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In-situ characterization of nanoscale opto-electronic devices through optical spectroscopy and electron microscopy

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In-situ characterization of nanoscale opto-electronic devices through optical spectroscopy and electron microscopy

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Content IN-SITU CHARACTERIZATION OF NANOSCALE
OPTO-ELECTRONIC DEVICES THROUGH OPTICAL
SPECTROSCOPY AND ELECTRON MICROSCOPY

by

Rohan Dhall

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 2016

Copyright 2016 Rohan Dhall
ii

EPIGRAPH

“Not failure, but low aim, is the crime.”
- Bruce Lee
iii

DEDICATION

To my parents

iv

ACKNOWLEDGMENTS

Any expression of gratitude that fits within the two-page requirement of the
graduate school, would fall miserably short of expressing the sentiments I wish to
convey. The people, places, and experiences, which have shaped me as an individual are
far too numerous, and this is just a small subset of those who deserve credit for holding
my hand through this process of growing up.
I have been fortunate to have a wonderful set of inspirational teachers through my
entire life, starting with my parents and grandparents. I still have memories of sitting in a
Cario Dust Maruti 800, on winter afternoons, eating peanuts, and reciting multiplication
tables, and I will go through life, always being grateful for those moments. My family has
given me more support and affection than I could have ever asked for.
Through my “work” life, I have also been fortunate to be surrounded by a set of
truly remarkable people. Research advisors, such as Steve and Mandar, who I have relied
on for guidance, support, and inspiration. Teachers such as Prof. Mehrotra and Prof.
Madhukar, who have taught me not be fear my own ignorance. Chris, Shaul and Matt,
who let me play with TEMs.
And to my wonderful friends- who have carried me through life so far. Your
compassion, care, and selflessness shall always be a source of hope to me. Thank you for
always being there to give me a helping hand. So it goes.
v

TABLE OF CONTENTS
Epigraph .................................................................................................................. ii
Dedication .............................................................................................................. iii
Acknowledgments.................................................................................................. iv
List of Figures ....................................................................................................... vii
Abstract ................................................................................................................ xiii
Chapter 1: Introduction ........................................................................................... 1
1.1 Low dimensional material systems ......................................................... 1
1.2 Graphene and the honeycomb lattice ...................................................... 2
1.3 Carbon nanotubes .................................................................................... 5
1.4 Raman spectroscopy and carbon nanotubes ............................................ 9
1.5 Low energy interactions in graphitic materials ..................................... 13
1.6 Perturbation formalism .......................................................................... 14
Chapter 2: Electron-phonon interactions in suspended quasi-metallic
carbon nanotubes .................................................................................................. 17
2.1 Abstract ................................................................................................. 17
2.2 Introduction ........................................................................................... 17
2.3 Experimental details .............................................................................. 19
2.4 Results and discussion ........................................................................... 21
2.5 Conclusion ............................................................................................. 35
Chapter 3: Determination of gate capacitance in metallic carbon nanotubes
transistors using phonon renormalization ............................................................. 37
3.1 Abstract ................................................................................................. 37
3.2 Introduction ........................................................................................... 37
3.3 Experimental Details ............................................................................. 38
3.4 Theoretical Model ................................................................................. 39
3.5 Results and Discussion .......................................................................... 43
3.6 Conclusions ........................................................................................... 45
Chapter 4: in-situ Electron diffraction of suspended carbon nanotubes ............... 46
4.1 Introduction ........................................................................................... 46
4.2 Coupled electrical and thermal transport in carbon nanotubes at high
bias voltages ................................................................................................ 47
4.3 The need for electron microscopy of carbon nanotubes........................ 52
4.4 Sample fabrication ................................................................................. 53
4.5 Electron diffraction in carbon nanotubes .............................................. 56
vi

4.5.1 The Born Approximation in Electron Diffraction .................... 57
4.5.2 Electron diffraction in carbon nanotubes .................................. 58
4.6 Nanobeam electron diffraction: Preliminary data ................................. 63
4.7 Conclusions and future work ................................................................. 64
Chapter 5: Fabrication of ultra-clean, suspended, carbon nanotube devices
with known chirality for opto-electronic devices ................................................. 66
5.1 Abstract ................................................................................................. 66
5.2 Device Fabrication: Carbon Nanotube Growth and Aligned Transfer.. 66
5.2.1 Fabrication of the Substrate ...................................................... 66
5.2.2 Fabrication of transfer compatible electrodes ........................... 68
5.2.3 Transfer of CNTs to electrical contacts .................................... 70
5.3 Photoluminescence Imaging for High Throughput Chirality Screening 72
5.4 Electrical Characteristics of Two Terminal Devices ............................. 75
5.5 Fabrication of Field Effect Transistors and Other Future Steps ............ 76
5.6 Conclusions ........................................................................................... 77
Chapter 6: Engineering Transition Metal Di-Chalcogenides for enhanced
efficency of opto-electronic devices ..................................................................... 78
6.1 Abstract ................................................................................................. 78
6.2 Introduction ........................................................................................... 79
6.3 Experimental Details ............................................................................. 79
6.4 Proposed Mechanism ............................................................................ 87
6.5 Results and Discussion .......................................................................... 90
6.6 Conclusions ........................................................................................... 94
Chapter 7: Strong Circularly Polarized Photoluminescence from few-layer
Molybdenum di-Sulfide through plasma driven direct gap transition .................. 95
7.1 Abstract ................................................................................................. 95
7.2 Introduction ........................................................................................... 96
7.3 Experimental details .............................................................................. 97
7.4 Proposed mechanism ........................................................................... 103
7.5 Conclusions ......................................................................................... 108
Bibliography……………………………………………………………………110
Appendix A: MATLAB Code for generating atomic coordinates of a
carbon nanotube .................................................................................................. 116
Appendix B: MATLAB code for generating diffraction patterns of carbon
nanotubes ............................................................................................................ 117

vii

LIST OF FIGURES
Figure 1-1: The lattice in real space (a) and reciprocal space (b) of graphene. .................. 3
Figure 1-2: (a) Shows the electronic band structure of graphene, and the creation
of an electron-hole pair due to electron-phonon creation is symbolized
in (b). Figure from [5]. ...................................................................................... 4
Figure 1-3: Structure of a carbon nanotube based on graphene. (left) A 2-D
graphene sheet with chiral vector
h
C
defined on hexagonal lattice by
chiral angle θ with respect to
1
a .(right) Examples of capped (a)
armchair, (b) zigzag, and (c) chiral nanotubes, with chiralities of (5,5),
(9,0), and (10,5), respectively. Taken from ref [8]. .......................................... 6
Figure 1-4: Electronic dispersion relation in graphene and extended to carbon
nanotubes. (a) Electron energy dispersion for graphene. (b)
Circumferential and axial wavevectors for carbon nanotube. (c) 2-D
graphene dispersion relation plotted with zigzag nanotube cutting lines
satisfying the cylindrical quantization of the wavevector. (d) Electron
conduction (white) and valence (yellow) bands near the Fermi level.
From ref [9]. ...................................................................................................... 8
Figure 1-5: Electronic density of states for a (10,0) and (9,0) carbon nanotube.
The dashed lines represent the dispersion relation for graphene. Taken
from ref [10]. ..................................................................................................... 9
Figure 1-6: Measuring and visualizing atomic vibrations in carbon nanotubes. (a)
Raman spectrum of two CNTs on a silicon/silicon dioxide substrate,
showing the prominent bands used to characterize the CNT structure
and properties. (b) Schematic diagram of the RBM and the two G
mode vibrations for a CNT. Adapted from ref [12]. ....................................... 12
Figure 2-1: (a) Schematic diagram and (b) SEM image of a suspended CNT FET
device. (c) Typical room temperature electrical current versus bias
voltage characterization of a metallic SWNT. The inset shows the low
bias conductance versus gate voltage. ............................................................ 20
Figure 2-2: G- band Raman shift plotted as a function of gate voltage at 300K for
sample 527-1m. The inset shows a typical Raman spectrum of a
pristine metallic SWNT taken at 300K at Vg=0V. .......................................... 23
Figure 2-3: (a)A waterfall plot showing the evolution of the Raman G band as a
function of gate voltage (Vg) for device 753 at 300K. .................................... 24
viii

Figure 2-4: Room temperature gate voltage dependence of the G- band Raman
shift and intensity for (a) device 435-8m, showing the signature W
shape profile indicating breakdown of the Born-Oppenheimer
approximation(Regime 1) and (b) device 498-16m, showing no
evidence of non-adiabatic behavior (Regime 2). ............................................ 25
Figure 2-5: Gate voltage dependence of the G band Raman shift and G band
Raman intensity for device 359 at (a) T= 300K, consistent with
Regime 2, and (b) at T=4.2K, consistent with Regime 1. ............................... 26
Figure 2-6 Correlation between the ratio of gated and ungated G band Raman
intensities for various devices plotted as a function of the maximum
gate-induced downshift of the G band Raman frequency due to the
non-adiabatic Kohn anomaly. Each point on this plot corresponds to a
different nanotube sample. .............................................................................. 28
Figure 2-7: Relative Raman shift of the G-band with respect to Vg=0 for (a) device
491-15 and (b) device 527-1 taken at various temperatures. .......................... 30
Figure 2-8: The renormalization of phonon energy is caused by a virtual electron-
hole pair created under light doping conditions as shown in (a).
However, when the Fermi level is lowered or raised sufficiently (𝐸𝐹 >
ℏ𝜔𝐺 2) , these virtual transitions are blocked and non-adiabatic phonon
renormalization is turned off, demonstrated in (b). Figure from Tsang
et.al. ................................................................................................................. 30
Figure 2-9 The real part of Π( ω,EF) from Equation 1 at T=300K and T=150K,
with (a) no bandgap in the electron band structure and (b) a bandgap of
120meV. .......................................................................................................... 34
Figure 3-1: The gate voltage dependence of G band Raman shift of a metallic
carbon nanotube. The signature "W shape" is a consequence of the
Kohn anomaly in this system, with the separation between the two
minima corresponding to change in Fermi energy of 0.196eV. ..................... 39
Figure 3-2: (a) The calculated dependence of the Fermi level of the nanotube on
externally applied gate voltage for three different values of gate
capacitance (𝐶𝐺 ). The band gap is assumed to be 0 eV. (b) The
calculated dependence of the Fermi level of the nanotube on externally
applied gate voltage for three different values of band gap. The non-
linearity in the dependence arises due to the presence of a band gap.
The offset of the charge neutrality point (CNP) is determined by
finding the minima in the transconductance plot. ........................................... 42
ix

Figure 3-3: The conductance of the nanotube as a function of applied gate voltage.
The data (shown in blue) is fitted to a Landauer model for ballistic
transport (shown in red), allowing us to determine the band gap. .................. 43
Figure 4-1: Current-voltage curves of a single, metallic carbon nanotube, as a
function of the effective length of the nanotube channel, adapted from
the work of Park et.al. ..................................................................................... 49
Figure 4-2: Schematic of optical phonon emission by electrons accelerated under
a strong applied field (high bias voltage). lT is the threshold distance
the electron must travel before it gathers sufficient kinetic energy to
emit an optical phonon. ................................................................................... 50
Figure 4-3: The device geometry (a) and schematic (b) for a nanotube device
using the same nanotube on and off a substrate. (c) Shows the current-
voltage characteristics seen in the two segments of the nanotube. ................. 51
Figure 4-4: The fabrication process for creating field effect transistors using ultra
clean, suspended carbon nanotubes, compatible with TEM imaging. ............ 54
Figure 4-5: SEM image of a suspended CNT device compatible with TEM
imaging. .......................................................................................................... 55
Figure 4-6: The current-gate voltage and current-voltage (inset) curves for a
metallic CNT suspended across a TEM compatible trench. ........................... 55
Figure 4-7: (a) Shows a schematic representation of the calculation of electron
diffraction from carbon nanotubes. (b) Shows one such calculated
diffraction pattern. The nanotube axis is aligned with the X-axis in this
diffraction pattern............................................................................................ 60
Figure 4-8: Calculated diffraction pattern for a (12,0) carbon nanotube with
differnt values of externally applied strain. .................................................... 62
Figure 4-9: Comparison of electron diffraction patterns recorded using select area
diffraction (SAD) and nano-beam diffraction(NBD). The illuminated
area diameter is 250nm in the former, and about 50nm for the latter,
leading to improved signal to noise ratio. ....................................................... 64
Figure 5-1: Fabrication of the optically transparent substrate for templated growth
of suspended carbon nanotubes. After the final step, nanotubes grown
by chemical vapor deposition are indicated schematically in black. .............. 67

x

Figure 5-2: (a) Shows an array of pillars, etched into a quartz wafer, along with
alignment markers for easy identification of suspended carbon
nanotubes. (b) Shows one such suspended carbon nanotube, bridging
the tops of neighboring pillars. ....................................................................... 68
Figure 5-3: (a) The steps involved in the fabrication of silicon chips with raised
metal electrodes, suitable for carbon nanotube transfer. The low
magnification and high magnification SEM images of one such device
are shown in (b) and (c) respectively. ............................................................. 69
Figure 5-4: (a) Low magnification SEM image of a three terminal electrical
device, compatible with the aligned optical transfer scheme. The
higher magnification image in (b) shows how the source and drain
electrodes are at a higher elevation than the gate. .......................................... 70
Figure 5-5: (a) The schematic layout of the micro-positioning and transfer stage
for the fabrication of carbon nanotube electrical devices. The steps for
aligned transfer are shown in (b) - (d), as described in the text. ..................... 72
Figure 5-6: Schematic layout for photoluminescence imaging setup. .............................. 73
Figure 5-7: (a) Shows the optical transitions involved in the PL emission process
in carbon nanotubes, and a typical PL spectrum from a single nanotube
is shown in (b), along with the transmission response of the band pass
filter used. ....................................................................................................... 74
Figure 5-8: Typical photoluminescnce image showing PL emission from a single,
suspended carbon nanotube. ........................................................................... 74
Figure 5-9: SEM image of an electrical device created using a transferred carbon
nanotube. ......................................................................................................... 75
Figure 5-10: I-V curves for a suspended carbon nanotube device, using palladium
and ITO coated aluminum as the source and drain electrodes. ....................... 76
Figure 6-1: Optical microscope image of a few layer MoS2 flake (a) before and
(b) after 3 minutes of oxygen plasma treatment. (c) Photoluminescence
spectra before and after oxygen plasma treatment, plotted on different
Y scales, highlighting the blue shift of the A exciton, the narrowing of
the spectral linewidth, and the emergence of the asymmetry in PL
lineshape after plasma treatment at 300K. (d) Inset shows the
emergence of a distinct, low energy peak at 100K. The relative
intensity of the low energy PL peak is shown as a function of
temperature. .................................................................................................... 82
xi

Figure 6-2: AFM (height) images of a MoS2 flake taken (a) before and (b) after a
3 minute oxygen plasma treatment. The step height profiles along the
dashed lines are shown in (c). A significant increase in sample
thickness, of about 2nm, is observed after plasma treatment. ........................ 85
Figure 6-3: Optical microscope image of a few layer MoS2 flake (a) before and
(b) after 3 minutes of oxygen plasma treatment. (c) Raman spectra
before and after plasma treatment. No significant shift in the Raman
peaks is observed, although the Raman intensity for both peaks is
reduced, and a slight narrowing of the peaks is observed............................... 87
Figure 6-4: (a) Atomistic structure of the 4L- MoS2 with the equilibrium vdW
gap, dvdw, and the modified vdW gap, dvdw (new), and (b) Direct gap
(solid) and indirect gap (dotted) energy transitions for 2L, 3L and 4L
MoS2 for a range of increases in the vdW gap ( dvdw). The dotted
vertical lines indicate the indirect to direct transition vdW gaps for 2L
(green), 3L (blue), and 4L (red) MoS2 . .......................................................... 88
Figure 7-1: (a) Optical microscope image, (b) photoluminescence spectra, and (c)
Raman spectra of a 3-4 layer flake of MoS2 taken before and after the
remote oxygen plasma treatment. ................................................................. 100
Figure 7-2: Circularly polarized photoluminescence spectra from an oxygen
plasma treated few layer flake (3-4 layers) of MoS2 collected at 30K
with (a) σ
+
excitation and (b) σ
-
excitation. The degree of polarization,
ρ, is plotted in (c). Inset shows the valley contrasted selection rules for
optical transition, with strong oscillator strength, similar to the case
observed for direct gap (monolayer) MoS2. .................................................. 102
Figure 7-3: Circularly polarized photoluminescence spectra from a “as-exfoliated”
few layer flake of MoS2. The emission spectra, collected using σ+
excitation at 633nm are shown in (a). The spectra for σ+ and σ-
polarization are nearly identical, exhibiting only a weak (~10%)
degree of polarization below 640nm, shown in (b). The inset
represents the absence of valley contrasted selection rules for optical
transitions. The degree of polarization from few layer MoS2 before
and after plasma treatment is compared to that of pristine “as-
exfoliated” monolayer MoS2 in (c). .............................................................. 104
Figure 7-4: The calculated interlayer coupling parameter tp and the polarization
corresponding to the localization within the top or bottom layer of
each spin in each valley and also the spin polarization of the excited
carriers due to circularly polarized optical absorption. ................................. 106
xii

Figure 7-5: Temperature dependence of the degree of polarization of circularly
polarized photoluminescence spectra, showing strong co-polarization
with the excitation up to T=300K. ................................................................ 107

xiii

ABSTRACT
This dissertation presents several in-situ investigations of nanoscale electronic
devices through a variety of experimental probes. These experiments shed light on some
of the fundamental physical interactions at play in these devices, and could pave the way
for a more rational device design to boost performance.
Chapter 1 provides background material that will aid in understanding the
research presented in this dissertation. It provides a brief overview of properties of carbon
nanotubes and graphene, their atomic structure, as well as their electronic band structure.
A brief discussion of interaction of excitations (electron-electron, and electron-phonon)
as well as the Kohn anomaly is included here. For the most part, however, the theoretical
background needed to understand each topic is covered within the relevant chapter.
Chapter 2 presents some in-situ Raman spectroscopy experiments on suspended,
metallic carbon nanotube devices. These experiments reveal a strong electron-phonon
interaction due to the Kohn anomaly in these suspended nanotubes, as well as the
interplay of Kohn anomaly with energy gaps created in the excitation spectrum of these
tubes due to electron-electron interactions.
Chapter 3 takes advantage of these experimental results presented in Chapter 2,
and couples them with a careful theoretical analysis to measure the carbon nanotube
capacitance. Surprisingly, this analysis reveals a significantly larger capacitance than
expected, which can be attributed to the electron-electron repulsion.
In Chapter 4, we discuss some work on the fabrication of suspended carbon
nanotube devices compatible with in-situ Transmission Electron Microscopy
xiv

experiments. Some preliminary data showing high quality diffraction patterns obtained
through nano-beam electron diffraction are discussed in this chapter.
Chapter 5 details the fabrication process and experimental setup for a home built
aligned transfer scheme to create electrical devices of known chiralities. The screening of
nanotube chirality is done through a home built photoluminescence imaging setup.
Preliminary electrical data, showing photodetector capability using such devices is also
presented.
Chapters 6 and 7 focus on a class of layered semiconductors, transition metal di-
chalcogenides. In particular, a simple method for perturbing the atomic structure of few
layer MoS2 is shown. This method pulls the atomic layers in this material system apart,
leading to a dramatic change in optical properties, such as a transition to a direct band
gap. Further, this material also acts as a source of strong, circularly polarized photons due
to broken inversion symmetry.

1

CHAPTER 1: INTRODUCTION

1.1 Low dimensional material systems
In the brief history of civilized human existence, curiosity about the universe we
inhabit has constantly let us to look forever “deeper” for patterns. Whether this be
through telescopes, which look deeper into the universe, or through microscopes, which
look deeper into the material makeup of the world around us. Recent advances in
neurological and cognitive science have revealed that this philosophical concept of
“depth” is intimately tied to the spatial dimensions of our surroundings, which are
mapped out within the human brain, in the connectivity of our neural networks. From this
perspective, it is of no surprise whatsoever, that our curiosity has led us to field of
nanoscience.
While postulates regarding the atomic theory of matter have existed since at least
as far back as ancient Greece, it has only been since the advent of the quantum theory of
matter, that scientists have found a reasonable framework, within which a handful of
tractable problems have been solved. However, just these few basic models have led to
tremendous advances in both science and technology. Lasers and transistors are two
wonderful examples of how this understanding of matter at the atomic scale, has
benefited society at large. In both these devices, the quantum confinement of electrons
(and holes) in nano-meter thick layers of materials, was the critical component in
boosting efficiency, and making them truly useful for practical applications. These
2

inventions have also motivated the search for new nanomaterials, which would
potentially improve existing electrical and optoelectronic devices, or even enable an
entirely new class of devices. In this thesis, we focus on experimental investigations of a
handful of such novel material systems, and discuss some of the physics behind them.
1.2 Graphene and the honeycomb lattice
The famous Schrodinger equation, which forms the basis of non-relativistic
quantum mechanics, is exactly solvable, only under very specific conditions, and after
making a set of assumptions regarding the system under study. Typically, this requires
that the system under investigation be small, such as a hydrogen atom, or that the system
possesses some symmetry, which allows one to simplify the Schrodinger equation. One
such symmetry is translational symmetry, which is present in materials with long range
atomic order, i.e., crystals. The simplest crystal system, the cubic system, encompasses
several metals and semiconductors, which are critical to modern technology.
The hexagonal crystal system possesses an entirely different symmetry, which
leads to several unique properties. In particular, graphene, which is a single atomic layer
of sp
2
hybridized carbon atoms, in a honeycomb lattice, has been contemplated
theoretically for several decades. As early as 1947[1], the theory of graphene had been
explored as a means to understanding graphite. However, the fabrication of graphene,
was only very recently made possible[2].
Due to its hexagonal symmetry, in reciprocal space, graphene possesses a
hexagonally symmetric two-dimensional Brillouin zone (Figure 1-1), and within the
simplest tight binding approximation, the conduction and valence bands of graphene are
3

known to touch at the vertices of reciprocal space Brillouin zone. Hence, graphene is
thought to be a “semi-metal”, or a zero band gap semiconductor.

