K) temperature difference, which arises from the difference in
thermal expansion coefficients of graphene and the underlying silicon. Subtracting the
Sample
Graphene
Layers
Graphene
Thickness
(nm)
Raman Upshift
After Cycling
(ω
sub
- ω
sus
)
(cm
-1
)
Compression
Estimated
from Raman
Upshift (%)
Effective
Compression
(Δl/l) from AFM
Data (%)
1 Single Layer 0.33 22.7 0.39 0.40
2 Bilayer 0.74 10.4 0.18 0.25
3 Triple Layer 0.94 5.3 0.09 N/A
4 Multiple Layer 3.24 0.5 0.01 0.058
Table 1. Raman and AFM data summary of four samples before and after thermal
cycling.
35
TEC due to the underlying silicon substrate (4.7 × 10
-6
/K)[44, 55] gives a value of -5.3 ×
10
-6
K for the TEC of single layer graphene. This is consistent with the values given in
our previous work, verifying the classical elasticity theory model used to interpret those
results[44]. This value is much larger in magnitude than the TEC of graphite in the basal
plane, -1 × 10
-6
/K, and roughly one and a half times larger than the value predicted for
graphene from theoretical calculations[54].
We note that Berciaud et al. have also observed significant shifts in the Raman
spectra of suspended graphene relative to on-substrate graphene[56]. However, in that
work, the shifting of these Raman peaks was attributed to a doping effect, which is
known to cause upshifts and linewidth narrowing of the G band in graphene through the
blockage of the decay channel of phonons into electron-hole pairs[5, 57, 58]. The data
shows a broadening of the G band linewidth in the suspended region, which can be
explained by inhomogeneous broadening. Since the period of the ripples is smaller than
the laser spot, local variations in the Raman frequency will be spatially averaged over the
collection area (laser spot), resulting in a broadened Raman linewidth after the ripples are
formed. The on-substrate graphene, however, shows a narrowing of the G band linewidth
from approximately 13cm
-1
to 9cm
-1
, which may indicate doping due to charge transfer
from the underlying substrate. However, the doping required to achieve this linewidth
narrowing is relatively small and corresponds to upshifts of just several cm
-1
[58].
Another alternative is that a compression-induced band gap is created[45, 46, 59, 60]. If
the band gap is larger than the G band phonon energy, it will block the decay of phonons
into electron-hole pairs, causing the observed upshift and linewidth narrowing. Further
studies must be conducted in order to separate these possible effects. The additional
36
topographical information provided by AFM corroborates the existence of compression,
which we believe is the primary effect on the observed Raman spectra.
Conclusion
We observe significant upshifts in the Raman spectra of suspended graphene
(25cm
-1
) after thermal cycling treatment (300K-700K-300K). For single layer graphene,
these upshifts correspond to compressions in the substrate region up to 0.4% and ripple
formation in the suspended region of the graphene. The effective change in length, as
determined from AFM measurements of the ripple amplitude and wavelength, are
consistent with the values of compression estimated from the Raman upshifts. These
independent measurements verify that the ripples originate from the change in lattice
constant in the compressed region. Lastly, the thickness dependence of the compression
induced by thermal cycling was ascertained, and was found to decrease with increasing
graphene thickness.
37
Chapter 3
Raman Spectroscopy of Substrate-Induced Compression and
Substrate Doping in Thermally Cycled Graphene
Introduction
By thermally cycling single layer graphene in air, we observe irreversible upshifts
of the Raman G and 2D bands of 24 cm
-1
and 23 cm
-1
, respectively. These upshifts are
attributed to an in-plane compression of the graphene induced by the mismatch of
thermal expansion coefficients between the graphene and the underlying Si/SiO
2
substrate, as well as doping effects from the trapped surface charge in the underlying
substrate. Since the G band is sensitive to doping and the 2D band is not, we can separate
the effects of compression and doping associated with thermal cycling. By performing
the thermal cycling in an argon gas environment and by comparing suspended and on-
substrate regions of the graphene, we can separate the effects of gas doping and doping
from the underlying substrate. Variations in the ratio of the 2D to G band Raman
intensities provide an independent measure of the doping in graphene that occurs during
thermal cycling. During subsequent thermal cycles, both the G and 2D bands downshift
linearly with increasing temperature, and then upshift reversibly to their original
frequencies after cooling. This indicates that no further compression or doping is induced
after the first thermal cycle. The observation of ripple formation in suspended graphene
after thermal cycling confirms the induction of in-plane compression. The amplitude and
wavelength of these ripples remain unchanged after subsequent thermal cycling,
corroborating that no further compression is induced after the first thermal cycle.
38
In the study of graphene, Raman spectroscopy is used widely for identifying the
thickness, carrier concentration, temperature, and strain[51, 61-63]. Recently, Late et al.
investigated the Raman spectra of single layer graphene on Si/SiO
2
substrates from 77K
to 573K, and calibrated the temperature coefficient of the G and 2D band Raman modes
to be ∂ω
G
/∂ε = − 0.016 cm
-1
/K and ∂ω
2D
/∂ε = − 0.026 cm
-1
/K[64]. Abdula et al. have also
reported temperature coefficients of ∂ω
G
/∂T = − 0.035 cm
-1
/K and ∂ω
2D
/∂T = − 0.07 cm
-
1
/K for single layer graphene[65], which are significantly different from those of Late et
al. Changes in the Raman G and 2D bands are also used to estimate the effect of strain in
graphene[12, 46, 66, 67]. Mohiuddin et al. have observed strain-induced shifts in the
Raman G and 2D bands of graphene of ∂ω
G
/∂ε = − 58 cm
-1
/% and ∂ω
2D
/∂ε = − 144 cm
-1
/%
for graphene under biaxial strain[68]. Ni et al. have reported ∂ω
G
/∂ε = − 14.2 cm
-1
/% and
∂ω
2D
/∂ε = − 27.8 cm
-1
/% of Raman G and 2D bands shifts on graphene under uniaxial
strain[69]. In addition to temperature and strain, doping also causes changes in the
Raman spectra[70]. By applying a top gate voltage to single layer graphene, Das et al.
observed that the intensity ratio of the 2D band to G band reduces, and that the G and 2D
band frequencies upshift with increasing doping [5].
While the temperature and strain coefficients of graphene Raman spectra have
been reported in many previous works, the effects of strain and doping induced by the
underlying substrate are usually not taken into consideration when estimating the Raman
temperature coefficient. However, graphene’s negative thermal expansion coefficient[71-
73] causes a geometric mismatch with most supporting substrates. In addition, graphene
is often observed to be doped when the ambient temperature is varied, which implies that
the effects of strain and doping cannot be neglected when calibrating the temperature
39
coefficient of the Raman modes of graphene. In this work, we measure the Raman spectra
of both suspended and supported graphene before, during, and after thermal cycling from
300K to 700K. Both the Raman G and 2D bands are studied systematically. Atomic force
microscopy (AFM) is used to determine the suspended graphene profile variation before
and after thermal cycling. Thermal cycling in air and Ar gas environments enables us to
indentify changes associated with gas doping. In doing so, we are able to separate the
effects of doping, compression, and temperature in graphene through the interpretation of
the resulting Raman spectra.
Experiment
In this work, graphene flakes are deposited on Si/SiO
2
substrates using
mechanical exfoliation[74, 75]. The number of graphene layers are identified using
Raman spectroscopy by curve fitting the 2D band[76-78]. Figure 3-1 shows an optical
microscope image of a single layer graphene flake sample (SLG1) deposited on a Si/SiO
2
substrate. Thermal cycling from 300K to 700K and then back to 300K is performed in air
using a Linkam THMS temperature controlled stage, while Raman spectra are taken
during the thermal cycling process.
The Raman spectra are collected by using a Renishaw
spectrometer with a 532 nm laser focused in a 0.5 µm spot through a Leica microscope
with a 100X objective lens.
Figure 3-1. Optical image of single layer graphene (SLG1).
40
The G band and 2D band Raman spectra of the single layer graphene sample
(SLG1) taken during thermal cycling are shown in Figures 3-2a and 3-2b. During heating,
the G band Raman shift remains approximately constant while the 2D band downshifts
monotonically. Since the G band is sensitive to both temperature and doping, the
temperature-induced downshift[79] is approximately canceled by the effect doping,
which upshifts the mode. The 2D band, on the other hand, is not sensitive to doping, and
exhibits the expected temperature-induced downshift. During cooling, linear upshifts are
observed in both the G and 2D bands, with temperature coefficients of ∂ω
G
/∂T = − 0.057
cm
-1
/K and ∂ω
2D
/∂T = − 0.092 cm
-1
/K, which are slightly higher than those observed in
previous works
[64, 65, 80]. By comparing the G and 2D band Raman modes before and
after thermal cycling (at 300K), the G band exhibits an irreversible upshift of 24.4 cm
-1
,
while the 2D band upshifts by 23.2 cm
-1
. This G band upshift is consistent with our
previous work on suspended graphene, which showed a 25 cm
-1
upshift in the supported
region, while the suspended region remained constant after thermal cycling[81]. In this
previous work, ripple formation in the suspended region of the graphene indicated that
the G band upshift originated from the compression of the graphene lattice created by the
mismatch of thermal expansion coefficients between the graphene and the underlying
Si/SiO
2
substrate[55, 71, 72, 82]. In addition to compression, doping effects can also
cause the G and 2D bands upshifts. Das et al. have reported G band upshifts of 25 cm
-1
and 7cm
-1
linewidth narrowing due to electrostatic doping, while the 2D band upshifts by
only 15 cm
-1
[5]. In the experiment presented here, both G and 2D bands show similar
irreversible upshifts, while the G band FWHM narrowing is less than 2 cm
-1
after thermal
41
300 400 500 600 700
2650
2660
2670
2680
2690
2700
Cooling
Heating Raman Shift (cm
-1
)
Temperature (K)
300 400 500 600 700
1575
1580
1585
1590
1595
1600
1605
1610
Raman Shift (cm
-1
)
Temperature (K)
Heating
Cooling
cycling. These results indicate that, in addition to substrate-induced doping effects, a
significant amount of compression is created.
A second thermal cycle was carried out on the same sample (SLG1) to 700K and
back to 300K. The Raman G and 2D bands taken during the second thermal cycling are
shown in Figures 3-3a and 3-3b. In the second thermal cycle, both the Raman G and 2D
bands downshift linearly with increasing temperature and upshift linearly to their original
frequencies reversibly after cooling to 300K. Here, we observe Raman temperature
coefficients of ∂ω
G
/∂T = − 0.055 cm
-1
/K and ∂ω
2D
/∂T = − 0.083 cm
-1
/K. It is important to
note that no irreversible upshifts or downshifts of the G or 2D bands are observed after
the second thermal cycling. This implies that no further compression or doping has
occurred in the graphene, and that these coefficients represent the true temperature
dependence of the G and 2D bands.
Figure 3-2. (a) G band and (b) 2D band Raman data of single layer graphene taken during
the first thermal cycling.
(a)
(b)
42
Figure 3-3. (a) G band and (b) 2D band Raman data of single layer graphene taken during
the second thermal cycling.
(a)
(b)
In order to confirm the assumption that no further compression is induced in the
graphene after the first thermal cycle, a triple layer graphene (TLG) flake suspended
across a 3µm trench, shown in Figure 3-4c, was thermally cycled twice to 700K, while
observing its Raman spectra. Figure 3-4a shows the height profiles of the suspended TLG
measured by atomic force microscopy before and after the first thermal cycling, which
exhibits uniform and periodic ripples after the first thermal cycle, indicative of
compression. Spatially mapped Raman spectra taken before and after the first thermal
cycle are shown in Figure 3-4b. G band upshifts of 9cm
-1
and 4cm
-1
are observed in the
supported and suspended regions, respectively. The magnitude of these shifts are
consistent with our previous work obtained for triple layer graphene.
