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Electronic and optoelectronic devices based on quasi-metallic carbon nanotubes
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Electronic and optoelectronic devices based on quasi-metallic carbon nanotubes
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Content
i
Electronic and Optoelectronic Devices
Based on Quasi-Metallic Carbon
Nanotubes
by
Mohammed (Moh) Amer
A Thesis Presented to
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
Thesis Approved by:
___________________________
Stephen Cronin, Chair
___________________________
Chongwu Zhou, Member
___________________________
Wei Wu, Member
August 2014
ii
To my Beloved Parents,
Dr. Amr and Dr. Bakhsh
I Love You
iii
Acknowledgments:
I would like to thank my adviser, Professor Stephen Cronin, for his tremendous help
throughout my career as a Ph.D. student and as an older brother. His guidance and his mentoring
help have offered so much to my experience. Research can be very discouraging, but looking up
to Steve’s passion and his perseverance have made research experience easier than it actually is.
The world of nanotechnology and nanotubes has so much potentials and it needs brilliant minds
to realize these potentials. Steve’s bright ideas and his critical help to my work and my
suggestions have always inspired me to give out the best of me in research. I will never forget
the day I found the diminishing of the band gap of metallic nanotubes on a substrate and his
awesome response to me. I will also never forget the days he inspired and encouraged me to try
and think from a different angle whenever experimental measurements go wrong.
I would also like to thank my family, especially my beloved mother, Dr. Bakhsh, on her
unlimited and constant support. Raising a child while being a single mother has always been a
challenging task, but her various supports to me has made me who I am today. I will always be
grateful to have a mother like her. Special thanks to my close sisters, Roaa and Marwa, for
standing beside me throughout my PhD years. Their support has made my graduate years very
enjoyable. Thanks to my best friend, Joe Nazzal, for being there with me along the PhD years.
I would also like to thank all my colleagues, Shermin Arab, Shun-Wen Chang, Chaun-
Chung Chen, Rohan Dhall, Bingya Hou, Zhen Li, Jing Qiu, Guangtong Zeng, Nirakar Poudel,
Mehmet Aykol, Chia-Chi Chang, Wenbo Hou, I-Kai Hsu, Wei-Hsuan Hung, Zuwei Liu,
iv
Prathamesh Pavaskar, and Ioannis Chatzakis. Special thanks to Adam Bushmaker and Jesse
Theiss for their help with the electrical, Raman, and photocurrent experimental setups. Their
discussions have made fruitful results published in high impact journals.
Thanks to all the research funding and tuition support agencies, Office of Naval
Research, Department of Energy, Department National Science Foundation, Ming Hsieh Scholar
award, Saudi Commission scholarship, and Ming Hsieh Department of Electrical Engineering
teaching assistantship. The research and the results would have never been obtained without their
support.
v
Table of Contents
Dedication ii
Acknowledgments iii
List of Figures 1
Abstract 7
Chapter 1: Nanotechnology and the Future of Electronics 8
Chapter 2: Physical Properties of Carbon nanotubes 11
2.1 - Carbon nanotube from Graphene 11
2.2 - Phonon dispersion relation and band structure of carbon nanotubes 12
2.3 - Raman scattering in carbon nanotubes 14
Chapter 3: Overview of the Electron Transport in 1-D Systems 17
3.1 - Introduction 17
3.2 - Landauer model and carbon nanotubes 17
3.3 - Effective mean free path 19
3.4 - Fermi energy and gate voltage 20
3.5 - Optical phonon (OP) emission and absorption 21
3.6 - Temperature dependent effective mean free path 22
Chapter 4: Kink Behavior in the I-V
b
Characteristics of Suspended Nanotubes 25
4.1 - Introduction 25
4.2 - Device fabrication and characterization 26
4.3 - Field Effect Transistor Ion/Ioff ratio and carrier mobility 28
4.4 - Current-Voltage characteristics in-situ with Raman spectroscopy Experiments 31
4.4.1 - Raman shift and the sudden downshift 31
4.4.2 - (FWHM) of Raman spectra and its relation to the kink 33
4.5 - Gate voltage dependence of the kink and optical phonon emission 35
4.6 - Temperature dependence of the kink 37
4.7 - The Dynamics of the Kink in Different Gaseous Environments 40
4.7.1 - Inert gases in room temperature 40
4.7.2 - the abrupt change in the non-equilibrium phonon population 41
4.8 - Spatial Dependence of Raman Downshifts Above and Below the Kink Bias Voltage 46
4.9 - Effect of temperature annealing on the I-V characteristics 47
4.10 - Summary 50
vi
Chapter 5: Effect of the Substrate in Determining the Band Gap of Metallic Carbon
Nanotubes 51
5.1 - Introduction 51
5.2 - Device Fabrication 53
5.3 - I-V Characteristics of on and off the substrate devices 54
5.4 - Suspended nanotubes incased in ice 59
5.5 - Summary 61
Chapter 6: Band to Band Tunneling in Metallic Carbon Nanotube pn Devices 63
6.1 - Introduction 63
6.2 - Band-to-band (Zener) Tunneling in small band gap carbon nanotubes 65
6.3 - Fabrication of suspended carbon nanotubes pn devices 66
6.4 - band-to-band (Zener) tunneling behavior in metallic nanotube pn devices 68
6.5 - Switching between ohmic behavior and rectifying Behavior 73
6.6 - Anomalous tunable breakdown voltage behavior 74
6.7 - Dependence of the breakdown voltage on the Conductance band gap 75
6.8 - Room temperature carbon nanotube tunnel field-effect-transistor based on pn devices 76
6.9 - Summary 78
Chapter 7: Photocurrent Generation in Metallic Nanotube pn Devices. 80
7.1 - Introduction 80
7.2 - Photocurrent generation in quasi-metallic nanotube pn devices 81
7.3 - Photocurrent spectroscopy and chirality assignment 83
7.4 - Summary 88
Chapter 8: Competing Photocurrent Mechanisms in Quasi-Metallic Carbon Nanotube pn
Devices 89
8.1 - Introduction 89
8.2 - Photothermoelectric effect and photovoltaic effect 90
8.3 - Mechanism underlying the photocurrent in quasi-metallic nanotubes 91
8.4 - Conductance modulation and the associated mechanism behind the photocurrent 98
8.5 - Summary 99
vii
Chapter 9: Opto-mechanical Self-Oscillations in Metallic Carbon Nanotube pn Devices 100
9.1 - Introduction 100
9.2 - Oscillations in current-voltage characteristics of metallic nanotubes pn devices 102
9.3 - Coupling of zener tunneling model with thermal oscillations 106
9.4 - Summary 108
Chapter 10: Conclusion and Future Outlook 109
10.1 - Terahertz emission and detection with qausi-metallic carbon nanotube pn devices 109
10.2 - Near infrared photocurrent spectroscopy 110
10.3 - high frequency NDC based oscillator 110
10.4 - Conclusion and final remarks 112
Bibliography 115
1
List of Figures:
Figure 2.1. Classifications of carbon nanotubes (a) armchair, (b) zigzag, and (c) chiral nanotubes
Dresselhaus et al.[1] 11
Figure 2.2. Graphene unit vectors and carbon nanotube unit cell. Dresselhaus et al.[1] 12
Figure 2.3. Electronic band structure of (a) (10,10) metallic nanotube and (b) (10,0)
semiconducting nanotube 13
Figure 2.4. (a) 3D model of the electronic band structure of graphene showing the Dirac points
(b,c) Quantization of the nanotube’s wavevector in the circumferential direction 13
Figure 2.5. (a) Typical Raman spectra of metallic and semiconducting nanotubes. (b) radial
breathing mode vibrational direction. Vibrational directions of the G band peaks (c) TO mode (d)
LO mode 15
Figure 3.1. Schematic diagram showing the optical phonon emission process in the applied
linear electric field (Ɛ). The electron will have to travel some threshold distance before it has
enough energy to emit an optical phonon. The red arrow represents the threshold distance that
electrons need to attain in the applied electric field (1st term in equation 3.10), while the green
arrow represents the additional scattering length that electrons need to travel before emitting an
optical phonon (2nd term in equation 3.10) 22
Figure 3.2. (a) Current–bias voltage charactistic simulated using the landauer model (equation
3.7) (b) the optical phonon temperature calculated as a function of the applied bias voltage, (c)
The simulated temperature profile along the length of the nanotube. The middle of the nanotube
is taken to be the origin 24
Figure 4.1. (a) cross sectional diagram with the accurate silicon oxide profile of the final device
structure. (b) SEM image of the device. The red line indicates the nanotube’s location. High bias
transport for a (c) semiconducting nanotube and (e) a metallic nanotube. Each nanotube is
suspended over a 2μm wide trench 27
Figure 4.2. Conductance of a suspended nanotube at different gate voltages for a constant
applied bias voltage (Vbias=0.2V). The current IOn/Ioff ratio is 107. (b) The effective mobility
of the nanotube device in (a) using Cg =8 pF/m 29
Figure 4.3. Schematic diagram of the simultaneous electrical and optical measurement setup 31
2
Figure 4.4. (a) I-V characteristics and Raman data of a 2 μm metallic nanotube measured in
argon at a gate voltage of -7 V plotted as a function of the applied bias voltage (b) Raman spectra
at Vbias=0 V (bottom curve) and 1 V (top curve) . (c) Preferential heating of the G+ band
phonon mode for a 5μm sample measured in argon and (d) downshifting of both G+ and G-
phonon modes for a 2μm semiconducting nanotube. 32
Figure 4.5. (a) Current-voltage characteristics and G band Raman (b) frequency and (c)
linewidth for a (L~2 μm) suspended metallic nanotube measured in argon (blue circles) and
vacuum (red triangles) plotted as a function of bias voltage 34
Figure 4.6. (a,b) Current-voltage characteristics of a 2 μm nanotube measured in argon at
different applied gate voltages. (c) Kink bias voltage and low bias resistance plotted as a function
of the applied gate voltage. (d) Current-voltage characteristics of the nanotube in (a) plotted as a
function of the voltage drop across the nanotube. 36
Figure 4.7. (a) I-Vbias data of L= 5 μm suspended metallic carbon nanotube taken at different
base substrate temperatures in argon. Inset shows the kink bias voltage for different substrate
temperatures. (b) G band Raman shifts observed when the nanotube is biased at the kink at
various substrate temperatures. Insets (left) Raman spectra taken at the kink and (right) zero bias
G band Raman data with polynomial fit. (c) Raman shift at different substrate temperatures in He
and CO2 for L ~ 5μm semiconducting nanotube. 38
Figure 4.8. (a,b) I-V characteristics of two different L=2 μm metallic nanotubes exhibiting
different kink locations for CO2, He, and Ar. (c) I-V characteristics of sample in (b) under
different applied gate voltages in Ar and vacuum. Notice the kink behavior towards low bias