The band structure of graphene is described by the equation:
𝐸 ( 𝒌 𝒙 , 𝒌 𝒚 ) = ±𝑡 √
1 + 4 cos
2
(
𝑘 𝑦 𝑎 2
) + 4 cos(
𝑘 𝑦 𝑎 2
) cos (
√ 3𝑘 𝑥 𝑎 2
)
In this expression, t is the hopping matrix element between nearest neighbors, and
a is magnitude of the lattice vector. Based on this treatment, the conduction and valence
bands are mirror images of one another. Further, at specific points, labelled in Figure 1-1
as K and K’, E = 0, and the valence and conduction bands meet. This leads to tremendous
richness in the low-energy excitation spectrum of graphene, and the electrons near the
Fermi level are prone to excitation (real or virtual) through various mechanisms, such as
their interaction with phonons, or with other electrons. Such an interaction is illustrated in
Figure 1-2[3].
Figure 1-1: The lattice in real space (a) and reciprocal space (b) of graphene.
4

In the vicinity of the K and K’ points, the band structure of graphene is often
considered to be linear, given by 𝐸 = ℏ𝑣 𝐹 |𝒌 |. These linear bands imply that the carriers
in graphene behave as massless Fermionic particles, which are more accurately described
by the relativistic Dirac equation, than the Schrodinger equation. Nevertheless,
significant insights into the properties of graphene can be gained using this simple linear
band structure. Furthermore, this massless Dirac Fermionic nature leads to the exciting
mobility of electrons and holes in graphene (~10
6
cm
2
/V-s).
While this band dispersion is tremendously interesting from a theoretical
standpoint, the lack of a band gap makes it impossible to switch off a graphene based
electronic device. However, a class of materials, the transition metal di-chalcogenides,
possesses a similar honeycomb lattice. This leads to several parallels in the theory of
TMDCs and graphene, but TMDCs offer the additional benefit of a finite bandgap, useful
for electronic device application.

Figure 1-2: (a) Shows the electronic band structure of graphene, and the creation of an
electron-hole pair due to electron-phonon creation is symbolized in (b). Figure from [5].
5

1.3 Carbon nanotubes
Graphene is also closely related to its one dimensional counterpart, carbon
nanotubes (CNTs), which are hollow cylinders of rolled up sheets of graphene. They
possess some of the same exciting mechanical and electronic properties of graphene, and
have been studied in great detail since their discovery in 1991 [4]. The result of this
collective body of research has resulted in over 50,000 publications, which span studies
of the electrical, thermal, and mechanical properties of CNTS. CNTs have been shown,
both experimentally and theoretically, to have exceptionally high electron mobilities of
100,000 cm
2
/V·s, thermal conductivities as high as 6,600 W/m·K, and Young’s modulus
values reaching up to 1.8 TPa [5-7], making them promising materials for nanoelectronic,
thermal management, and nanomechanical applications.
Thinking of single-walled carbon nanotube as a seamless rolled up sheet of two-
dimensional graphene has also allowed scientists to borrow heavily from the well-
established theory of graphene, in order to explain the electrical, optical, and mechanical
properties of carbon nanotubes. The nanotube structure can be uniquely identified by a
combination of two integer indices, (n,m), known as “chiral indices”, which determine
the direction in which the sheet of graphene is rolled up, with respect to the underlying
honeycomb lattice of graphene itself. Equivalently, the structure can be characterized by
the diameter dt and chiral angle θ, of the nanotube, as shown in Figure 1-3. The
hexagonal grid has basis vectors
1
a and
2
a , and the unit cell of the nanotube is indicated
by the box OAB’B, where the circumferential chiral vector,
h
C
, forms an angle θ with
1
a
. The chiral indices, (n,m), define the circumferential vector,
2 1
a a C m n
h
 
. The length
6

of this chiral vector is the circumference of the carbon nanotube and can be written as
t
d 
. The cases of 0  m and
n m 
specify two special classes of achiral CNTs called
armchair and zigzag nanotubes. All other nanotubes are chiral nanotubes.

Figure 1-3: Structure of a carbon nanotube based on graphene. (left) A 2-D graphene
sheet with chiral vector
h
C
defined on hexagonal lattice by chiral angle θ with respect to
1
a .(right) Examples of capped (a) armchair, (b) zigzag, and (c) chiral nanotubes, with
chiralities of (5,5), (9,0), and (10,5), respectively. Taken from ref [8].
The periodic boundary condition applied, which can be applied both in the axial
direction, and in the circumferential direction, leads to further constraints on the
eigenfunctions which may satisfy Schrodinger’s equation in CNTs. In particular, in
cylindrical coordinates, this implies the electron wavefunction must satisfy the criterion:
𝜓 ( 𝑟 , 𝜃 , 𝑧 ) = 𝜓 ( 𝑟 , 𝜃 + 2𝜋 , 𝑧 )
If the electron wavefunction is a Bloch state, this leads to an additional constraint,
𝒌 ⊥
∙ 𝑪 𝒉 is an integer multiple of 2𝜋 . Only those wavevectors in the graphene reciprocal
space, which satisfy this criterion would give rise to allowed electronic states in a one
dimensional nanotube. This leads to the idea of “cutting lines”, as shown in Figure
7

1-4(d). These allowed wavevectors lie on lines, as shown in red, which cut across the
graphene reciprocal space lattice. Each individual line, which corresponds to a different
integer multiple of 2𝜋 , forms a “band” within the Brillouin zone unit cell of graphene. In
calculating the band structure of a nanotube, it is assumed that the act of rolling these
sheets of graphene is a tiny perturbation on the electronic states in graphene. Only, the
addition of a constraint in the azimuthal direction allows states of only specific
wavevectors to exist within nanotubes, as opposed to graphene. In other words, the states
are quantized in the radial direction.
The chirality of the tube also determines the electronic properties of the CNT, and
carbon nanotubes can be either metallic or semiconducting, if the cutting lines pass
through the K and K’ points or not.
8

Figure 1-4: Electronic dispersion relation in graphene and extended to carbon nanotubes.
(a) Electron energy dispersion for graphene. (b) Circumferential and axial wavevectors
for carbon nanotube. (c) 2-D graphene dispersion relation plotted with zigzag nanotube
cutting lines satisfying the cylindrical quantization of the wavevector. (d) Electron
conduction (white) and valence (yellow) bands near the Fermi level. From ref [9].
The one-dimensional CNT band structure creates sharp van-Hove singularities in
the electronic density of states. Examples for a metallic (9,0) CNT and a semiconducting
(10,0) CNT are shown in Figure 1-5. The electronic energy differences for transitions
between singularities (symmetric about zero energy) are often labeled Eii, where 1  i
represents the lowest energy transition between the van-Hove singularities closest to zero
energy. For the metallic tube, we note a finite density of states between the singularities
a)
b)
c) d)
9

near zero energy. The other nanotube shows no electron density between the singularities
at zero energy, where E11 denotes the bandgap of the semiconducting CNT.

Figure 1-5: Electronic density of states for a (10,0) and (9,0) carbon nanotube. The
dashed lines represent the dispersion relation for graphene. Taken from ref [10].
1.4 Raman spectroscopy and carbon nanotubes
Raman spectroscopy is an optical spectroscopy tool, used commonly to study
different materials. The process involves inelastic scattering of an incident photon, in
which the photon loses a small amount of energy to atomic vibrations in the scattering
object. The scattered photon then has an energy slightly below (Stokes process) or
10

slightly above (anti-Stokes process) the energy of the incident photon. The difference in
these energies (Raman shift), allows one to access energies of certain (Raman active)
vibrational modes in the solid.
As shown earlier, the chirality of a CNT determines the band structure of a carbon
nanotube and whether it has metallic or semiconducting behavior. It also determines the
allowed values of wave vectors for electrons in a particular nanotube. These same
wavevectors selection rules (cutting lines) are also also applicable to phonon modes, and
in much the same fashion, one can calculate the phonon dispersion of a nanotube from
that of graphene, given its chirality.
Certain features, however, make Raman spectroscopy especially useful tool for
studying 0-, 1-, 2-, and 3-D carbon-based materials. As shown earlier, the chirality of a
CNT determines the band structure of a carbon nanotube and whether it has metallic or
semiconducting behavior. Wrapping of 2-D graphene into a “1-D” tubule produces
unique van Hove singularities in the electronic density of states. Photons that match the
energy difference between these singularities can resonantly excite electrons from the
valence and conduction bands in the CNT, with significantly higher cross sections of
interaction. If this electron then undergoes an inelastic scattering event with a phonon,
and decays back to the valence band, the CNT produces a Raman-scattered photon. The
intensity of Raman scattering, is thus greatly enhanced by the electronic resonance.
Similarly, the intensity of scattering events where the emitted photon is resonant with the
electronic transitions is also greatly enhanced. Even though a CNT has an extremely tiny
geometric cross section, its effective Raman scattering cross section is remarkably high
11

(estimated to be on the order of 10
-22
cm
2
/sr compared to 10
-31
cm
2
/sr for non-resonant
molecules) [11].
The Raman scattering spectrum features several prominent modes or bands that
reveal a wealth of information about the CNT. The most significant Raman modes are the
radial breathing modes (RBMs) and the higher energy D (disorder), G (graphite), and G’
or 2D (second-order D-band) modes, observed in the spectral scattering of Figure 1-6.
The RBM mode is a unique feature of CNTs which does not occur in 2D and 3D carbon
allotropes. This mode is associated with the tube’s isotropic radial expansion or the
symmetric vibration of the carbon atoms in the radial direction. The Raman shift of the
RBM is inversely related to the diameter of the nanotube, and hence, can provide
structural information about the nanotube being studied.
12

Figure 1-6: Measuring and visualizing atomic vibrations in carbon nanotubes. (a) Raman
spectrum of two CNTs on a silicon/silicon dioxide substrate, showing the prominent
bands used to characterize the CNT structure and properties. (b) Schematic diagram of
the RBM and the two G mode vibrations for a CNT. Adapted from ref [12].
The D band is a longitudinal optical phonon referred to as the disorder or defect
mode, because it requires a defect (e.g. substitutional atom, vacancy, grain boundary) or
other disorder (finite-size effect, edges) that break the symmetry of the semi-infinite sp
2

13

carbon lattice. Thus, its relative intensity compared to other bands can give information
about the quality of the nanotube lattice. The G’ band is a second order mode of the D
band that does not require defects or disorder to be observed.
Finally, the G band is an optical phonon characterized by the tangential shear
stretches in the 2-D plane of graphene. However, the mode splits into a lower energy G-
mode and higher energy G+ mode due to electron-phonon interaction. In general, the G-
band can be used to distinguish between a metallic and semiconducting CNT, where a
metallic tube typically exhibits a broad peak, with a unique BWF lineshape, and a
semiconducting tube exhibits a sharp peak [13]. The origin of the BWF lineshape lies in
the interaction of phonons with electrons[6].

1.5 Low energy interactions in graphitic materials
In pristine, undoped graphene (and metallic CNTs), the Fermi energy lies at E=0,
at the K and K’ points in the Brillouin zone. Thus, unlike most conventional
semiconductors, graphene is capable of supporting electronic states in the vicinity of the
Fermi surface. This leads to particularly strong interactions of excitations in graphene. In
particular, electron-phonon interaction and electron-electron interactions play a unique
role in governing the properties of graphene. This situation is even more obvious in
metallic nanotubes, where the reduced dimensionality leads to even stronger interactions
between these excitations. An excellent description of the physics of interacting particles
is provided by Ziman[14]. This description is generic enough to allow one to handle
distinct phenomena such as electron-electron, as well as electron-phonon interactions.

14

1.6 Perturbation formalism
Considering a free electron gas, subject to a time dependent perturbation, given by
𝛿𝒰 ( 𝒓 , 𝑡 ) = 𝒰 𝑒 𝑖 𝒒 .𝒓 𝑒 𝑖𝜔𝑡 𝑒 𝛼𝑡
, which is a damped oscillatory potential of wavevector q, and
frequency ω. Acting on a state |𝒌 ⟩ = exp {𝑖 ( 𝒌 . 𝒓 + ℰ( 𝒌 ) . 𝑡 /ℏ) }, this potential leads to a
mixing of states, and the new wavefucntion is given by:
𝜓 𝒌 ( 𝒓 , 𝑡 ) = |𝒌 ⟩ + 𝑏 𝒌 +𝒒 ( 𝑡 ) |𝒌 + 𝒒 ⟩
Where, using first order perturbation theory,
𝑏 𝒌 +𝒒 ( 𝑡 ) =
⟨𝒌 + 𝒒 |𝒰 𝑒 𝑖 𝒒 .𝒓 𝑒 𝑖𝜔𝑡 𝑒 𝛼𝑡
|𝒌 ⟩
ℰ( 𝒌 )− ℰ( 𝒌 + 𝒒 )+ ℏ𝜔 − 𝑖 ℏ𝛼
The numerator in above expression is readily simplified assuming a perturbation
of wavevector q, only couples states with wavevectors differing by the same q. Since the
presence of the perturbation potential modifies the wavefunctions of the electronic states,
the charge density in the material is also redistributed, and the change in charge density is
given by
𝛿𝜌 ( 𝒓 , 𝑡 ) = 𝑒 ∑{|𝜓 𝒌 ( 𝒓 , 𝑡 ) |
2
− 1}
𝒌
Assuming that the original perturbation potential was real simply means we need to add
the complex conjugate to each of the above equations, and we arrive at:
𝛿𝜌 = 𝑒𝒰 ∑ {
𝑓 ( 𝒌 )− 𝑓 ( 𝒌 + 𝒒 )
ℰ( 𝒌 )− ℰ( 𝒌 + 𝒒 )+ ℏ𝜔 − 𝑖 ℏ𝛼 }
𝒌 𝑒 𝑖 𝒒 .𝒓 𝑒 𝑖𝜔𝑡 𝑒 𝛼𝑡
+ 𝑐 . 𝑐
In this equation, the summation is now included over all k states, “occupied” or
“unoccupied”. The redistribution of this charge is associated with a corresponding
15

potential given by Poisson equation, ∇
2
( 𝛿𝜙 ) = −4𝜋𝑒𝛿𝜌 , which allows one to determine
the potential due to the external perturbation as:
𝜙 = {
4𝜋 𝑒 2
𝑞 2
∑ {
𝑓 ( 𝒌 )− 𝑓 ( 𝒌 + 𝒒 )
ℰ( 𝒌 )− ℰ( 𝒌 + 𝒒 )+ ℏ𝜔 − 𝑖 ℏ𝛼 }
𝒌 }𝒰
Assuming that the actual external potential applied (if any) is 𝛿𝒱 , for our equations to be
self consistent, this perturbation (𝛿𝒰 ) must contain 𝛿𝜙 , or 𝛿𝒰 = 𝛿𝒱 + 𝛿𝜙 and as per the
definition of permittivity, 𝛿𝒰 =
𝛿𝒱
𝜖 ( 𝑞 ,𝜔 )
, giving us the Linhard expression for permittivity
as:
𝜖 ( 𝑞 , 𝜔 ) = 1 + {
4𝜋 𝑒 2
𝑞 2
∑ {
𝑓 ( 𝒌 )− 𝑓 ( 𝒌 + 𝒒 )
ℰ( 𝒌 + 𝒒 )− ℰ( 𝒌 )− ℏ𝜔 + 𝑖 ℏ𝛼 }
𝒌 }
From this expression, it is easy to derive the permittivity in the case of static screening,
when 𝜔 = 0, giving us 𝜖 ( 𝑞 , 𝜔 ) = 1 +
𝜆 2
𝑞 2
, where 𝜆 2
= 4𝜋 𝑒 2
𝒩 ( ℰ
𝐹 ) .
The case of dynamic screening is somewhat more complex, where the complete
expression of 𝜖 ( 𝑞 , 𝜔 ) must be considered for large values of 𝜔 . This summation depends
on the band structure of the material under consideration, through the ℰ( 𝒌 ) terms in the
denominator. For a free electron gas model, this can be summed to give:
𝜖 ( 𝑞 , 𝜔 ) = 1 +
4𝜋 𝑒 2
𝑞 2
𝑛 2
3
ℰ
𝐹 {
1
2
+
4𝑘 𝐹 2
− 𝑞 2
8𝑘 𝐹 𝑞 𝑙𝑛 |
2𝑘 𝐹 + 𝑞 2𝑘 𝐹 − 𝑞 |}
This is a simplified expression for the Kohn effect at T=0K. What it reveals is that at
specific wavevectors, the perturbation potential diverges, and states couple very strongly.
However, in three dimensions, this leads to a mild discontinuity in the permittivity. The
16

summation over k diverges only for a select few (nested) wavevectors, which connect
two points on the Fermi surface.
In one dimensional systems, however, the Fermi surface consists only of two distinct
points, and hence is completely nested. This leads to a significantly stronger singularity
in screening at select wavevectors, and manifests itself as strong electron-electron
interaction (when the perturbation is a Coulombic potential), or strong electron-phonon
interaction (when the perturbation is a deformation potential). This concept is critical to
explaining several quantum anomalies observed in both graphene and metallic single
wall carbon nanotubes.

17

CHAPTER 2: ELECTRON-PHONON INTERACTIONS IN
SUSPENDED QUASI-METALLIC CARBON NANOTUBES
This chapter is similar to Dhall et al.[15], published in Physical Review B.

2.1 Abstract
Pronounced electron-phonon interactions in suspended, nearly defect-free metallic
carbon nanotubes, are observed through a Kohn anomaly (KA) of greater strength than
theoretically predicted. This KA is accompanied by a gate-induced modulation of the G
band Raman intensity. By establishing a quantitative correlation between the strength of
the non-adiabatic Kohn anomaly and the modulation of Raman intensity, we determine
that the underlying cause that leads to both these effects is the same. By varying
temperature, we find that metallic nanotubes can switch between a regime in which the
non-adiabatic Kohn anomaly is clearly observed and a regime where the non-adiabatic
Kohn anomaly is absent. The regime that does not exhibit a non-adiabatic Kohn anomaly
is accompanied by a suppression of the Raman intensity under electrostatic gating,
whereas in the regime where the non-adiabatic Kohn anomaly is clearly observed, strong
enhancement of the Raman intensity with gating is observed.
2.2 Introduction
Carbon nanotubes (CNTs) have been studied extensively over the last two
decades due to their remarkable mechanical, electronic, and thermal properties. Despite
this large collective body of research effort, there are still several important aspects of
carbon nanotubes that are not well understood, with significant discrepancies between
18

experiment and theory. Recently, the ability to fabricate ultra-clean, nearly defect-free,
suspended single wall carbon nanotubes (SWNTs) has been developed [16-18]. This has
allowed scientists to study many interesting physical phenomena such as negative
differential conductance (NDC)[19], breakdown of the Born-Oppenheimer
approximation[20], Wigner crystallization[21], Raman intensity modulation[22], and
Mott insulator behavior[17, 22]. Because of their one-dimensional nature, pristine,
defect-free SWNTs provide an excellent experimental platform to study the exotic
physical phenomena of one-dimensional systems.
The especially strong electron-phonon coupling in this one-dimensional system
has a significant effect on the G band of metallic nanotubes, which gives rise to a Kohn
anomaly (KA)[23-26], and is even predicted to cause a Peierls distortion (PD) at T=0K
[27, 28]. The G band for metallic SWNTs consists of two peaks, a G- peak that
corresponds to the LO phonon mode and a G+ peak, corresponding to the TO phonon
mode. In metallic SWNTs, the G- peak is downshifted and broadened due to a strong
coupling of this phonon mode to the continuum of electronic states[29]. Time dependent
density functional theory (DFT) calculations predict a breakdown of the Born-
Oppenheimer approximation[30, 31], which leads to the non-adiabatic Kohn
anomaly[32]. In the non-adiabatic KA regime, the gate voltage (Vg) dependence of the G-
phonon frequency follows a W shape profile[30], which provides a signature of the non-
adiabatic behavior[32, 33]. This phenomenon has been investigated previously, both in
carbon nanotubes and graphene, using Raman spectroscopy[28, 33-35]. It is not
surprising that the Born-Oppenheimer approximation breaks down in carbon nanotubes,
19

given the fast vibrational motion of their tightly bound carbon atoms (0.02ps) and long
electron lifetimes (0.2-3.0ps)[36]. However, it is surprising that a vast majority of the
literature on Raman spectroscopy of gated metallic CNTs shows no evidence of a non-
adiabatic KA[25, 28]. In these previous studies, the nanotubes were lying on a substrate
and had undergone lithographic processing, which may induce defects and surface
contaminants. In fact, clear non-adiabatic effects have only been observed in ultra-clean,
nearly-defect free, suspended carbon nanotubes[20]. This is a testament to the acute
sensitivity of this one-dimensional system to perturbations from substrate interactions and
surface contaminants. Furthermore, in the work presented here, the strength of this effect
is found to be considerably greater than both previous experimental work and predictions
made theoretically[35, 37]. We have also found that nanotubes can transition between a
regime in which the non-adiabatic KA is clearly evident to a second regime where there
is no sign of the non-adiabatic KA, by varying the temperature.
2.3 Experimental details
In this work, platinum source and drain electrodes are patterned on a
Si/SiO2/Si3N4 wafer, along with a platinum gate electrode in an 800nm deep, 2μm wide
trench, as described previously[22, 33]. A ferric nitrate catalyst for carbon nanotube
growth is dispersed in de-ionized water and deposited in lithographically-defined
windows patterned on the source and drain electrodes. CNTs are then grown by chemical
vapor deposition (CVD) using a mixture of argon gas bubbled through ethanol and
hydrogen at 825°C, yielding suspended single wall carbon nanotubes in a field effect
transistor (FET) geometry, as shown in Figure 2-1(a) and Figure 2-1(b). The nanotube
growth is the final processing step in the sample fabrication, which ensures that these
20

-1 0 1
-5.0
0.0
5.0
300K
Current ( A)
Bias Voltage (V)
nanotubes are not contaminated by any chemical residues from lithographic processes.
Also, since these nanotubes are suspended, there are no effects induced by the underlying
substrate.