300 400 500 600 700
2660
2670
2680
2690
Raman Shift (cm
-1
)
Temperature (K)
Heating
Cooling
300 400 500 600 700
1580
1585
1590
1595
1600
1605
1610
Raman Shift (cm
-1
)
Temperature (K)
Heating
Cooling
43
Figure
3-‐4a
Figure
3-‐4b
(c)
Figure 3-5. (a)
Spatially-‐mapped
Raman
spectral
data
and
(b)
AFM
height
profile
of
the
bilayer
graphene
show
in
Figure
4
before
and
after
the
second
thermal
cycling
to
700K.
After a second thermal cycle to 700K, this TLG sample exhibited only slight
variations in the amplitude and wavelength of the ripples and in the spatially-mapped
Raman spectra, as shown in Figures 3-5a and 3-5b. The consistency of these results
before and after the second thermal cycling confirms that no further compression or
doping are induced after the first thermal cycle.
Figure
4b
0 1 2 3 4 5 6 7
-100
-50
0
50
100
Height (nm)
Distance (µm)
After
Before
0 2 4 6 8 10 12 14 16
1578
1581
1584
1587
1590
1593
1596
Before
After
Raman Shift (cm
-1
)
Distance (µm)
Trench
(a)
(b)
Figure 3-4. (a) AFM height profile
of suspended triple layer graphene
before and after the thermal cycling.
(b) Spatially-mapped Raman spectral
data of the triple layer graphene
before and after thermal cycling. (c)
Optical microscope image of the
triple layer suspended graphene
sample.
Figure
5.
(a)
Spatially-‐mapped
Raman
spectral
data
and
(b)
AFM
height
profile
of
the
bilayer
graphene
show
in
Figure
4
before
and
after
the
second
thermal
cycling
to
700K.
0 1 2 3 4 5 6 7
-40
-20
0
20
40
After 1st
After 2nd
Height (nm)
Distance (µm)
0 2 4 6 8 10 12
1584
1585
1586
1587
1588
1589
1590
1591
After 1st
After 2nd
Raman Shift (cm
-1
)
Distance (µm)
Trench
(a)
(b)
44
Figure 3-6. (a)
G
band
and
(b)
2D
band
Raman
data
of
single
layer
graphene
taken
during
three
thermal
cycles
to
500K,
600K,
and
700K.
We also measured the effect of sequential thermal cycling to incrementally higher
temperatures. Another single layer graphene sample (SLG2) was first thermally cycled to
500K, then to 600K, and then to 700K. Figures 3-6a and 3-6b show the G and 2D band
Raman data taken during these three thermal cycles. For the first thermal cycle to 500K,
the G band shows an initial upshift during the heating process, while the 2D band does
not. This phenomenon can be attributed to the doping effect from the surrounding air
molecules and/or the underlying substrate. In Figure 3-6, the room temperature positions
of both the G and 2D bands are observed to upshift after every subsequent thermal cycle.
After the third thermal cycle to 700K, net upshifts of 25 cm
-1
for the G band and 27 cm
-1
for the 2D band are observed, which are consistent with the upshifts of sample SLG1
shown in Figure 3-1a after a single thermal cycling to 700K. This observation confirms
that the equilibrium between the graphene and the underlying Si/SiO
2
substrate is not
broken until the graphene is taken to a higher temperature. For this sample, the Raman
temperature coefficients of the G and 2D bands are ∂ω
G
/∂T = − 0.055 cm
-1
/K and
∂ω
2D
/∂T = − 0.085 cm
-1
/K during the third cooling process, which are also consistent with
the previous results.
300 400 500 600 700
1580
1585
1590
1595
1600
1605 1st Heating
1st Cooling
2nd Heating
2nd Cooling
3rd Heating
3rd Cooling
Temperature (K)
Raman Shift (cm
-1
)
300 400 500 600 700
2660
2670
2680
2690
1st Heating
1st Cooling
2nd Heating
2nd Cooling
3rd Heating
3rd Cooling
Raman Shift (cm
-1
)
Temperature (K)
Figure
6.
(a)
G
band
and
(b)
2D
band
Raman
data
of
single
layer
graphene
taken
during
three
thermal
cycles
to
500K,
600K,
and
700K.
45
Figure 3-7. Raman
intensity
ratio
of
the
2D
and
G
bands
taken
during
the
first
and
second
thermal
cycles.
In this work, we attribute the irreversible upshifts observed in the Raman spectra
to in-plane compression and doping effects in the graphene[83, 84]. The in-plane
compression effects can also be studied through the observation of ripple formation in
suspended graphene, and the doping level in SLG samples can be studied by observing
the Raman intensity ratio of the 2D and G bands (I
2D
/I
G
). This intensity ratio reduces with
increasing carrier concentration[56, 85]. Malard et al. have also thermally cycled on-
substrate single layer graphene to 515K in Ar. In their experiment, no significant 2D band
upshifts were observed, and all G band upshifts and I
2D
/I
G
Raman intensity ratio changes
were attributed to doping alone[86]. Figure 3-7 shows the intensity ratio of the 2D and G
bands of SLG1 sample shown in Figures 3-1 and 3-2 taken during the first and second
thermal cycles. This data indicates that the doping effects from the surrounding air
molecules and underlying substrate cause a factor of 5 reduction in the relative intensity
of the 2D band after the first thermal cycle, while the variation of the intensity ratio after
the second thermal cycle is negligible. These results imply that the SLG1 sample is doped
during the first thermal cycle only[5, 87].
300 400 500 600 700
2
3
4
5
6
7
8
1st Heating
1st Cooling
2nd Heating
2nd Cooling
I
2D
/I
G
Temperature (K)
46
Table
2.
Summary
of
Raman
data
taken
on
three
different
SLG
samples
after
thermal
cycling
to
700K.
In order to further investigate the effects of doping, a fresh single layer graphene
sample (SLG3) was thermally cycled to 700K in an Ar gas environment to reduce the
effect of gas doping, while the Raman spectra are monitored. The Raman data of sample
SLG3 (not shown) measured in Ar shows that during the cooling process the Raman
temperature coefficients, ∂ω
G
/∂T = − 0.048 cm
-1
/K and ∂ω
2D
/∂T = − 0.080 cm
-1
/K, are
slightly reduced compared with that in air. Both the G and 2D bands still show large
irreversible upshifts (21.2 cm
-1
and 27.1 cm
-1
) after thermal cycling in Ar. These results
prove that the large upshifts observed in both air and Ar are dominated by compression
and doping induced by the underlying substrate.
Table 2 shows a summary of the Raman spectra of three different single layer
graphene samples after thermal cycling to 700K. In this table, the SLG1 and SLG2
samples show similar temperature coefficients and G and 2D band upshifts, even though
SLG2 has been cycled sequentially to 500K, 600K, and then 700K. The temperature
coefficient of SLG3 is slightly lower than that of SLG1 and SLG2. The lower I
2D
/I
G
variation of SLG3 after 700K thermal cycling indicates that the gas doping effect is
reduced by the Ar atmosphere.
Sample
Changes in the Raman frequency after
700K thermal cycling (cm
-1
)
Gas
𝑰
𝟐𝑫
𝑰
𝑮
𝑩𝒆𝒇𝒐𝒓𝒆
−
𝑰
𝟐𝑫
𝑰
𝑮
𝑨𝒇𝒕𝒆𝒓
𝑰
𝟐𝑫
𝑰𝑮
𝑩𝒆𝒇𝒐𝒓𝒆
Raman temperature
coefficient (K
-1
)
G band 2D band
1
st
cycle 2
nd
cycle 1
st
cycle 2
nd
cycle 1
st
cycle 2
nd
cycle ∂ω
G
/∂ε ∂ω
2D
/∂ε
SLG1 24.4 -0.03 23.2 -3.86 Air 0.69 -0.086 -0.055 -0.083
SLG2 24.8 NA 26.9 NA Air 0.69 NA -0.055 -0.085
SLG3 21.3 NA 27.2 NA Ar 0.42 NA -0.048 -0.080
47
Conclusion
G band and 2D band upshifts of 24 cm
-1
and 23 cm
-1
were observed after thermal
cycling single layer graphene to 700K. These upshifts are attributed to the compression of
the graphene induced from the underlying SiO
2
/Si substrate and doping effects from the
trapped charges in the underlying substrate. No irreversible upshifts were observed after a
second thermal cycle to 700K, indicating that no further compression or doping is
induced after the first thermal cycle. By separating the effects of doping, compression,
and temperature in graphene, through the interpretation of the resulting Raman spectra,
we are able to determine the true temperature dependence of the G and 2D bands.
Repeatable Raman temperature coefficients are observed after the first thermal cycle,
giving SLG Raman temperature coefficients of the G and 2D bands of ∂ω
G
/∂T = -0.055
cm
-1
/K and ∂ω
2D
/∂T = -0.085 cm
-1
/K, respectively. These results provide a more complete
understanding of the graphene-substrate interaction, which can result in significant
variations of graphene’s electrical, mechanical, and optical properties.
48
Chapter 4
Graphene-Silicon Schottky Diodes
Introduction
We have fabricated graphene-silicon Schottky diodes by depositing mechanically
exfoliated graphene on top of silicon substrates. The resulting current-voltage
characteristics exhibit rectifying diode behavior with a barrier energy of 0.41 eV on n-
type silicon and 0.45 eV on p-type silicon at the room temperature. The I-V
characteristics measured at 100K, 300K, and 400K indicate that temperature strongly
influences the ideality factor of graphene-silicon Schottky diodes. The ideality factor,
however, does not depend strongly on the number of graphene layers. The optical
transparency of the thin graphene layer allows the underlying silicon substrate to absorb
the laser light and generate a photocurrent. Spatially resolved photocurrent measurements
reveal the importance of inhomogeneity and series resistance in the devices.
Extensive transport studies have been performed on individual-, double- and few-
layer graphene,[88-95] since it was first exfoliated from graphite onto dielectric
substrates in 2004[1]. Researchers have made p-n junctions by electrostatically gating
single layer graphene (SLG) [96] [97] [98]. Due to its high electron mobility (200,000
cm
2
/V s), and high electric current carrying capacity (>10
8
A/cm
2
), graphene is an
excellent candidate for next-generation field effect transistors[3, 99-102]. Graphene has
the advantages over carbon nanotubes of being naturally compatible with thin film
processing, enabling large device areas and, hence, high operating powers. Also,
graphene is more readily scalable and has lower contact resistance. Nagashio et al. have
successfully evaluated the contact resistance between graphene and several most common
49
electrodes, including Ti/Au, Cr/Au, and Ni, which are patterned and deposited on
graphene using electron-beam lithography and electron gun evaporation. Through four
probe measurements, the lowest contact resistance ~ 500 Wµm was observed from the
interface of graphene and Ni[103, 104].
Schottky barriers of energy ~0.7 eV have been observed in graphene/graphene-
oxide junctions, and can be easily tuned by changing the oxidation temperature [105].