voltages as more negative gate voltage is applied in Ar. 39
Figure 4.9. I-V curve fitting for L=2 μm metallic nanotube using the Landauer model (a) helium,
(b) carbon dioxide, and (c) argon. 44
Figure 4.10.(a) I-V characteristics of a 2μm nanotube in argon showing NDC after the kink. (b)
Spatial Raman shift mapping for the G- phonon mode taken near the electrodes (left and right)
and at the center of the nanotube when the device is unbiased (open red circle) and biased above
(upside green triangle) and below the kink. Linear fit is used to fit the unbiased and before the
kink data while a quadratic fit is used for the data after the kink. 47
Figure 4.11. (a) Current voltage characteristics before and after annealing at 400oC for 40
minutes. (b) Device conductance before and after annealing (c) I-V curve fitting in argon and
before annealing. (d) I-V curve fitting in argon and after annealing. Notice that the kink
disappears after annealing and the conductance of the nanotube decreased indicating the kink
requires high conductance 49
3
Figure 5.1. (a) Cross-sectional diagram and (b) SEM image of a carbon nanotube sample for
comparing on-substrate and suspended CNT devices 53
Figure 5.2. (a) I-Vbias characteristics of the suspended and on-substrate regions taken from the
same nanotube. The blue solid curve is measured between electrodes Pt1 and Pt2 in Figure 1a
and the red dashed curve is measured between electrodes Pt2 and Pt3. (b) I-Vgate characteristics
of the suspended and on-substrate regions. (c) Normalized conductance (G/Gmax) plotted as a
function of gate voltage 54
Figure 5.3. The measured conductance (open blue circles) fitted to the Landauer model (red
curve) for (a) suspended and (b) on-substrate segments of the nanotube. (c) The relation between
the Fermi energy and gate voltage for the suspended and on-substrate segments. (d) Band
structure of the suspended metallic nanotube showing a 100 meV band gap 57
Figure 5.4. Schematic diagram illustrating the spatial fluctuations of the energy bands due to the
trapped charges in the nanotube obscuring the mini-gap 59
Figure 5.5. (a) picture showing the formation of ice on the chip as seen from the optical window
(b) I-Vb characteristics of the suspended quasi-metallic nanotube at 300K (red curve) with no ice
and at 77K (blue curve) when ice formed on the entire chip. (c) I-Vgate characteristics of the
nanotube before (red curve) and after (blue dots) ice formation 61
Figure 6.1. (a) Qualitative analysis of the drain current vs. gate voltage for various device
structures. The inset triangle shows a slope of 60mV/decade for comparison. (b) schematic
representation of band to band tunneling mechanism 64
Figure 6.2.Fabrication processes involved to fabricate suspended carbon nanotube pn devices 67
Figure 6.3. Current-bias voltage characteristics taken at (a) room temperature and (c) 4K with
the device gated in a pn configuration (i.e., Vg1=-Vg2). Here, no rectifying behavior is observed
at room temperure because of the small band gap. Rectifying behavior is observed at 4K with
tunable forward and reverse breakdown voltages. (b) Current-gate voltage characteristics at
300K showing a minimum near 0V. This dip in the conductance arises from the existence of a
band gap. (d) Forward and reverse bias breakdown voltages observed under different doping
conditions, demonstrating tunability between 1V and 0.2V. 69
4
Figure 6.4. (a) Schematic diagram of the device geometry and energy band diagram illustrating
Zener tunneling (b) Forward and reverse sweeps for a quasi-metallic pn diode, showing no
hysteresis. (c) A fit of the measured rectifying behavior (black circles) to the Zener model (red
curve). (d) The extracted barrier width (L) and the built-in voltage used to fit the measured
rectifying I-Vbias curves 71
Figure 6.5. Zener model fits for different electrostatic doping conditions (Vg1=-Vg2). (a) 1.5V,
(b) 2V, (c) 4V, and (d)5V. 72
Figure 6.6. Tunability between rectifying behavior and ohmic behavior for (a) device 1 and (b)
device 2. 73
Figure 6.7. Zener breakdown for 4 different samples showing 2 opposite behaviors. Samples in
(a) and (b) exhibit a decrease in the breakdown voltage with increasing homogenous electrostatic
doping conditions, while samples in (c) and (d) show an increase in the zener breakdown with
increasing homogenous electrostatic doping conditions. 74
Figure 6.8. Maximum breakdown voltage measured as a function of the extracted conductance
band gap for six different samples. 76
Figure 6.9. (a) Rectifying behavior observed at room temperature. (b) zoomed-in view of (a)
showing the reverse breakdown voltage. (c) log plot of the current showing regions with steep
slopes. (d) Extracted sub-threshold swing at different electrostatic pn doping concentrations. 77
Figure 7.1. Measured current-bias voltage of a qausi-metallic carbon nanotube pn devices for
Vg1= -Vg2= 7 and (b) Vg1= -Vg2= -7. The nanotube exhibits increasing photocurrent
magnitude with increasing incident laser power. 81
Figure 7.2. (a) Measured photocurrent as a function of the incident laser power for the sample in
figure 7.1. (b) measured photocurrent for different combinations of gate voltage 1 and gate
voltage 2. 82
Figure 7.3. Photocurrent spectroscopy setup using a lock-in technique. 83
Figure 7.4. (a,b) Photocurrent spectra taken under different pn gating conditions showing the
evolution of a prominent excitonic peak corresponding to the metallic transition. (c) Kataura plot
showing unique chiral identification based on the nanotube’s RBM at 215.7 cm-1 and the energy
at 2.14eV. The intercept identifies a nanotube chirality of (13,1). (d) The optical transition
energy (red) and photocurrent magnitude (blue) plotted at various electrostatic doping
conditions. 85
5
Figure 7.5. (a) Photocurrent spectra map of the sample in figure 7.4 with additional doping
conditions showing a peak occurring at 2.14eV. Additional photocurrent spectra for (b) (22,13)
(c) (28,13), and (d) (25,7). The spectra show the evolution of prominent peaks which are
attributed to Eii excitonic transition 87
Figure 8.1. (a) Schematic diagram illustration photothermoelectric in carbon nanotube pn
devices. Hot-free carriers diffuse from the hot side (right) to the cold side (left). (b) Photovoltaic
effect schematic showing electon-hole pair separation. 91
Figure 8.2.(a) Schematic diagram of the final device structure. (b) Experimental setup showing
the focused incident laser on the nanotube when it is biased in a pn configuration. 92
Figure 8.3.Photocurrent maps for all different combinations of gate voltage 1 and 2 of (c) device
1, and (d) device 2. 93
Figure 8.4. Measured photocurrent at different homogeneous electrostatic pn doping
concentration of 4 different devices. The measured photocurrent shows a non-monotonic profile
for (a) device 1 and (b) device 3. The measured photocurrent saturates for with increasing
electrostatic doping for (b) device 2 and (b) device 4. The insets are the measured conductance
vs. gate voltage of each device. 95
Figure 8.5. Photocurrent power dependence for homogeneous pn/np doping of (a) device 3, and
(b) device 4. For each case, the photocurrent reserves its profile for all incident laser powers. The
calculated thermoelectric power of (a) device 3 and (b) device 4. For device 3 the thermoelectric
power profile is in excellent agreement with the measured photocurrent profile. While for device
4, the measured photocurrent profile does not follow the calculated thermoelectric power profile
96
Figure 8.6. (a) Measured conductance of device 1 (blue solid curve) and device 2 (dotted red
curve). (b) a zoomed-in view of device 1 showing the conductance modulation is miniscule due
to a small band. 98
Figure 9.1. (a) Schematic diagram showing the metallic carbon nanotube suspended over a
trench. (b) SEM image of the device structure. The nanotube location is highlighted in red. (c)
thermal excitation experimental setup, The laser power is large enough to induce heating when
the nanotube is gated in a pn junction configuration 101
Figure 9.2. (a) I-Vbias of a quasi-metallic carbon nanotube with and without thermal excitation
for. The inset shows the conductance of the nanotube at various gate voltages. (b) A zoomed-in
view of the induced current oscillations showing the periodicity of the oscillations 103
6
Figure 9.3. (a) Current dependence of the thermal oscillations as a function of time showing a
sinusoidal like wave. (b) Fast Fourier Transform of the data in (a) showing the dominant peak
happens at 1.562 Hz. 104
Figure 9.4. (a) Temperature dependence of the I-Vbias curves demonstrating zener tunneling is
very sensitive to temperature and occurs at T~ 4K. (b) I-Vbias in dark and under thermal
excitations with 633nm laser. The measured laser power is 6.9mW (red curve) and 17mW (blue
curve). (c) Schematic diagram showing thermal self-oscillations of the nanotube for node (red
nanotube) and anti-node (blue nanotube). 105
Figure 9.5. (a) Measured current oscillations under 6.9mW of 633nm. (b) Zener tunneling model
I-Vbias curves when the nanotube oscillates between 200K and 350K. 107
Figure 10.1 (a) Suspended carbon nanotube pn device structure, and (b) schematic diagram of
the light emission process of a suspended CNT pn-junction device 109
Figure 10.2. (a) Measured photocurrent and (b) normalized photocurrent in the near infrared
regime for (13,1) nanotube shown in figure 7.5a. 110
Figure 10.3. Schematic diagram of self-sustaining oscillator 111
Figure 10.4. (a) Schematic diagram of a tapered transmission line fixture. (b) Circuit model of
the nanotube device. 111
7
Abstract
Electronic devices have become the backbone of our daily life usage. In recent years, new
types of electronics have emerged such as wearable electronics, flexible electronics, and
optoelectronics. In particular, the idea of converting light into electricity with high efficiency, by
carefully engineering the device structure, has become an active area of research. In this thesis,
carbon nanotube electronic and optoelectronic devices are investigated which are based on
suspended quasi-metallic carbon nanotubes. These quasi-metallic nanotube electronics exhibit
semi-ballistic electron transport at room temperature, which gives them high sensitivity to
gaseous environment. Once the nanotube is in contact with a substrate, the mini-gap in their
energy band structure diminishes due to fixed charges in the oxide. Moreover, quasi-metallic
carbon nanotube tunnel field-effect-transistors (TFETs) using an electrostatically tunable pn
junction are engineered and studied. Although these devices do not show any diode behavior at
room temperature, they show a finite photocurrent due to the existence of a space charge region.