Current-bias voltage (I-Vb) and conductance-gate voltage (I-Vg) characteristics of
each device are measured on a probe station in order to distinguish metallic nanotubes
from semiconductors. High bias transport measurements are performed in an inert gas
environment to determine whether the device is suspended, which is indicated by a region
of negative differential conductance (NDC), as shown in Figure 2-1(c). The value of the
maximum current is used to determine whether the device is a single isolated CNT or a
(
c)
(
a)
-4 -2 0 2 4
0
20
40
300K
Conductance ( S)
Gate Voltage (V)

Gate Electrode
CNT
Pt Electrode

(
b)
Source
Drain
Trench
Gate
CNT
Figure 2-1: (a) Schematic diagram and (b) SEM image of a suspended CNT FET device.
(c) Typical room temperature electrical current versus bias voltage characterization of a
metallic SWNT. The inset shows the low bias conductance versus gate voltage.
(
(a)
(
(b)
(
(c)
21

bundle, as established by Pop et al.[19]. Single metallic CNTs that pass these selection
criteria are selected and wire-bonded for further characterization. Raman spectra of these
CNT devices are collected using either 633nm or 532nm wavelength radiation. The laser
beam is attenuated by neutral density filters, to ensure that heating is minimal, and
focused to a 1 m spot size using a cover-glass corrected 40X objective lens. The
measurements are performed in an optical cryostat (Cryo Industries, Inc.) under vacuum
at various temperatures between 4K and 400K. As a further selection criterion, we ensure
that each nanotube does not exhibit a defect-induced D band Raman mode near 1350 cm
-1
[38]. G band Raman spectra are collected at different gate voltages and fitted to both
Breit-Wigner-Fano (BWF) and Lorentzian lineshapes. The Raman shift, peak height, full
width at half maximum (FWHM), and the electron-phonon coupling factor (Fano factor
from the BWF lineshape[29]) are extracted from these fits and plotted as a function of the
applied gate voltage.
2.4 Results and discussion
Figure 2-2 shows the G- band Raman shift plotted as a function of the applied gate
voltage, which clearly shows the W shape profile predicted for the non-adiabatic KA
(Figure 7). The inset shows the raw Raman spectrum at Vg=0V. Time-dependent density
functional theory predicts the maximum downshift in phonon frequency with gate voltage
(from the ungated sample) at room temperature to be approximately 3 cm
-1
[30, 31, 35].
However, as shown in Figure 2-2, this device shows maximum downshifts of 15 cm
-1
at
300K, a stronger dependence of phonon energy on gate voltage than theoretically
predicted. A similar W shape profile has been observed in graphene, but only at very low
22

temperatures (T=12K)[39]. For graphene, however, the depth of this W shape is only
about 1 cm
-1
. The significantly more pronounced W shape profiles observed in CNTs are
indicative of strong electron-phonon interaction in metallic nanotubes, and of the
cleanliness of suspended CNT samples fabricated in this fashion. Graphene samples,
prepared on Si/SiO2 substrates, are prone to spatial fluctuations of Fermi level, making it
harder to observe these effects. Comparing our results with the calculations of Tsang et.
al[35], we conclude that the electron-phonon interaction matrix element squared is
approximately 500 eV
2
Å
-2
for these suspended pristine metallic CNTs, which is about 5
times greater than values reported previously, both by experimental methods[35] and
theoretical calculations[30]. For a majority of our devices, the G- peak is significantly
more intense than the G+ peak, and hence, the term “G band” refers to the G- vibrational
mode. Raw spectra for one such device are plotted in Figure 2-3(a). A color plot is shown
in Figure 2-3(b), which also shows the gate dependence of the G- band linewidth. On
devices that clearly show a G+ band, we find that the G+ band Raman shift and intensity
do not change with gate voltage.

23

-10 -5 0 5 10
1550
1560
1570
1580

G
-
Band Raman Shift (cm
-1
)
Gate Voltage(V)
1300 1400 1500 1600 1700
G
-
peak
Raman Intensity
Raman Shift (cm
-1
)
V
g
=0V
G
+
peak
T=300K
15cm
-1

Figure 2-2: G- band Raman shift plotted as a function of gate voltage at 300K for sample
527-1m. The inset shows a typical Raman spectrum of a pristine metallic SWNT taken at
300K at Vg=0V.

24

-8 -6 -4 -2 0 2 4 6 8
1500
1550
1600
1650
Gate Voltage (V)
Raman Shift (cm
-1
)

Figure 2-3: (a)A waterfall plot showing the evolution of the Raman G band as a function
of gate voltage (Vg) for device 753 at 300K.
All 25 nanotubes characterized in this study were found to exhibit only two types
of behavior, which we refer to as Regime 1 and Regime 2. In Regime 1, shown in Figure
2-4(a), the G band Raman shift exhibits a strong non-adiabatic Kohn anomaly, or W
shape profile. These devices also show a suppression of the Raman intensity near Vg=0V,
as shown by the data corresponding to the right vertical axis. Not all of our samples
exhibit a W shape profile. In fact, a slight majority of samples do not exhibit this
behavior. In Regime 2, shown in Figure 2-4(b), no gate voltage dependence is observed
in the G band Raman shift, however, significant enhancement in the Raman intensity is
1450 1500 1550 1600 1650
Raman Shift (cm
-1
)
Vg= -8V

Vg= 8V

(a)
(b)
25

observed near the charge neutrality point. Regime 1 behavior was observed in 11 of the
25 nanotubes measured in this study, showing a clear W shape profile in the Raman shift
versus Vg dependence and a gate-induced enhancement of the G band Raman intensity.
As mentioned above, this W shape profile indicates strong electron-phonon coupling and
phonon energy renormalization due to the non-adiabatic Kohn Anomaly. The fact that
this profile is not observed in Figure 2-4(b) indicates that neither the Kohn anomaly, nor
the breakdown of Born-Oppenheimer approximation, make a significant contribution to
the phonon renormalization energy in Regime 2 and the electron-phonon coupling is
weak.

Interestingly, many of the devices measured in this study were found to transition
from Regime 2 to Regime 1 as the temperature was lowered. Figure 2-5 shows the gate
dependence of the G- band for the same device measured at two different temperatures.
At room temperature, the device shows no sign of the non-adiabatic Kohn anomaly
(
b)
-6 -4 -2 0 2 4 6
1572
1576
1580
1584
1588
Raman Intensity
Raman Shift
Raman Intensity
Raman Shift (cm
-1
)
Gate Voltage (V)

-6 -4 -2 0 2 4 6
1572
1576
1580
1584
Raman Intensity
Raman Shift
Raman Intensity
Raman Shift (cm
-1
)
Gate Voltage (V)

(a)
(b) Regime 1 Regime 2
Figure 2-4: Room temperature gate voltage dependence of the G- band Raman shift and
intensity for (a) device 435-8m, showing the signature W shape profile indicating
breakdown of the Born-Oppenheimer approximation(Regime 1) and (b) device 498-16m,
showing no evidence of non-adiabatic behavior (Regime 2).
26

(Figure 2-5(a)), and the Raman intensity is enhanced around Vg=0V, consistent with
devices in Regime 2. At 4.2K, however, we observe the signature W shape profile
(Figure 2-5(b)) and Raman intensity suppression around Vg=0V, consistent with devices
in Regime 1. It should be noted that, in the case of this particular device, the full W shape
profile cannot be seen, simply because the device was not gated strongly enough to
clearly observe the upshift that follows, completing the W shape profile. This change
from 300K to 4.2K in gate dependence was reversible and repeatable as we cooled down
and warmed up the device. Hence, any contamination or damage to the nanotube can be
ruled out as an underlying cause of this temperature-induced transition. Data was also
collected at intermediate temperatures, and the temperature at which the device
transitioned from Regime 1 to Regime 2 was found to lie between 4.2K and 100K for
device 359.

-6 -4 -2 0 2 4 6
-10
-8
-6
-4
-2
0
Raman Shift
Raman Intensity
Raman Intensity
Relative Raman Shift (cm
-1
)
Gate Voltage(V)

-6 -4 -2 0 2 4 6
-10
-8
-6
-4
-2
0
2
Raman Shift
Raman Intensity
Raman Intensity
Relative Raman Shift (cm
-1
)
Gate Voltage(V)

Figure 2-5: Gate voltage dependence of the G band Raman shift and G band Raman
intensity for device 359 at (a) T= 300K, consistent with Regime 2, and (b) at T=4.2K,
consistent with Regime 1.
T=300K T=300K (a) (b)
27

These results indicate that there is a relation between the Raman intensity
modulation and the non-adiabatic Kohn anomaly. In order to further establish this
correlation, we first quantify the intensity modulation using the ratio of the Raman G
band intensities of the gated and ungated CNT. Similarly, we quantify the strength of the
non-adiabatic Kohn anomaly from the maximum downshift observed in G band Raman
frequency from Vg=0V. This corresponds to the depth of the minima in the W shape
profile. By plotting the intensity ratio against the maximum phonon energy downshift, we
obtain the linear correlation shown in Figure 2-6. While both a bandgap and the
electronic lifetime affect non-adiabaticity, based on our limited dataset, we are unable to
clearly distinguish between changes brought upon due to a bandgap and due to a change
in electronic lifetimes. It should be noted that, in this scheme, all the devices in Regime 2
(showing an enhanced Raman intensity around Vg=0V and no non-adiabatic KA) lie near
the (0,0) point, since the Raman intensity of the doped CNT is much smaller than the
undoped CNT. The G- band linewidths for the 25 samples measured in this study spanned
a wide range from 33 cm
-1
to 83 cm
-1
.This data is given in Table 2-1 along with the
relative strengths of the non-adiabatic effects. No correlation could be established
between the G- band linewidth and either the maximum Raman downshift in the W-shape
profile, or the intensity modulation ratio.

28

The depth of the minima in the W shape profile is directly proportional to the
electron-phonon coupling matrix element, and the wide range of values obtained for this
depth can be explained by the chirality dependence of electron-phonon coupling in
SWNTs[37]. The linear correlation between this depth and the intensity modulation, as
shown in Figure 2-6, suggests that intensity modulation is a manifestation of the same
underlying mechanism, i.e., electron-phonon interaction. An abrupt change in the Raman
intensity, as shown in Figure 2-4(a), can arise from a structural phase transition. For
example, a Mott insulator transition or Peierls transition can result in a charge density
wave, which lowers the symmetry of the crystal and can change these vibrational modes
from Raman active to Raman inactive, thus resulting in an abrupt drop in Raman
intensity near the charge neutrality point. However, from our limited datasets, we are
0 5 10 15 20
0
5
10
15
Intensity Modulation Ratio
Maximum Raman Downshift (cm
-1
)
Figure 2-6 Correlation between the ratio of gated and ungated G band Raman intensities
for various devices plotted as a function of the maximum gate-induced downshift of the
G band Raman frequency due to the non-adiabatic Kohn anomaly. Each point on this plot
corresponds to a different nanotube sample.
29

unable to establish exactly which instability is producing these effects, and further studies
are needed in this direction.
Table 2-1: Various metallic SWNT FET devices showing the non-adiabatic Kohn
anomaly, as well as intensity modulation of the Raman G band.
Device Name Temperature (K) G - linewidth (cm
-1
) Maximum Raman
Downshift (cm
-1
)
359 300 53.6 -
200 47.5 7.9
100 51.4 9.4
4.2 66.2 8.8
498-16m 300 43.0 1.2
4.2 37.4 4.1
435-8m 300 54.5 9.7
4.2 33.7 6.4
508 300 63.0 7.1
75 75.1 -
526 15m 300 43.9 5.2
10 48.8 14.4
491-15m 300 83.4 2.2
10 68.8 7.8
525-3m 300 40.8 6.8
524 300 32.2 2.1
527 300 69.2 9.2
314 300 62.1 14.4
753 300 46.0 6.5

The minima in the W shape profile have been predicted to deepen significantly as
the temperature is lowered for graphene and metallic carbon nanotubes [30, 35, 37].
These calculations assume linear bands for electron dispersion, with no bandgap. This
general trend is observed on several devices, although, the effect is still not as
pronounced as theoretically predicted. For a significant fraction of our devices, however,
we do not see this trend. Figure 2-7 shows the gate dependence of the G- band Raman
shift relative to the Raman shift at Vg=0, at different temperatures for two different CNT
devices. Both devices show the W shape profile, indicating a strong non-adiabatic KA.
30

However, at low temperatures, the device in Figure 2-7(a) clearly shows a deepening of
the minima in Raman shift. In contrast, for a number of other devices, such as the one
shown in Figure 2-7(b), we saw no appreciable change in the gate dependence of the
Raman shift at different temperatures.

-10 -5 0 5 10
-20
-15
-10
-5
0
5
10
15
20

300K
150K
4.5K
Relative Raman shift (cm
-1
)
Gate Voltage

(V)
Figure 2-7: Relative Raman shift of the G-band with respect to Vg=0 for (a) device 491-
15 and (b) device 527-1 taken at various temperatures.
(a) (b)
-5 0 5
-9
-6
-3
0

300K
4.5K
Relative Raman Shift (cm
-1
)
Gate Voltage (V)
(
a)
(
b)
Figure 2-8: The renormalization of phonon energy is caused by a virtual electron-hole
pair created under light doping conditions as shown in (a). However, when the Fermi
level is lowered or raised sufficiently (|𝐸 𝐹 | >
ℏ𝜔 𝐺 2
) , these virtual transitions are blocked
and non-adiabatic phonon renormalization is turned off, demonstrated in (b). Figure from
Tsang et.al.
(a) (b)
31

The Kohn anomaly occurs in metallic CNTs when a phonon excites an electron-
hole pair across the tiny bandgap of the metal[30]. The creation of this electron-hole pair
renormalizes the phonon self energy. A visual representation of this process is given in
Figure 2-8. When the Fermi level is raised or lowered sufficiently, these virtual electron-
hole pair excitations are Pauli blocked, and these translate to minima in the phonon
energy at specific Fermi levels (𝐸 𝐹 = ±
ℏ𝜔 2
) . A renormalized phonon self energy is
written as the sum of the unrenormalized energy, ℏ𝜔 , and the real part of the phonon self
energy, Π( 𝜔 , 𝐸 𝐹 ) . The imaginary part of this self energy gives the phonon lifetime, and
hence the width of the phonon mode. From second order time dependent perturbation
theory, the self energy is given as
Π( 𝜔 , 𝐸 𝐹 ) = 2 ∑(
|𝑉 𝑘 |
2
ℏ𝜔 −𝐸 𝒌 𝑒 ℎ
+𝑖 Γ/2
−
|𝑉 𝑘 |
2
ℏ𝜔 +𝐸 𝒌 𝑒 ℎ
+𝑖 Γ/2
)
𝒌 ( 𝑓 ℎ
− 𝑓 𝑒 ) , (1)
where the prefactor 2 comes from spin degeneracy[37]. Here, 𝑓 ℎ,𝑒 are the Fermi
distribution functions for holes and electrons, 𝐸 𝑘 𝑒 ℎ
= 𝐸 𝑘 𝑒 − 𝐸 𝑘 ℎ
, where 𝐸 𝑘 𝑒 ( 𝐸 𝑘 ℎ
) is the
electron (hole) energy, and 𝑉 𝑘 is the electron-phonon matrix element that converts a
phonon into an electron-hole pair. By doping the nanotube, we increase its Fermi energy
so that states in the conduction band are occupied. At T=0K, when 𝐸 𝐹 =
ℏ𝜔 2
, all the
electronic states that can be excited by a phonon are occupied, which switches off the
Kohn anomaly and dramatically changes the electronic screening of phonons. As a result,
this phonon renormalization is extremely sensitive to the band gap of the nanotube. Since
metallic nanotubes actually have non-zero band gaps, we must consider a model that
32

includes the finite effective mass of the electrons. Using a finite-mass Dirac dispersion
relation ( 𝐸 = √𝑚 2
+ ( ℏ𝜐 𝐹 𝑘 )
2
) in the non-adiabatic case at T=0, we obtain
Re[Π( 𝜔 , 𝐸 𝐹 ) ] =
−𝛼 2
[𝐸 𝐶 − 𝐸 𝐹 − {
( ℏ𝜔 )
2
−( 2𝑚 )
2
4ℏ𝜔 }ln |
|𝐸 𝐹 |−
ℏ𝜔 2
|𝐸 𝐹 |+
ℏ𝜔 2
|], (2)
where 𝛼 and 𝐸 𝐶 are constants and 2𝑚 is the band gap[37]. In this case, we see
that the logarithmic singularity can be eliminated if the band gap nears the phonon
energy, thus explaining why some nanotubes do not show a strengthening of the Kohn
anomaly at lower temperatures, as in Figure 2-7(b). In order to more accurately interpret
the experimental observations presented in this study, both the functional form of the
matrix element, Vk, and the curvature induced mini gap must be considered.
Unfortunately, this requires a precise knowledge of the nanotube chirality.
According to Engelsberg and Schrieffer[40], non-adiabatic phonon frequencies
are observed when the electronic momentum relaxation is slower than the phonon
frequency. One can, thus, switch from adiabatic to non-adiabatic frequencies by changing
the electronic relaxation time (that is, by changing the parameter Γ in Equation 1). The
observed transition away from non-adiabatic behavior, as shown in Figure 5, is brought
upon by varying the temperature only. While the underlying nature of this change is not
fully illuminated by this data, one possibility is that the electron lifetime (and hence Γ)
changes with temperature. However, if that is the case, one expects to see a monotonic
phonon hardening, as reported by Farhat et al[25]. That fact that this is not observed in
our experiment indicates that the change in behavior is due to a change in the electron-
phonon interaction matrix element, Vk. This is further corroborated by the observed G-
band linewidths at different temperatures, which do not change considerably.
33

Figure 2-9(a) shows the calculated real part of the phonon self energy (based on
Equation 1) plotted as a function of the applied gate voltage, for two different
temperatures, assuming there is no bandgap in the electron band structure of the metallic
CNT. In this case, we can clearly see a deepening of the minima in the W shape profile,
which has been reported previously [26, 30, 35]. This behavior agrees with the trend
observed in Figure 2-7(a). However, the inclusion of a mini bandgap (120 meV) at
T=150K in the band structure of the CNT, can reduce the renormalization of phonon
energy, as shown in Figure 2-9(b). Small bandgaps of ~100meV (≫ 𝑘 𝐵 𝑇 ) have been
observed experimentally in metallic nanotubes[17, 22], and have been attributed to the
effect of curvature[37] and electron-electron interactions[17]. These calculations indicate
that the experimental data shown in Figure 2-7(b) can be explained if a bandgap opens up
in the metallic CNT as the temperature is lowered[22]. The electron-phonon coupling
matrix element,|𝑉 𝑘 |, is assumed to be the same for all cases in Figure 2-9. One must note,
however, that these calculations involve several simplifications, making it difficult to
provide an exact estimate for the electron-phonon interaction from our experimental data.
Ideally, the electron-phonon matrix element, Vk, depends on the electron wavevector k. In
a more detailed analysis, one could calculate the electron and hole wavefunctions using
an extended tight binding model[41], and thereby obtain the bare electron-phonon matrix
element (g), using a deformation potential form of interaction[37, 42, 43]. Given the
nanotube chirality, it is then possible to assign a functional form to the k dependence of
Vk, which is proportional to g. However this simplification qualitatively captures the
physical understanding of how a bandgap influences the phonon renormalization[35]. A
34

more rigorous analysis would require information about the chirality of the nanotube to
precisely calculate this matrix element, since the functional form of Vk varies with
chirality. Unfortunately, none of the nanotubes presented in this study exhibited a radial
breathing mode. We were, therefore, unable to identify the chirality of the nanotubes, and
this issue is yet to be investigated experimentally.