Schottky barriers made from graphene nanoribbons have been simulated theoretically. In
simulations performed by Jiménez et al., the Schottky barrier depletion width reduces and
the tunneling current increases as the gate voltage increases [106]
,
[107]. Epitaxially-
grown graphene/graphene-oxide junctions have also demonstrated Schottky diode
behavior, as a consequence of the band gap in graphene oxide [108]. While many
previous studies have explored electron transport in graphene, the Schottky barriers
between graphene and silicon have not been studied thoroughly. Tongay et al. have
observed the Schottky barriers at bulk HOPG graphite-silicon interfaces[109]. Here, no
photocurrents could be measured, and a comparison of n- and p-type substrates was not
given in this prior work. Also, the local effect of light absorption on the I-V
characteristics of graphene/silicon interfaces has not been studied. We present a detailed
study of the graphene-silicon interface, including temperature dependence, graphene
layer thickness dependence, and spatial mapping of photocurrents, which will likely be
important for the future integration of graphene with silicon.
Experiment
We fabricate graphene-silicon Schottky diodes by depositing graphene on top of
the Si/SiO
2
/Si
3
N
4
/Cr/Au structure shown in Figure 4-1a. To obtain a clean Si-graphene
50
interface, the SiO
2
is removed by BOE 7:1 wet etching. The samples are then rinsed with
DI water and baked on a hot plate at 120
o
C to remove any water from the surface. After
wet etching, we perform dry etching using CF
4
RIE[110]. These processing steps remove
the native oxide on the Si and passivate the surface[111]. Graphene is then deposited by
mechanical exfoliation in air. All samples were fabricated under the exact same
conditions. While we have no way of knowing the precise atomic configuration at the Si-
graphene interface, the dry etching step is crucial in order to fabricate devices with finite
resistance exhibiting rectifying I-V characteristics. According to Bunch et al., graphene
flakes are gas impermeable[112], which ensures that no further oxidation of the Si
surface occurs at the Si-graphene interface through the graphene flakes once they are
deposited. In addition, Chen et al. also demonstrated that graphene, grown by chemical
vapor deposition on copper, is able to prevent the underlying copper surface from air
oxidation[113], further corroborating that no oxidation is taking place after the graphene
deposition. Since the native oxide on silicon surfaces is usually less than 10 Ǻ thick[114],
the native oxide should only affect a very small region near the outer edge of the
graphene device. We have evaluated the stability and time dependence of these devices
by comparing the I-V characteristics taken immediately following device fabrication with
those taken after one week in an ambient environment. This data is presented in the
online supplemental document, which shows no change or degradation in I-V behavior,
and therefore no increased oxide or tunnel barrier. To characterize the device, a bias
voltage (V
b
) is applied between the Au electrode and Si substrate, as shown in Figure 1a.
All measurements were taken at room temperature and ambient conditions, unless
otherwise stated. A graphene bilayer deposited on an n-type Si substrate (n ~ 2.5 ×
51
n/p-‐type
Si
SiO
2
Si
3
N
4
Cr/Au
Graphene
V
b
graphene
silicon gold
Laser spot
10µm
grid marker
silicon gold
graphene
(a)
(b)
(c)
Figure 4-1. (a) Schematic
diagram, (b) optical micrograph,
and (c) SEM image of a graphene
on n-type silicon Schottky diode.
10
15
cm
-3
) with a Au electrode can be seen in the optical microscope and scanning
electron microscope (SEM) images shown in Figures 1b and 1c. Figure 1b shows
illumination from an approximately 0.5µm diameter 532nm wavelength laser spot.
Figure 4-2 is the measured I-V
bias
characteristics of the graphene-silicon device
shown in Figure 1 taken with and without illumination. Here, the Au makes an Ohmic
contact to the graphene, while the silicon-graphene interface forms a Schottky barrier,
which exhibits rectifying behavior. The contact resistances between Au and graphene are
estimated from four-probe measurements to be approximately 212 × 10
-6
Ω cm
2
[103,
104]. Based on this result, the contact resistances between silicon and graphene are
estimated to be ~73.6 × 10
-6
Ω cm
2
from the linear region of the I-V
bias
characteristics
(from 0.6 to 1.0 V), as shown on Figure 2. The lower contact resistance indicates the
bonding energy of graphene-silicon interface (151 ± 28 mJ/m
2
) is slightly higher than that
52
Figure 4-2. Current-voltage characteristics of a graphene on n-Si device with and without
illumination. The inset figure shows current on a log scale.
of graphene-Au interface ( ~ 160 mJ/m
2
)[115, 116]. In these experiments, approximately
30mW of laser power uniformly illuminate the graphene flake. The finite photocurrent
and open circuit voltage can be seen more clearly in the inset, indicating photoexcitation
of carriers and photocurrent generation.
Graphene bilayers deposited on the p-type Si substrates (p ~ 1.25× 10
14
cm
-3
) were
also studied. As shown in Figure 4-3, the I-V
bias
data of this device taken with and
without uniform laser illumination exhibits rectifying behavior under negative applied
voltages. In the inset of Figure 4-3, the rectifying I-V
bias
curve taken without illumination
is enlarged, demonstrating the Schottky barrier formed between graphene and p-Si. In
this device, a 250 µA photocurrent is observed at V
bias
= 3 V under 532 nm laser
illumination.
-1.0 -0.5 0.0 0.5 1.0
-30
0
30
60
90
120
150
180
210
-1.0 -0.5 0.0 0.5 1.0
1E -10
1E -9
1E -8
1E -7
1E -6
1E -5
1E -4
Bias V oltage (V )
Log (| I |)
Light Off
Light On
Bias Voltage (V)
Current (µA)
53
3 2 1 0 -1 -2 -3
250
200
150
100
50
0
-50
Light Off
Light On
Current (µA)
Bias Voltage (V)
3 2 1 0 -1 -2 -3
0
-2
-4
-6
-8
Dark Current (µA)
Bias Voltage (V)
Spatially mapped photocurrents were also measured on the graphene-silicon
device shown in Figure 4-1. Figure 4-4a shows an optical image of the device, together
with the grid used to measure the photocurrents shown in Figure 4-4b. Here, a 10 mW
laser beam is focused to a 0.5mm spot size and irradiated at every intersection of the grid,
separately, while I-V data is taken. The photocurrent map presented in Figure 4-4b plots
the current distribution over the device area at V
b
= 0V. The current map shows very
weak photocurrent generation in regions without graphene, and the current tends to be
higher in the region closer to the Au electrodes. A plot of the spatial dependence of the
short circuit photocurrent (Figure 4-4c) exhibits a linear spatial dependence, which is
consistent with the series resistance hypothesis put forth in this paper. Here, the in-plane
resistance creates an effective load resistance in the circuit, which causes the measured
photocurrent to be reduced when illuminating away from the gold electrode under the
same laser intensity. An alternative explanation of the spatial dependence of the
photocurrent is oxidation driven by oxygen diffusion from the graphene-silicon edge.
Figure 4-3. Current-voltage characteristics of a graphene on p-Si Schottky diode with and
without illumination. Inset shows the enlarged dark current-voltage characteristics.
54
However, if it were due to oxidation, any spatial variation in photocurrent due to
the oxide thickness would result in large changes spanning orders of magnitude, rather
than the ~4× changes observed in our measurements.
Au electrode
graphene
3µm
6
5
4
3
2
1
-0.8580
-0.7540
-0.6500
-0.5460
-0.4420
-0.3380
-0.2340
-0.1300
-0.02600
X-axis
I
sc
, V
bs
= 0 V
µA
1 2 3 4 5 6
0.0
-0.2
-0.4
-0.6
-0.8
Slope = 0.058
I
sc
(µA)
Position along X-axis
(b)
Au electrode
(c)
(a)
Figure 4-4. (a) Optical microscope image of a graphene flake and gold electrode. (b)
Short-circuit photocurrent spatial map. (c) Short-circuit photocurrent along the X-axis
of the short-circuit photocurrent map in (b).
55
-1.0 -0.5 0.0 0.5 1.0
-50
0
50
100
150
200
250
300
350
400
-1.0 -0.5 0.0 0.5 1.0
1E-10
1E-9
1E-8
1E-7
1E-6
1E-5
1E-4
Bias Voltage (V)
Log (| I |)
100K
300K
400K
Current (µA )
Bias Voltage (V)
3 2 1 0 -1 -2 -3
2
0
-2
-4
-6
-8
-10
-12
3 2 1 0 -1 -2 -3
1E-12
1E-11
1E-10
1E-9
1E-8
1E-7
1E-6
1E-5
Bias Voltage (V)
Log (| I |)
100K
300K
400K
Current (µA )
Bias Voltage (V)
(b)
(a)
The current-voltage characteristics of the graphene on n-type and p-type silicon
devices were also measured at temperatures T = 100 K, 300 K, and 400 K without
illumination, as shown in Figure 4-5. Here, the current increases as the temperature
increases in both n-type and p-type devices, due to thermally excited electrons, which
enhance the carrier concentration in the underlying silicon substrates[117, 118]. The
current measured at T = 400 K is over 400 times that observed at T = 100 K in p-Si
devices at V
b
= -3V, as shown more clearly in the inset of Figure 4-5b.
The current flowing across a Schottky diode can be expressed by the ideal diode
equation:
𝐼= 𝐼
!
𝑒
!!
!"#$
!
!"
!
!
!
−1 ,
(4-‐1)
where I
o
is the reverse saturation current and n
id
is the ideality factor. For an ideal diode,
n
id
= 1, and n
id
>
1 for non-ideal diodes[119]. A fit of the data shown in Figure 4-2 yields
Figure 4-5. Current-voltage characteristics measured at T = 100 K, 300 K, and 400 K for (a)
an n-Si device and (b) a p-Si device. The inset figures show current on a log scale.
56
an ideality factor of 4.89. The ideality factors of several devices are listed in Table 3, and
range from 4.89 to 7.69 for n-Si devices and 29.67 to 33.50 for p-Si devices at room
temperature. The largest ideality factor among the n-Si diodes, 7.69, corresponds to a
three
layer graphene-silicon diode, however, no obvious dependence of the ideality factor
on graphene layers was observed.
Sample
Number
of
Graphene
Layers
Graphene-‐Si
Contact
Area(µm
2
)
Substrates
Ideality
Factor
𝜑
!"/!
(eV)
100K
300K
400K
100K
300K
400K
N7P1
2
64.2
n-‐Si
12.6
5.39
6.67
0.128
0.415
0.495
N7P2
2
24.2
n-‐Si
11.8
4.89
4.25
0.127
0.416
0.403
N7P3
2
19.0
n-‐Si
13.4
5.80
5.82
0.118
0.406
0.480
N5P1
3
92.0
n-‐Si
16.6
7.69
NA
0.128
0.425
NA
P1P3
2
16.9
p-‐Si
89.0
29.7
27.6
0.131
0.436
0.491
P1P1
Multiple
57.9
p-‐Si
82.6
33.5
24.9
0.144
0.46
0.558
Figures 4-2 and 4-3 illustrate three major differences between n-Si and p-Si
substrate graphene Schottky diodes, including turn-on bias, current intensity, and
photocurrent. First, the n-Si device is turned on with a positive bias and p-Si device with
a negative bias, due to the different majority carriers in the substrate. Second, the
magnitude of the current density in the n-Si devices is significantly higher than those
Table 3. Summary of data taken on several different graphene-silicon Schottky diode devices.
57
measured in the p-Si devices. For instance, the current density of sample N7P2 is 8.24 ×
10
6
A/m
2
at V
b
= 1 V, while that of sample P1P3 is only 4.59 × 10
5
A/m
2
at V
b
= -3 V.
The saturation current, I
o
, in Equation 1 can be expressed as:
𝐼
!
=𝐴
∗
𝑇
!
𝑒
!
!!
!"/!
!
!
!
𝐴
(4-2)
and
𝜑
!"/!
=
!
!
!