At cryogenic temperatures, these transistors show a tunable band-to-band (zener) tunneling with
sub-threshold swing ~1mV/decade. At room temperature, these devices can produce
photocurrent upon light exposure. The mechanism underlying the generated photocurrent in
these devices reveals two different mechanisms. Devices with small band gaps (E
gap
< 75meV )
exhibit photothermoelectric effect, while devices with larger band gaps, photo-induced electron
hole separation by a built-in electric field (photovoltaic effect) dominates the photocurrent
transport. Upon photothermal heating of these devices at cryogenic temperatures, an oscillatory
behavior occurs in the current-voltage characteristics with a very low frequency of oscillation.
This oscillatory behavior is found to be caused by opto-mechanical action where the nanotube is
thermally coupled to an optical cavity.
8
Chapter 1
Nanotechnology and Carbon Nanotubes
During the past couple of decades, research in technology has made it possible to
implement integrated circuits in the micro- level. The discovery of Metal Oxide Semiconductor
Field- Effect- Transistor (MOSFET) has revolutionized the semiconductor industry. Integrated
circuits that implement MOSFETs have gained much attention due to their vast applications. In
the last few decades, a dramatic increase in the number of transistors has been observed. This
increase has been formalized by Gordon Moore which states that the number of transistors in an
integrated circuit doubles every two year. Reduction in the length of the transistor’s gate terminal
and advances in semiconductor fabrication processes enable the scaling of Moore’s law.
To this end, shrinking the gate width causes some quantum effects to occur such electron
tunneling leading to uncontrollable electron density in the MOSFET channel. Although low
electric power consumption is one of the main advantages that makes shrinking the gate size,
desirable, the uncontrollable electron density in the channel will create fluctuations in the output
of the designed integrated circuit. Thus, another alternative technology shall be sought with
optimal electronic performance.
Single wall carbon nanotubes, cylindrically shaped carbonaceous material with a
diameter in the range of 0.7-3 nm and a length up to millimeters, have been extensively studied
over the past two decades. With such an extremely tiny size, this novel material exhibit
extraordinary optical and electronic properties. Electron mobility in a single wall carbon
9
nanotube can reach 390 times larger than that of commercially available silicon technology[2].
With this high performance, ballistic transport (i.e., electrons travel without being scattered) has
been observed in carbon nanotube devices[3]. Zhong et al. from Cornell University measured the
ballistic electron resonance of a single wall carbon nanotube [4]. These ballistic resonances are a
clear indication of the absence of scattering in such a nanomaterial.
To date, there have been over 50,000 publications on the subject of carbon nanotubes.
Remarkably, publications in recent years have shown phenomena that never been observed
before. Our ability to fabricate ultra clean, defect-free, carbon nanotube devices with a rigorous
pre-screening process have enabled us to observe features only available to defect-free carbon
nanotubes [5-9]. These features include, but are not limited to, ballistic electron transport at room
temperature[6], breakdown of the Born-Oppenheimer Approximation (BoA)[10], Mott insulator
transition[11], and the observation of optical phonon emission[12]. Our group was also able to
create electronic devices out of this structure such as Nanoelectromechanical resonator[13],
meristor from defected carbon nanotube [14], and high frequency inductors [15].
This thesis discusses recent results published on carbon nanotube electronic and
optoelectronic devices. The thesis is divided into the following chapters: carbon nanotube
physical properties and electronic characteristics (chapters 2and 3), previous work done which
includes exploring the anomalous kink in the current voltage (I-V
bias
) characteristics of
suspended carbon nanotube devices (chapter 4), and band gap alteration by substrate support
(chapter 5). Zener tunneling and rectifying behavior in quasi-metallic carbon nanotube pn
devices (chapter 6), photocurrent generation and chirality assignment using photocurrent
10
spectroscopy (chapter 7), origin of the photocurrent in qausi-metallic carbon nanotube pn devices
(chapter 8), opto-mechanical self-oscillations in qausi-metallic carbon nanotube pn devices, and
future outlook for nanoelectronics and nanoscale photonic devices (chapter 10)
11
Chapter 2
Physical Properties of Carbon Nanotubes
2.1- Carbon Nanotube from Graphene:
Starting with the graphene unit cell, carbon nanotubes can be formed by rolling a sheet of
graphene. The way the rolling occurs gives different types of nanotubes, armchair, zigzag, and
chiral nanotubes which can be specified from the end caps. Figure 2.1 shows these 3 different
caps. For all these different types, we can specify any nanotube by its chiral vector (C
h
), or the
chirality. In figure 2.2, a
1
and a
2
are the unit vectors which construct the chiral vector. Since the
nanotube has to be periodic in the circumferential direction, the chiral vector depends on the unit
vectors and is given by
̅ ̅ ̅
̅ ̅ ̅
where n and m are the chiral indices. By only knowing the chiral vector, all other nanotube
properties can be determined. That is, the circumference is given by |
| √
,
the diameter is given by
|
| and a chiral angle being √
Figure 2.1. Classifications of carbon nanotubes
(a) armchair, (b) zigzag, and (c) chiral
nanotubes Dresselhaus et al.[1]
(2.1)
12
2.2- Phonon dispersion relation and the band structure of carbon nanotubes:
Due to their periodicity in the circumferential direction, the wavevector around the
circumference is quantized and can be derived from the graphene band structure which is given
by
̅ ̅ ̅ ̅
|
̅ ̅ ̅ ̅|
̅ ̅ ̅
,
where
√
(
√
) (
)
(
) is the energy dispersion
relation of graphene (figure 2.4a),
̅ ̅ ̅
and
̅ ̅ ̅
are given by
̅
̅ ̅ ̅
and
̅
̅ ̅ ̅
, respectively.
̅
and
̅ ̅ ̅
are the reciprocal lattice vectors of graphene. Figures 2.3 a and b
show the simulated band structure of (10, 10) nanotube and for (10,0) nanotube, respectively.
Figure 2.2. Graphene unit vectors and carbon nanotube unit cell. Dresselhaus et al.[1]
(2.2)
13
From the figure, a 0.4 eV band gap occurs for (10,0) nanotube. The existence of the band
gap can be explained by looking at the cutting lines that show the quantization of
in figure
2.4c on the graphene band structure. At the Dirac point, these cutting lines can form a linear
relationship with the Dirac cone (metallic nanotubes) or a hyperbolic relationship
(semiconductor nanotubes with a band gap). However, as will be discussed later in chapter 5,
metallic nanotubes are not truly metallic. They have an intrinsic small band gap.
Figure 2.3. Electronic band structure of (a) (10,10) metallic nanotube and (b) (10,0)
semiconducting nanotube
Figure 2.4. (a) 3D model of the electronic band structure of graphene showing the Dirac points
(b,c) Quantization of the nanotube’s wavevector in the circumferential direction.
(a) (b)
(a)
(b)
𝑘
𝑘 𝑝 𝑎𝑟𝑎𝑙𝑙𝑒 𝑙
𝐷
𝑘
𝑘 𝑝 𝑎𝑟𝑎𝑙𝑙𝑒 𝑙
(c)
14
2.3- Raman spectrum of carbon nanotubes:
Raman scattering occurs when an incident light scatters off the vibration of the lattice
(phonon). In this process, a phonon is either emitted (stokes) or absorbed (anti-stokes). In carbon
nanotubes, the relative intensities between stokes and anti-stokes gives the
Where I
S
is the stokes intensity, I
AS
is the anti- stokes intensity, C is a constant determined
experimentally, E
ph
is the phonon energy, K
B
is the Boltzmann constant, and T is the temperature.
There are several active Raman bands in carbon nanotubes. The radial breathing mode (RBM),
the disorder induced (D) band, the tangential mode (G) which gives rise to two bands due to the
nanotube’s curvature, and the 2
nd
order disorder induced (2D or G’) band. In figure 2.5, a
metallic nanotube and a semiconducting nanotube show different spectral properties.
The RBM band is the nanotube’s signature since all carbon atoms vibrate in the radial
direction. The nanotube’s diameter can be calculated by knowing the frequency of RBM (ω
RBM
)
and using
where A and B are constants determined experimentally [1]. The G
band is split into G
-
(LO) and G
+
(TO). The G band can differentiate between metallic and
semiconducting nanotubes. For metallic nanotubes, the broad G- occurs due to the existence of
Khon Anomaly [16]. In addition to the Khon Anomaly effect in metallic nanotubes, the
frequency of this band is correlated with the diameter of the nanotube [1]. Small diameter
nanotubes have lower frequency shift while large diameter nanotubes have frequencies closer to
(2.3)
15
G
+
band. The 2D band is the 2
nd
order active disorder induced Raman band. Unlike the G band,
the 2D can give better measure of the optical phonon temperature in carbon nanotubes.
Figure 2.5. (a) Typical Raman spectra of metallic and semiconducting nanotubes. (b) radial breathing
mode vibrational direction. Vibrational directions of the G band peaks (c) TO mode (d) LO mode.
(a)
(b)
(c) (d)
Raman Shift (cm
-1
)
Intensity (a.u.)
Me tallic
Semicond ucting
16
There have been several methods to determine the temperature of the nanotube. One
method that gives the true temperature of the phonon mode is by measuring the relative
intensities between stokes and anti-stokes given in equation 2.2. However, this method requires a
resonant sample with the incident laser in order to get noticeable intensities for both stokes and
anti-stokes, which is not the usual case for suspended carbon nanotubes. Another much more
common method is the use of G band frequency downshift. As the nanotube heats up, the G band
phonon mode tends to downshift [17, 18]. An increase in the downshift can be interpreted as an
increase in the phonon mode temperature. This downshift can be calibrated with the environment
temperature to give a measure of the G band temperature. For nanotubes in thermal equilibrium,
the temperature measured for both cases will be the temperature of the nanotube.
17
Chapter 3
Overview of the Electron Transport in a 1-D System
3.1- Introduction:
The current voltage characteristics of carbon nanotubes have attracted the attention of
many engineers and scientists. It is essential to understand how electrons behave in such an
exceptional 1-D material. The observation of high current carrying abilities up to 25 µA at high
bias in carbon nanotubes and the ballistic transport are features that make carbon nanotubes
interesting to study [19]. In this chapter, the 1-D Landauer model will be discussed. This model
has been used to fit the current-voltage characteristics of individual suspended carbon nanotubes.