As mentioned above, the W shape profiles observed in this work, and hence
electron-phonon interaction matrix elements, are significantly larger than values reported
previously, both by experimental methods[35] and theoretical calculations[30]. A recent
study of graphene has indicated that the presence of long range electron-electron
interactions renormalize both the phonon dispersion curve and the strength of the
electron-phonon coupling matrix element using more accurate calculations of the electron
-7.5 -5.0 -2.5 0.0 2.5 5.0 7.5

Real( )
Gate Voltage (V)
300K, E
g
=0eV
150K, E
g
=120meV
-7.5 -5.0 -2.5 0.0 2.5 5.0 7.5

Real( )
Gate Voltage (V)
300K, E
g
=0eV
150K, E
g
=0eV
Figure 2-9 The real part of Π( ω,EF) from Equation 1 at T=300K and T=150K, with (a) no
bandgap in the electron band structure and (b) a bandgap of 120meV.
(a) (b)
35

band structure through the GW approximation[44]. The electron-phonon coupling matrix
element calculated in this manner was found to be about 50% larger than the value
obtained using the local density approximation. In view of this result, we feel similar
theoretical studies are needed for metallic SWNTs to explore the role electron-electron
interactions may have in enhancing the electron-phonon interaction and possible
structural phase change.

2.5 Conclusion
In conclusion, the immense strength of the electron-phonon interactions in
metallic carbon nanotubes causes their phonon energies to depend strongly on the free
carrier density. We find that these pristine nanotubes exist in one of two regimes – (1)
having no sign of the breakdown of the Born Oppenheimer approximation and showing a
suppression of the G- band Raman intensity with electrostatic gating and (2) showing a
breakdown of the adiabatic approximation and accompanied by a dramatic gate-induced
enhancement of G- band Raman intensity. We establish that the coupling between
electrons and phonons in metallic CNTs is approximately five times stronger than
previous theoretical and experimental reports, and that the strength of this coupling is
correlated with the gate-induced Raman intensity modulation. The abrupt changes in the
Raman intensity can arise from a structural phase transition, (e.g., charge density wave),
which lowers the symmetry of the crystal, and can change these vibrational modes from
Raman active to Raman inactive. We feel that, in light of this evidence, the electron-
phonon interactions in metallic carbon nanotubes should be theoretically re-examined.
36

This research was supported in part by ONR Award No. N000141010511, DOE
Award No. DE-FG02-07ER46376, and NSF award No. CBET-0854118. A portion of this
work was done in the UCSB nanofabrication facility, part of the NSF funded NNIN
network.

37

CHAPTER 3: DETERMINATION OF GATE CAPACITANCE IN
METALLIC CARBON NANOTUBES TRANSISTORS USING
PHONON RENORMALIZATION
3.1 Abstract
A novel technique to determine the gate capacitance of metallic carbon nanotube
field effect transistors is presented. The method relies on the strong electron-phonon
interaction in metallic carbon nanotubes, which leads to the non-adiabatic
renormalization of phonon energy with electrostatic doping. The phonon energy goes
through minima when the Fermi energy is half the optical phonon energy (𝐸 𝐹 = ±
ℏ𝜔 2
).
Analyzing the experimentally observed dependence of the G band Raman shift on applied
gate voltage allows us to accurately determine the Fermi energy as a function of gate
voltage, and hence estimate the capacitance of the field effect device. The estimated gate
capacitance is found to be up to a factor of two larger than the geometric capacitance,
indicating the possible role of electron-electron interactions in modifying the carbon
nanotube gate capacitance.

3.2 Introduction
The attractive electrical properties of single wall carbon nanotubes (CNTs) have
been studied extensively since their initial discovery. Due to the long electron lifetimes,
and near perfect crystalline order, nanotubes, and more recently graphene, have attracted
interest as materials suited for novel electronic devices. However, real device application
of CNT based field effect transistors (FETs), requires precise knowledge of the gate-
38

capacitance of the device, along with the band gap of the carbon nanotube. While
electronic band gaps can be measured both by optical techniques, and using transport
measurements, measurement of the gate capacitance (𝐶 𝐺 ) is more challenging. Typical
capacitance measurements use AC transport data to extract circuit impedance, and hence
determine capacitance. However, such AC measurements are adversely affected by stray
parasitic capacitances. In this study, a novel characterization technique is demonstrated,
which allows the determination of this gate capacitance using Raman spectroscopy.
This technique relies on strong interaction of optical phonons and electrons in
metallic carbon nanotubes, which gives rise to the non-adiabatic Kohn anomaly. This
Kohn anomaly leads to a distinctive dependence of the longitudinal optical (LO) phonon
energy on the charge density in the nanotube. Both time dependent density functional
theory, and perturbation theory calculations predicted a ''W-shape'' dependence of the LO
phonon energy on the nanotube Fermi level (𝐸 𝐹 ), with two minima occurring when the
Fermi energy exactly equals half the phonon energy (𝐸 𝐹 = ±
ℏ𝜔 2
). Studying the gate
voltage dependence of the G band Raman shift, allows us to determine the gate voltages
at which these minima in phonon energy occur. Since the phonon energy itself is known
precisely (0.196 eV), the position of the Fermi level at these gate voltages is known
exactly, and we can estimate a gate capacitance from this data.
3.3 Experimental Details
Suspended FET devices are fabricated with pre-patterned electrodes for
source/drain and gate. Catalyst nanoparticles are dispersed in lithographically defined
windows to enable nanotube growth by chemical vapor deposition as described in the
39

previous chapters. Metallic nanotubes are distinguished from semiconductors using their
transport characteristics, and selected for Raman characterization. Raman spectra are
collected at different applied gate voltages, and the phonon energy of the LO mode
(Raman G band) is extracted from these spectra. Plotting this phonon energy, as a
function of applied gate voltage gives the characteristic W-shape profile, shown in Figure
3-1. The experimentally observed data can give us a wealth of information about
electron-phonon interaction in metallic nanotubes. In this study, however, we mainly use
the separation in gate voltage (Δ𝑉 𝜔 𝑚𝑖𝑛 ) at the two minima in renormalized phonon energy
to accurately determine the relationship between the externally applied gate voltage (𝑉 𝐺 )
and nanotube Fermi energy.

Figure 3-1: The gate voltage dependence of G band Raman shift of a metallic carbon
nanotube. The signature "W shape" is a consequence of the Kohn anomaly in this system,
with the separation between the two minima corresponding to change in Fermi energy of
0.196eV.
3.4 Theoretical Model
The elementary theoretical concepts needed to describe the gate-nanotube
coupling are described briefly. The charge density (ρ) on the nanotube is electrostatically
40

tuned using the capacitive coupling between the gate electrode and the suspended
nanotube (𝐶 𝐺 ). In nanostructures, the reduced density of states means that it is not always
possible to accumulate enough charge to completely screen an externally applied
electrostatic field. Following the work by Luryi[45] for the case of two dimensional
electron gases, it was shown that the gate capacitance (𝐶 𝐺 ) per unit length for a CNT-FET
is given by
1
𝐶 𝐺 =
1
𝐶 𝑔𝑒𝑜𝑚 +
1
𝐶 𝐷𝑂𝑆 +
1
𝐶 𝑥𝑐

Where 𝐶 𝑔𝑒𝑜𝑚 is the electrostatic capacitance, governed by the geometry of the
capacitor, and 𝐶 𝐷 𝑂𝑆
is the quantum capacitance, which arises from the energy cost of
adding charge to a system with a finite density of available states (and the requirement
that Pauli’s exclusion principle be satisfied). However, the presence of electron-electron
interaction in metallic nanotubes, and the requirement of anti-symmetry of the many
body wavefunction, lead to additional energy costs in adding charge to a nanotube, not
accounted for by geometric and quantum capacitances. Hence, the exchange-correlation
capacitance, 𝐶 𝑥𝑐
, must be included in the equation above.
The geometric capacitance is given by 𝐶 𝑔𝑒𝑜 =
2𝜋 𝜖 0
log(
4ℎ
𝑑 )
, where ℎ is the separation
between the nanotube and the gate electrode, and 𝑑 is the diameter of the carbon
nanotube. The quantum capacitance depends on the density of available electronic states
in the carbon nanotube (𝐷 ( 𝐸 ; 𝐸 𝑔𝑎𝑝 )), and hence, on it’s electronic band structure. While
metallic carbon nanotubes in the one-electron approximation are expected to possess a
linear band structure, where 𝐸 = ℏ𝑣 𝐹 𝑘 , the presence of a finite bandgap is included into
41

picture by assuming a hyperbolic band structure, given by 𝐸 =
√
ℏ𝑣 𝐹 𝑘 2
+ (
𝐸 𝑔𝑎𝑝
2
)
2
,
where 𝑣 𝐹 is the Fermi velocity (~8×10
5
m/s)[46], 𝑘 is the electron wavevector, and 𝐸 𝑔𝑎𝑝
is the band gap of the quasi-metallic carbon nanotube. At finite temperatures, the
quantum capacitance is given by
𝐶 𝐷𝑂𝑆 ( 𝐸 ; 𝐸 𝑔𝑎𝑝 ) = ∫ 𝑑𝐸 (−
𝑑𝑓 𝑑𝐸 )𝐷 ( 𝐸 ; 𝐸 𝑔𝑎𝑝 )
where 𝑓 ( 𝐸 ; 𝐸 𝐹 , 𝑇 ) is the Fermi distribution function. The effects of exchange and
correlation have so far been ignored in existing literature. The gate capacitance (𝐶 𝐺 ) of
the nanotube modulates the Fermi level (𝐸 𝐹 ) with applied gate voltage (𝑉 𝐺 ) as given by
𝜕 𝐸 𝐹 𝜕 𝑉 𝐺 =
𝜕 𝐸 𝐹 /𝜕𝑛
𝜕 𝑉 𝐺 /𝜕𝑛
=
𝐶 𝐺 𝐶 𝐷𝑂𝑆
Solving this equation numerically allows us to determine the relationship between
applied gate voltage and Fermi energy. The calculated dependence is non-linear due to
the band gap of the nanotube, and depends on the gate capacitance and band gap, as
shown in Figure 3-2. Using the minima of the renormalized phonon energy, shown in
Figure 3-1, we know the gate voltages at which the Fermi level is exactly half the phonon
energy, i.e.,
𝐸 𝐹 (𝑉 𝐺 = ±
∆𝑉 𝜔𝑚𝑖𝑛 2
) = ±
ℏ𝜔 2
= 0.098𝑒𝑉

42

In a truly gapless metallic nanotube, it would be possible to directly determine the
capacitance by ensuring that the calculated dependence of Fermi level on gate voltage
satisfies this condition, since we would have one equation and one unknown (𝐶 𝐺 ).
However, the finite band gap in metallic nanotubes introduces a non-linearity in the
dependence of applied gate voltage on the nanotube Fermi level. Hence, we must
supplement the Raman measurements with electrical transport (transconductance) data, as
shown in Figure 3-3, in order to estimate the band gap of the nanotube. Fitting our
transconductance curves to a simple Landauer model provides us with one constraint on
the values of capacitance and band gap. The second constraint comes from enforcing
Equation, based on our Raman data, yielding two coupled transcendental equations,
(a) (b)
Figure 3-2: (a) The calculated dependence of the Fermi level of the nanotube on
externally applied gate voltage for three different values of gate capacitance (𝐶 𝐺 ). The
band gap is assumed to be 0 eV. (b) The calculated dependence of the Fermi level of the
nanotube on externally applied gate voltage for three different values of band gap. The
non-linearity in the dependence arises due to the presence of a band gap. The offset of the
charge neutrality point (CNP) is determined by finding the minima in the
transconductance plot.
CNP
43

which can be solved self consistently to determine both the band gap and the gate
capacitance.

Figure 3-3: The conductance of the nanotube as a function of applied gate voltage. The
data (shown in blue) is fitted to a Landauer model for ballistic transport (shown in red),
allowing us to determine the band gap.
3.5 Results and Discussion
While analyzing the values obtained for the capacitance, we separate the term in
Equation corresponding to the density of states capacitance (𝐶 𝐷𝑂𝑆 ), which can be easily
calculated. The residual capacitance, 𝐶 𝑔𝑥𝑐 = ( 𝐶 𝑥𝑐
−1
+ 𝐶 𝑔𝑒𝑜𝑚 −1
)
−1
, is assumed, as a first
approximation, to be independent of the gate voltage. For the data shown in Figure 3-3,
the band gap from the transport measurements was found to be 148 meV, and the
corresponding residual capacitance (𝐶 𝑔𝑥𝑐 ) was found to be 1.408×10
-11
F/m. Similarly,
transport and Raman datasets for other devices have been analyzed, and used to extract
the band gap and the gate capacitance, as shown in Table 3-1.
Upon extracting the residual capacitance,𝐶 𝑔𝑥𝑐 , one finds that it is over twice as
large as the geometric capacitance. This is most surprising, because the geometric and
exchange-correlation capacitances add in series, and hence, the net capacitance,𝐶 𝑔𝑥𝑐 , is
44

expected to be smaller than each of the individual capacitances. Hence, it leads to the
conclusion that the effect of exchange and correlation is to introduce a negative
capacitance. Essentially, this implies a negative compressibility of the “sea” of free
electrons in metallic carbon nanotubes, which would arise due to the electron-electron
interaction. In conventional systems, such as bulk metals, with positive compressibility of
electrons, the addition of charges (electrons) to the system leads to an increase in the
overall energy of the system due to mutual repulsion. However, in systems with negative
electron compressibility, the addition of charges screens the mutual repulsion that
individual electrons experience, thereby reducing the energy of the overall many body
system. While previous reports in literature have explored the possibility of a Mott like
gap due to strong correlations in these suspended, quasi metallic CNTs, no consensus
exists in literature with regards to existence of such a state. Very recent reports in
literature have put forth theories supporting such an argument. In particular, the
experimental work of Ilani[47], as well as the theoretical model put forth by Fu[48] are
some recent efforts in this direction. In particular, the model by Fu puts forth a more
accurate approximation for the gate capacitance of a suspended carbon-nanotube FET.
Correlation effects are found to be of especial importance in the case of low charge
density, when the average separation between electrons is comparable to the distance
between the nanotube and the gate electrode. In these suspended, ultra-clean nanotubes, it
is indeed possible to achieve such low charge densities, as these tubes are free from
issues of unintentional doping due to surface adsorbates. In particular, it is suggested that
the electrons in a nanotube are likely to lower the energy of the system by spatially
45

avoiding one another. This would lead to an enhancement of capacitance, given by the
expression,
𝐶 𝐶 𝐺 ≈ 1 +
log(
2
𝑛𝑑
) − 1.384
ln( 2𝑛 ℎ)+ 1.384

Where 𝑑 is the diameter of the nanotube, 𝑛 is the charge density, and ℎ is the
height above the gate electrode.
Device Temp(K) ℎ( 𝑛𝑚 ) Δ𝑉 𝜔 𝑚𝑖𝑛
( 𝑉 ) 𝐸 𝑔𝑎𝑝 ( 𝑚𝑒𝑉 ) 𝐶 𝑔𝑒𝑜𝑚 ( 𝐹 /𝑚 ) 𝐶 𝑔𝑥𝑐 ( 𝐹 /𝑚 ) 𝐶 𝑥𝑐
( 𝐹 /𝑚 )
498 300 500 6.6 150 7.58×10
-12
1.41×10
-11
-1.641×10
-11

435 300 500 8.4 138 7.58×10
-12
1.10×10
-11
-4.085×10
-11

774 300 300 6.6 148 8.15×10
-12
1.41×10
-11
-5.171×10
-11

Table 3-1: Extracted values of band gap and residual capacitance from three different
metallic carbon nanotube devices using both the electrical transport data, and the gate
induced renormalization of phonon energy.
3.6 Conclusions
In summary, we have shown a novel technique to determine the gate capacitance
of CNT FET devices using Raman spectroscopy. Since the method utilizes a purely
optical probe, under DC gating conditions, issues of electrical contact resistances,
parasitic capacitances, and impedance mismatches do not affect the measurement. The
values of gate capacitance found using this method was 7.5×10
-12
F/m, which is larger
than the geometric capacitance, indicating the possible role of electron-electron
interactions in these suspended, ultra-clean CNTs which warrants more detailed
theoretical modeling.

46

CHAPTER 4: IN-SITU ELECTRON DIFFRACTION OF
SUSPENDED CARBON NANOTUBES
4.1 Introduction
The earlier sections of this thesis have focused on experimental studies of
suspended, nearly defect free carbon nanotubes. The absence of defects and substrate
interactions have revealed a rich variety of physical effects, such as strong electron-
phonon interaction through the non-adiabatic Kohn anomaly[15], and strong electron-
electron interactions leading to a Mott like phase transition[21]. These effects had
previously not been observed in nanotubes grown on substrates such as Si/SiO2 wafers,
due to the perturbation caused by the presence of lithographic residue on the surface of
the tubes, as well as interaction with the underlying substrate.
By following the device fabrication protocol highlighted in the previous chapters,
one is able to overcome these issues through the fabrication of nearly defect free carbon
nanotubes by chemical vapor deposition (CVD). However, one major drawback of the
CVD process is the lack of control over the atomic structure of the particular nanotube
species which forms the channel of the device. Instead, what we end up with is a mixture
of chiralities, which are not always possible to identify. At best, through careful screening
using high-bias transport data, we can distinguish devices with one or multiple nanotubes,
and use only those which have one suspended tube between the source and drain.
47

However, several properties of carbon nanotubes, such as electrical conductivity,
optical excitation energies, and electron-phonon coupling, are known to be sensitive to
the chirality of the tube. Hence, it would be a worthy effort to grown chirality selective
nanotubes through a CVD process similar to the one used in our lab. Recent reports have
demonstrated two techniques to achieve this very goal: engineering the metallic
nanoparticles used to catalyze the growth of nanotubes[49, 50], and the use of small
segments of chirality sorted nanotubes as seeds for an epitaxial growth process[51].
However, these strategies are challenging to reproduce, and not always compatible with
the device geometry required for suspended nanotubes.
Instead, two strategies are suggested as possible alternatives to this problem: (1)
nanotubes are grown in a device geometry which is compatible with Transmission
Electron Microscopy, and (2) the deterministic transfer of suspended nanotubes onto a
device structure, after chirality determination through high throughput optical screening.
While the latter strategy is discussed in the next chapter, this chapter discusses our work
on the fabrication of suspended, nearly defect free carbon nanotube devices on TEM
compatible substrates, along with some preliminary data on in-situ electron microscopy
experiments.
4.2 Coupled electrical and thermal transport in carbon nanotubes at high
bias voltages
Joule heating is a common phenomenon, in which energy from electrons
accelerated by a externally applied electric field is dissipated as heat. While heat
dissipation is a problem with significant practical implications, especially in nanoscale
electronic devices, it is also an interesting problem from an academic standpoint. This
48

process of heat dissipation is made possible by the interaction of electrons and phonons
within the system under study, and depends on various factors such as material
dimensionality, the phonon and electron band structures, the strength of electron-phonon
interaction, as well as defect density in the material.
Ultra-clean, suspended carbon nanotubes offer a unique one-dimensional system,
in which this electron-phonon interaction may be studied. Due to the limited phase space
available for a travelling electron to scatter into (only forward and backward scattering
are permitted in one dimension), electrons travelling through a carbon nanotube may not
scatter for distances as long as 1μm at room temperatures, i.e., the mean free path of
acoustic phonon scattering is very long. At higher “bias voltages” however, the electrons
may be accelerated to a point where they possess sufficient kinetic energy to emit optical
phonons. This leads to a heat dissipation process unlike that observed in any other
material system. The current understanding of this process is based on two fundamental
experiments performed on a metallic carbon nanotube on a substrate[46] and on a
suspended carbon nanotube[19]. The results of these two previous studies are
summarized in this section.
The work of Park [46] studied electron phonon interaction on carbon nanotubes
lying on a substrate. An atomic force microscope (AFM) tip was used as one electrode
for a current-voltage (I-V) measurement. By measuring the nanotube resistance as a
function of the applied source-drain voltage, as well as the position of the AFM tip, the
mean free path of phonon emission was measured on these carbon nanotubes.