!
𝑙𝑛[
!!
∗
!
!
!
!
] (4-3)
where 𝐴 is the graphene-Si contact area, 𝐴
∗
is the effective Richardson’s constant, which
is 112 A cm
-2
K
-2
for n-Si and 32 A cm
-2
K
-2
for p-Si substrates[120], and 𝜑
!"/!
is the
Schottky barrier. From Equations 4-2 and 4-3, the Schottky barriers are estimated to be
0.41 eV on average for the bilayer graphene n-Si devices and 0.44 eV for the bilayer
graphene p-Si device at 300K, which is consistent with the higher current densities
observed in n-Si devices versus p-Si devices. These values are considerably smaller than
the Schottky barrier heights (~0.7eV) measured previously in graphene/graphene-oxide
interfaces [105]. The third difference between n-Si and p-Si devices is the photocurrent.
Unlike the dark current, the photocurrent is more pronunced in p-Si devices (under
positive bias) than in n-Si devices (under negative bias). The photocurrent in p-Si devices
is 45.8 µA (under V
bias
= 1 V and 30 mW uniform laser illumination), while it is only
11.7 µA in n-Si devices (under V
bias
= -1 V and 30 mW uniform laser illumination).The
steady-state photocurrent density of Schottky diode is expressed as:
𝐽
!
=𝑒𝑊 𝐺
!
(4-4)
58
where 𝐺
!
is the generation rate of excess carriers, and 𝑊 is the space charge region width,
and is expressed as:
𝑊= [
!!
!
(!
!"
!!
!
)
!!
!/!
]
!/!
(4-5)
where 𝑉
!"
= 𝜑
!"/!
− 𝜑
!/!
(4-6)
and 𝜑
!/!
= 𝐸
!/!
−𝐸
!"
=𝐾𝑇𝑙𝑛(
!
!/!
!
!/!
) (4-7)
𝑁
!
(~ 2.5 × 10
15
cm
-3
) and 𝑁
!
(~ 1.25 × 10
14
cm
-3
) are the carrier concentrations, 𝜖
!
is permittivity of silicon, 𝑉
!
is the applied reverse-bias voltage, and 𝑁
!
(~ 2.8 × 10
19
cm
-3
)
and 𝑁
!
(~ 1.09 × 10
19
cm
-3
) are effective density of states function in conduction and
valence bands [14]. Taking, for example, samples N7P2 and P1P3 at V
R
= -1 V and 300K,
Equation 4-5, 4-6 and 4-7 gives, 𝜑
!
= 0.242 eV, 𝜑
!
= 0.295 eV, and W(N7P2) = 9.51 ×
10
-5
cm, W(P1P3) = 3.82 × 10
-4
cm. The contact area of sample N7P2 is 24.2 µm
2
and
16.9 µm
2
for sample P1P3, these result in the photocurrent ratio (I
N7P2
/ I
P1P3
) to be 0.356
which is slightly higher than the experimental value (0.255). However, the differences of
space charge region width here are still believed to be the major factor for the higher
photocurrents observed in p-Si devices. Equation 4-3 indicates that the ambient
temperature has major influence on the Schottky barriers. This can be seen in Table 3,
which shows how Schottky barrier heights vary with temperature. Unlike the I-V
characteristic shown in Figure 4-5, Table 3 indicates that the Schottky barriers decrease
as the temperature decreases, while Figure 4-5 shows the current increases at high
temperature. These results imply that the current intensity is dominated by thermal
excitation instead of Schottky barriers height.
59
2 1 0 -1 -2
0
-2
-4
-6
-8
-10
2 1 0 -1 -2
1E -11
1E -10
1E -9
1E -8
1E -7
1E -6
1E -5
Bia s V ilta g e (V )
Log | I |
Current (µA)
Bias Voltage (V)
Before
After
Figure 4-6 shows the I-V characteristics of a p-Si diode measured in air at 300K
before and after the device was annealed in vacuum at 200
o
C for 20 hours. The Raman
spectra exhibit G band upshifts of 4.6 cm
-1
and linewidth narrowing of 2.8 cm
-1
after the
vacuum annealing. According to Remero et al., graphene FET devices exposed in air for
several days are found to be p-type and after kept in vacuum for 20 hours at 200 °C, the
devices became n-type[121]. Therefore, the variations in the Raman spectra and I-V
characteristics in vacuum shown in Figure 4-6 are believed to be due to the n-type doping
of the graphene in vacuum [122]. This n-type doping results in the observed G band
upshift and linewidth narrowing, and causes a 0.036eV increase in the Schottky barrier.
This observation implies that the Schottky barrier between graphene and the underlying
silicon substrate can be modified by individually doping the graphene.
Strain in the intermediate region between the Si and gold contact regions could
also affect the device transport characteristics. We have ruled out the possibility of strain
in this intermediate region by measuring the Raman spectra, which show G band modes
in the range of 1582 to 1585 cm
-1
, which is similar to normal unstrained graphene [77]
Figure 4-6. Current-voltage characteristics of a graphene on p-Si Schottky diode before and
after vacuum annealing.
60
[123]. Any appreciable strain would result in a significant downshift of this vibrational
mode (14.2 cm
-1
/% for single layer and 12.1 cm
-1
/% for three layer graphene), as
observed by Ni et al. and Yu et al[45] [46].
Conclusion
The I-V characteristics of graphene-silicon interfaces indicate that a Schottky
barrier is formed at the interface between the graphene and silicon. The magnitude of the
photocurrent flowing across the graphene-silicon devices is spatially dependent, possibly
due to the in-plane series resistance of the graphene. The electrical current of these
devices is also affected by the temperature. Devices at higher temperatures tend to
conduct more strongly. Lastly, both current intensity and ideality factor do not show
obvious dependence on the graphene thickness.
61
Chapter 5
Gate Tunable Graphene-Silicon Ohmic/Schottky Contacts
Introduction
We show that the I-V characteristics of graphene-silicon junctions can be actively
tuned from rectifying to Ohmic behavior by electrostatically doping the graphene with a
polymer electrolyte gate. Under zero applied gate voltage, we observe rectifying I-V
characteristics, demonstrating the formation of a Schottky junction at the graphene-
silicon interface. Through appropriate gating, the Fermi energy of the graphene can be
varied to match the conduction or valence band of silicon, thus forming Ohmic contacts
with both n- and p-type silicon. Over the applied gate voltage range, the low bias
conductance can be varied by more than three orders of magnitude. By varying the top
gate voltage from -4 to +4 V, the Fermi energy of the graphene is shifted between –3.78
and −5.47 eV; a shift of ±0.85eV from the charge neutrality point. Since the conduction
and valence bands of the underlying silicon substrate lie within this range, at −4.01 and
−5.13 eV, the Schottky barrier height and depletion width can be decreased to zero for
both n- and p-type silicon under the appropriate top gating conditions. I-V characteristics
taken under illumination show that the photo-induced current can be increased or
decreased based on the graphene-silicon work function difference.
Metal-semiconductor interfaces form Schottky junctions due to the mismatch of
their work functions and electron affinities[124]. These junctions are characterized by a
Schottky barrier, a depletion width, and rectifying behavior. In typical MOSFET devices,
regions of heavily doped semiconductor are needed in order to reduce the high resistance
associated with these metal-semiconductor junctions. However, these p
+
and n
+
regions
62
present several problems as the channel lengths of transistors are scaled down to the
22nm node and beyond. For example, diffusion of dopants into the active channel region
can cause a significant reduction in the gain of these devices. Therefore, a method for
producing low (or zero) Schottky barrier metal-semiconductor junctions without doping
the semiconductor is highly desirable.
Polymer electrolyte doping has been reported as an effective way of doping
carbon nanotubes and graphene[125-128]. Lu et al. fabricated polymer electrolyte-gated
carbon nanotube transistors[129], and Das et al. reported electrochemical top-gated
graphene transistors, which show that the Fermi energy of graphene can be shifted by
over 0.7 eV[5]. From these previous works, the Fermi energy of graphene in our
experiment is estimated to be shifted by ± 0.85 eV from the charge neutrality point by
polymer electrolyte doping.
In our previous work, Schottky diode behavior was demonstrated in graphene-
silicon junctions using a simple fabrication technique[130]. Tongay et al. have observed
Schottky contacts between bulk graphite and Si, GaAs, 4H-SiC, and GaN
substrates[131]. In these previous works, however, the Fermi energy of the graphene was
not varied by an external gate. The Schottky junction behavior at graphene-
semiconductor interfaces and graphene’s highly transparent nature have also been
extended to photovoltaic applications[132-136]. Graphene-silicon nanowire Schottky
junctions have reported solar conversion efficiencies of 1.25%. The conversion efficiency
of these graphene-silicon devices could be further improved by exposing the graphene to
SOCl
2
and HNO
3
vapors, which leads to p-type doping of the graphene[137, 138]. In this
prior work, the enhancement in energy conversion efficiency was attributed to the
63
increased graphene conductance caused by p-type doping. However, it is also likely that
the variation of the Schottky junction with doping also contributed to their experimental
observations. Tongay et al. have studied the effect of bromine intercalation of graphite on
the Schottky barrier height formed at many-layer-graphene (MLG)/GaN interfaces[139,
140]. These previous works suggest that the electron transport in these devices can be
changed by shifting of the graphene work function.
Experiment
In this work, we measure the I-V characteristics of graphene-silicon contacts
while varying the work function (i.e., Fermi energy) of graphene. We explore the effects
of both n- and p-doping of graphene on the conductance of the interface, for both n- and
p-type silicon substrates. Photocurrent generation in these graphene-silicon junctions is
also studied as a function of graphene doping, in order to further understand the
Schottky/Ohmic nature of the junction.
Graphene is grown on copper foil by chemical vapor deposition (CVD)[141-146].
Poly(methyl methacrylate) (PMMA) is then spin coated on the graphene surface right
after the growth to avoid unwanted doping from air and to prevent the graphene film
from breaking during the graphene transfer process. The underlying copper foil is then
etched away using copper etchant to separate the graphene film from the copper foil.
Before transferring the graphene film, an oxidized silicon wafer is patterned
photolithographically to expose 300×300 µm windows, which are subsequently etched
using buffered oxide etch (BOE) 7:1 in order to remove the SiO
2
and expose the
underlying silicon. Pd/Ti (50/5 nm thickness) electrodes are deposited 100 µm away from
the silicon windows, as shown in Figure 5-1a. Graphene films are then transferred to the
64
(b)
Figure 5-1. (a) Optical microscope image of the graphene-on-silicon device before depositing the
electrolyte top gate, and (b) schematic diagram of the device structure.
(a)
prepared substrates, and the PMMA is removed by acetone vapor. Another
photolithography step is performed to etch all of the graphene in between adjacent
devices. The polymer electrolyte is prepared by dissolving poly (ethylene oxide) (PEO)
and lithium perchlorate (LiClO
4
) (1:0.12 by weight) in methanol[129]. It is then applied
locally to the graphene-silicon contact region of the device, as shown schematically in
Figure 5-1b. A small bias voltage is applied between the graphene (through the Pd
electrode) and the underlying silicon substrate. The top gate voltage is applied by
inserting a small probe into the polymer.
Figure 5-2a shows the I-V
bias
characteristics taken at various top gate voltages
ranging from -4V to +4V for a p-type silicon wafer (100 Ω/cm, p ~ 1.25 × 10
14
cm
-3
). The
inset figure shows the I-V
bias
characteristics of the device taken at V
gate
= 0V, which
exhibits rectifying behavior, indicating the formation of a Schottky junction. As a large
negative (p-doping) gate voltage is applied, the I-V
bias
characteristics evolve to Ohmic
behavior, indicating a reduction of the Schottky barrier height and depletion width.