3.2- Landauer Model and carbon nanotubes:
The current voltage (I-V) characteristics of suspended nanotubes have been discussed
extensively by many research groups [3, 20-23]. However, most of these studies are either
measured or simulated in a vacuum environment which ultimately terminates the appearance of
the sudden drop in current observed in defect free, suspended nanotubes measured in gaseous
environment (discussed in details in chapter 4). Generally, the DC resistance of the nanotube can
be described according to
CNT contacts
R R R (3.1)
18
where
contacts
R is the contact resistance at the electrodes, and
is the nanotube resistance.
can be calculated from the conductance of the nanotube. In general, for a perfect
transmission (T=1) the current in a 1-D system is given by:
Where
v
g is the valley degeneracy (equals to 2 for CNT) [24], g(E) is the density of states, v is
the group velocity, and f is the Fermi function. For the first sub-band, |
|
, and
while
, then the product of g(E)∙v = 1/ħ. The conductance of such a 1D system,
which is a measurable parameter, can be found by dividing the current by the applied bias
voltage.
here T is the transmission coefficient due to scattering processes, f (E,eV
s
) and f (E,eV
d
) are the
Fermi-Dirac distributions at the source and the drain, respectively, and V
bias
is the applied voltage
between the source and the drain terminals.
dE
E
f
T
h
e
V
dE eV E f eV E f
h
e
V
I
T E G
bias
d s
bias
CNT
2
4
)] , ( ) , ( [
4
) , (
(3.3)
dE v E g eV E f eV E f
e g
I
d s
v
) ( )] , ( ) , ( [
2
(3.2)
19
We can relate the transmission coefficient to the total scattering rate using the so called multiple
scattering technique. The resultant transmission coefficient from this technique is
L
T
eff
eff
where
eff
is the effective mean free path for a scattered electron in the system and L is the
nanotube’s channel length. With this in mind, the nanotube conductance is given as
For a fixed applied gate voltage, the integral over the energies in the band structure is constant
and hence, the resistance of the nanotube will be temperature (bias voltage) dependent only. The
nanotube’s total resistance will become the superposition of two terms, the quantum resistance
term, and the scattering resistance term. Therefore,
, or
3.3- Effective Mean Free Path (MFP):
The effective mean free path,
eff
, is composed of different scattering processes. Due to
the circumferential confinement of carbon nanotube devices, the optical phonon dispersion
(3.5)
dE
E
f
L T E
T E
h
e
R
G
eff
eff
CNT
CNT
) , (
) , (
4 1
2
(3.4)
L T
T
h
e
G
eff
eff
E
CNT
F
) (
) (
4
2
constant
scattering quantum
eff eff
eff
CNT
R R
T
L
e
h
e
h
T
L T
e
h
T R
) ( 4 4 ) (
) (
4
) (
2 2 2
(3.6)
(3.7)
20
relations are different than graphene. The phonon dispersion relations of carbon nanotubes
reported by different groups contain more phonon modes than graphene. Thus, we expect
different electron transport behavior and different electron-phonon coupling in nanotubes than in
graphene. Fortunately, some of these phonon branches have weak interaction with electrons,
while others have significant contributions to the electron transport in certain regimes as will be
shown later. However, the effective mean free path that an electron has to travel before scattering
in this 1D system can be divided into: Acoustic phonon mean free path, optical phonon emission,
optical phonon absorption. The effective mean free path is given by Mathiessen’s rule:
where
, is the acoustic phonon mean free path which depends on the
acoustic mean free path at room temperature(
) and is inversely proportional to the
nanotuibe’s temperature [23]. Recently, it has been found that
is proportional to the
diameter of the nanotube (d) according to
nm [25].
and
are the
optical phonon emission and absorption mean free paths, respectively. Section 3.5 discusses
these 2 terms thoroughly.
3.4- Fermi energy and gate voltage:
Applying a gate voltage (V
g
) on the nanotube can change the Fermi energy (E
F
) position,
and hence the energy of the charge carriers that contribute to transport. The Fermi energy can be
calculated numerically which is given as a function of the applied gate voltage according to
(3.8)
1
,
1
,
1 1
ems op abs op ac eff
21
g
F
F
eV
C
E Q
E
) (
,
where C is the geometric capacitance, and Q is the charge induced on the CNT. The inclusion of
the Fermi energy is to account for the density of states capacitance of the nanotube (gate voltage
changes the electrochemical potential not the electrostatic potential only) [26].
3.5- Optical Phonon (OP) emission and absorption:
OP emission has been very successful in explaining high bias electron transport in carbon
nanotubes, and was used to explain the observed current saturation in metallic nanotube devices
[19]. In this model, electrons accelerate ballistically until they reach a threshold energy, above
which they back-scatter by emitting an OP, as shown schematically in Figure 3.1.
Mathematically, the scattering length for emitted OPs is given by
1 ) (
1 ) (
300
min , ,
T N
N
qe
L
op
op
op
op
ems op
where
is the (contact resistance-corrected) electric field along the nanotube and
OP
E = 0.2 eV
is the OP energy. In this equation,
min
OP
is the scattering length for electron scattering from OP
emission in the nanotube after the electron has accelerated to the threshold energy,
OP
E , and has
been found to be on the order of 15d nm, where d is the nanotube’s diameter [27]. Thus, λ
op,ems
decreases as the bias voltage increases. When this is the dominant contribution to the MFP,
current saturation of the order of 25 µA results [28]. However, in the OP emission in suspended
carbon nanotube devices cannot explain the occurrence of NDC alone. Thus, OP absorption
(3.9)
(3.10)
22
process should be included in the effective MFP in this high bias regime. Here, the OP
absorption is given as .
1
300
min ,
OP
OP
op abs op
N
N
where
abs op,
is the OP absorption MFP, N
OP
, is
the OP population and follow Bose-Einstein distribution.
3.6- Temperature dependent effective mean free path
So far, we have not included the temperature of the nanotube in the system. The effective
mean free path is a strong function of temperature and cannot be ignored. Theoretical and
experimental results show that the temperature of the opitcal phonon modes in carbon nanotubes
can rise up to thousands of Kelvins in high bias regime. Thus, it is advisable to find the
temperature of the dominant optical phonon modes at a constant (contact resistance corrected)
x(nm)
E(eV)
e
-
1 2
Figure 3.1. Schematic diagram showing the optical phonon emission process in the applied linear
electric field ( ). The electron will have to travel some threshold distance before it has enough energy
to emit an optical phonon. The red arrow represents the threshold distance that electrons need to attain
in the applied electric field (1
st
term in equation 3.10), while the green arrow represents the additional
scattering length that electrons need to travel before emitting an optical phonon (2
nd
term in equation
3.10).
23
applied electric power (P
CNT
). The temperature of such devices follows the heat diffusion
equation which is solved numerically and is given by:
where ,
, and , are the cross sectional area, thermal conductivity, and the thermal
boundary conductance of the gas, respectively [29]. The negative differential conductance
observed in suspended carbon nanotubes is associated with the sudden emission of optical
phonons at high bias. These optical phonons will eventually decay into acoustic phonons which
appear as heat elongated across the nanotube out to the contacts. Due to the presence of hot
phonons observed at high bias, the dis-equilibrium between optical and acoustic phonons is
specified by a non-equilibrium factor (α), which is affected by the surrounding environment as
explained in chapter 4. The optical phonon temperature is given by:
where
,
, and
are the temperatures of the optical phonons, the acoustic
phonons, and the environment, respectively [22, 23]. In our case, I will take room temperature as
T
o
=300K. It is worth mentioning that the non-equilibrium factor α depends on the optical phonon
lifetime (
) according to
, where C
op
is the heat capacity (constant at high bias).
For a given nanotube length L, equation 3.11 is solved numerically for each applied bias
voltage in a self-consistent fashion in order to extract the temperature distribution along the
(3.12)
0
) ( ) (
2
2
th
o
th
CNT
A
T T g
A
P
dx
x T d
(3.11)
) (
o acoustic acoustic optical
T T T T
24
nanotube. The values of the thermal boundary conductance of the gases were taken from the
experimental measurements done by Hsu et al. [30]. Figure 3.2 shows the simulated device I-
V
bias
for an electrostatically heavily doped device. Figure 3.2b shows the optical phonon
temperature at different bias voltages. As noticed, the optical phonon temperature can reach as
high as 1000K for 1 volt across the device. For each applied bias voltage value, the optical
phonon temperature profile along the length of the nanotube is simulated. Figure 3.2c shows the
simulated temperature profile along a 2µm long nanotube at high bias regime (V
bias
= 1V) in an
argon environment.
Figure 3.2. (a) Current–bias voltage
characteristic simulated using the
landauer model (equation 3.7). (b) The
optical phonon temperature calculated as
a function of the applied bias voltage. (c)
The simulated temperature profile along
the length of the nanotube. The middle of
the nanotube is taken to be the origin.
0.0 0.2 0.4 0.6 0.8 1.0
0
1
2
3
4
5
Current (µA)
Bias Voltage (V)
0.0 0.2 0.4 0.6 0.8 1.0
300
400
500
600
700
800
900
1000
T
optical phonon
(K)
Bias Voltage (V)
-1.0 -0.5 0.0 0.5 1.0
300
400
500
600
700
800
900
1000
Temperature (K)
Nanotube Length (µm)
(a) (b)
(c)
25
Chapter 4
Anomalous Current-Voltage Characteristics of Suspended
Single Wall Carbon Nanotubes
4.1- Introduction:
Measurements performed on suspended carbon nanotubes in gaseous environment shows
a sudden drop in current (kink). No group was able to understand the origin of this kink at high
bias which is mostly related to the electron-phonon coupling in carbon nanotubes. In this chapter,
I will discuss my findings on the origin of this kink by performing Raman spectroscopy on
carbon nanotubes to elucidate the underlying mechanism of energy loss and to further explore
the electron-phonon interactions on which it is based upon. A systematic study of this kink
feature was performed on a total of 17 CNT samples at various gate voltages, substrate
temperatures, and in different gas environments. Raman spectroscopy provides additional
information about the optical phonon dynamics in this system, which interestingly shows an
abrupt change at high bias voltages. The current voltage characteristics data are fitted to the
Landauer model in order to extract the underlying changes in the phonon population. The work
in this chapter is published in [31].
26
4.2- Device fabrication and characterization:
Several fabrication schemes have been implemented to produce a suspended nanotube field
effect transistor. Typically, nanotubes are grown on an oxidized silicon substrate , followed by
etching of a trench, and then patterning of the source and drain electrodes [32]. In this method,
lithography residues such as PMMA, photoresist, and other processing contaminants may affect
physical or electronic behavior, and hence offer a disadvantage when attempting to measure the
intrinsic properties of the carbon nanotube. In contrast, the as-grown method minimizes
contaminants on the nanotube surface that could otherwise scatter electrons by ensuring that the
nanotube growth is the last step in the sample fabrication process. Several research groups have
explored CNT device fabrication using this approach [33, 34]. Briefly, a 500 nm deep trench is
etched on a p-type silicon substrate with a pre-grown silicon oxide (1µm) and silicon nitride (100
nm). Electrodes are patterned on top of the silicon nitride, which serve as the source and a drain.