49

It is known that in the limit of long device length (𝐿 > 𝜆 ) , the resistivity should
be linearly dependent on the channel length, and resistivity 𝜌 =
𝑑𝑅
𝑑𝐿
= (
ℎ
4𝑒 2
)
1
𝜆 , for a one
dimensional channel with 4 sub-bands (degenerate bands at K and K’ points in the
Brillouin zone, and spin-up and spin-down carriers). Whereas, for short device lengths,
𝐿 < 𝜆 , the transport is ballistic, and resistance is not a function of channel length, for
longer devices, the mean free path of electron scattering (λ) can be extracted from the
slope of the low bias resistance vs. length. In the same manner, the mean free path can
also be calculated at higher applied bias voltages, when optical phonon emission needs to
be accounted for. The conclusion of this study were as follows:
1. At low bias acoustic phonon emission is the dominant process, and a
scattering time of 𝜏 𝑎𝑐
= 3.0 × 10
−12
sec, or equivalently, a mean free path,
Figure 4-1: Current-voltage curves of a single, metallic carbon nanotube, as a function of
the effective length of the nanotube channel, adapted from the work of Park et.al.
50

𝜆 𝑎𝑐
= 2.4𝜇 m is calculated, which is comparable to the value extracted from
experimental data.
2. At higher bias voltages, when electrons possess sufficient kinetic energy to
emit optical phonons, this process becomes the dominant scattering
mechanism. It was found (using tight binding calculations) that only specific
phonon modes made a significant contribution to the scattering rate. In
particular, optical modes (q=0) polarized in the longitudinal direction would
scatter with a 𝜏 𝑜𝑝
= 2 × 10
−13
sec, or a 𝜆 𝑜𝑝
= 180nm. One zone boundary
optical mode phonon (with q=-2kF) also couples strongly to the accelerated
electrons, and 𝜆 𝑧𝑜
= 37nm. Due to the stronger interaction of these phonon
modes with accelerated electrons, scattering due to optical phonon emission is
very effective at high bias voltages, which explains current saturation at high
bias voltages. A schematic sowing the process of optical phonon emission
from an electron accelerated by an electric field is shown in Figure 4-2.

Figure 4-2: Schematic of optical phonon emission by electrons accelerated under a strong
applied field (high bias voltage). lT is the threshold distance the electron must travel
before it gathers sufficient kinetic energy to emit an optical phonon.
51

The work of Pop et al, revealed even more surprising effects in suspended carbon
nanotubes. In particular, the I-V characteristics observe in suspended carbon nanotubes
showed negative differential conductance at high bias voltages, as shown in Figure 4-3

This unusual negative differential conductivity at high bias voltages was
attributed to self-heating effects in the suspended carbon nanotube. The lack of an
underlying substrate makes it harder for heat to escape the carbon nanotube. Furthermore,
being a one dimensional system, heat can only be removed from the nanotube by
conduction, along the length of the tube, and into the source and drain electrodes (which
act as thermal sinks). However, as shown by the work of Park, most of the generated heat
at these high bias voltages, is supplied to the optical phonon branches. Optical phonons,
being almost dispersionless, possess very slow group velocities, and are inefficient
carriers of heat. A combination of these factors leads to intense heating in suspended
CNTs at high bias voltages, which, in turn leads to negative differential conductance.
In order to justify these claims, coupled thermal and electrical transport were
modeled by Pop et al. The model had several floating parameters, such as the thermal
(c)
Figure 4-3: The device geometry (a) and schematic (b) for a nanotube device using the
same nanotube on and off a substrate. (c) Shows the current-voltage characteristics seen
in the two segments of the nanotube.
52

conductivity of the tube, the contact resistance of the device, as well as the mean free
path of acoustic and optical phonon scattering. A self-consistent approach was used to
iteratively tune these parameters to try and reproduce the I-V curves, using a Landauer
model for conductance in a one dimensional channel, without satisfactory results.
Further, the carbon nanotube lattice temperature extracted in this fashion was around
1500K, and it was surprising that nanotubes were found to survive such elevated
temperatures in atmospheric conditions. Hence, it was argued that a situation of thermal
non-equilibrium must exist in these suspended carbon nanotubes. The optical phonon
modes, are in effect, hotter than the acoustic phonon modes. A parameter for the degree
of non-equilibrium (which represented the ratio of thermal resistance of optical-acoustic
decay to that of acoustic conduction along the tube) was introduced into the model. Based
on this, the non-equilibrium phonon populations of the optical and acoustic modes were
calculated, and included in the electron-phonon scattering rate. The self-consistent fitting
process was repeated, yielding more satisfactory fits to the measured I-V curves. It was
hence argued that non-equilibrium phonon populations must exist.
4.3 The need for electron microscopy of carbon nanotubes
However, we believe that further verification of some of these claims needs to be
made. In particular, no chirality dependence was attributed to electron-phonon interaction
in these metallic carbon nanotubes. Furthermore, the mean free paths of phonon
scattering, while measured on nanotubes on a substrate, were only inferred for suspended
carbon nanotubes. Also, no direct measurement of the thermal strain in the nanotube was
made in these studies. Nor was the dependence of the low-energy band structure of the
CNT on any strain effects considered. Each of these facts requires the careful design of a
53

novel experimental scheme, along with significant theoretical modeling. It is for this
reason, that we have designed, and fabricated suspended carbon nanotubes over 1-2μm
long trenches. These trenches penetrate the entire chip, and hence, these samples are
compatible with transmission electron microscopy, which can yield information at the
length scale below the resolution offered by optical probes. Since the mean free paths of
optical phonon emission in suspended CNTs have been estimated to be ~ 37nm, such an
effect would only ever be directly visualized through electron microscopy.
4.4 Sample fabrication
Any sample for TEM studies has to obviously be electron transparent. Often, a
carbon or silicon nitride grid or thin membrane is used as a substrate. However, these
substrates are typically 10 nm thick, considerably thicker than the diameter of a carbon
nanotube (1-2nm). Furthermore, substrate interaction would create perturbations in the
environment of the carbon nanotube. Hence, having suspended carbon nanotubes is
essential for TEM measurements.
54

Figure 4-4: The fabrication process for creating field effect transistors using ultra clean,
suspended carbon nanotubes, compatible with TEM imaging.
The fabrication process is schematically represented in Figure 4-4. A double sided
Si/SiO2/SiN wafer is used for fabrication. Anisotropic etching of Silicon from the back
side of the wafer using KOH removes the bulk of the material from the wafer. After that,
small windows are etched into the SiN on the top face of the wafer. Aligning the back
face lithography to the second lithography step is done using the optical contrast offered
by the etched window from the first etch step.
After this, source, drain and side gate electrodes are deposited on the wafer, and
the remaining SiO2 is etched away, creating a trench which goes through the wafer.
Catalyst windows are then patterned on the source and drain electrodes as before,
followed by CNT growth in our CVD system. A scanning electron microscope image of
one such device is shown in Figure 4-5. The electrical transport data in Figure 4-6, shows
that it is possible to effectively gate such samples using the side gate electrode.
55

Figure 4-6: The current-gate voltage and current-voltage (inset) curves for a metallic
CNT suspended across a TEM compatible trench.

Figure 4-5: SEM image of a suspended CNT device compatible with TEM imaging.
CNT
Contact
Electrode
Catalyst
56

4.5 Electron diffraction in carbon nanotubes
Information at the atomic length scale can be gleaned through scattering
experiments with waves having wavelengths comparable to the atomic separation. In
particular, electrons accelerated to high kinetic energies, offer one such experimental
probe. At a typical TEM acceleration voltage of 200kV, the de Broglie wavelength of the
electron wave is 2.5pm, which is considerably smaller than the interatomic separation in
most solids, making atomic resolution imaging possible (as long as the microscope lenses
are relatively aberration free).
Several schemes are adopted to image using these accelerated electrons, including
conventional high resolution TEM imaging, scanning TEM (STEM) imaging, as well as
the formation of diffraction patterns, which provide the Fourier transform of the crystal
potential of the scattering object (in this case, the nanotube). Currently, STEM and high
resolution imaging of carbon nanotubes is challenging, due to issues of high electron
dose, which is delivered to the nanotube. This high dose of accelerated electrons has been
shown to cause damage. This problem is of particular concern in STEM imaging, where
the electron beam is focused down to a sub-nanometer spot, and rastered across the
sample. However, STEM does offer the capability of looking at inelastically scattered
electrons, and thus allows one to probe collective excitations such at plasmons, at the
spatial resolution of a few nanometers. This topic is left as a possible course of action for
future experiments.
The focus of this chapter will be the discussion of electron diffraction, especially
in the case of carbon nanotubes. The usefulness of probing thermal effects through
electron diffraction is explored through some simple calculations. A relatively new
57

technique of “nano-beam” electron diffraction is shown to provide significantly better
experimental results.
4.5.1 The Born Approximation in Electron Diffraction
The theory of electron diffraction is well reviewed by standard texts on electron
microscopy, and the standard principles of the theory of diffraction apply in this case as
well. Diffraction can be thought of as a scattering phenomenon, in which a wave
coherently interacts with a periodic arrangement of scattering objects. The primary
condition for scattering, is that the wavelength of the wave must be comparable to the
characteristic spacing between the scattering objects. As the wave travels through this
periodic arrangement of scattering objects, each scattering site serves as source for
secondary wavelets, which then add in phase, as well as amplitude, in accordance with
the principle of superposition. If the secondary waves add in phase, and interfere
constructively, the wave amplitude is increased, or equivalently, the wave is
preferentially scattered into directions where the condition for constructive interference is
met.
This condition, which is known as the Bragg condition (or equivalently the Laue
condition for crystallographers), says that electrons are scattered preferentially into
directions, such that the change in wavevector of the electron wave is equal to a
reciprocal space lattice vector, i.e., Δ𝒌 = 𝑮 .
Various forms of diffraction, such as neutron diffraction, X-ray diffraction, and
electron diffraction, have been utilized to obtain fundamental structural information about
58

materials. Although they very in their scattering cross sections, and their characteristic
wavelengths, the theory behind each of these experimental tools is almost the same.
For the particular case of electron diffraction, one particularly important
approximation, called the Born approximation, allows us to greatly simplify the
calculations of electron diffraction patterns, which assumes that electrons do not suffer
multiple scattering events while traversing the thickness of the sample. This
approximation is particularly useful for carbon nanotubes, which offer a very low mass-
thickness.
4.5.2 Electron diffraction in carbon nanotubes
Within the first Born approximation, we can use the scattering amplitude of the
incident electron wave, as given by:
𝐹 ( 𝒒 ) = ∫ 𝑑 𝒓 𝑉 ( 𝒓 ) exp ( 2𝜋𝑖 𝒒 . 𝒓 )
Here 𝒒 is the change in wavevector of the electron wave, which hence specifies
the direction of scattering. 𝑉 ( 𝒓 ) is the scattering potential, which in this case, is the
screened atomic potential of the arrangement of atoms within the carbon nanotube.
An analytical theory of crystal diffraction by tubular structures was first given by
Francis Crick, which enable the identification of the crystal structure of DNA.
Unsurprisingly, this theory represents plane waves in cylindrical co-ordinates, using
Bessel functions to describe the various harmonics[52]. While the algebra is somewhat
cumbersome, the results can be expressed intuitively fairly easily.
The repetition of carbon atoms along the axial direction of the tube, leads to
periodicity, which in turn, leads to certain preferred values of scattering angles. In the
59

radial direction too, the nanotube crystal potential repeats itself every 2π radians. This
lends itself to an intensity distribution which follows Bessel functions of specific orders,
in the direction normal to the nanotube axis. The separation between peaks in the radial is
inversely proportional to the nanotube diameter.
These selection rules are a handy guide for quick identification of the carbon
nanotube chirality, but are not particularly useful beyond that. Instead, numeric
computation, by simply adding up the scattered waves from each of the scattering sites
(atoms in the nanotube), also yields a suitable procedure to calculate diffraction patterns
of carbon nanotubes. In this numeric scheme, the scattering amplitude is calculated at
each pixel on the detector, which is placed on the back focal plane of the TEM.
Parameters such as pixel dimension, camera length, and acceleration voltage are chosen
to match the experimental conditions. The scattering amplitude is given by:
∑ 𝑒 𝑖 ℎ
𝐴 𝑝𝑎𝑡 ℎ𝑠 = 𝑐 1
𝑒 𝑖𝑘 𝑟 𝑆𝐷
𝑟 𝑆𝐷
+ 𝑐 1
2
∑
1
𝑟 𝑆 𝐴 𝑛 . 𝑟 𝐴 𝑛 𝐷 𝑒 𝑖𝑘 𝑟 𝑆 𝐴 𝑛 𝑓 𝑛 𝑒 𝑖𝑘 𝑟 𝐴 𝑛 𝐷 𝑛
Here, 𝑆 denotes the position of the source, 𝐷 , the position of a particular pixel on
the detector, 𝐴 𝑛 denotes the position of a particular atom in the carbon nanotube, 𝑓 𝑛 is the
atomic scattering factor, which is assumed to be independent of the angle of scattering,
and 𝑐 1
is a constant. This formula essentially treats each atom in the carbon nanotube as
the source for a secondary wavelet, which itself is a spherical wave.
One example of simulations performed in this manner is shown here in Figure
4-7. Only up to first order scattering is considered in this calculation. The nanotube axis
is aligned along the X-axis in the diffraction pattern shown. The parameters for the
simulation are indicated in the calculated image.
60

Pixels
Pixels

200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000 0
0.5
1
1.5
2
2.5
3
3.5
x 10
6

One straightforward extension to this calculation is the inclusion of lattice strain.
At elevated temperatures, due to phonon anharmonicity, the lattice is expected to undergo
thermal expansion (or thermal strain), which may be simulated by simply adjusting the
positions of the individual atoms, and running the same simulations. One such calculation
is shown here, using realistic TEM parameters. The diffraction pattern is calculated for a
(12,0) carbon nanotube, with its axis aligned along the X-axis of these diffraction
patterns. Three values of lattice strain (applied along the nanotube axis) are applied, and
the diffraction patterns are show in Figure 4-8(a)-(c).
As is evident from these plots, a clear shift in the diffraction peaks is seen with
increasing values of lattice strain. In particular, a yellow dotted line is used to indicate the
position of the second order diffraction peak in the diffraction pattern of the unstrained
CNT. As strain values are increased, this second order peak moves away from this dotted
yellow line, and the deviation is shown with the lines in red.
(12,0)
80kV
L = 200nm
Camera L = 160cm
Source L = -1.6m
Figure 4-7: (a) Shows a schematic representation of the calculation of electron diffraction
from carbon nanotubes. (b) Shows one such calculated diffraction pattern. The nanotube
axis is aligned with the X-axis in this diffraction pattern.
61

However, this is an oversimplified description of a hot lattice. Thermal vibrations
lead to oscillatory motion of atoms about their mean position, in the time domain. This
has been approximated by assuming the motion of atoms is uncorrelated, and that each
atom exists in its own thermal ellipsoid. The size of the ellipsoid changes with increasing
amplitude of atomic vibration. This allows one to average over all potential instantaneous
configurations of atoms in a hot lattice, without a significant increase in required
computational resources.
The more detailed approach includes the correlation between the motion of
different atoms in the lattice, which can be accounted for by using the entire phonon band
structure of the material, and is considerably more computationally intensive.

62

However, qualitatively, these effects show up as what is known as the “Debye-
Waller” factor. Since an experimentally recorded diffraction pattern averages (in time)
over all possible atomic configurations, electrons lose their preferences to be scattered
Pixels
Pixels

200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000 0
0.5
1
1.5
2
2.5
3
3.5
x 10
6
Pixels
Pixels

200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000 0
0.5
1
1.5
2
2.5
3
3.5
x 10
6
Pixels
Pixels

200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000 0
0.5
1
1.5
2
2.5
3
3.5
x 10
6
Strain = 0%
Strain = 5%
Strain = 10%
Figure 4-8: Calculated diffraction pattern for a (12,0) carbon nanotube with differnt values of
externally applied strain.
63

into directions satisfying the Bragg condition. This leads to a dampening of intensity in of
the peaks in the diffraction pattern. The dampening factor, or the Debye Waller factor, is
given by:
𝐷𝑊𝐹 ( 𝒒 ) = exp ( −〈[𝒒 . 𝒖 ]
2
〉)
Where 𝒒 is the scattering wave vector, and 𝒖 is the amplitude of atomic motion.
Thus, higher order Bragg peaks (with larger 𝒒 ) are damped more strongly. In principle, a
careful analysis of the Debye Waller factor in the diffraction peaks at different
temperatures is capable of yielding information about the population of different phonon
modes within the lattice.
4.6 Nanobeam electron diffraction: Preliminary data
While a detailed theoretical calculation, as proposed in the previous section,
would be a challenging undertaking, the collection of diffraction patterns of carbon
nanotubes with sufficient signal to noise ratio is also a non-trivial task. Increasing the
electron dose on the nanotube (increasing integration time) while collecting diffraction
patterns can only help up to a certain point. Eventually, beam induced deposition on the
nanotube surface, or knock on damage and the subsequent creation of defects, become
serious issues. In our work, we found that using the TEM in a specific “Nano beam”
mode, allowed us to significantly improve our experimental results.
In conventional TEM, under parallel beam illumination, the illuminated area is
about 250nm. This is much larger than the diameter of the nanotube itself, and a majority
of the electrons tend to never interact with the CNT, and hence, do not contribute to the
diffraction pattern. By forming a parallel beam about 20nm in diameter, one is able to
64

significantly enhance the cross section of interaction of electrons with the suspended
nanotube. We have been able to accumulate high quality diffraction patterns at the JEOL
2100-F TEM at the Center for Electron Microscopy and Microanalysis using this
technique. Using a TEM holder specifically designed with electrical feedthroughs for
electrical biasing (Hummingbird Inc.), we have been able to load and bias these
nanotubes successfully in the TEM, and the preliminary datasets are presented in the
section below.

4.7 Conclusions and future work
While this chapter demonstrates the successful fabrication of these unique
samples with suspended carbon nanotubes, as well as the development of the nano-beam
electron diffraction method, needed to obtain high quality electron diffraction patterns
from nanotubes, much work remains to be done. The first and simplest measurements
would allow us to experimentally determine the lattice strain in suspended carbon
SAD
NBD
Figure 4-9: Comparison of electron diffraction patterns recorded using select area
diffraction (SAD) and nano-beam diffraction(NBD). The illuminated area diameter is
250nm in the former, and about 50nm for the latter, leading to improved signal to
noise ratio.
65

nanotubes under high bias voltages. A sudden onset of lattice strain would be
unambiguous proof for suppressed acoustic phonon scattering, and the emission of hot
optical phonons. Furthermore, with spatially resolved nanobeam diffraction patterns, it
would also be possible to measure the mean free paths of optical and acoustic phonon
emission in these nanotubes, through a careful comparison with theoretical calculations.
Also, these experiments would allow us to simultaneously determine the chirality of the
nanotube being studied. Chirality dependent studies would also shed light on the
interaction of electrons with the nanotube lattice, in these unique suspended, one-
dimensional structures, and provide a means to verify the claims made so far in literature.

66

CHAPTER 5: FABRICATION OF ULTRA-CLEAN, SUSPENDED,
CARBON NANOTUBE DEVICES WITH KNOWN CHIRALITY FOR
OPTO-ELECTRONIC DEVICES
5.1 Abstract
The predominant focus of this thesis is on the characterization of ultra-clean
carbon nanotube devices. Previously utilized strategies, such growth of carbon nanotubes
directly onto pre-patterned field effect transistors have yielded a variety of surprising
experimental results, arising due to quantum anomalies in this unique one-dimensional
system. However, the lack of chirality control in the chemical vapor deposition technique
limits any studies on samples prepared in such fashion. While it is possible to create
electrical devices using known chirality nanotubes, prepared using separation and density
gradient ultracentrifugation, such samples suffer from lithographic residues and surface
contaminants. In this chapter, we describe a unique method to prepare ultra clean, known
chirality electrical and opto-electronic devices, using a home built, flip-chip transfer
scheme. Details of the fabrication scheme, as well as a high throughput chirality
screening process are presented, along with preliminary electrical transport data.

5.2 Device Fabrication: Carbon Nanotube Growth and Aligned Transfer
5.2.1 Fabrication of the Substrate
Sample fabrication begins with optically transparent fused silica wafers, using
which, we create a substrate for the growth of carbon nanotubes through chemical vapor
deposition. Arrays of pillars, about 1µm in diameter, separated by a distance of
67

approximately 5µm, are created by photolithography, followed by oxygen based reactive
ion etching of the quartz substrate, with an etch depth of about 4µm. Subsequently, a
second step photolithography is used to open up windows on the tops of the pillar
structures, followed by deposition of a 1 nm film of iron, which serves as the catalyst for
nanotube growth. These steps are schematically represented in Figure 5-1.