65
Figure 5-2. I-V
bias
characteristics taken at different gate voltages of (a) graphene-Si (p-type)
and (b) graphene-Si (n-type) devices. The inset figures show the I-V characteristics at V
G
=
0V.
(a) (b)
Figure 5-2b shows the I-V
bias
characteristics of a graphene-silicon interface for an n-type
silicon wafer (15 Ω/cm, n ~ 2.5 × 10
14
cm
-3
). In this dataset, the opposite behavior is
observed, in which Ohmic behavior appears at large positive (n-doping) gate voltages.
Figures 5-3a and 5-3b show the low bias conductance plotted as a function of the
Fermi energy of graphene for p- and n-type silicon substrates, respectively. Over the
applied gate voltage range, the conductance is varied by more than three orders of
magnitude. The charge neutrality point was determined from the I-V characteristics of a
similar graphene sample with source and drain electrodes in a field-effect transistor
geometry[147, 148]. The graphene Fermi energy is determined from the applied gate
voltage using a top gate capacitance of 2.2×10
-6
F/cm
2
, as described by Das et al.[5]. In
Figure 5-3, the work function of graphene is shifted between -3.78 and -5.47 eV, which
corresponds to +0.82 and -0.87 eV from the charge neutrality point[14, 149]. The solid
vertical lines in the plots correspond to the conduction and valance bands of silicon, and
the dashed line indicates the Fermi energy of the silicon substrate. For the p-type silicon
-1.0 -0.5 0.0 0.5 1.0
-60
-40
-20
0
20
40
60
-1.0 -0.5 0.0 0.5 1.0
0
10
20
30
40
50
Vg = 0 V
Current (µA)
Bia s V o lta g e (V )
Vg=4V
Vg=2V
Vg=1.5V
Vg=1V
Vg=-2V
Vg=-3V
Vg=-4V
V
g
=4V V
g
=2V V
g
=1.5V
V
g
=1V
Bias Voltage (V)
Current (µA)
-1.0 -0.5 0.0 0.5 1.0
-30
-20
-10
0
10
20
30
-1.0 -0.5 0.0 0.5 1.0
-8
-6
-4
-2
0
Vg=0V
Current (µA )
Bias Voltage (V)
Vg=-4V
Vg=-2V
Vg=-1.5V
Vg=-1V
Vg=2V
Vg=3V
Vg=4V
V
g
=-4V
V
g
=-2V
V
g
=-1.5V
V
g
=-1V
Current (µA )
Bias Voltage (V)
66
Figure 5-3. Low bias conductance plotted as a function of graphene Fermi energy for (a)
graphene-Si (p-type) and (b) graphene-Si (n-type) devices. The right and left solid vertical
lines represent the conduction and valence bands of silicon, and the middle dashed line
represents the Fermi energy of silicon.
(a) (b)
sample (Figure 5-3a), the low bias conductance increases as the graphene Fermi energy is
decreased and tends to saturate after passing the valence band of silicon. For the n-type
sample (Figure 5-3b), the conductance increases as the graphene Fermi energy
approaches the conduction band of silicon. These observations indicate that p-type (n-
type) doping of graphene leads to a decrease of the Schottky barrier formed with the
underlying p-type (n-type) silicon, thus, leading to a transition from rectifying to Ohmic
behavior, as observed in Figure 5-2.
Here, we build a model to provide a theoretical study of the electron transport in
graphene-silicon interface, and simulate the device conductance. The model simulates the
individual electron distribution in graphene and silicon, and then combines both of them
to conclude the electron conductance of graphene-silicon interface with respect to the
shifting of graphene Fermi energy.
First, the graphene-electron distribution can be expressed as:
-0.9 -0.6 -0.3 0.0 0.3 0.6 0.9
0
10
20
30
40
50
60
70
Low Bias Conductance (µS)
Fermi Energy (eV)
E
V
(Si) E
F
(Si) E
C
(Si)
-0.9 -0.6 -0.3 0.0 0.3 0.6 0.9
0
50
100
150
200
Low Bias Conductance (µS)
E
V
(Si) E
F
(Si) E
C
(Si)
Fermi Energy (eV)
[ ] [ ]
F
G
F
E E f S GrapheneDO E E , , • =
67
where
Graphene-hole distribution:
Second, silicon-electron distribution is:
Where
and
By combining electron transports in graphene and silicon, the electron conductance is
concluded as:
[ ]
KT
E E F
F
e
E E f
−
+
=
1
1
,
0 / 10 11 . 1
0 / 10 04 . 1 : :
6
6
< ×
> ×
F
F F
E s m
E s m Velocity Fermi υ
[ ] [ ] [ ]
F
G
F
E E f S GrapheneDO E E , 1 , − • =
[ ] ( ) [ ] [ ]
Si
F
Si
F
E E f E DOS electron Silicon E E , _ _ , • =
( ) ( )
otherwise
E E if E E N E DOS electron Silicon
Si
C
Si
C C
0
_ _
=
> − • =
Band Conduction in DOS Effective cm N
C
3 19
10 8 . 2
−
× =
[ ] ( ) [ ] [ ]
Si
F
Si
F
E E f E DOS hole Silicon E E , 1 _ _ , − • =
Band Valence in DOS Effective cm N
V
3 19
10 04 . 21
−
× =
[ ]
[ ] [ ]
[ ] [ ]dE E E on distributi hole Silicon E E on distributi hole Graphene
dE E E on distributi electron Silicon E E on distributi electron Graphene
Si
F
G
F
Si
F
G
F
∫
∫
∞
∞ −
∞
∞ −
•
+
•
=
, _ _ , _ _
, _ _ , _ _
E e Conductanc
F
68
E
barrier
X
2
-X
1
X
Potential Energy (eV)
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
− ≅
E
E m
T
Barrier
t
! 3
2 4
exp
2
3
*
0
2
,
2
=
⎟
⎠
⎞
⎜
⎝
⎛
− = Ex
E
x x
Barrier
Barrier
Barrier
E Ex
E
x x = ⎟
⎠
⎞
⎜
⎝
⎛
− − =
2
,
1
Assuming the potential barriers in graphene-silicon interface is a triangular barrier, as
show in the Figure, and the tunneling potential can be expressed as:
The simulated conductance is plot together with the experimental data in Figure
5-4. Both experimental and simulated results show the sudden increasing and saturation
2
1
2
1
2
3
*
2
*
2
2
3
4
exp
2
2
2 exp
x
x
barrier
x
x
Barrier
t
Ex
E
E
m
dx Ex
E m
T
−
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
− =
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
− − ≅
∫
!
!
[ ]
[ ] [ ]
[ ] ( )
[ ] [ ]dE E E on distributi hole Silicon E E on distributi hole Graphene
dE E E probility tunneling electron type n
E E on distributi electron Silicon E E on distributi electron Graphene
E E type n
Si
F
G
F
G
F
Si
F
G
F
G
F
∫
∫
∞
∞ −
∞
∞ −
•
+
+ •
•
= −
, _ _ , _ _
, _ _ _ _ 1
, _ _ , _ _
, _ e Conductanc _ Full
69
-0.9 -0.6 -0.3 0.0 0.3 0.6 0.9
0.00
0.25
0.50
0.75
1.00
Normalized Low Bias Conductance
Experimental Data
normolized
E
V
(Si) E
F
(N-Si) E
C
(Si)
Fermi Energy (eV)
-0.9 -0.6 -0.3 0.0 0.3 0.6 0.9
0.00
0.25
0.50
0.75
1.00
Fermi Energy (eV)
Experimental Data
Modeling Data
E
V
(Si) E
C
(Si) E
F
(P-Si)
Normalized Low Bias Conductance
Figure 5-4. Both experimental and modeling normalized low bias conductance plotted as a
function of graphene Fermi energy for (a) graphene-Si (p-type) and (b) graphene-Si (n-type)
devices. The right and left solid vertical lines represent the conduction and valence bands of
silicon, and the middle dashed line represents the Fermi energy of silicon.
of the low bias conductance when the graphene Fermi energy shifts to the conduction or
valence bands of silicon from the charge neutrality point.
Figure 5-5a shows the graphene-silicon I-V
bias
characteristics for a p-type silicon
substrate taken at different gate voltages under illumination with a 50W fiber optic
illuminator. For large negative gate voltages, we observe Ohmic behavior with no photo-
generated current or voltage. Figure 5-5b shows the short circuit current (I
sc
) dependence
on the graphene Fermi energy, which increases sharply when the Fermi energy of the
graphene exceeds that of the silicon substrate, and then saturates in the region near the
conduction band of silicon. This implies that the depletion region in the underlying
silicon substrate increases with the electron carrier concentration in the graphene. The
increased depletion region is able to collect more light, thus resulting in an increased
photocurrent. As mentioned above, Fan et al. also observed I
sc
enhancement in their
70
Figure 5-5. (a) Graphene-silicon I-V
bias
characteristics taken under illumination at different
gate voltages. (b) Short circuit current (I
sc
) with and without illumination plotted as a function
of graphene Fermi energy.
(a) (b)
graphene-silicon device with chemical vapor doping, and attributed the I
sc
enhancement
to the increase in graphene conductance[137]. However both p- and n-type doping cause
an increase in graphene conductance. Therefore, the increased depletion width provides a
more plausible explanation of the I
sc
enhancement with graphene doping.
Conclusion
The I-V characteristics of graphene-silicon contacts can be tuned from rectifying
to Ohmic behavior by electrostatically doping the graphene with a polymer electrolyte
gate. We explore the effects of both n- and p-type doping of graphene on the I-V
characteristics of the interface, for both n- and p-type silicon substrates. Through
appropriate gating, the Fermi energy of the graphene can be varied to match the
conduction or valence band of silicon, thus forming Ohmic contacts with both n- and p-
type silicon. Similarly, the Schottky barrier height and depletion width can also be
increased with electrostatic gating, resulting in rectifying diode behavior and large
-0.9 -0.6 -0.3 0.0 0.3 0.6 0.9
0
2
4
6
8
10
12
14
Dark I
sc
Light I
sc
E
C
(Si) E
F
(Si) E
V
(Si)
Fermi Energy (eV)
Short Circuit Current (µA)
-0.8 -0.4 0.0 0.4 0.8
-20
-10
0
10
20
Vg=4V
Vg=2V
Vg=0V
Vg=-2V
Vg=-4V
Current (µA)
Bias Voltage (V)
V
g
=2V
V
g
=0V
V
g
=4V
V
g
=-4V V
g
=-2V
71
photocurrents. Over the applied gate voltage range, the low bias conductance can be
varied by more than three orders of magnitude.
72
Chapter 6
Thermal Interface Conductance across a
Graphene/Hexagonal Boron Nitride Heterojunction.
Introduction
We measure thermal transport across a graphene/hexagonal boron nitride (h-BN)
interface by electrically heating the graphene and measuring the temperature difference
between the graphene and BN using Raman spectroscopy. Because the temperature of the
graphene and BN are measured optically, this approach enables nanometer resolution in
the cross-plane direction. A temperature drop of 60 K can be achieved across this
junction at high electrical powers (14mW). Based on the temperature difference and the
applied power data, we determine the thermal interface conductance of this junction to be
7.4 × 10
6
Wm
-2
K
-1
, which is below the 10
7
-10
8
Wm
-2
K
-1
values previously reported for
graphene/SiO
2
interface.