A third electrode is deposited in the bottom of the trench as a gate. Iron nanoparticle catalyst is
patterned on top of the source and drain electrodes followed by carbon nanotube growth for 10
minutes using ethanol as the carbon feedstock [17]. The growth temperature, which ranges from
825
o
C to 875
o
C [35] can be optimized to tune the resulting nanotube diameter. Figures 4.1a,b
show the device schematics and the cross sectional view, and figure 4.1c shows the SEM image
of the final device structure. Out of 30 electrode pairs, 3-4 nanotubes are suspended with their
maximum current (I
max
) is proportional to the trench width (L in µm) according to I
max
~10/L (µA)
[34]. The relationship between the maximum current and the trench width is a good starting
method to characterize suspended nanotubes electrically [34]. . The yield ratio depends on the
channel length (or trench width) used. For instance, for a 5µm long nanotube; the yield is 1 out
27
of 60 devices. However, this can be improved by modifying the growth conditions. Figure 4.1c,d
show I-V
bias
characteristics for quasi-metallic and semiconducting nanotubes, respectively. The
negative differential conductance (NDC) observed at high bias is a signature of a suspended
nanotube [34], and is not observed in carbon nanotube devices grown on a substrate. Both
devices are suspended over a 2µm wide trench and exhibit I
max
~ 5µA. Tunable Raman
measurements [1, 36-39], scanning photocurrent microscopy [40-45], and thermal emission
spectra [46, 47], are additional methods used to confirm the individuality of a suspended
nanotube.
0.0 0.2 0.4 0.6 0.8 1.0
0
2
4
6
Current (µA)
V
bias
(V)
V
gate
= -3V
-4 -2 0 2 4
0
10
20
30
Conductance (µS)
V
gate
(V)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
2
4
6
Current (µA)
V
bias
(V)
V
gate
=-5V
-4 -2 0 2 4
0
4
8
12
16
20
Conductance (µS)
V
gate
(V)
I
max
Figure 4.1. (a) cross sectional diagram with the accurate silicon oxide profile of the final
device structure. (b) SEM image of the device. The red line indicates the nanotube’s
location. High bias transport for a (c) semiconducting nanotube and (e) a metallic
nanotube. Each nanotube is suspended over a 2µm wide trench.
I
max
(a)
(b)
(c)
(d)
28
4.3- Field Effect Transistor I
on
/I
off
ratio and carrier mobility:
One desired feature for logic gate transistors is the ratio of on-state current to the off- state
current, referred to as the current on/off ratio (I
on
/I
off
). In digital devices, it is preferred to have as
low Off-state current as possible to minimize power consumption [48]. Rouhi et al measured
I
on
/I
off
ratio ranging between 10-10
5
for solution based semiconducting CNT-FET devices [49].
Although their devices exhibit high I
on
/I
off
ratio, the mobility has values of ~10 cm
2
/V∙s,
significantly lower than those obtained from as-grown devices. Solution processing induced
defects and impurities, and the nanotube-nanotube contact resistance can restrict the charge
carrier mobility in the channel by introducing additional scattering into the system. Thus, it is
essential to study the electronic performance of a single wall carbon nanotube.
In Figure 4.2a, the current-gate voltage characteristic (I-V
gate
) of a suspended semiconducting
nanotube is shown. The measured I
on
/I
off
ratio for this sample is ~10
7
. The measured I
on
/I
off
values range between 10
6
-10
7
for different semiconducting devices. The underlying reason
behind high I
on
/I
off
ratios of our devices is related to the device structure where the suspension of
the nanotube eliminates any additional charges (trapped oxide charges) that could contribute to
larger off-state current and hence, lower I
on
/I
off
ratio. Our measured I
on
/I
off
ratio is higher than
those measured on substrate supported single nanotube devices [50] .
Device applications such as logic circuits require high I
on
/I
off
ratio which can be achieved by
incorporating additional semiconducting nanotubes in the channel. Zang et al and Wang et al
measured I
on
/I
off
ratios in the order of 10
5
, which is 2 orders of magnitude lower than single
suspended nanotube devices [51, 52].
29
Another figure of merit for transistors is the carrier mobility. For a 1-D system in a diffusive
regime, the mobility is given by [53-55]:
Where G is the nanotube channel conductance, L is the nanotube length, and C
g
is the gate
capacitance per unit length. The extraction of C
g
is an important parameter in calculating the
accurate channel mobility.
For suspended nanotube devices, the theoretically predicted gate capacitance C
g
for a 500nm
deep trench with d=2 nm is 8.05 pF/m [26, 56]. Our fits to the conductance curves using the
Landauer model produce C
g
values in the range of 7-10 pF/m [56], which are close to the
theoretical value. Figure 4.2b illustrates the calculated mobility of device in figure 4.2a using
equation 4.1. We use C
g
= 8 pF/m and L= 2 µm. The peak mobility reaches ~7,000 cm
2
/V∙s.
(4.1)
-4 -3 -2 -1 0 1 2 3 4
1E-15
1E-13
1E-11
1E-9
1E-7
1E-5
1E-3
Conductance (S)
Gate Voltage (V)
V
bias
= 0.2V
(a) (b)
-4 -2 0 2 4
0
1000
2000
3000
4000
5000
6000
7000
8000
Mobility (cm
2
/V.s)
Gate Voltage (V)
Figure 4.2. Conductance of a suspended nanotube at different gate voltages for a constant
applied bias voltage (V
bias
=0.2V). The current I
On
/I
off
ratio is 10
7
. (b) The effective
mobility of the nanotube device in (a) using C
g
=8 pF/m.
30
Zhou et al measured the peak mobility of semiconducting nanotubes with diameters ranging
between 1-4 nm [55]. They found a strong dependence of the nanotube’s mobility with the
square of its diameter (~d
2
). For a nanotube with d= 2 nm, the theoretically predicted peak
mobility is 5,000 cm
2
/V∙s [55]. Given the uncertainty of the capacitance value used in the
calculations (±2 pF/m), the nanotube channel exhibits the theoretically predicted mobility.
Related to Equation 4.1, the mobility of the nanotube channel can also be calculated according to
[53]
,
where n is the carrier density which depends on the threshold voltage (V
th
) according to
n=C
g
(V
th
-V
g
). However, the extracted mobility becomes less accurate as the gate voltage
approaches the threshold voltage due to the division by a small number in equation 4.2. For the
purpose of intrinsic mobility extraction, the conductance of the nanotube can be calculated by the
modified formula
,
where R
C
is the contact resistance. This method, however, requires knowledge of the contact
resistance of the device which is gate voltage dependent and varies from one device to another.
One way to estimate the contact resistance is by calculating the resistance of the low bias I-V
bias
characteristics. The resistance obtained from the low bias transport approximately equals the
resistance of the contacts. This method is applicable only for short devices as the contact
resistance dominates the electron transport at low bias regime.
(3)
(3)
(3)
(3)
(4.2)
(4.3)
31
4.4- Current-Voltage characteristics in-situ with Raman spectroscopy:
In order to measure the Raman optical phonons with the applied bias voltage, I have
created the setup shown in figure 4.3, Raman spectra are taken with a Renishaw InVia
spectrometer using 532 nm and 633 nm wavelength lasers.
4.4.1- Raman Shift and the sudden downshift:
Figure 4.4a shows the current-voltage characteristics of a metallic suspended carbon
nanotube plotted together with the G
+
and G
-
band Raman shifts. A sudden drop or “kink” in the
I-V curve can be seen between 0.9 and 1 V. An abrupt drop in the G
-
band frequency also occurs
at the kink bias voltage, while the G
+
band remains constant. Figure 4.4b shows the detailed
Raman spectra which illustrate this type of selective downshift [5]. The sudden downshift of the
G
-
band at the kink bias voltage indicates an abrupt change in the nanotube temperature and/or
phonon populations[57]. The striking difference in behavior between the G
+
and G
-
bands
indicates thermal non-equilibrium phonon populations, as reported previously[6]. Figures
Figure 4.3. Schematic diagram of the simultaneous electrical and optical measurement setup.
32
4.4(c,d) show similar data taken on nanotubes exhibiting preferential G
+
band downshifts and
semi-equilibrium downshift for G
+
and G
-
bands .
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
1
2
3
4
5
6
IV
Current (µA)
V
bias
(V)
1565
1570
1575
1580
1585
1590
1595
G
-
G
+
Raman Shift (cm
-1
)
Ar
Figure 4.4. (a) I-V characteristics and Raman data of a 2 μm metallic nanotube measured in
argon at a gate voltage of -7 V plotted as a function of the applied bias voltage (b) Raman
spectra at V
bias
=0 V (bottom curve) and 1 V (top curve) . (c) Preferential heating of the G
+
band
phonon mode for a 5µm sample measured in argon and (d) downshifting of both G
+
and G
-
phonon modes for a 2µm semiconducting nanotube.
1450 1500 1550 1600 1650 1700
Normalized Intensity (a.u)
Raman Shift (cm
-1
)
(b) (a)
V
bias
=1 V
V
bias
=0 V
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
1
2
3
4
5
6
IV
Current (µA)
Bias Voltage (V)
1540
1560
1580
G
-
G
+
Raman Shift (cm
-1
)
Ar
0.0 0.2 0.4 0.6 0.8 1.0
0
1
2
3
4
5
6
IV
Current (µA)
Bias Voltage (V)
Ar
1572
1578
1584
1590
G
-
G
+
Raman Shift ( cm
-1
)
(c) (d)
33
The existence of preferential heating in these devices is not yet understood. The different
electron-phonon coupling for the G
+
and G
-
causes these devices to be out of equilibrium. The
observation of different phonon coupling has been hypothesized before to be due to the existence
of Kohn Anomaly in carbon nanotubes. However, more experiments are essential to have a
conclusive explanation of the preferential heating effect.