These chips are then inserted into a tube furnace, and carbon nanotubes are grown
using chemical vapor deposition, at 800-850C, using a mixture of hydrogen, and argon
bubbled through ethanol as the precursors. The thickness of the iron film deposited on the
pillars controls the mean diameter of the nanotubes, although, precise control of diameter
is still an unsolved problem. The growth process yields nanotubes which grow outward
from the tops of pillars. A fraction of these tubes will end up bridging the tops of pillars,
Figure 5-1: Fabrication of the optically transparent substrate for templated growth of
suspended carbon nanotubes. After the final step, nanotubes grown by chemical vapor
deposition are indicated schematically in black.
68

as indicated by the nanotubes encircled in green in Figure 5-1. Some nanotubes might
grow not successfully bridge the tops of pillars, but would still have a segment of
suspended length, similar to those encircled in red. This latter category of tubes are not
suitable for transfer to electrical devices.

Suspended nanotubes can be identified through scanning electron microscope
(SEM) images, as shown in Figure 5-2, and then transferred to a carefully designed set of
electrical contacts. However, for rapid identification of specific chiralities of CNTs, an
optical microscopy scheme is used, which is discussed in the next section.
5.2.2 Fabrication of transfer compatible electrodes
Once suspended carbon nanotubes are created on the quartz pillars, are described
in the previous section, they are transferred onto silicon chips which have metal
electrodes, designed specifically to be compatible with the transfer process.

(
(a)
(
(b)
Figure 5-2: (a) Shows an array of pillars, etched into a quartz wafer, along with
alignment markers for easy identification of suspended carbon nanotubes. (b) Shows
one such suspended carbon nanotube, bridging the tops of neighboring pillars.
69

The crucial parameters in designing the silicon chips are the dimensions of the
raised metal electrodes. The height of the pillars, created using the Bosch process is
almost equal to that of the quartz pillars used for nanotube growth. Further, the electrodes
must be narrow enough to fit within the separation between two pillars in the quartz
chips.
This fabrication scheme has yielded a good rate of success in the nanotube
transfer process (described in the next section). We are currently in the process of
extending this scheme to different kinds of devices. In particular, two geometries are
being explored:
1. The fabrication of two terminal devices with different metal electrodes used
for the source and drain metals. This geometry is particularly useful for opto-
Figure 5-3: (a) The steps involved in the fabrication of silicon chips with raised metal
electrodes, suitable for carbon nanotube transfer. The low magnification and high
magnification SEM images of one such device are shown in (b) and (c) respectively.
70

electronic devices, such as photodetectors and light emitters. By selecting
metals with very different work functions for the source and drain electrodes,
we are able to create an in-built electric field, which enables efficient
separation of optically generated electron-hole pairs.
2. Three terminal devices, with a separate gate electrode have also been
designed. These devices would allow us to perform measurements as a
function of the charge density on the carbon nanotube, which may be tuned by
applying an external gate voltage.

5.2.3 Transfer of CNTs to electrical contacts
The transfer process involves a home built, flip chip micro-positioning stage,
accompanied by an optical imaging system. The setup resembles a photolithography
contact aligner in terms of its design, and a schematic is shown in Figure 5-3Error!
Reference source not found.. The fabrication process proceeds as follows:
(a) (b)
Source
Drain
Gate
Figure 5-4: (a) Low magnification SEM image of a three terminal electrical device,
compatible with the aligned optical transfer scheme. The higher magnification image in
(b) shows how the source and drain electrodes are at a higher elevation than the gate.
71

1. A quartz chip with a suspended carbon nanotube at a predetermined location
is identified. The chip is glued onto a transparent glass slide, inverted, and
loaded onto a X-Y micro-positioner.
2. A prefabricated silicon chip with contact metal deposited on tall pillars is
placed on an X-Y-Z micro-positioner under the inverted quartz chip (with a
suspended carbon nanotube).
3. Since the quartz chip is optically transparent, it is possible to image the silicon
chip through the inverted quartz chip. Both the quartz and silicon chips can be
carefully moved in order to position the raised electrodes directly under the
pair of quartz pillars between which a nanotube is suspended.
4. Using the Z-micro-positioner, the quartz chip (with a suspended nanotube),
and the silicon chip (with raised contact electrodes) are brought into contact.
The nanotube transfers onto the silicon chip, due to a stronger van der Waals
binding to metal electrodes.

72

5.3 Photoluminescence Imaging for High Throughput Chirality Screening
The main advantage offered by this device fabrication scheme, is that we can also
perform high throughput screening of suitable chirality carbon nanotubes through wide
field photoluminescence imaging. As described earlier, the chirality of a carbon
nanotube, determined by a pair of chiral indices, (n,m), determines the electronic band
structure of the nanotube, i.e., determines the energy of the fundamental band gap, as
well as the higher interband transitions in nanotube. These transition energies are
typically labelled as Eii (i=1,2,3…). Typically, the cross-section of photon emission (or
absorption) is maximized when the photon energy matches the energy of interband
transitions. In particular, the photoluminescence process in carbon nanotubes has been
understood fairly well by previous studies on individual nanotubes suspended in
Figure 5-5: (a) The schematic layout of the micro-positioning and transfer stage for the
fabrication of carbon nanotube electrical devices. The steps for aligned transfer are
shown in (b) - (d), as described in the text.

73

solution[53]. Semiconducting nanotubes are normally excited at the second interband
transition (E22); the excited photon relaxes to a lower lying available conduction band
state, and then emits a photon matching the energy of the lowest allowed optical
transition (E11). By performing emission-excitation spectroscopy, one is able to uniquely
determine the chiral indices of carbon nanotubes.
In our scheme, we use a fixed excitation wavelength at λ=785nm. Instead of
confocal excitation of the specimen, however, the laser is defocused on the sample
surface, to cover an illuminated area of ~ 20µm in diameter. The reflected light is then
focused onto a InGaAs infra-red sensor, through a band pass filter. This allows us to
eliminate the elastically scattered photons from the image, and only the inelastically
scattered photons, matching the E11 transition contribute to image formation. A schematic
diagram of the experimental layout is shown in Figure 5-6, and the optical transitions
involved are shown in Figure 5-7.

Figure 5-6: Schematic layout for photoluminescence imaging setup.
50:50
785nm
50X
Band Pass Filter
Sample
50:50
IR LAMP
IR
CCD
IR Lamp
74

A typical PL image taken with a 785nm illumination source is shown in Figure
5-8. The sample used is a quartz wafer with pillars etched into it, after growth of carbon
nanotubes. The bright lines connecting individual pillars are PL emission from suspended
nanotubes suitable for transfer using the flip chip transfer scheme.

50 100 150 200 250 300
50
100
150
200
250
600
700
800
900
1000
1100
1200
1300
1400
1500
Energy
Bandgap
(b) (a)
Figure 5-7: (a) Shows the optical transitions involved in the PL emission process in
carbon nanotubes, and a typical PL spectrum from a single nanotube is shown in (b),
along with the transmission response of the band pass filter used.
Figure 5-8: Typical photoluminescnce image showing PL emission from a single,
suspended carbon nanotube.
75

5.4 Electrical Characteristics of Two Terminal Devices
The flip chip transfer scheme described here has allowed us to successfully create
electrical devices using carbon nanotubes. The SEM image of one such device is shown
in Figure 5-9. This particular device used two dissimilar metals for the source and drain
electrodes. One electrode was made using Palladium (work function ~ 5.3eV) and a
second electrode using Gadolinium (work function ~ 2.9eV).

The use of two dissimilar metals at source and drain pins the Fermi level at the
two ends of the tube to two very different levels, and creates a built-in electric field. For
these devices, the suspended length of the carbon nanotube is ~300nm, and the difference
between the work functions of the two metals is ~2.2eV, leading to a built-in field of
about ~7000eV/m. Any electron-hole pairs generated in the carbon nanotube are
immediately separated by this strong electric field, generating a significant photocurrent
(~2nA), even under very weak illumination.
Figure 5-9: SEM image of an electrical device created using a transferred carbon
nanotube.
76

However, gadolinium is an unstable metal, which oxidizes over time. In order to
overcome this issue, devices using aluminum coated with 10nm of indium tin oxide
(ITO) were also used. Current-voltage (I-V) characteristics for one such device shown in
Figure 5-10: I-V curves for a suspended carbon nanotube device, using palladium and
ITO coated aluminum as the source and drain electrodes. The I-V curves shown a p-n
junction like behavior, with strong photo-response. It is important to point out that these
I-V curves were recorded under defocused illumination with different lamps in our lab.

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
-50
0
50
100
150
200
250
300
350
After EL Imaging
IR Lamp On
Dark
Visible Lamp On
Current (nA)
Bias Voltage (V)

Figure 5-10: I-V curves for a suspended carbon nanotube device, using palladium and
ITO coated aluminum as the source and drain electrodes.

5.5 Fabrication of Field Effect Transistors and Other Future Steps
Thus, we have demonstrated the capability to successfully isolate known
chiralities of suspended, ultra-clean carbon nanotubes through rapid optical screening.
Further, we have been able to create simple opto-electronic devices using a flip-chip
transfer scheme. In order to further extend our device fabrication capabilities, we are now
77

making silicon chips with a third gate electrode, at a depth of about 500nm below the
source and drain electrodes. This is achieved by using photolithography to pattern the
source and drain electrodes, followed by metal deposition and the first round of dry
etching of silicon. The source and drain electrodes serve as self-aligned masks for the dry
etch. After etching to a depth of about 500nm, another step of photolithography is used to
pattern the gate electrode, followed by a second step of dry etching to create the 5µm
deep pillar structure. An SEM image of one such device is shown in Figure 5-4.
Transfers onto such a device geometry would extend our experimental capabilities
and provide us another knob to tune the carbon nanotube system under study, opening up
the possibility of performing optical, and electronic measurements on ultra-clean,
suspended carbon nanotubes of known chiralities.

5.6 Conclusions
In conclusion, a novel scheme for fabrication known-chirality devices using
suspended, nearly defect free carbon nanotubes is demonstrated. A rapid optical
screening process is seen to effectively identify carbon nanotubes with desired optical
properties, and a flip-chip transfer method yields electrical devices using these pre-
defined nanotubes as channels. Photo-detection using one such device is demonstrated
using metal electrodes with dissimilar work functions. Chips for three-terminal electrical
devices are also fabricated.

78

CHAPTER 6: ENGINEERING TRANSITION METAL DI-
CHALCOGENIDES FOR ENHANCED EFFICENCY OF OPTO-
ELECTRONIC DEVICES
This chapter is similar to Dhall et al.[54] published in Advanced Materials.
6.1 Abstract
In this chapter, we report a robust method for engineering the optoelectronic
properties of few layer MoS2 using low energy oxygen plasma treatment. Gas phase
treatment of MoS2 with oxygen radicals generated in an upstream N2-O2 plasma is shown
to enhance the photoluminescence (PL) of few layer, mechanically exfoliated MoS2
flakes by up to 20 times, without reducing the layer thickness of the material. A blue shift
in the photoluminescence spectra and narrowing of linewidth is consistent with a
transition of MoS2 from indirect to direct band gap material. Atomic force microscopy
and Raman spectra reveal that the flake thickness actually increases as a result of the
plasma treatment, indicating an increase in the interlayer separation in MoS 2. Ab-initio
calculations reveal that the increased interlayer separation is sufficient to decouple the
electronic states in individual layers, leading to a transition from an indirect to direct gap
semiconductor. With optimized plasma treatment parameters, we observed enhanced PL
signals for 32 out of 35 few layer MoS2 flakes tested, indicating this method is robust and
scalable. Monolayer MoS2, while direct band gap, has a small optical density, which
limits its potential use in practical devices. The results presented here provide a material
with the direct band gap of monolayer MoS2, without reducing sample thickness, and
hence optical density.
79

6.2 Introduction
Two dimensional materials, such as graphene and few layer transition metal
dichalcogenides (TMDCs) have attracted great research interest in the past decade, since
mechanical exfoliation of these materials from their three dimensional bulk counterparts
was demonstrated[55]. Graphene, in particular, is of tremendous interest from a scientific
standpoint due to its linear band dispersion[56], and excellent carrier mobility[57],
allowing observation of phenomena such as the quantum hall effect[58-60], non-adiabatic
phonon anomalies[34], and Dirac Fermion nature of electrons[34, 35]. However, due to
its gapless dispersion, its utility in the field of optoelectronics is limited. Transition metal
dichalcogenides, such as MoS2, WS2, and WSe2, on the other hand, are found to exist in
similar layered structures and exhibit finite band gaps in the visible wavelength range[61-
63]. TMDCs have traditionally been used as lubricants and host materials for
intercalation compounds[64, 65]. The optical properties of these TMDCs vary
significantly with layer thickness[63]. While monolayer MoS2 and WSe2 are direct band
gap materials, their few layer counterparts are indirect semiconductors, which show a
greatly suppressed photoluminescence(PL)[63, 66]. Consequently, most recent research
efforts have been directed towards monolayer TMDCs. Monolayers, while direct band
gap, have small optical densities, which limits their potential use in practical devices.
6.3 Experimental Details
In the work presented here, a gentle oxygen plasma treatment is shown to produce
a direct band gap transition in few layer MoS2. This transition is studied using
photoluminescence spectroscopy, Raman Spectroscopy, atomic force microscopy (AFM),
and electron energy loss spectroscopy (EELS). Ab-initio calculations provide a clear
80

insight into the layer decoupling mechanism responsible for this indirect to direct gap
transition. Low power, remote (or downstream) plasma treatment has been effectively
used to remove hydrocarbon impurities in situations where the sample itself is known to
be susceptible to damage by fast moving ionic species[67]. For example, remote plasma
has been used to selectively etch away metallic carbon nanotubes and surface
contaminants, to enable fabrication of semiconducting single wall carbon nanotube field
effect transistors[68]. We use an XEI Evactron Soft Clean plasma cleaner, in which the
plasma is generated by flowing room air past an electrode supplied with 20W of RF
power at 200mTorr. The sample is placed a certain distance (6-10cm) away from the
plasma source, and ionized oxygen atoms diffuse towards the sample chamber with low
kinetic energies. Samples were exposed to the O2 plasma for about 3 minutes. While
typical plasma cleaners used in semiconductor fabrication operate using a “sputtering”
mechanism, wherein the sample is bombarded with ions carrying significant kinetic
energy, remote plasma cleaners rely mainly on the chemical reactivity of the ionized
oxygen to remove surface contaminants. Despite the presence of nitrogen in the gas
mixture, the plasma itself mainly consists of oxygen radicals, since the N2 molecule has a
much higher bonding energy.
Figure 6-1 shows the optical microscope image of a mechanically exfoliated flake
of MoS2 on an oxidized silicon wafer. The photoluminescence (PL) spectra of these
flakes are obtained using a 532nm excitation laser focused to a 0.5µm spot, attenuated in
power to 10µW/µm
2
, to minimize sample heating. The PL spectra of the same MoS2 flake
taken before and after three minutes of oxygen plasma treatment are shown in Figure
81

6-1(c). The two peaks labeled A and B correspond to transitions between the conduction
band and the two (spin-orbit split) valence bands at the K point in the Brillouin zone. In
this particular case, there is a sixteen fold enhancement of the PL intensity after the
oxygen plasma treatment, along with significant (about 46%) narrowing of the spectral
linewidth, indicating an improvement in material quality. The PL peak also shifts from
typical energies between 1.81-1.83eV before O2 plasma to 1.86 eV after the plasma
treatment. This is consistent with the observations of Mak et. al on suspended,
monolayer, direct gap MoS2[63]. Table 6-1 provides a list of PL peak positions and
linewidths measured before and after oxygen plasma treatment for 35 MoS2 flakes
measured in this study. We observed enhanced PL intensities for 32 out of 35 few layer
MoS2 flakes tested, indicating this method is robust and scalable.
The large intensity enhancement and blueshift of the PL peak observed after
oxygen treatment is not the result of a reduction in the layer thickness of the MoS 2, as
shown by AFM and Raman measurements. The AFM images taken before and after
oxygen treatment, surprisingly, reveal an increase in flake thickness, as shown in Figure
6-2(c). For the AFM data shown in Figure 6-2(c), the step height along the white dashed
lines in Figure 6-2(a) and Figure 6-2(b) increases by about 20Å due to the treatment with
oxygen plasma. The 20Å increase in the film thickness, distributed across the 9 nm MoS2
film consisting of 11 to 13 monolayers, corresponds to an average increase in each van-
der-Waals (vdW) gap of 1.5Å to 1.8Å. Density functional theory calculations described
below show that this increased interlayer distance is sufficient to cause an indirect to
82

direct band gap transition suggesting that the enhanced PL observed is the result of
plasma-assisted layer decoupling of the MoS2 lattice.

Raman spectra taken before and after oxygen treatment also indicate that no
thinning of the sample is occurring. In Figure 6-3(c), the Raman spectra of an MoS2 flake
exhibit two peaks corresponding to the E
1
2g (in plane) and A1g (out of plane) vibrational
modes[69]. The separation between these two peaks provides a good measure of the layer
thickness of the material, varying from 19cm
-1
for monolayer to 25cm
-1
for N-layer (N>6)
(a) (b)
before
after
5μm 5μm
1.4 1.6 1.8 2.0 2.2
Intensity
Energy (eV)
Pre O
2
x16
Post O
2
1.70 1.75 1.80 1.85 1.90 1.95 2.00
Intensity
Energy (eV)
100 150 200 250
0.15
0.20
0.25
0.30
0.35
0.40
Relative PL Intensity A
d
/A
Temperature (K)
(c)
x
16
(d)
A
A
d

A
Figure 6-1: Optical microscope image of a few layer MoS2 flake (a) before and (b) after 3
minutes of oxygen plasma treatment. (c) Photoluminescence spectra before and after
oxygen plasma treatment, plotted on different Y scales, highlighting the blue shift of the A
exciton, the narrowing of the spectral linewidth, and the emergence of the asymmetry in
PL lineshape after plasma treatment at 300K. (d) Inset shows the emergence of a distinct,
low energy peak at 100K. The relative intensity of the low energy PL peak is shown as a
function of temperature.

83

MoS2[69]. We studied the Raman spectra of 17 flakes of MoS2, before and after O2
plasma treatment. On average, the separation between the two Raman peaks reduced
from 22.6 cm
-1
to 21.4 cm
-1
after plasma treatment, indicating that the flakes are still
multilayer MoS2. We consistently see a downshift in the A1g (out of plane) Raman mode
position and a narrowing of the Raman linewidth. However, no consistent and systematic
change of the in plane (E
1
2g) mode is observed, which is also seen to upshift slightly at
times. These results indicate that the intralayer spring constant is unaffected by the
plasma treatment, and the interlayer “spring constant” is consistently weakened (albeit by
a small amount). This shows that a mere flake thinning is not the mechanism responsible
for the enhanced PL intensity observed after O2 plasma treatment. On the contrary, an
increase in the flake thickness shown by AFM, and the softening of the interlayer spring
constant seen in the Raman spectra, point to a mechanism in which the interlayer van der
Waals coupling is weakened. The reduction in Raman intensity is a possible consequence
of the change in lattice symmetry, which determines the matrix elements and selection
rules for Raman active vibrational modes. A tabulated summary of our Raman data is
given in Table 6-2.

Sno Pre O 2 Treatment Post O 2 Treatment

A Peak A Peak

Height
(Counts)
Center
(eV)
Width
(meV)
Height
(Counts)
Center
(eV)
Width
(meV)
PL Blueshift
(meV)
Δwidth
(meV)
PL
Enhancement
1 6532 1.832 58 121040 1.867 29 35 -29 18.5
2 3680 1.826 60 24498 1.863 40 37 -20 6.7
3 3860 1.816 56 6600 1.808 72 -8 16 1.7
4 4378 1.822 55 30406 1.856 44 35 -10 6.9
5 7351 1.832 57 20096 1.837 53 5 -3 2.7
84

Table 6-1: Photoluminescence peak height, position, and linewidth for the A exciton peak
for 35 flakes of MoS2 before and after O2 plasma treatment. The narrowing in peak
linewidth and blueshift of peak position are also listed. Overall, 32 out of 35 flakes show
an enhanced PL intensity. The last line indicates on average PL is enhanced 6.7 times,
blueshifted by 26.4 meV, and the peak linewidth reduces by 14 meV due to the plasma
treatment.