During the past two years, a number of novel 2 dimensional (2D) heterostructure
devices have emerged, such as graphene/h-BN, graphene/MoS
2
, and InAs/WSe
2
[29, 150-
153]. For in-plane electron transport in graphene, much higher electron mobility is
observed in graphene/h-BN devices than graphene/SiO
2
devices[17]. Moreover, novel
vertical 2D heterostructure devices have achieved much larger on/off ratios than lateral
graphene devices, and show interesting transport phenomena such as rectification and
negative differential resistance[130, 154-156]. In these types of devices, a large cross-
plane electric field exists across a thin 2D stack, and can result in localized heating[18].
Despite the large in-plane thermal conductivity of graphene, even when supported on an
73
amorphous substrate[157-159], heat dissipation from 2D devices has been found to be
limited by vertical heat transfer[19, 20]. Consequently, the operating temperature of 2D
devices is strongly influenced by the interface thermal conductance between the 2D
materials and the materials in contact.
There have been several measurements of graphene/SiO
2
, graphene/metal,
graphene/Si, and graphene/SiC interfaces[25, 26, 28, 130, 154, 160-163], as well as
theoretical calculations of thermal interface transport across such interfaces. It has been
predicted that high interface conductance can be achieved in graphene/h-BN interfaces
because of the similar crystal structure[164-166]. However, experimental measurement of
interface thermal conductance across such an interface is still lacking.
Experiment
Here, we measure the thermal interface conductance across the graphene/h-BN
interface by depositing graphene on h-BN substrates and passing electric current through
the graphene to electrically heat the graphene. The temperature variation of the graphene
and the underlying h-BN substrate during the electrical heating is monitored by Raman
spectroscopy[167]. Because of the optical transparency of graphene[132, 133, 145],
Raman spectroscopy of both the graphene and h-BN can be monitored at the same time.
The most prominent features in the Raman spectra of graphene are the G (1580 cm
-1
) and
2D (2680 cm
-1
) bands, which downshift with increasing temperature[51, 78, 168-172].
The Raman frequency of the optical phonon mode in h-BN can be observed at 1370 cm
-1
.
This mode also downshifts significantly with increasing temperature, enabling the lattice
temperature to be determined from the Raman spectra. From these Raman frequencies,
the temperature of the graphene and the h-BN can be obtained during the electrical
74
heating process to obtain the temperature drop across the graphene/h-BN interface and,
thus, the interfacial thermal conductance[173-175].
Figure 6-1a shows an optical microscope image of the graphene/h-BN device.
Here, the h-BN flake is exfoliated from bulk BN by the “Scotch tape” method and
deposited on a Si/SiO
2
substrate. Graphene is grown on a copper substrate at 1000
o
C by
chemical vapor deposition (CVD) using CH
4
as the carbon feedstock[141]. The graphene
is then transferred to the BN flake using a polymethyl methacrylate (PMMA) transfer
layer and wet chemical etching. Electron beam lithography (EBL) and oxygen plasma
etching are then used to pattern a 3 µm by 10µm graphene strip on the h-BN surface, as
shown in Figure 6-1a. This procedure patterns a PMMA mask that protects the active
graphene device area during the etch process[176]. Raman spectroscopy confirms that
this graphene is monolayer with a single 2D peak[70, 170]. The Ti/Au electrodes are
patterned and deposited using another EBL step and metal evaporation. The device is
baked under vacuum at 150
o
C for 5 hours to anneal the graphene/h-BN interface. Once
annealed, the device is more robust against any further substrate-induced doping and
strain associated with the elevated temperatures reached during the electrical heating
process[177, 178]. The device is then subsequently mounted in a vacuum cryostat. Figure
6-1b shows the schematic diagram of the device and the experiment setup. Electric
current is passed through the graphene strip ranging from 0 to 1.5 mA. Raman spectra are
collected with a Renishaw inVia spectrometer using a 40X/0.6 NA objective lens to focus
a 532 nm excitation laser at the center of the graphene strip. Raman spectra are also
collected every 0.25 mA increment in current to monitor the temperature changes in the
graphene and underlying h-BN.
75
Figure 6-1. (a) Optical imageand (b) schematic diagram of the graphene/h-BN device and
experiment setup.
Figures 6-2a and 6-2b show the Raman frequencies of the G and 2D bands of the
graphene monolayer plotted as a function of the applied electric power. Both modes show
a significant downshift with increasing applied power, indicating heating in the graphene.
The Raman frequency of the h-BN optical phonon mode is also monitored, as shown in
Figure 6-2c. This mode also downshifts indicating a temperature rise in the h-BN flake.
The Joule heating-induced peak shifts of these Raman modes downshift linearly with the
applied power, as one would expect from increasing lattice anharmonicity with
temperature[179]. The experiment was then repeated to ensure that no irreversible
changes occur in this structure during the measurement, such as strain or compression
caused by the mismatch of the thermal expansion between graphene and h-BN due to the
electrical heating[81, 180]. We observe consistent results in the Raman frequency shifts
during the first and second electrical heating measurements, and the Raman spectra taken
before and after the measurement, which is provided in the supplemental information
document, show no significant changes, indicating that no oxidation or irreversible
damage occur during this procedure. Electrostatic doping by an applied voltage can also
(a) (b)
76
Figure 6-2. Raman frequency shifts of
the (a) G and (b) 2D bands of the
graphene, and (c) h-BN optical phonon
mode plotted as a function of the
electrical heating power.
result in changes in the Raman peak positions and linewidths, however, the full width at
half maximum (FWHM) of the 2D and G bands are FWHM
2D
(0A) = 35.8 cm
-1
,
FWHM
G
(0A) = 20.5 cm
-1
, and FWHM
2D
(1.5mA) = 35.6cm
-1
, FWHM
G
(1.5mA) = 20.2
cm
-1
. These variations with applied voltage/current are less than 1 cm
-1
, indicating that
electrostatic doping effects are negligible in these measurements[181].
The temperature-induced downshifts of the Raman modes of the graphene and h-
BN are calibrated in a temperature-controlled stage from 300K to 400K, as shown in
Figure 6-3. These downshifts show a linear dependence on temperature with coefficients
of -0.0102 and -0.0215 cm
-1
/K for the graphene G and 2D bands, respectively, and -
0.0246 cm
-1
/K for the h-BN. Based on these coefficients, we can convert the Raman
downshifts observed in Figure 6-2 to temperature, and plot the temperature as the
0 4 8 12 16
2697
2698
2699
2700
2701
Raman Shifts (cm
-1
)
Power (mW)
0 4 8 12 16
1369
1370
1371
1372
Raman Shifts (cm
-1
)
Power (mW)
0 4 8 12 16
1585.6
1586.0
1586.4
1586.8
1587.2
1587.6
Raman Shifts (cm
-1
)
Power (mW)
(a) (b)
(c)
77
Figure 6-3. Temperature calibration of
the Raman frequency shifts of the (a) G
and (b) 2D bands of the graphene, and
(c) h-BN optical phonon mode plotted
as a function of temperature.
Figure 6-4. Temperature of the graphene and h-BN calibrated with Gand 2D bands and BN
optical phonon Raman frequencies during the (a) first and (b) second electrical heating.
function of the applied power, as shown in Figure 6-4. Figure 6-4b shows the temperature
data from a second subsequent data run, showing excellent agreement with the first, as
shown in Figure 6-4a, indicating that no irreversible changes took place during initial
electrical heating measurement.
300 320 340 360 380 400
1586.0
1586.4
1586.8
1587.2
Slope : -0.0102
Raman Shifts (cm
-1
)
T (K)
300 320 340 360 380 400
2697.0
2697.5
2698.0
2698.5
2699.0
2699.5
Slope : -0.0215
Raman Shifts (cm
-1
)
T (K)
300 320 340 360 380 400
1369.5
1370.0
1370.5
1371.0
1371.5
1372.0
Slope : -0.0246
Raman Shifts (cm
-1
)
T (K)
(a)
(b)
(c)
0 4 8 12 16
280
320
360
400
440
480
BN
G
2D
T (K)
Power (mW)
0 4 8 12 16
280
320
360
400
440
480
BN
G
2D
T (K)
Power (mW)
(a) (b)
78
The measured temperature drop across the graphene-BN interface, (ΔT = T
Graphene
– T
BN
), shown in Figure 6-5, increases with the electrical heating power, Q = I
2
R. The
slope of the curve normalized by the interface area (A = 30 µm
2
) is the interface thermal
conductance (G
th
) of the graphene/h-BN interface, G
th
= Q/(A×ΔT), where A is the
graphene-BN contact area[21]. Based on the G band and 2D band temperatures,
respectively, the G
th
values are 6.88 MWm
-2
K
-1
and 7.73 MWm
-2
K
-1
during the first
electrical heating (Figure 6-5a), and 7.57 MWm
-2
K
-1
and 7.47 MWm
-2
K
-1
from the
second electrical heating (Figure 6-5b). These values are averaged to obtain G
th
of
7.41±0.43 MWm
-2
K
-1
, which is substantially lower than the theoretically calculated value
of 1.87×10
8
Wm
-2
K
-1
[164] and previously reported values of 10
7
-10
8
Wm
-2
K
-1
for
graphene/SiO
2
, graphene/Ti/Au, and graphene/Au interfaces, but higher than the value of
1.89×10
4
Wm
-2
K
-1
reported for graphene/SiC interfaces[26, 28, 160, 161, 163]. We
expect the thermal interface conductance of these randomly stacked heterostructures
obtained by mechanical exfoliation and PMMA transfer to be significantly lower than
that of lattice-matched graphene grown on BN, which more closely resembles theoretical
calculations[164]. This is a current limitation of our experimental approach that may be
resolved technically in the future. However, lower thermal interface conductance is
advantageous for applications in thermoelectric energy conversion. Moreover it is likely
that contaminations of the interface by liquid or organic residues have resulted in further
discrepancies between the measured and theoretical results, as well as, variations between
different experimental results.
79
Figure 6-5. Temperature difference across the interface of graphene/h-BN calibrated with
2D, G bands and BN optical phonon Raman frequencies of the (a) first and (b) second
electrical heating.
Conclusion
Motivated by a recent Raman measurement of thermal interface conductance
between graphene and the SiC substrate[163], this experiment shows that the thermal
interface conductance of a graphene/h-BN interface can be obtained by electrical heating
of the graphene sheet while monitoring the temperatures of the graphene and BN using
Raman spectroscopy. While the depth resolution of the measured SiC temperature was
set by the optical penetration depth in the SiC substrate in the earlier measurement[163],
the current measurements can achieve atomic scale depth resolutions in the measured
temperatures in both graphene and h-BN. As such, the current experiments are able to
resolve the temperature drop over atomic distance between the graphene and underlying
h-BN, which allows for direct probing of the graphene/h-BN thermal interface
conductance. In contrast to theoretical predictions of high thermal interface conductance
across a clean graphene/h-BN interface[164], the results show that the thermal interface
conductance for the graphene/h-BN device prepared by the PMMA transfer method is
0 4 8 12 16
0
20
40
60
80
Slope (with G) : 4.314
Calibrated with G
Calibrated with 2D
ΔT (K)
Power (mW)
Slope (with 2D) : 4.848
0 4 8 12 16
0
20
40
60
80
Calibrated with G
Calibrated with 2D
ΔT (K)
Slope (with G) : 4.464
Slope (with 2D) : 4.402
Power (mW)
(a) (b)
80
7.41±0.43 MWm
-2
K
-1
, which is lower than those reported for graphene/SiO
2
,
graphene/Ti/Au, and graphene/Au interfaces, and higher than that reported for
graphene/SiC interface. The results suggest the importance in improving the interface
quality in order to increase the interface conductance.