4.4.2 (FWHM) of Raman Spectra and Its Relation to The Kink:
Figure 4.5a shows the I-V data taken from a suspended, metallic CNT in argon and in
vacuum. The low bias resistance of this device is not affected by the gaseous or vacuum
environment. Only the high bias data is affected by the gas/vacuum environment. The
corresponding Raman data is shown in Figures 4.5b and 4.5c, which plot the G band Raman shift
and FWHM as a function of the applied bias voltage, respectively. In Ar, there is an abrupt
change in the G band vibrational frequency (ω
G
) at the kink bias voltage, consistent with Figure
4.4a. In vacuum, however, the Raman data does not exhibit an abrupt change in ω
G
, but, instead,
downshifts consistently over the whole bias voltage range. The full width half maximum
(FWHM) data in Figure 4.5c shows similar results. The temperature-induced G band downshifts
observed in vacuum are larger than those observed in argon, because the gas molecules affect the
optical phonon population, which in turns affects the thermal transport of the system [8]. At a
given bias voltage, the electric current is lower in vacuum than in argon because the temperature
of the nanotube is higher, and hence there is more scattering in the nanotube. The mechanism
34
underlying this kink behavior can be understood by considering that, below the kink, gas
molecules are adsorbed on the surface of the nanotube. These gas molecules, in turn, assist in
the decay of hot optical phonons. These hot phonons then decay rapidly into acoustic phonons,
1550
1560
1570
1580
argon
vacuum
Raman Shift (cm
-1
)
0
2
4
6
argon
vacuum
Current (µA)
0.0 0.4 0.8 1.2
0
5
10
15
20
25
vacuum
argon
FWHM (cm
-1
)
Bias Voltage (V)
(b)
(a)
(c)
Figure 4.5. (a) Current-voltage
characteristics and G band Raman
(b) frequency and (c) linewidth for
a (L~2 µm) suspended metallic
nanotube measured in argon (blue
circles) and vacuum (red
triangles) plotted as a function of
bias voltage.
35
which carry the heat out of the nanotube. Above the kink, gas molecules desorb due to the
population of the optical phonons, which causes a reduction in the hot phonon decay rate,
causing the nanotube to heat up abruptly. That is, the desorption of gas molecules results in
longer phonon lifetimes, and hence higher OP (and intermediate frequency phonon) populations,
which cause the abrupt downshift in the G band and the drop in current due to the increased
electron-phonon scattering.
4.5- Gate voltage dependence of the kink and optical phonon emission:
Figures 4.6a and 4.6b show the current-voltage characteristics of another suspended,
quasi-metallic carbon nanotube measured in argon at different gate voltages between 0 and +5 V
and between 0 and -5 V, respectively. A sudden drop or “kink” in the I-V curve can be seen in
each dataset. The voltage at the kink (V
kink
) varies with the applied gate voltage, as shown in the
inset of Figure 4.6a. This kink voltage follows the same general trend as the low bias resistance
of the device (Figure 4.6c), which exhibits a maximum when the Fermi energy of the nanotube
lies inside the small band gap of this quasi-metallic nanotube.
The total device resistance can be expressed as
R
device
= 2R
contact
+ R
CNT
= 2R
contact
+ R
quantum
+ R
ac
+ R
op
,
where R
contact
is the contact resistance, R
quantum
= h/4e
2
= 6.5 kΩ is two units of quantum
conductance 4e
2
/h [28, 58], R
ac
is the resistance due to acoustic phonon scattering, and R
op
is the
resistance associated with optical phonon scattering. R
contact
and R
ac
depend strongly on the
applied gate voltage[23, 59]. In low bias regime, R
op
is negligible since the optical phonon
populations are extremely low at room temperature[23]. Therefore, the low bias resistance can be
(4.4)
36
approximated as R
low bias
= 2R
contact
+ R
quantum
+ R
ac
. Since we are mainly interested in
understanding the high bias behavior of these nanotubes, in particular the optical phonon
dynamics at high bias, we can subtract the bias voltage-independent resistance as follows: V
op
=
V
bias
– (2IR
contact
+ IR
quantum
+ IR
ac
) = IR
op
. Figure 4.6d shows the current through the nanotube
plotted as a function of the voltage drop corresponding to optical phonon scattering, V
op
. Here,
for heavily gated and ungated I-V curves, all the kinks occur at approximately V
op
=0.2 V, which
corresponds to the energy of the highest optical phonon branches (1590cm
-1
= 197 meV). These
0.0 0.2 0.4 0.6 0.8 1.0
0
1
2
3
4
5
Current (µA)
Bias Voltage (V)
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
1
2
3
4
5
Current (µA)
Bias Voltage (V)
0.0 0.2 0.4 0.6 0.8 1.0
0
2
4
6
Current (µA)
V
op
(V)
(b) (a)
V g= 5V
V g= 0
(d)
(c)
V g= -5V
V g= 1
-10 -8 -6 -4 -2 0 2 4 6 8 10
0.3
0.4
0.5
0.6
0.7
0.8
Kink Bias Voltage (V)
Gate Voltage (V)
0
40
80
120
160
200
240
Resistance (k )
Ar
Figure 4.6. (a,b) I-V characteristics of a 2 µm nanotube measured in argon at different applied gate
voltages. (c) Kink bias voltage and low bias resistance plotted as a function of the applied V
g
. (d) I-
V characteristics of the device in (a) plotted as a function of the voltage drop across the nanotube.
37
phonon modes are known to couple strongly to the electrons through a Kohn anomaly[5, 60, 61].
This optical emission process is illustrated schematically in the inset of Figure 4.6d, where
electrons accelerating in the applied electric field ( ) gain a kinetic energy that is linearly
proportional to the distance they travel ( ), until they have enough energy to emit optical
phonons (0.2 eV).
4.6- Temperature dependence of the kink:
The current-voltage characteristics of carbon nanotubes changes with changing the
substrate temperature. Accompanied with that changing, the kink bias voltage also changes with
the substrate temperature. Interestingly, the kink disappears for low cryogenic temperatures in
gaseous environments. This may be due to gas adsorption. However, the origin of this behavior
is not fully understood. I have measured I-V characteristics in situ with Raman spectroscopy for
3 different samples which showed the same behavior for different substrate temperatures. Figure
4.7a shows the I-V characteristics of a quasi-metallic, suspended carbon nanotube taken at
various substrate temperatures between -185
o
C and 100
o
C in an argon environment. The kink
voltage varies with the substrate temperature, as shown in the inset of Figure 4.7a. For
temperatures below -130
o
C, no kink was observed in the I-V characteristics. Figure 4.7b shows
the Raman shift of the G
+
phonon mode of the same device at various substrate temperatures,
when biased at the kink. There are many temperature-dependent variables that affect the kink
bias voltage, including contact resistance, thermal conductivity of the nanotube, and mean free
paths. For this nanotube, these competing effects cause the kink bias voltage to peak at -40
o
C.
Despite the large variations in kink bias voltage, the G
+
band Raman shift is observed at a
38
consistent wavenumber (1575 cm
-1
) when biased at the kink over the whole range of substrate
temperatures. The G
+
band Raman shifts measured at zero bias voltage are plotted in the inset of
Figure 4.7b, together with a polynomial fit. This data shows the typical temperature dependence
of the G
+
band mode in carbon nanotubes[57]. From the calibrated G
+
band downshifts, we can
estimate the nanotube temperature at the kink to be approximately 400
o
C, which is consistent
with the kink temperature measured for the other samples with a pronounced kink in their I-V
Figure 4.7. (a) I-V
bias
data of L= 5 µm suspended metallic carbon nanotube taken at different base
substrate temperatures in argon. Inset shows the kink bias voltage for different substrate temperatures. (b)
G band Raman shifts observed when the nanotube is biased at the kink at various substrate temperatures.
Insets (left) Raman spectra taken at the kink and (right) zero bias G band Raman data with polynomial fit.
(c) Raman shift at different substrate temperatures in He and CO2 for L ~ 5µm nanotube.
-120 -80 -40 0 40
1500
1515
1530
1545
1560
1575
Raman Shift (cm
-1
)
Substrate Temperature (
o
C)
V
b
=V
kink
V
b
=0V
-150-100 -50 0 50 100 150
1589
1590
1591
1592
1593
1594
Substrate Temperature (
o
C)
Raman Shift (cm
-1
)
1400 1600
Raman Intensity
Raman Shift (cm
-1
)
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
1
2
3
4
Current ( A)
Bias Voltage (V)
-80 -40 0 40 80 120
0.0
0.3
0.6
0.9
Kink V
bias
(V)
Substrate Temperature (
o
C)
-185ºC
100ºC
(b) (a)
-40 -20 0 20 40 60 80 100
1568
1572
1576
1580
1584
He
CO
2
Raman Shift (cm
-1
)
Substrate Temperature (
o
C)
1400 1600
Raman Intensity
Raman Shift (cm
-1
)
(c)
39
characteristics. However, this temperature value is not accurate because of the non-equilibrium
phonon populations associated with these devices[5, 6]. Figure 4.7c shows another set of Raman
measurements taken at different substrate temperatures in He and CO
2
gas environments for a
semiconducting nanotube.
0.0 0.2 0.4 0.6 0.8 1.0
0
1
2
3
4
5
6
Current (µA)
V
bias
(V)
CO
2
He
Ar
V
gate
=-3V
0.0 0.2 0.4 0.6 0.8 1.0
0
1
2
3
4
5
6
V
bias
(V)
Current (µA)
CO
2
He
Ar
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
1
2
3
4
Current (µA)
V
bias
(V)
Vg=-3V, Ar
Vg=-2V, Ar
Vg=0V, Ar
Vg=-3V, Vac
Vg=-2V, Vac
Vg=0V, Vac
(a) (b)
Figure 4.8. (a,b) I-V characteristics of two different L=2 μm metallic nanotubes exhibiting different
kink locations for CO
2
, He, and Ar. (c) I-V characteristics of sample in (b) under different applied gate
voltages in Ar and vacuum. Notice the kink behavior towards low bias voltages as more negative gate
voltage is applied in Ar.
40
4.7- The dynamics of the kink in different gaseous environments:
4.7.1 Inert gases in room temperature:
I have specifically chosen inert gases to separate the effect of Van der Waals binding
from any chemical binding which would result in chemical doping of the nanotube and hence, a
change in the Fermi level in the I-V characteristics. To this end, argon, helium, and carbon
dioxide are picked for the measurements. Figure 4.8 (a,b) show the I-V characteristics of two
suspended metallic carbon nanotubes measured in Ar, He, and CO
2
environments at a pressure of
1 atm. The kink bias voltage is highest in CO
2
and lowest in Ar. This trend is observed
consistently on all other samples measured in this study. Here, the samples were first measured
in argon, then helium, and then carbon dioxide. To eliminate any irreversible effects arising from
permanent changes in the nanotube structure (such as defects), the gases are pumped into the
chamber several times in different orders while electrical data are taken, to ensure the
repeatability and reproducibility of these results. Before taking any electrical measurements,
samples are annealed at high bias, beyond the kink, in order to remove any unwanted surface
species from the previously flown gas.
Although there is small variations in the kink’s bias voltage for all measured gases, when
the contact resistance is subtracted from the I-V characteristics (section 4.4), the all kinks line up
at the optical phonon emission voltage (0.2V) suggesting the kink is the onset of the optical
phonon emission as discussed earlier.