6 10881 1.830 57 163812 1.861 33 31 -24 15.1
8 11592 1.827 58 222173 1.868 33 41 -25 19.2
9 11614 1.831 59 192731 1.866 35 35 -24 16.6
10 7574 1.814 55 12338 1.821 65 8 10 1.6
11 17039 1.815 62 80517 1.848 41 33 -21 4.7
12 13355 1.807 60 5461 1.825 54 18 -6 0.4
13 13037 1.811 63 48597 1.865 31 54 -32 3.7
14 16616 1.824 60 121148 1.861 38 37 -22 7.3
16 17513 1.825 63 28747 1.869 43 44 -20 1.6
17 23582 1.816 55 12098 1.845 59 29 4 0.5
18 11144 1.831 45 6109 1.832 61 1 16 0.6
19 19399 1.839 53 102603 1.863 35 25 -19 5.3
20 3499 1.838 45 6104 1.836 52 -2 7 1.7
21 4617 1.841 51 37555 1.863 33 22 -18 8.1
23 3404 1.830 66 15016 1.869 35 38 -31 4.4
25 2882 1.828 53 12194 1.876 34 48 -19 4.2
27 4145 1.839 52 59454 1.867 33 28 -19 14.3
34 6580 1.851 49 35625 1.873 27 22 -22 5.4
37 2859 1.845 47 12304 1.872 28 28 -18 4.3
38 3632 1.849 46 35641 1.872 27 23 -18 9.8
39 4847 1.852 46 26829 1.872 28 20 -18 5.5
41 2553 1.845 40 6383 1.883 35 38 -5 2.5
43 3043 1.841 38 30866 1.845 28 22 -10 10.1
47 2284 1.849 48 15510 1.871 31 28 -17 6.8
49 3233 1.836 46 20282 1.873 28 22 -18 6.3
50 3178 1.839 46 19232 1.874 29 21 -17 6.1
51 1731 1.844 42 10963 1.877 28 33 -13 6.3
52 1571 1.845 41 9902 1.878 29 33 -12 6.3
53 2735 1.853 43 26206 1.872 28 19 -15 9.6
54 2804 1.851 44 27625 1.872 28 21 -16 9.9
Avg 7393 1.837 52 45905 1.857 37.9 26.4 -13.9 6.7
85

-4 -2 0 2 4 6
0
2
4
6
8
10 Post O
2
Pre O
2
Height (nm)
Distance ( m)

(a)
(b)
(c)
before
after
2μm 2μm
Figure 6-2: AFM (height) images of a MoS2 flake taken (a) before and (b) after a 3 minute
oxygen plasma treatment. The step height profiles along the dashed lines are shown in (c). A
significant increase in sample thickness, of about 2nm, is observed after plasma treatment.
86

Sno E
1
2g Peak A 1g Peak
Pre O 2 Treatment Post O 2 Treatment Pre O 2 Treatment Post O 2 Treatment
Centre Width Centre Width Centre Width Centre Width
1 383.8 3.7 385.2 4.0 405.3 8.5 405.1 5.8
2 382.5 3.9 383.1 4.2 405.9 7.1 405.8 5.8
3 382.3 3.7 382.9 3.6 406.6 5.2 406.6 6.0
4 383.0 3.9 382.9 3.6 406.3 6.9 404.2 6.0
5 384.0 4.8 382.7 4.5 406.1 8.0 405.0 6.1
6 384.3 3.5 384.3 4.4 407.3 8.2 404.3 6.7
8 384.2 4.3 384.9 4.2 406.0 7.5 404.5 6.4
9 384.2 3.4 382.7 4.0 406.7 8.0 405.1 6.5
10 384.1 3.7 382.8 3.4 407.6 6.5 405.0 6.8
11 383.8 4.4 383.8 3.6 405.3 9.7 404.3 7.0
12 383.4 4.6 383.0 3.7 405.2 10.7 406.6 5.5
13 382.9 4.1 383.4 3.5 406.3 8.5 405.8 6.0
14 384.1 4.5 385.8 3.3 405.9 9.1 404.6 8.1
16 384.0 3.9 385.5 4.4 405.8 8.7 405.2 6.6
17 383.9 4.7 384.4 3.8 405.9 8.4 406.2 6.4
18 383.8 4.4 383.5 4.2 407.9 6.0 407.0 6.0
19 384.5 4.2 385.6 4.1 406.4 8.7 405.3 6.8
Avg: 383.7 4.1 383.9 3.9 406.3 8.0 405.3 6.4
Table 6-2: Raman scattering peak position and width for the E
1
2g and A1g Raman modes
for 17 flakes measured before and after optimized oxygen plasma treatment. No
systematic change in the peak position is observed for all 17 samples. However, the A 1g
peak width is seen to consistently reduce after the plasma treatment. Raman data was not
collected for all samples in Table 6-1, however, sample numbers given in Tables 6-1 and
6-2 correspond to the same flakes of MoS2.

87

6.4 Proposed Mechanism
To explain the observed change in the PL peak with oxygen intercalation, we
attribute the emergence of the PL peak at 1.8 eV to an increase in the van-der-Waals
(vdW) gap between the adjacent layers of MoS2. To support this argument, we calculate
the electronic band structure of bilayer (2L), trilayer (3L) and quad-layer (4L) MoS2, as
shown in Figure 6-4, for a range of vdW gap distances between the adjacent layers. Our
calculations are based on first-principles density functional theory (DFT) using the
projector augmented wave method as implemented in the software package VASP[70].
(a) after before
6μm
6μm
360 380 400 420 440
Raman Intensity
Raman Shift (cm
-1
)
Before O
2
After O
2
(c)
Figure 6-3: Optical microscope image of a few layer MoS 2 flake (a) before and (b) after 3
minutes of oxygen plasma treatment. (c) Raman spectra before and after plasma treatment. No
significant shift in the Raman peaks is observed, although the Raman intensity for both peaks
is reduced, and a slight narrowing of the peaks is observed.
(b)
88

The screened Heyd-Scuseria-Ernzerhof (HSE) hybrid functional has been
employed for this study[71]. Spin-orbit coupling was included self-consistently within
the band structure calculations. The HSE calculations incorporate 25% short-range
Hartree Fock exchange, and the screening parameter is set to 0.4Å[72]. A Monkhorst-
Pack scheme was adopted to integrate over the Brillouin zone with a k-mesh 9 x 9 x 1 for
the bilayer and trilayer structures. The k-mesh was reduced to a converged 4 x 4 x 1 grid
for the quad-layer structure HSE calculations. A plane-wave basis kinetic energy cutoff
of 300 eV was used. The lattice constants for the bilayer and trilayer structures are
d
vdW
S
S
Mo
d
vdW
(new)
(b)
(a)
Figure 6-4: (a) Atomistic structure of the 4L- MoS2 with the equilibrium vdW gap, dvdw,
and the modified vdW gap, dvdw (new), and (b) Direct gap (solid) and indirect gap (dotted)
energy transitions for 2L, 3L and 4L MoS2 for a range of increases in the vdW gap
( dvdw). The dotted vertical lines indicate the indirect to direct transition vdW gaps for 2L
(green), 3L (blue), and 4L (red) MoS2 .

89

obtained from our prior calculations on the bulk structure of MoS 2 that have been
optimized with vdW interactions accounted for using a semi-empirical correction to the
Kohn-Sham energies[73]. A vacuum spacing of 15 Å is added along the z-axis for all the
structures. The atomic coordinates for each structure were optimized in all directions
using the DFT-D2 dispersion corrections[74] until all the interatomic forces are below
0.01 eV/Å. The default level of theory in all calculations is HSE with spin-orbit coupling.
Only deviations from the defaults are noted. The equilibrium vdW gap, d vdW, is 3.12Å for
the 2L, 3L and 4L MoS2 structures.
The valence band edge, Гv, is composed of 28% pz orbitals from the S atoms and
67% dz
2
orbitals from Mo atoms. The valence bands at Kv contain no dz
2
or pz
components and are primarily composed of dx
2
, and dxy orbitals. Because of the large pz
orbital component of the S atoms, the Гv valley has the largest interlayer coupling and is,
therefore, most sensitive to the presence of adjacent layers. When two monolayers are
brought together, the Гv valleys of the two layers couple and split. At the equilibrium
interlayer distance of 3.12Å, the energy splitting is 620 meV. The corresponding energy
splitting at Kv due to interlayer coupling is 74 meV. Thus, the interlayer coupling causes
the Гv valley to rise above the Kv valley as two monolayers are brought into close
proximity.
The orbital composition of the conduction band at Kc is 67% dz
2
with no pz
component. The next closest conduction band valley is at Σc composed of 36% dz
2
and a
minor contribution from the pz orbitals of the S atoms. The conduction band at Kc has no
pz components from the sulfur atoms. Thus, the Kc valley is only weakly affected by the
90

proximity of an adjacent layer, and as two monolayers are brought together, the
conduction band remains at Kc for the 2L, 3L and 4L structures.
The electronic band structures for 2L, 3L, and 4L MoS2 are calculated for a range
of vdW gap distances starting from the equilibrium value of dvdW = 3.12Å and increasing
it up to a maximum of 1.6 times the equilibrium value. When the vdW gap is increased
by a factor of 1.6 in a 2L structure, the energy of Гv decreases by 470 meV with respect
to the vacuum energy. The Kv-Kc direct gap transition changes by only 2 meV. A
crossover from an indirect to direct gap transition occurs when the equilibrium vdW gap
in 2L, 3L, and 4L MoS2 is increased by 1.0 Å, 1.13 Å, and 1.45 Å, respectively. At these
separation distances the direct gap and indirect gap energies are equal. With further
increases in the vdW gap the band gap becomes direct. The direct gap Kv-Kc and the
indirect gap Гv-Kc band gap energies calculated using DFT are illustrated for the 2L ,3L,
and 4L structures in Figure 6-4(b). The calculated increases in the vdW gaps that produce
the indirect to direct transition are consistent with the experimentally measured increase
in the film thickness shown in Figure 6-2: AFM (height) images of a MoS2 flake taken (a)
before and (b) after a 3 minute oxygen plasma treatment. The step height profiles along
the dashed lines are shown in (c). A significant increase in sample thickness, of about
2nm, is observed after plasma treatment.(c).
6.5 Results and Discussion
The consistency between the increase in interlayer separation revealed by AFM
and Raman spectroscopy, and the corresponding increase in PL yields with theoretical
calculations point to a mechanism in which exposure to oxygen plasma disturbs the
interlayer van der Waals bonding. One scenario which could lead to this effect is
91

intercalation of van der Waals gap of MoS2 by a foreign species during expose to oxygen
plasma. Electrochemical techniques, using liquid phase solvents, have been shown to
enable intercalation of small chemical species (such as lithium ions) into lattices of
layered materials like graphite[75]. More recently, such methods have been used to
completely separate the individual layers of two dimensional materials[76-79]. Layer
separation is achieved by completely saturating the interlayer gaps in the host TMDC
lattice with guest species, followed by mechanical agitation. From intercalation
chemistry, we know that a guest species need not distribute itself evenly in the interlayer
gaps of the host lattice. It is common to find staging of guest atoms, which is the
occupation of every other interlayer gap[64, 65, 80]. Similarly, the guest species may
cover only a fraction of the area in any one interlayer gap, leaving the host atomic layers
weakly bound to one another. It would be expected, that completely saturating the
interlayer spaces with guest species would lead to complete exfoliation of MoS 2. We do
indeed see that overexposure of MoS2 flakes to the plasma treatment sometimes leads to
complete removal of the flakes. However, unlike previous liquid based exfoliation
methods, by controlling the plasma treatment parameters, we are able to ensure only
partial coverage of the interlayer spaces, and hence prevent complete exfoliation.
In MoS2, such an engineered system is tremendously advantageous for device
applications. By reducing the inter-planar overlap of electronic states in few layer MoS2,
one would expect the material to behave as a stack of isolated “monolayer” MoS 2, each
with a direct band gap desirable for optoelectronic applications. One of the challenges in
creating an optoelectronic device such as a p-n junction from a “monolayer” crystal arises
92

from local fluctuations in charge densities due to surface impurities, which precludes
controlled doping of the material. The direct band gap “bulk” crystal obtained in this
work would be far less susceptible to surface effects. Furthermore, bulk, direct band gap
MoS2 would enable cross plane p-n junctions to be fabricated with finite space charge
regions, as in conventional p-n junctions.
Another aspect of the oxygen plasma treatment, evident from the AFM images in
Figure 6-2, is the dramatic reduction in surface contaminants arising from lithographic
and exfoliation residues, which is expected to contribute to the dramatic increase in PL
efficiency shown in Figure 6-1. The plasma cleaning treatment also leads to a consistent
narrowing of the PL linewidth, as evident in Figure 6-1(c). We also observe that while
the intensity of the A exciton luminescence is greatly enhanced, the intensity of the B
exciton is actually diminished. This is also to be expected, since optically generated
higher energy (B) excitons, due to their increased lifetimes, now have more time to find a
decay path to the more energetically favorable (A) state before radiative recombination.
This transition from B to A is disallowed in defect free MoS2, since those states are
orthonormal. However, oxygen plasma treatment perturbs the crystal potential, thereby
allowing this transition, and explaining the reduction of B exciton luminescence. This
observed blue shift in the PL peak is consistent with previous studies on suspended
MoS2[63] and MoS2 passivated by ionic liquids[81]. The lineshape of the observed
luminescence from the A exciton is found to be asymmetric, with a significant shift of the
spectral weight towards the low energy side, as shown in Figure 6-1(c). This apparent
asymmetry is the result of the emergence of a peak near the low energy shoulder of the A
93

excitonic peak. Photoluminescence spectra taken at cryogenic temperatures provide
insight into the underlying nature of this lineshape asymmetry. Here, we are able to
distinguish the lower energy peak clearly, shown in the inset of Figure 6-1(d). As shown
recently by Korn et. al[82], this peak (labeled A
d
) is characteristic of the formation of a
localized excitonic state, due to the creation of defects, or alternatively, the emergence of
disorder. Figure 6-1(d) shows the relative intensity of this low energy A
d
peak to the
dominant A exciton peak, as a function of sample temperature. At room temperature, the
excitonic state is no longer well localized, leading to a diminished intensity of the
observed disorder related peak. As a consequence of disorder, one would expect the PL
intensity to vary spatially. However, in our 2D PL maps, we were unable to detect
inhomogeneity of PL intensity over a MoS2 flake of uniform thickness. We believe this is
because both the exciton radius, and the size of any defect state, are expected to be at
least an order of magnitude smaller than the diffraction limit. While interpretation of far
field optical spectroscopy, as presented in this work, sheds some light on the possible
mechanisms at play, more direct evidence may be found by near field optical studies.
Similarly, a more detailed ab-initio calculation by including guest species in the van der
Waals gap would prove to be useful.
A recent report in literature[83] also observes similar PL enhancement,
attributed to formation of Mo-O bonds based on XPS signals. However, XPS
measurements are ill suited to flakes of MoS2, as the illuminated spot size is typically 15-
20μm, which is considerably larger than the typical flake size. We believe such a bond
formation should have a dramatic impact on the Raman spectrum, due to a change in the
94

atomic mass. No such shift was observed in our work, hence ruling out Mo-O bond
formation.
6.6 Conclusions
In summary, we demonstrate an indirect to direct band gap transition in bulk
MoS2 using a simple, scalable oxygen plasma induced process. The PL efficiency is
found to increase due to the decoupling of electronic states in individual layers.
Furthermore, a significant narrowing in spectral linewidth is observed, indicating an
increase in the exciton lifetime in MoS2, due to removal of surface contaminants. The
mechanism for the photoluminescence enhancement relies on incomplete filling (or
intercalation) of the interlayer gap with a guest species, with a very slight change in
doping. While the increase in interlayer separation confines the carriers in two
dimensions, the possible creation of defects in MoS2 likely gives rise localized excitonic
states with longer lifetimes. This simple processing step could have vast implications for
future generations of optoelectronic devices by providing direct band gap transition metal
dichalcogenides with large optical densities.

95

CHAPTER 7: STRONG CIRCULARLY POLARIZED
PHOTOLUMINESCENCE FROM FEW-LAYER MOLYBDENUM
DI-SULFIDE THROUGH PLASMA DRIVEN DIRECT GAP
TRANSITION
7.1 Abstract
We report circularly polarized photoluminescence spectra taken from few layer
MoS2 after treatment with a remotely generated oxygen plasma. Here, the oxygen plasma
decouples the individual layers in MoS2 by perturbing the weak interlayer van der Waals
forces without damaging the lattice structure. This decoupling causes a transition from an
indirect to a direct band gap material, which causes a strong enhancement of the
photoluminescence intensity. Furthermore, up to 80% circularly polarized
photoluminescence is observed after plasma treatment of few layer MoS 2 flakes,
consistent with high spin polarization of the optically excited carriers. A strong degree of
polarization continues up to room temperature, further indicating that the quality of the
crystal does not suffer degradation due to the oxygen plasma exposure. Our results show
that the oxygen plasma treatment not only engineers the van der Waals separation in
these TMDC multilayers for enhanced PL quantum yields, but also produces high quality
multilayer samples for strong circularly polarized emission, which offers the benefit of
layer index as an additional degree of freedom, absent in monolayer MoS2.

96

7.2 Introduction
While bulk transition metal dichalcogenides (TMDCs) are known to be indirect
gap semiconductors, recent interest in this material system has been stimulated by the
discovery of spin and pseudospin physics in atomically thin TMDCs[84]. In the
monolayer limit, a direct band gap arises due to quantum confinement of electronic
states[61, 85], making these materials attractive for potential optoelectronic device
applications[86-88]. The crossover to a direct band gap in monolayer TMDCs is also
accompanied by a breaking of inversion symmetry, which leads to several interesting
physical phenomena, such as a coupling of spin and valley degrees of freedom and valley
dependent optical selection rules for interband transitions[89]. On the other hand, bilayer
TMDCs show a unique interplay between spin, valley, and layer degrees of freedom. As
previously described, the spin orientation in bilayer is locked to the layer index for a
fixed valley[90, 91]. Specifically, in the K valley, the up spin resides primarily on one
layer and the down spin resides primarily on the other layer. In the K’ valley, the spins
are reversed. Optical probing of the spin layer locking has been achieved in bilayer WSe2
in which the direct and indirect transitions are nearly degenerate[91]. In MoS2, optical
measurement of these effects is harder to observe due to the indirect nature of the band
gap, which dramatically reduces the photoluminescence (PL) quantum yields.
The photonic device performance of monolayer TMDCs is limited by their finite
absorption (5-10% in the visible region of the electromagnetic spectrum)[92]. Ideally,
one would like to exploit the larger absorption cross section offered by multiple layer
TMDCs while retaining the direct band gap structure and highly polarized light emission
of monolayer TMDCs. The weak nature of the van der Waals coupling between
97

individual TMDC layers opens up the possibility of perturbing these systems for band
structure engineering, allowing one to create such a system ideally suited for spin
polarized optoelectronics.
Liquid phase intercalation of molybdenum disulfide with lithium ions has been
shown to separate the individual layers of MoS2[93, 94]. The resulting lithium-MoS2
complex is unstable and leads to “chemical exfoliation” of individual layers of the
TMDC in solution[95]. In the previous chapter, we demonstrated that a low fluence of
remotely generated oxygen plasma perturbs the crystal structure of few layer MoS 2,
leading to a slight increase (about 1Å) in interlayer separation[96]. This increased
interlayer separation decouples the electronic states in the atomic layers of MoS 2,
inducing an indirect-to-direct band gap transition accompanied by a huge enhancement
(up to 20X) in the photoluminescence (PL) intensity. However, those studies were
performed using linearly polarized light, which prohibited us from exploring the layer-
spin selective physics. In the work presented here, up to 80% circularly polarized
photoluminescence is observed in plasma treated few layer MoS2 flakes, consistent with
our DFT calculations of weakly coupled TMDC multilayers.
7.3 Experimental details
Sample preparation begins with thin flakes of MoS2 being mechanically
exfoliated from bulk MoS2 crystals onto a Si/SiO2 wafer. Few layer flakes (2-6 layers) of
MoS2 are located using optical microscopy, and the layer thickness of the flakes is
confirmed using PL spectroscopy, Raman spectroscopy, and atomic force microscopy
(AFM). This study primarily focuses on indirect gap N-layer flakes (N between 2 and 6),
which may be considered to be representative of bulk MoS2, since the band structure of
98

N-layer MoS2 approaches that of the true bulk band structure in the limit of N>4. The
samples are then exposed to a stream of oxygen plasma (XEI Scientific, Inc.) for 2-3
minutes at a pressure of 200mTorr. The plasma is generated from ambient air at low RF
powers (20W) ensuring a low fluence of oxygen radicals. Furthermore, the sample is not
placed directly between the RF electrodes for plasma generation (local plasma
generation), but instead at a distance of about 10 cm from the plasma generation
electrodes (remote plasma generation). This remote plasma configuration ensures that the
sample is not directly bombarded by ionic species being accelerated in a strong electric
field. The time of exposure to plasma is somewhat important. While under-exposed
flakes of MoS2 show no change in optical properties, over-exposure to remote oxygen
plasma does lead to damage of the MoS2 crystal, and a drop in PL intensity, presumably
due to defect creation. The optimal exposure time was found to be ~ 2 minutes in this
study. However, this time is dependent on parameters such as flake thickness, pressure in
the plasma chamber, and the RF power used to generate plasma. A combination of the
low RF power used and remote generation of plasma allows one to minimize any damage
to the surface of MoS2 from exposure to the oxygen plasma. Instead, as reported in our
previous study, it is found that the interlayer separation in MoS 2 is increased by about 1Å
after exposure to oxygen plasma[96]. Ab-initio calculations showed that such an increase
in interlayer separation is sufficient to cause a transition to a direct gap band structure in
MoS2.
Figure 7-1(a) shows an optical microscope image of a typical exfoliated flake of
MoS2. The PL spectrum of the as-exfoliated flake, using linearly polarized 532nm
99

excitation, exhibits weak peaks at 1.85 and 2.05 eV, corresponding to the A and B
excitonic states, split by spin orbit coupling in the valence band, as shown in Figure
7-1(b). There is also a broad peak at 1.4 eV, which corresponds to emission from the
indirect gap of this few layer MoS2 flake. After oxygen plasma treatment, the PL
emission from the A exciton (1.86eV) is strongly enhanced (16 times) with narrower
linewidth, while the indirect band gap peak at 1.4 eV is no longer observed. All these
observations imply a transition to a direct gap semiconductor. Raman spectra taken both
before and after oxygen plasma treatment are shown in Figure 7-1(c). The two observed
Raman peaks correspond to the in plane and out of plane vibrational modes. The
separation between these two peaks is measured to be 22.5 cm
-1
, indicating that the flake
is about 3-4 layers in thickness, based on previous reports in literature[97]. This
separation between the Raman peaks remains unchanged after exposure to oxygen
plasma.