81
Chapter 7
Thermoelectric Transport Across Graphene/Hexagonal
Boron Nitride/Graphene Heterostructures
Abstract
We report thermoelectric transport measurements across a graphene/hexagonal
boron nitride (h-BN)/graphene heterostructure device. Using an AC lock-in technique, we
are able to separate the thermoelectric contribution to the I-V characteristics of these
important device structures. The temperature gradient is measured optically using Raman
spectroscopy, which enables us to explore thermoelectric transport produced at material
interfaces, across length scales of just 1-2 nm. Based on the observed thermoelectric
voltage (∆V) and temperature gradient (∆T), a Seebeck coefficient of 99.3 µV/K is
ascertained for the heterostructure device. The obtained Seebeck coefficient can be useful
for understanding the thermoelectric component in the cross-plane I-V behaviors of
emerging 2D heterostructure devices. These results provide an approach to probing
thermoelectric energy conversion in two-dimensional layered heterostructures.
Electron transport in the cross-plane direction of layered material heterostructures
has recently shown interesting new functionalities that extend far beyond lateral graphene
devices. Graphene-based heterojunction devices, such as graphene/silicon and
graphene/gallium arsenide diodes, have demonstrated rectifying behavior and gate-
tunable photovoltaic responses[130, 182-190]. Heterostructure devices made by
combining graphene with other 2D materials, such as graphene/hexagonal boron nitride
(h-BN)/graphene and graphene/MoS
2
, have shown interesting electron tunneling
82
transport, negative differential conductance, and light absorption behaviors[29, 150, 152,
191, 192]. In addition to electron transport and light absorption in these graphene-based
heterojunctions, heat dissipation in these types of devices is found to be dominated by
vertical heat transfer[19, 20]. Unlike the large in-plane thermal conductance in graphene
and h-BN, the graphene/h-BN junction demonstrates relatively low interface thermal
conductance. While the low interface thermal conductance is not desirable for electronic
devices, it has stimulated interest in utilizing 2D layered heterostructures for
thermoelectric conversion. For example, Xie et al. have reported a theoretical study of
ballistic thermoelectric properties in boron nitride nanoribbons[193], while Yang et al.
have simulated the thermoelectric properties in hybrid graphene/boron nitride
nanoribbons[194]. However, there have been few experimental studies of thermoelectric
effects in 2D heterostructures.
Here, we report a thermoelectric transport measurement across a graphene/h-
BN/graphene heterostructure. The thermovoltage is measured between the top and
bottom graphene layers using an AC lock-in technique at frequency 2ω, based on Joule
heating created in the top graphene layer with an AC voltage at ω. The temperatures of
the top and bottom graphene layers are determined by monitoring their 2D band Raman
frequencies, revealing temperature drops (∆T) as high as 39 K between the top and
bottom graphene layers. Since the temperatures are measured optically using Raman
spectroscopy, we are able to explore thermoelectric transport across length scales of just
1-2 nm. From the measured thermoelectric voltage (∆V) and the acquired temperature
drops (∆T) between the top and bottom graphene layers, the Seebeck coefficient (S) of
the heterostructure device is established.
83
Experiment
Figures 7-1a and 7-1b show an optical image and schematic diagram illustrating
the profile structure of the graphene/h-BN/graphene
device and the experimental setup.
Here, the monolayer graphene is grown by chemical vapor deposition (CVD) with CH
4
at
1000
o
C on a copper foil, which is then transferred to a Si/SiO
2
substrate, and patterned to
form a 3×100 µm
2
bottom graphene strip using electron beam lithography (EBL) and
oxygen plasma etching[141]. Another EBL and metal evaporation step is then performed
to deposit Ti/Au electrodes on the bottom graphene strip. Multilayer (~5 layers) h-boron
nitride (h-BN) is exfoliated using the ‘Scotch tape’ method and deposited on another
substrate. The multilayer h-BN flake is then transferred onto the center of the bottom
graphene layer with careful alignment, using a sacrificial polymethyl methacrylate
(PMMA) carried layer [195]. The top graphene strip is also fabricated by CVD growth on
copper foil, transferred to another Si/SiO
2
substrate, electron beam lithography (EBL)
patterned and oxygen plasma etched, and then subsequently transfered with careful
alignment to the bottom-graphene/h-BN overlapping region. During the last EBL and
metal evaporation step, electrodes are deposited on the top graphene layer. Next, atomic
layer deposition (ALD) is used to deposit a 60 nm insulating layer of Al
2
O
3
on the
surface of graphene/h-BN/graphene heterosructure to make the device more robust. The
fabricated device is then wire-bonded to a chip carrier for measurements carried out in
vacuum.
84
Figure 7-1. (a) Optical image and (b) schematic diagram of the graphene/h-
BN/graphene/Al
2
O
3
heterostructure device and measurement setup.
Figure 7-2 shows the in-plane and cross-plane I-V characteristics of the bottom
and top graphene strips. Unlike the in-plane I-V characteristics, the cross-plane transport
shows a non-linear I-V curve, indicating electron tunneling through the graphene/h-
BN/graphene heterojunction with a low-bias conductance (G) of 154 nS [150, 196], while
the in-plane conductance are 20 and 23 µS, 2 orders of the magnitude higher than that of
the cross-plane conductance. AC voltages with frequencies ω = 100 and 200 Hz are
applied to the top graphene to provide a temperature gradient between the graphene
layers and induce a thermoelectric voltage across the graphene/BN/graphene
heterostructure at the second harmonic frequencies, 200 and 400 Hz. The 2ω component
of the thermoelectric voltage is a result of e the 2ω component in the Joule heating in the
top graphene layer. The applied AC voltages are kept below 2 Volts to protect the device
and avoid unwanted substrate-induced doping and compression effects in the
graphene[81, 180].
(a)
(b)
85
0.0 0.5 1.0 1.5 2.0
0
1
2
3
4
Temperature (K)
ω=60Hz
ω=120Hz
ΔV
AC
(2ω) (mV)
V
AC
(ω) (V) & V
DC
(V)
300
310
320
330
340
DC
In Figure 7-3, the measured second harmonic thermoelectric voltage is plotted as
a function of the applied AC voltage for both 100 and 200 Hz. Both datasets show the
measured thermoelectric voltage increasing quadratically with the applied AC voltage,
reaching 4 mV at 2 V of the applied voltage.
-0.2 -0.1 0.0 0.1 0.2
-4
-2
0
2
4
-0.2 -0.1 0.0 0.1 0.2
-25
0
25
Top-Bottom Graphene
Current (nA)
Voltage (Volts)
Top Graphene
Bottom Graphene
Top-Bottom Graphene
Voltage (Volts)
Current (µA)
Figure 7-2. In-plane and cross-plane I-V characteristics of the bottom and top graphene
strips of the heterostructure, the inset figure plots the cross-plane I-V characteristics with
the unit of nA.
Figure 7-3. The 200 and 400 Hz thermoelectric voltages across the graphene/BN/graphene
heterostructure as a function of the applied 100 and 200 Hz AC voltages together with the
corresponding DC voltages measured at top graphene temperature (right axis).
86
0.0 0.5 1.0 1.5 2.0
300
310
320
330
340
Point 1
Point 2
Point 3
Temperature (K)
DC Voltage (Volts)
In order to calibrate the temperature of the graphene layers, the Raman spectra of
the graphene layers are measured as a function of the applied voltage. However,
independent measurement of temperature of two graphene layers at the region of the
heterojunction where the two graphene layers overlap is not possible, since the acquired
Raman signal from the top and bottom graphene layers cannot be distinguished. The
temperatures of the two graphene layers can only be observed next the heterojunction,
between the junction and the electrodes, as indicated as points 1, 2, and 3 in Figure 7-4a.
The 2D band Raman frequencies taken from the top graphene layer at point 1 and 2
downshift linearly with the increasing applied voltage, indicating Joule heating in the top
graphene layer, while no frequency shift is observed in the bottom layer at point 3, as
shown in Figures 7-5b, 7-5c, and 7-5d. The temperature coefficients of the Raman
frequencies for the top graphene layer are then calibrated in a temperature controlled
stage and plotted in Figures 7-6a and 7-6b, giving coefficients of -0.029 and -0.035 cm
-
1
/K at point 1 and point 2, respectively.
Figure 7-4. (a) Optical image indicating the locations of Raman spectrum taken near the
heterojunction. (b) Temperature of the graphene at the indicated location with respect to the
applied voltage.
(a) (b)
87
0.0 0.5 1.0 1.5 2.0
2693.0
2693.5
2694.0
2694.5
2695.0
2695.5
2696.0
Point 3
Raman Shifts (cm
-1
)
Voltage (Volts)
0.0 0.5 1.0 1.5 2.0
2696.0
2696.4
2696.8
2697.2
Raman Shifts (cm
-1
)
Voltage (Volts)
Point 1
0.0 0.5 1.0 1.5 2.0
2684.8
2685.2
2685.6
2686.0
2686.4
Point 2
Raman Shifts (cm
-1
)
Voltage (Volts)
Figure 7-5. (a) Optical image indicating the locations of Raman spectrum taken near the
heterojunction. Raman 2D band frequencies as functions of the applied voltage taken at (b)
point 1, (c) point 2 for the top graphene, and (d) point 3 for the bottom graphene.
(a) (b)
(c) (d)
300 320 340 360 380 400
2693
2694
2695
2696
2697
Point 1
Raman Shifts (cm
-1
)
Temperature (k)
Slope : -0.02913 cm
-1
/K
300 320 340 360 380 400
2689
2690
2691
2692
2693
Raman Shifts (cm
-1
)
Point 2
Slope : -0.03504 cm
-1
/K
Temperature (k)
(a) (b)
Figure 7-6. Temperature coefficient of the Raman 2D band frequency for the top graphene
at (a) point 1, and (b) point 2.
88
Here, the thermoelectric voltage is measured with AC Joule heating applied to the
top graphene layer, while the temperature of the top graphene layer is calibrated as a
function of DC heating. In order to ensure that an accurate comparison can be made
between AC and DC heating, we calculate that the thermal time constant of the measured
device is faster than the heating frequency. Because the thermal conductivity of the Si
substrate is much larger than the 300 nm thick SiO
2
layer, heating is assumed to occur
only in and above the SiO
2
layer. As such, the thermal time constant is controlled by the
thermal resistance (R) and thermal capacitance (C) of the SiO
2
layer under the 3×3 µm
2
heated graphene region. The thermal resistance of the SiO
2
layer is, thus, calculated to be
on the order of 25,000 K/W. For the thermal capacitance, we conservatively assume that
the heated region extends in the lateral direction 5 times beyond that of the
heterostructure, which gives an area of 15×15 µm
2
and a thermal capacitance of 1.8 × 10
-
10
J/K. Thus, the thermal time constant is obtained as τ = RC = 4.5 µsec, which
corresponds to a cutoff frequency of 36 kHz. This value is more than two orders of
magnitude higher than the AC frequencies applied here, so that the AC thermal
impedance of the system can be reduced to the DC case, namely the ratio between the AC
temperature rise and AC heating power is very close to that between the DC temperature
rise and DC heating power[197, 198]. This conclusion is further supported by our
measurement results conducted with heat frequencies of 100 and 200 Hz, which yield
approximately the same results.