41
4.7.2 The abrupt change in the non-equilibrium phonon population:
This kink behavior can be modeled using a Landauer electron transport model together
with a diffusive thermal transport model, coupled through the electron-phonon coupling in this
system. Here, both the electron transport equations and thermal transport equations are solved
self-consistently, as described previously [22, 23, 59]. The negative differential resistance
observed in suspended carbon nanotubes is associated with the emission of optical phonons at
high bias, which eventually decay into acoustic phonons that carry the heat out to the contacts at
the ends of the nanotube. In this model, the non-equilibrium between optical and acoustic
phonons is specified by a non-equilibrium factor α given by:
,
where
,
, and
are the temperatures of the optical phonons, the acoustic
phonons, and the substrate, respectively [21-23]. In this case, the substrate is at room
temperature, giving
. For a constant electric power ( applied to the nanotube, the
spatial temperature profile assumed in the model is calculated by solving the heat diffusion
equation:
where ,
, and , are the cross sectional area, thermal conductivity, and heat transfer
coefficient to the surrounding gas, respectively [8]. We calculate the cross sectional area as
where d is the diameter of the nanotube and δ is the interlayer spacing of graphite. We
also calculate the thermal conductivity of the nanotube as
where
is the room
(4.6)
(4.5)
42
temperature thermal conductivity of the nanotube[23, 62]. In Figure 4.9, we use
W/m·K and d = 2 nm [23]. The non-equilibrium factor, , is directly proportional to the
optical phonon lifetime (τ
op
) [22]. Adsorbed gas molecules enable the optical phonons to decay
into lower energy phonons at a faster rate, compared with vacuum. This change in the decay rate
is associated with a change in the non-equilibrium factor (Δα).
The model consists of two processes describing the thermal and electrical transport. Since
the two processes are coupled through electron-phonon scattering, we must solve these
iteratively, in a self-consistent fashion. The electrical conductance of our devices can be
described as
where λ
eff
is the effective mean free path of an electron, L is the device length, and
is the
derivative of the Fermi-Dirac distribution[25]. The effective mean free path in the nanotube can
be calculated according to Mathiessen’s rule:
(4.8)
(4.7)
dE
E
f
L T E
T E
h
e
R
G
eff
eff
CNT
CNT
) , (
) , (
4 1
2
1
,
1
,
1 1
ems op abs op ac eff
43
where
,
, and
, as described previously[22, 23, 63]. For a constant applied gate
voltage, the Fermi energy level does not change. Hence, equation 4.7 can be simplified to:
(
)(
)
In our fits, we take the room temperature mean free path for acoustic and optical phonon
scattering to be
= 280d nm and
= 15d nm where d is the diameter of the nantube in
accordance with previously published work [6, 21-23, 25, 27, 63]. In order to reproduce the
experimental I-V curves, Equations 4.2 and 4.4 are solved iteratively for each bias voltage in a
self-consistent fashion until the current converges to the experimentally measured value. The
values of the thermal boundary conductance of the gases used in the study were taken from Hsu
et al. [8].
Within this theoretical framework, the sudden drop in current can be explained by a
change in the non-equilibrium factor (α). Figure 4.9(a) shows fits of our I-V data taken in helium
(4.9)
44
above and below the kink. Once the data below the kink is fit to the model, α is varied to achieve
a fit to the high bias data. That is, the only difference between fitting 1 and fitting 2 is the value
of α, which ranges from 2.5 at low bias to 4.2 at high bias for helium. Figure 4.9(b and c) shows
the fits for carbon dioxide and argon, respectively using the same technique adopted for helium.
0.0 0.2 0.4 0.6 0.8
0
1
2
3
4
5
Experiment
Fitting 1
Fitting 2
Current (µA)
Bias Voltage (V)
Ar
0.0 0.2 0.4 0.6 0.8 1.0
0
1
2
3
4
5
6
Current (µA)
Bias Voltage(V)
Experiment
Fitting 1
Fitting 2
CO
2
0.0 0.2 0.4 0.6 0.8 1.0
0
1
2
3
4
5
6
V
bias
(V)
Current (µA)
Experiment
Fitting 1
Fitting 2
He
(a)
Figure 4.9. I-V curve fitting for L=2 µm metallic nanotube using the Landauer model (a) helium,
(b) carbon dioxide, and (c) argon.
(b)
(c)
45
The extracted change in the non-equilibrium factor (∆α) for argon, carbon dioxide, and
helium is 0.8, 1.2, and 1.7, respectively. Table 4.1 shows the extracted ∆α values for several
other samples, determined by fitting the I-V characteristics of each sample. From this Table, the
general trend of
is observed for all nanotubes. The change in the non-
equilibrium factor (Δα), corresponds to an increase in the hot phonon decay lifetime (Δτ
op
),
which leads to increased electron-phonon scattering and a lower electrical current. This gives rise
to the ordering for the change in the optical phonon decay lifetime as (
),
which is the same ordering measured on the ordering of the gases in Table 1. We notice that
neither the change in the optical phonon decay rate nor the kink bias voltage correlate with the
Device Type
∆
(µA)
∆
(µA)
∆
(µA)
∆α
Ar
∆α
CO2
∆α
He
Device 1
L=5µm
QM 0.31 N/A N/A
2 N/A N/A
Device 2
L=2µm
QM 0.26 0.48 0.6
0.55 0.7 1.2
Device 3
L=2µm
SC 0.16 0.2 0.26
0.3 0.6 1
Device 4
L=2µm
QM 0.25 0.55 0.6
0.4 0.55 1.3
Device 5
L=2µm
QM 0.25 N/A N/A
0.5 N/A N/A
Device 6
L=5µm
SC
N/A
0.2 0.25
N/A 1 1.1
Device 7
L=2µm
QM 0.23 N/A N/A
0.35 N/A N/A
Device 8
L=2µm
SC 0.12 N/A N/A
0.5 N/A N/A
Table 4.1. Change in the electrical current (∆ ) observed at the kink in Ar, He,
and CO
2
.
46
molecular mass of these gases or the number of atoms in these molecules, but is most likely
related to the degree to which they couple vibronically to the phonons in the nanotube, which has
not been studied previously.
4.8- Spatial dependence of Raman downshifts above and below the kink bias voltage:
In order to examine the optical phonon dynamics above and below the kink,
spatial
Raman measurements are taken along the length of the nanotube, while the device is biased
above and below the kink bias voltage. Figure 4.10a shows the I-V characteristic of a 2µm
suspended metallic nanotube with the kink occurring in the range 0.6V - 0.7V. Raman data are
taken in three different cases, when the device is unbiased, biased below the kink (V
b
< 0.6V),
and biased above the kink (V
b
> 0.6V). I will sacrifice the spatial resolution for the sake of the
applied bias resolution. Figure 4.10b shows the spatial Raman profile of the G
-
taken for these
cases. When biased above the kink, a uniform Raman downshift is observed, which, if converted
to temperature, a uniform phonon temperature distribution. The non-uniformity of the
temperature across the nanotube suggests that electrons are being transported ballistically into
the nanotube before the application of the kink [64, 65]. The generated hot optical phonons are
being relaxed by gas molecules surrounding the nanotube. Nevertheless, the Raman shift
measured after the kink shows a non-uniform Raman shift (quadratic) indicating diffusive
temperature distribution along the lattice with the center being the hottest spot[30, 63]. The
difference in the Raman shift at the edges of the nanotube is attributed to different thermal
contact resistances. Such a distribution after the kink follows the assumed temperature
distribution for the model used below at high bias voltages. Measurements performed on samples
exhibiting different G band downshift scenarios discussed above show similar behavior. The
47
quadratic temperature profile occurs directly after the onset of the kink. The behavior observed
after the kink at high bias is in good agreement with the discussion above [7].
4.9- Effect of temperature annealing on the I-V characteristics:
Another interesting effect observed on these devices is the absence of this kink in the I-V
characteristics after annealing which takes place at 400
o
C for 40 minutes while running a
constant flow of argon. All devices annealed at that temperature showed similar behavior. Figure
4.11a shows the I-V characteristics before and after annealing. Figure 4.11b shows the
conductance as function of applied gate voltage when a constant bias voltage is applied (V
bias
=30
mV). First, notice after annealing, the maximum current decreases by an amount of 2µA.
0.0 0.4 0.8 1.2 1.6 2.0
1540
1550
1560
1570
Vb=0
Vb=0.6V
Vb=0.8V
Vb=1V
Vb=1.2V
Vb=1.4V
Raman Shift (cm
-1
)
Position (µm)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Current (µA)
V
bias
(V)
Figure 4.10.(a) I-V characteristics of a 2µm nanotube in argon showing NDC after the kink. (b)
Spatial Raman shift mapping for the G
-
phonon mode taken near the electrodes (left and right)
and at the center of the nanotube when the device is unbiased (open red circle) and biased above
(upside green triangle) and below the kink. Linear fit is used to fit the unbiased and before the
kink data while a quadratic fit is used for the data after the kink.
(a)
(b)
48
Accompanied this reduction in current; the kink disappears in the I-V characteristics. Second, the
maximum conductance of the device decreases by half after annealing.
The effect of annealing has been studied by Kane et al. and is attributed to a change in
the contact resistance between the nanotube and the Pt electrodes when the annealing
temperature is < 880K [66]. With this in mind, we can model the I-V before and after annealing.
Figure 4.11c shows the fitting curves along with the measured I-V characteristics before
annealing. The thermal conductivity of this 2µm long nanotube is found to be 2700 W/(K·m),
with
,
, R
contact
=17 KΩ, and a diameter of about 2.5 nm. The
phonon non-equilibrium factor before and after the kink is 2.5 and 3.4, respectively. Figure 4.11d
shows the I-V characteristics after annealing. The same fitting parameters given above are used
to fit the after annealing I-V curve, while taking into account that the contact resistance increases
after annealing (R
contact
= 20 KΩ), the I-V model fails to generate the measured I-V curve.
However, changing only the effective electron mean free path by decreasing
and
to
8nm and 0.2µm, respectively, the I-V curve agrees well. The effect of decreasing the mean free
path of the OP and AC phonon modes after annealing is associated with the increase in the
nanotube resistance which causes an alteration in the measured conductance as figure 4.11b
shows. This effect is also observed on devices having large resistance which is associated with a
small NDC at high bias regime. In these particular devices, the kink does not appear and is more
likely to disappear among all large resistance devices. For large contact resistance devices
(R
contact
~ 1 MΩ), current saturation occurs at high bias. Other devices show a slight NDC at high
bias with a contact resistance in the order of ~200 kΩ. Devices in this study have low contact
49
resistance and are practically rare to grow compared to the ones with large contact resistance.