100

10 μm

We have also performed circularly polarized photoluminescence measurements
on these oxygen plasma treated flakes of few-layer MoS2, as shown in Figure 7-2.
Excitation is provided by a 633nm HeNe laser at moderate laser powers (80μW), to
(a)
(
b)
(
c)
1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1
Photoluminescence Intensity
Energy (eV)
After oxygen plasma
Before oxygen plasma
250 300 350 400 450 500
Raman Intensity
Raman Shift (cm
-1
)
Before oxygen plasma
After oxygen plasma
(b)
(c)
Figure 7-1: (a) Optical microscope image, (b) photoluminescence spectra, and (c) Raman
spectra of a 3-4 layer flake of MoS2 taken before and after the remote oxygen plasma
treatment.
101

ensure heating effects are minimal. Figure 7-2 shows the normalized circularly polarized
photoluminescence spectra measured at 30 K. The photoluminescence signal is strongly
co-polarized with either left (σ+) or right (σ-) circularly polarized excitation, as shown in
Figure 7-2(a) and (b). The sharp spectral features around 650nm correspond to Raman
peaks from the MoS2 and the underlying silicon. These features were removed from the
spectra before calculating the degree of polarization, which is given by ρ=
𝐼 +
−𝐼 −
𝐼 +
+𝐼 −
, where
𝐼 +( −)
is the intensity of PL emission of σ+ (σ-) polarization. As seen in Figure 7-2(c), the
PL emission is co-polarized by up to 80% with the excitation polarization (at λ=640nm).
In these spectra, the degree of polarization is most pronounced at shorter wavelengths
(i.e., 640nm), and tails off at lower energies due to intervalley scattering processes,
consistent with previous studies on monolayer MoS2[98]. This is considerably higher in
energy than the band gap (667nm), but closest to the circularly polarized excitation
(633nm). The slight difference in the spectra in Figure 7-1 and Figure 7-2 can be
attributed to the differences in substrate temperature, and excitation wavelength. The
633nm excitation also uses a long pass filter with a cutoff around 640nm, which slightly
distorts the emission lineshape. The large background observed in the PL spectra in
Figure 7-2 emerges as a red-shifted shoulder peak at low temperatures, and has been
previously attributed to defect related sub-band gap states[96]. In this work, we find that
this background is largely unpolarized (Figure 7-2(c)), as expected for emission from
sub-gap states.

102

640 660 680 700 720
0
10
20
30
40
50
T = 30 K
P = 20 W
+ excitation

+ emission
- emission
Intensity (counts/( W s))
Wavelength (nm)

(
c)
(
a)
(
b)
640 660 680 700 720
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0

+ excitation
- excitation

Wavelength (nm)
640 660 680 700 720
0
10
20
30
40
50
T = 30 K
- excitation

Intensity (counts/( W s))
+ emission
- emission
Wavelength (nm)
P = 20 W
(b)
(a)
(c)
Figure 7-2: Circularly polarized photoluminescence spectra from an oxygen plasma
treated few layer flake (3-4 layers) of MoS2 collected at 30K with (a) σ
+
excitation and
(b) σ
-
excitation. The degree of polarization, ρ, is plotted in (c). Inset shows the valley
contrasted selection rules for optical transition, with strong oscillator strength, similar to
the case observed for direct gap (monolayer) MoS2.

B
A A
K ’ K
B
103

Circularly polarized photoluminescence spectra were also collected on as-
exfoliated few layer MoS2 flakes (before exposure to remote oxygen plasma), as shown
in Figure 7-3. As expected, the PL emission from few layer flakes shows a negligible
degree of polarization, even at 30K. The lower quantum yield of PL emission in the
indirect gap few layer MoS2 leads to weaker PL signals. Thus, the degree of polarization
is dominated by sharp spectra features such as the Raman peaks of MoS 2 and the
underlying silicon substrate. At wavelengths longer than 680nm, the raw spectra are
dominated by the detector shot noise, leading to large fluctuations in the calculated
degree of polarization, ρ.
7.4 Proposed mechanism
As described above, bilayer TMDCs introduce a layer degree of freedom that
couples to the spin and valley degrees of freedom[89-91]. That is, in the K valley, the up
spin resides primarily in the lower layer, and the down spin resides primarily in the upper
layer. The spins are reversed in the K’ valley. The layer index is treated as a pseudospin
with layer amplitudes cL for the lower layer and cU for the upper layer. For a given spin
and valley, analysis of the low-energy, k·p Hamiltonian described in Ref. [7], shows that
the magnitude of the layer polarization is
c
U
2
- c
L
2
= l l
2
+t
p
2
,

104

640 660 680 700 720
0
10
20
30
40
Intensity (counts/( W s))
Wavelength (nm)
+ emission
- emission
 excitation

640 660 680 700 720
0.0
0.2
0.4
0.6
0.8
1.0

Few Layer - As Exfoliated
Monolayer - As Exfoliated
Few layer- After Oxygen Treatment

Wavelength (nm)
640 660 680 700 720
0.0
0.2
0.4
0.6
0.8
1.0

Wavelength (nm)
(b)
K ’ K
A A
B B
(a)
(c)
640 650 660 670 680 690 700 710 720
0
1
2
3
4
5

Intensity (counts/( W s))
Wavelength (nm)
+ emission
- emission
Figure 7-3: Circularly polarized photoluminescence spectra from a “as-exfoliated” few layer
flake of MoS2. The emission spectra, collected using σ+ excitation at 633nm are shown in
(a). The spectra for σ+ and σ- polarization are nearly identical, exhibiting only a weak
(~10%) degree of polarization below 640nm, shown in (b). The inset represents the absence
of valley contrasted selection rules for optical transitions. The degree of polarization from
few layer MoS2 before and after plasma treatment is compared to that of pristine “as-
exfoliated” monolayer MoS2 in (c).

105

where  is the valence band spin-orbit splitting and tp is the interlayer coupling.
This value is the same for each spin and each valley. This degree of layer polarization is
also the degree of spin polarized absorption from circularly polarized light given by
P
K
+
2
+ P
K '
+
2
- P
K¯
+
2
- P
K '¯
+
2
P
K
+
2
+ P
K '
+
2
+ P
K¯
+
2
+ P
K '¯
+
2
, where P
+
is the interband matrix element of the canonical
momentum Px + iPy for the indicated valley and spin. Even for an unperturbed bilayer of
MoS2, the spin polarization is large. Using values of  = 73.5 meV and tp = 43 meV[89],
the magnitude of the layer polarization and the spin polarization of the absorption is 0.86.
The O2 plasma treatment increases the thickness of the sample, presumably by
intercalating O2 between the layers pushing them apart. As the layers are pushed apart,
the interlayer coupling tp is reduced, and the polarization given by Eq. (1) is enhanced. To
understand the effect of layer separation (d) on the value of tp in the low-energy k·p
Hamiltonian, we perform density functional theory calculations as described previously,
however, now we turn off the spin-orbit coupling so that the valence band splitting Kv =
2tp resulting from the interlayer coupling is not obscured by the spin-orbit coupling.
Values for tp resulting from an increase in the interlayer distance ( d) are shown in
Figure 7-4. At the equilibrium position (d = 3.12 Å, d = 0), our value of tp = 35.3 meV is
close to the value of 43 meV from Ref. [2]. At d = 1.0 Å, tp = 4.8 meV, and the
polarization is 0.998. These calculated values are in close agreement with the recent work
of Liu et al.[99] Values of d between 1.0 to 1.5 Å are required to cause the indirect to
106

direct transition in few layer MoS2[96]. Therefore, for the O2 treated samples, we expect
nearly complete spin polarization of the excited carriers.

Figure 7-4: The calculated interlayer coupling parameter tp and the polarization
corresponding to the localization within the top or bottom layer of each spin in each
valley and also the spin polarization of the excited carriers due to circularly polarized
optical absorption.
Experimentally, the degree of circularly polarized PL will rely on the spin lifetime
and the radiative relaxation time of the excitons, which depends on the quality of the
samples. The interpretation of these circularly polarized PL spectra using Eq. (1) is
strictly valid in the long carrier lifetime limit, and a more rigorous model would also
include any change in the carrier lifetimes brought about by exposure to remote oxygen
plasma. However, intervalley scattering processes are strongly suppressed in TMDCs as
they must be accompanied by a spin flip, which leads to long carrier lifetimes. Hence,
only in highly defective samples is this assumption likely to be invalid, and to a first
order, we expect that the change in interlayer coupling, and not a change in carrier
lifetimes, plays a dominant role in the degree of polarization.
As the temperature is increased, the degree of polarization reduces due to phonon
assisted intervalley scattering. However, as shown in Figure 7-5, a strong degree of co-
107

640 660 680 700 720
0.0
0.2
0.4
0.6
0.8
1.0
T=30K
T=100K
T=200K
T=300K
Degree of Polarization ( )
Wavelength (nm)
polarization with the excitation is observed up to a temperature of about 300K, in
agreement with previous reports on pristine monolayer MoS2 samples[98]. In highly
defective samples with a high density of localized scattering sites, one would expect to
see strong intervalley scattering. The measured temperature dependence of the degree of
circular polarization confirms that the crystal quality of the MoS2 is not degraded by
exposure to this remote oxygen plasma. In contrast, before oxygen plasma treatment, few
layer MoS2 shows a weak degree of polarization, even at 30K.

Optical access to the valley and spin degrees of freedom would be essential for
future spintronic devices. However, the indirect gap nature and rapid relaxation of excited
carriers to the Γ point in multilayers dramatically suppresses the quantum yields in the
light emission from K valleys, which makes the observation of these effects challenging.
Our results show that, by engineering the van der Waals separation in these TMDCs, it is
possible to observe strong circularly polarized emission and absorption from multilayer
MoS2 with enhanced photoluminescence, which offers the additional benefit of layer
Figure 7-5: Temperature dependence of the degree of polarization of circularly polarized
photoluminescence spectra, showing strong co-polarization with the excitation up to
T=300K.
108

index as an additional degree of freedom, absent in monolayer MoS2. The transition to a
direct gap semiconductor is corroborated by the large enhancement in photoluminescence
quantum yield observed. Although bilayer indirect gap TMDCs such as WSe2 and WS2
have shown some degree of circular polarization[100] due to spin-layer-locking, previous
measurements of bilayer MoS2 show a much weaker degree of circularly polarized PL
emission (~15%), due to the larger energy difference between the direct and indirect
transitions. Furthermore, the quantum yield for PL emission is considerably lower in
bilayer MoS2, due to the indirect band gap. In this work, up to 80% circular polarization
in the PL emission spectrum is observed for samples 3-4 layers in thickness. Also, the PL
quantum yield is far stronger when compared with previous studies on multilayer MoS 2,
due to the transition to a direct band gap. Other approaches to modifying the van der
Waals gap, such as the application of cross-plane tensile strain could potentially also give
rise to similar effects.
7.5 Conclusions
In conclusion, we observe circularly polarized photoluminescence from few layer
MoS2 flakes after treatment with a remote oxygen plasma. These results confirm the
transition from an indirect to a direct band gap material induced by plasma assisted
decoupling of the electronic states in the individual layers of few layer MoS 2. An up to
20-fold enhancement of PL emission is observed due to the direct gap transition. While
as-exfoliated MoS2 exhibits only a weak degree of polarization, the PL resulting from
circularly polarized excitation is 80% polarized at T=30K, consistent with the predictions
of Liu et al.[99]. This simple and robust technique offers the possibility of creating
efficient multilayer TMDC spin polarized optoelectronic devices. Multilayer
109

molybdenum disulfide not only offers a higher absorption cross section, but is also
significantly less sensitive to surface scattering phenomena. Engineering the band
structure by plasma assisted layer decoupling gives multilayer MoS 2 the advantages of
single layer MoS2 (i.e., direct band gap) without sacrificing layer thickness.

110

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116

APPENDIX A: MATLAB CODE FOR GENERATING ATOMIC
COORDINATES OF A CARBON NANOTUBE
clear all;
format('long');
n=5;
m=5;
acc=1.4210e-10;
a=sqrt(3)*acc;
a1=[sqrt(3)/2, 1/2]*a;
a2=[sqrt(3)/2, -1/2]*a;
rad= a*sqrt(n^2 +m^2 +n*m)/(2*pi);
dR=gcd(2*n+m, 2*m+n);
Nhex=2*(n*n +m*m+ n*m)/dR;
Ch=n*a1+m*a2;
t1=(2*m+n)/dR; t2=-(2*n+m)/dR;
T=t1*a1+t2*a2;
atom=1;
pos3D=zeros(2*Nhex,3);
Aatoms=[];
Batoms=[];

for i1= -(n+20): n+20
for i2= -(m+20): m+20
pos2DA=i1*a1+i2*a2;
pos2DB=pos2DA+acc*[1 0];
% check if in unit cell
if (atan2(pos2DA(2), pos2DA(1)) >= atan2(Ch(2), Ch(1) ) )
if (atan2( pos2DA(2), pos2DA(1)) <= atan2(T(2),T(1)))
if ( sum(pos2DA.*Ch) - sum(Ch.*Ch) < -(acc*acc/20) &&
sum(pos2DA.*T)- sum(T.*T)<-(acc*acc/20) )
Aatoms=[Aatoms; pos2DA];
end
end
end

if (atan2(pos2DB(2), pos2DB(1)) >= atan2(Ch(2), Ch(1) ) )
if (atan2( pos2DB(2), pos2DB(1)) <= atan2(T(2),T(1)))
if ( sum(pos2DB.*Ch) - sum(Ch.*Ch) < -acc*acc/20 &&
sum(pos2DB.*T)- sum(T.*T)< -acc*acc/20 )
Batoms=[Batoms; pos2DB];
end
end
end
end
end
A3D=[];
B3D=[];

nA=size(Aatoms);
nB=size(Batoms);
117

for jA= 1: nA(1)
theta= sum(Aatoms(jA,:).*Ch)/norm(Ch);
theta= theta*2*pi/norm(Ch);
z= sum(Aatoms(jA, :).*T)/norm(T);
A3D=[A3D; rad*cos(theta), rad*sin(theta),z];
end
for jB= 1: nB(1)
theta= sum(Batoms(jB,:).*Ch)/norm(Ch);
theta= theta*2*pi/norm(Ch);
z= sum(Batoms(jB, :).*T)/norm(T);
B3D=[B3D; rad*cos(theta), rad*sin(theta),z];
end

APPENDIX B: MATLAB CODE FOR GENERATING
DIFFRACTION PATTERNS OF CARBON NANOTUBES
function [ Action ] = DP_RealSp(
HTVolt,n,m,CNTlength,c0,c1,fn,Source,CameraPos,NPixels,PixelSize )
%DP_REALSP Calculate Diffraction Pattern using path summation approach
%within first order Born Approximation
% Real space lattice sum to calculate diffraction pattern.
%Chirlaity n,m - CNTlength is in nm
%HTVolt is in kV
%All other lengths (pixel size...) in meters
%fn is atomic scattering
%Reference:Electron diffraction analysis of individual single-walled
carbon nanotubes
i=sqrt(-1);
gun=[-Source, 0,0]; %location of gun in meters (x,y,z)
%detector=[CameraPos,0,0]; %location of camera in meters (x,y,z)

atoms=CNTcoordinates(n,m,CNTlength,0); % this is in meters
natoms=size(atoms);
%Relativistic conversion of kV to lambda
V=1000*HTVolt;
echarge=1.6e-19;
me=9.1e-31; %mass electron in kg
c=3e8; %c in m/s
lambda= 12.25e-10/sqrt( V + echarge*V*V/(2*me*c*c));

k=2*pi/lambda;
%make camera array
%total camera has NPixels*NPixels size

Action=zeros(NPixels,NPixels);
118

%Use 1st Born approximation, so only zero and first order scattering

%Camera is positioned at (CameraPos,0,0) and is in Y-Z plane, so each
pizel
%has a (y,z) coordinate in meters
for jy=1:NPixels
for jz=1:NPixels
ypixel= -(NPixels-1)*PixelSize/2 +(jy-1)*PixelSize;
zpixel= -(NPixels-1)*PixelSize/2 +(jz-1)*PixelSize;
pixel=[CameraPos, ypixel,zpixel]; %pixel coordinates

rgc=norm(pixel-gun); %gun to camera distance
%this is the zero order path

Action(jy,jz)=c0*exp(i*k*rgc)/rgc;
for j=1:natoms(1)
atomj=atoms(j,:);
rga=norm(atomj-gun); % distance between gun and atom
rac=norm(atomj-pixel); %distance between atom and pixel
(camera)
Action(jy,jz)= Action(jy,jz) +
c1*exp(i*k*rga)*fn*exp(i*k*rac)/(rga*rac);
end

end
[jy,jz] %show progress
end

end

Abstract (if available)

Abstract This dissertation presents several in-situ investigations of nanoscale electronic devices through a variety of experimental probes. These experiments shed light on some of the fundamental physical interactions at play in these devices, and could pave the way for a more rational device design to boost performance. ❧ Chapter 1 provides background material that will aid in understanding the research presented in this dissertation. It provides a brief overview of properties of carbon nanotubes and graphene, their atomic structure, as well as their electronic band structure. A brief discussion of interaction of excitations (electron-electron, and electron-phonon) as well as the Kohn anomaly is included here. For the most part, however, the theoretical background needed to understand each topic is covered within the relevant chapter. ❧ Chapter 2 presents some in-situ Raman spectroscopy experiments on suspended, metallic carbon nanotube devices. These experiments reveal a strong electron-phonon interaction due to the Kohn anomaly in these suspended nanotubes, as well as the interplay of Kohn anomaly with energy gaps created in the excitation spectrum of these tubes due to electron-electron interactions. ❧ Chapter 3 takes advantage of these experimental results presented in Chapter 2, and couples them with a careful theoretical analysis to measure the carbon nanotube capacitance. Surprisingly, this analysis reveals a significantly larger capacitance than expected, which can be attributed to the electron-electron repulsion. ❧ In Chapter 4, we discuss some work on the fabrication of suspended carbon nanotube devices compatible with in-situ Transmission Electron Microscopy experiments. Some preliminary data showing high quality diffraction patterns obtained through nano-beam electron diffraction are discussed in this chapter. ❧ Chapter 5 details the fabrication process and experimental setup for a home built aligned transfer scheme to create electrical devices of known chiralities. The screening of nanotube chirality is done through a home built photoluminescence imaging setup. Preliminary electrical data, showing photodetector capability using such devices is also presented. ❧ Chapters 6 and 7 focus on a class of layered semiconductors, transition metal dichalcogenides. In particular, a simple method for perturbing the atomic structure of few layer MoS2 is shown. This method pulls the atomic layers in this material system apart, leading to a dramatic change in optical properties, such as a transition to a direct band gap. Further, this material also acts as a source of strong, circularly polarized photons due to broken inversion symmetry.

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Asset Metadata

Creator Dhall, Rohan (author)

Core Title In-situ characterization of nanoscale opto-electronic devices through optical spectroscopy and electron microscopy

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 03/11/2016

Defense Date 02/08/2016

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag carbon nanotubes,electronic properties,OAI-PMH Harvest,optical properties,opto-electronic devices,transition metal dichalcogenides,vibrational spectroscopy

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Cronin, Stephen (committee chair), Ravichandran, Jayakanth (committee member), Wu, Wei (committee member)

Creator Email rdhall@usc.edu,rohandhall@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-220163

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