89
0 10 20 30 40
0
1
2
3
4
Slope: 97.1 µV/K
V
AC
(2ω, 200Hz) (mV)
ΔT (K)
0 10 20 30 40
0
1
2
3
4
Slope: 99.3 µV/K
ΔT (K)
V
AC
(2ω, 400Hz) (mV)
By converting the Raman downshifts to the AC component of the temperature rise,
using the acquired temperature coefficients from the DC calibration, the temperature of
the top graphene can be obtained, as plotted in Figure 7-4b, showing the temperature rise
due to the Joule heating at point 1 and 2. Since no shift in the Raman frequency of the
bottom graphene layer is observed, we obtain an upper limit for the temperature drop, and
hence a lower limit of the Seebeck coefficient (S=∆V/∆T). Our ∆T measurement is
limited to an upper bound because lateral temperature gradients may exist, and thus, the
actual temperature drop directly across the heterostructure may be less than the measured
∆T. In this case, the Seebeck coefficient would be larger than that measured here.
Assuming no lateral temperature gradients, we plot the measured thermoelectric voltage
(∆V) as a function of the cross-plane temperature gradient (∆T) in Figure 7-7 for the 100
and 200 Hz datasets. Here, a consistent linear dependence is observed between the
voltage and the temperature gradient, yielding Seebeck coefficients of 97.1 µV/K and
99.3 µV/K for the 100 and 200 Hz datasets, respectively, which are higher than the in-
plane Seebeck coefficients of single layer graphene, ~ 50 µW/K, at room
Figure 7-7. (a) The 200, and (b) 400 Hz thermoelectric voltage as a function of the
maximum possible temperature drop (∆T) across the heterostructure.
(a)
(b)
90
0 40 80 120
0
10
20
30
40
ΔT (K)
Power (µW)
Slope : 0.3138 K/µW
temperature[199]. From these observations, we estimate the power factor (S
2
G) to be 1.46
and 1.51×10
-15
W/K
2
for the graphene/h-BN/graphene heterojunctions. While it is
possible that the cross-plane Seebeck coefficient consists of contributions from electron
tunneling[200, 201] in addition to thermionic emission [202, 203]across the energy
barrier[202, 203], further works are needed to determine what the dominant contribution
is. The temperature drop is plotted as a function of the applied electrical power in Figure
7-8. Based on this data, we estimate the thermal conductance (K) of the
graphene/BN/graphene heterostructure to be 4.25×10
-7
W/K[195, 204]. We further obtain
the thermoelectric figure of merit of this device as ZT = S
2
GT/K[193, 205], where T =
300K is the temperature of the device and K is the thermal conductance across the
heterostructure, yielding a ZT value of 1.05×10
-6
.
Figure 7-8. Temperature coefficient as a function of the applied power of the graphene/h-
BN/graphene heterostructure.
91
Conclusion,
We report Seebeck measurements across a graphene/h-BN/graphene
heterostructure by inducing a temperature gradient between the bottom and top graphene
layers and measuring the corresponding thermoelectric voltage (∆V) across the
heterostructure. A temperature gradient (∆T) of 39 K and thermoelectric voltage (∆V) of
almost 4 mV is observed in the device, which results in a Seebeck coefficient of 99.3
µV/K, a power factor (S
2
G) of 1.51×10
-15
W/K
2
, and a thermoelectric figure of merit of
ZT = 1.05×10
-6
for the graphene/h-BN/graphene heterostructure. These measurements
represent thermoelectric voltages produced at material interfaces, across length scales of
just 1-2 nm. While the overall thermoelectric energy conversion efficiency of this device
is small, the relatively large Seebeck coefficient and temperature drops observed here
indicate that the I-V characteristics of 2D heterostructures can contain an appreciable
thermoelectric component. The performance of graphene/BN/graphene heterostructure
devices (i.e., tunneling transistors and diodes) will, therefore, be influenced by such
thermoelectric effects.
92
Chapter 8
Future Work
Graphene/silicon interface future development
In chapter 5, we have demonstrated the direct Ohmic contact at graphene/silicon
interface using polymer electrolyte doping to reduce to Schottky barrier at the interface.
However, the polymer electrolyte can only last for less than two hours, which implies that
the doping effects are not permanent, and the reduced Schottky barrier will form after the
polymer electrolyte loses the doping effects. This would be a major difficulty for the
application of graphene either used as transparent electrodes to increase the energy
conversion efficiency of graphene/silicon solar cell, or used as electrodes for directly
Ohmic contact to silicon devices. In order to create permanent Ohmic contact at
graphene/silicon interface, the graphene has to be permanent n- or p-type doped. There
are several works which have reported synthesizing n- or p-type graphene by introducing
additional gases during the chemical vapor deposition process to provide extra carriers.
Wei et al. have reported synthesizing n-type graphene on Cu substrate by introducing
both CH
4
and NH
3
at high temperature simultaneously during the chemical vapor
deposition process. The synthesized graphene will contain nitrogen atoms and result in n-
type doped graphene. Figure 8-1 shows the XPS spectra and schematic diagram of their
synthesized graphene. Figure 8-2 is the SEM image, schematic diagram of a graphene
FET device and the electrical property of their n-type doped graphene
[206].
93
Figure 8-1. (a) XPS spectra of the pristine and the N-doped graphene. (b) XPS C 1s
spectrum and (c) XPS N 1s spectrum of the N-doped graphene. The C 1s peak can be split
to three Lorentzian peaks at 284.8, 285.8, and 287.5 eV, which are labeled by red, green,
and blue dashed lines. The N 1s peak can be split to three Lorentian peaks at 401.7, 400.1,
and 398.2 eV, which are labeled by red, green, and blue dashed lines. (d) Schematic
representation of the N-doped graphene. The blun, red, green, and yellow spheres represent
the C, “graphitic” N, “pyridinic” N, and “pyrrolic” N atoms in the N-doped graphene,
respectively[205].
94
Figure 8-2. Electrical properities of the N-doped graphene. (a) SEM image of an example
of the N-doped graphene device. (b) Bird’s-eye view of a schematic device configuration.
(c) and (d) I
ds
/ I
ds
characteristics at various V
g
for the pristine graphene and the N-doped
graphene FET device, respectively, The insets are the presumed band structures. (e)
Transfer characterictics of the pristine graphene (V
ds
at -0.5 V) and the N-doped graphene
(V
ds
at 0.5 and 1.0 V)[205].
95
In addition to the n-type doped graphene, Wang et al. have also reported boron-
doped graphene. Instead of CH
4
and boron powder, they use phenylboronic acid
(C
6
H
7
BO
2
) as the sole precursor to synthesize p-type doped graphene on Cu substrate.
The grown boron-doped graphene exhibits a p-type transport behavior with a carrier
mobility of about 800 cm
2
V
−1
s
−1
at room temperature. Figure 8-3 (a)-(c) are the
schematic diagram of boron-doped CVD graphene on Cu surface, and the optical and
SEM images of boron-doped CVD graphene on SiO
2
substrate
[207].
Figure 8-3. (a) Schematic diagram of CVD growth of boron-doped graphene on Cu surface
with phenyboronic acid as the carbon and boron sources. The red, grey, yellow, and green
spheres represent boron, caebon, oxygen and hydrogen atoms, respectively. (b) Optical
micrograph of a monolayer boron-doped graphene transferred onto SiO
2
/Si substrate. The
arrow points to blank SiO
2
/Si substrate. (c) SEM image of the boron-doped graphene film
transferred onto SiO
2
/Si substrate[206].
96
Figure 8-3 (d)-(g) are the AFM and UV-vis transmittance spectra of the boron-doped
graphene. Figure 8-4 shows the Raman spectra, and the electrical properties of the
intrinsic and boron-doped graphene.
Figure 8-3. (d) AFM image of the region pointed by black arrow in panel (b) with a z-scale
of 20 nm. (e) Histogram of thickness distribution from AFM height images. (f) Contrast
enhanced photograph of the B-doped graphene sample on 4-inch SiO
2
/Si substrate. (g) UV-
vis transmittance spectra of the boron-doped graphene and the reference intrinsic graphene
on quartz substrate. The intrinsic graphene monolayer was CVD grown on copper using
methane and then transferred on the quartz substrate. Inset: the photograph of boron-doped
graphene monolayer on a quartz substrate[206].
97
Those previous works have successfully synthesized both n-type and p-type
graphene, therefore the study of n-, p-type graphene/silicon junction are likely to generate
interesting electron transports phenomena, and is believed to provide useful knowledge
for future application of graphene/silicon devices.
Figure 8-4. (a) Typical Raman spectra of the boron-doped (red) and intrinsic (black)
graphene transferred on SiO
2
/Si substrate by dry transfer procedure. (b) Optical micrograph
of a boron-doped graphene device. (c) Raman map of D band intensity the channel region
of the boron-doped graphene device shown in (b). (d) Source-drain current (I
ds
) vs back
gate voltage (V
g
) with V
ds
= 0.1 V of the boron-doped (red) and intrinsic (black) graphene
device, respectively[206].
98
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Abstract (if available)
Abstract
This dissertation discusses the Raman spectroscopy of substrate-induced effects on graphene and electron transport at graphene-silicon interface. In the chapter 2 and 3, the discussion will be focused on Raman spectroscopy of thermally cycled graphene, which analysis the substrate-induced effects on graphene during the thermal cycling process by the Raman data taken before, during, and after the thermal cycling. The substrate-supported and suspended graphene samples are studied in the experiment, and demonstrate different Raman signal shifting. Both Raman G and 2D bands of the graphene show significant upshifts of after the thermal cycling, which indicate the compression and doping effects on graphene induced from the mismatch of the thermal expansion coefficients and the trapped charge transferring between graphene and the supported SiO₂ substrate. Uniform ripples are also observed in suspended graphene, after the thermal cycling, while similar Raman frequencies shifting in the suspended graphene are not observed. The electron transports at graphene-silicon interface will be presented in chapter 4 and 5, which demonstrates the formation of Schottky barrier with energy barrier height of 0.41 eV on n-type silicon and 0.45 eV on p-type silicon at the room temperature at graphene-silicon interface due to the energy difference between graphene Fermi energy and silicon electron affinity. This energy mismatch can be tuned to eliminate the Schottky barrier and result in Ohmic contact at graphene-silicon interface by using electrolyte chemical doping, which shifts graphene Fermi energy to match the conduction or valance bands of silicon. The experimental data proves the reducing of the Schottky barrier height and the observations of low bias conductance and short circuit photocurrent at graphene-silicon interface reveal the evolution of the graphene-silicon interface and corroborate the Ohmic contact at the interface. Also, a model of electron transports at graphene-silicon interface is presented, which simulates electron transports at graphene-silicon interface based on electron distributions, density of states, the Schottky barrier, and electron tunneling effects in both graphene and silicon to estimate the low bias conductance variation with respect to the graphene Fermi energy shifting. In addition to graphene, a heterostructure of graphene with another 2D material stack, hexagonal boron nitride (h-BN), will be discussed in chapter 6 and 7, including the investigations of interface thermal conductance and thermoelectric effects at the graphene/h-BN heterostructures.
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University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Chen, Chun-Chung
(author)
Core Title
Substrate-induced effects in thermally cycled graphene & electron and thermoelectric transports across 2D material heterostructures
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Electrical Engineering
Publication Date
01/12/2015
Defense Date
10/15/2014
Publisher
University of Southern California
(original),
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(digital)
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graphene,OAI-PMH Harvest
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application/pdf
(imt)
Language
English
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Electronically uploaded by the author
(provenance)
Advisor
Cronin, Stephen B. (
committee chair
), Goo, Edward K. (
committee member
), Zhou, Chongwu (
committee member
)
Creator Email
chunchuc@gmail.com,chunchuc@usc.edu
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https://doi.org/10.25549/usctheses-c3-524832
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The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
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graphene