Therefore, it is believed that the kink only appears for devices that exhibit ballistic transport in
the low bias regime and OP phonon domination at high bias (as discussed in section 4.5).
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
1
2
3
4
5
6
7
Current (µA)
V
bias
(V)
Before Annealing
After Annealing
-6 -4 -2 0 2 4 6
5.0
10.0
15.0
20.0
25.0
30.0
Condutacne (µS)
V
gate
(V)
Befoe annealing
After annealing
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
1
2
3
4
5
6
7
Current (µA)
V
bias
(V)
Fit 1
Fit 2
Experiment
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
1
2
3
4
Current (µA)
V
bias
(V)
Experiment
Fit
(d)
(c)
(b)
(a)
Figure 4.11. (a) Current voltage characteristics before and after annealing at 400
o
C for 40 minutes.
(b) Device conductance before and after annealing (c) I-V curve fitting in argon and before annealing.
(d) I-V curve fitting in argon and after annealing. Notice that the kink disappears after annealing and
the conductance of the nanotube decreased indicating the kink requires high conductance.
50
In order to satisfy the ballistic transport requirement, a typical device should have a low contact
resistance (R
contact
≤60 KΩ). Usually, devices that exhibit steep NDC at high bias (strong OP
emission) should be able to show the kink in the I-V curve.
4.10- Summary:
In summary, I have quantified several aspects of the sudden drop or “kink” in current
observed in the I-V characteristics of individual, suspended carbon nanotubes in gaseous
environments. After subtracting the voltage drop across the contact resistances, the I-V
characteristics of the carbon nanotube reveal that the kink occurs at 0.2V independent of the gas
environment and/or the gate voltage applied. This kink voltage corresponds to the energy of the
optical phonon emission threshold. Raman measurements reveal a sudden downshift in the G
band mode, indicating a sudden increase in the non-equilibrium phonon population. A strong
substrate temperature dependence and gate voltage dependence of the kink bias voltage are
observed. However, the Raman shift at the kink is constant over the measured range of substrate
temperatures, which suggests a constant G band temperature. Using the Landauer formalism, the
kink can be modeled as a change in the non-equilibrium optical phonon population, which
increases dramatically after the kink.
51
Chapter 5
Effect of the Substrate in Determining the Band Gap of
Metallic Carbon Nanotubes
5.1- Introduction:
Metallic carbon nanotubes are known to exhibit small band gaps on the order of 10-
100meV [67]. The origin and magnitude of these band gaps, however, is still a topic of
debate. Early scanning tunneling microscopy (STM) studies of metallic nanotubes
attributed these small energy gaps to the curvature of the nanotube[68]. Tight binding
calculations for armchair and metallic zigzag nanotubes do not predict the existence of a
band gap in the electronic structure [69]. More recent calculations of metallic nanotubes
show a small band gap caused by breaking of the bond symmetry due to curvature [68,
70-72]. Uniaxial strain can also result in a band gap opening in metallic nanotube [73,
74]. These types of symmetry-breaking band gaps (i.e., strain-induced, curvature
induced), however, can be closed with the application of an axial magnetic field. This,
however, was not observed experimentally[67], indicating that another underlying
mechanism is responsible for the observed band gaps. The relatively large band gaps
observed in ultra-clean, suspended small gap metallic (i.e., quasi-metallic) carbon
nanotubes have been attributed to a Mott insulator transition arising from strong electron-
electron interactions[67]. However, this mechanism has not been confirmed by other
experiments, and the exact nature of the Mott state is not known, whether it exhibits a
52
charge density wave, spin density wave, or otherwise [75, 76]. A large suppression of the
Raman intensity has been correlated to the magnitude of the band gap in quasi-metallic
nanotubes, which could result from a lattice distortion induced by a charge density wave
[11]. Another possible mechanism for the observed energy gap is a Peierls distortion[77],
which results from strong electron-phonon interactions. First principles calculations have
predicted a Peierls transition at temperatures as high as 300K [78] for small diameter
metallic CNTs with band gaps in the order of 0.25eV [79]. While a Peierls distortion
would result in a band gap and a large modulation of the Raman intensity through a
lowering of the crystal symmetry, it has been predicted theoretically only in nanotubes
with very small diameters, and is not expected to occur in the relatively large diameter
nanotubes grown in most experimental studies. Several phenomena have been observed
in these ultra-clean, suspended, nearly defect-free, metallic carbon nanotubes near zero
gate voltage, including breakdown of the Born Oppenheimer approximation (BOA)[80],
thermal non-equilibrium phonon populations[6], and large Raman intensity modulations
[11]. Yet, to date, no detailed comparison of these band gaps on- and off-substrate has
been made.
In this chapter, a detailed comparison of CNTs grown on- and off-substrate is studied
in order to quantify the effect of the substrate interaction on the band gap of quasi-
metallic nanotubes. Single wall carbon nanotubes are grown across two sets of electrodes,
resulting in one segment of the nanotube suspended across a trench and the other segment
supported on the substrate, as shown in Figures 5.1a and 5.1b. By comparing the band
gaps of the same exact nanotube on- and off-substrate, I was able to eliminate the
53
variations associated with different nanotube chiralities and growth conditions. The band
gaps is then characterized of these devices by fitting the I-V
gate
characteristics to a
Landauer transport model in order to identify the effect of the substrate on the electronic
properties of quasi-metallic nanotubes. The work in this chapter is published in [56]
5.2- Device Fabrication
Devices in this study are fabricated by first etching a 500 nm deep trench in a Si/SiO
2
/SiN
substrate. Pt electrodes are patterned on top of the substrate using photolithography. Iron
nanoparticle catalyst is then deposited on top of one of the electrodes close to the trench, as
shown schematically in Figure 5.1a. Carbon nanotube growth is carried out at 875
o
C for 15
minutes by flowing a mixture of argon, ethanol, and hydrogen. Figure 5.1b shows a scanning
electron microscope (SEM) image of a final device. The I-V
bias
characteristics of the suspended
CNT device are used to ensure that the device consists of only one nanotube, if the maximum
current (in A) satisfies the approximate relation I
max
~ 10/L, where L is the length of the
nanotube, as established by Pop, et al.[23].
Figure 5.1. (a) Cross-sectional diagram and (b) SEM image of a carbon nanotube sample for comparing
on-substrate and suspended CNT devices.
(a)
drain
Pt 2
source
electrode
Pt 3
CNT
gate
suspended
substrate
source
electrode
Pt 1
(b)
54
5.3- I-V Characteristics of on and off the substrate devices:
Figure 5.2a shows the measured I-V
bias
of a metallic nanotube on and off the substrate.
Negative differential conductance (NDC) appears for the suspended segment due to substantial
heating of the nanotube by optical phonon emission[6, 23].
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
0
2
4
6
8
10
12
14
Suspended
On substrate
Current (µA)
Bias Voltage (V)
-10 -8 -6 -4 -2 0 2 4 6 8 10
0
5
10
15
20
25
30
35
40
Suspended
On substrate
Conductance (µS)
Gate Voltage (V)
-10 -8 -6 -4 -2 0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
1.0
Suspended
On substrate
G/G
max
Gate Voltage (V)
(a) (b)
(c)
Figure 5.2. (a) I-V
bias
characteristics of the suspended and on-substrate regions taken from the
same nanotube. The blue solid curve is measured between electrodes Pt1 and Pt2 in Figure 1a and
the red dashed curve is measured between electrodes Pt2 and Pt3. (b) I-V
gate
characteristics of the
suspended and on-substrate regions. (c) Normalized conductance (G/G
max
) plotted as a function of
gate voltage.
55
The monotonic increase in current observed for the on-substrate segment indicates heat
dissipation to the underlying substrate[28]. Figure 5.2b shows the measured conductance of the
suspended and on-substrate segments plotted as a function of gate voltage. We used the Pt gate
electrode to measure the conductance of the suspended segment while the Si back gate was used
to measure the on substrate segment. For the suspended segment of the nanotube, the measured
conductance drops from 33.1 µS at V
g
=-10V to 5.3 µS at the charge neutrality point, giving a
conductance modulation of ∆G/G = 0.84. Whereas, for the on-substrate segment, the
conductance changes by only ∆G/G = 0.11. In order to illustrate the drastic difference in
conductance of each nanotube segment, Figure 5.2c shows the normalized conductance of each
segment as a function of gate voltage. This difference in conductance is attributed to an effective
reduction of the band gap in the metallic nanotube when it is in contact with the substrate. We
believe the primary effect of the substrate in determining the effective band gap is trapped
charges. Other effects, such as diameter deformation, can also lead to change in the band
gap[81]. However, these changes would result in a decrease in band gap for some chiralities and
an increase for others, which is not observed experimentally.
In order to quantify the changes observed in the effective band gap, we fit the I-V
gate
data
using a Landuaer model, as discussed previously[6]. Briefly, the low bias conductance of the
device can be expressed as:
(
)∫ (
)(
)
(5.1)
56
where λ
eff
is the effective mean free path (given by Matthiessen rule), L is the device length, and
is the derivative of the Fermi-Dirac distribution[25]. Using a hyperbolic energy dispersion
relation, we integrate over the density of states (n) which is given by
∑ |
|
Here, the density of states is zero inside the band gap, E
g
(see figure 5.3d). Figure 5.3a shows a
fit of the suspended I-V
gate
characteristics using this model with E
g
= 100 meV. Using the same
nanotube parameters in the fit (i.e., diameter), the on-substrate data is fitted by decreasing the
band gap of the device to E
g
= 5 meV, as shown in Figure 5.3b.
The Fermi energy in the nanotube is related to the applied gate voltage according to the
following relation [6, 9, 82]:
where E
F
is the Fermi energy, Q is the electric charge on the nanotube, and C is the geometric
capacitance. In our initial fits, the capacitance per unit length was calculated using the formula
C’=2π
r
o
/ln(4h/d
t
), where h and d
t
are the dielectric thickness (1 µm) and the nanotube diameter
(1.3nm), respectively[83]. From the schematic diagram of Figure 5.1a, the gates for the on-
substrate and suspended segments are structurally different. This geometric difference can
significantly affect the capacitive coupling and gating effect. These different geometries result in
capacitance values of 8.05 pF/µm and 20.6 pF/µm for the suspended and on-substrate segments,
respectively. We found that these fits could be improved by decreasing these capacitance values
(5.2)
(5.3)
57
to 7 pF/µm and 10 pF/µm. While these changes in the capacitance improve the fits, they do not
change the value of the band gap, which is strongly affected by the relative value of minimum
conductance ∆G/G. Figure 5.3c shows the Fermi energy plotted as a function of the gate voltage,
using the band gap and capacitance values in Equations 5.2 and 5.3. The Fermi energy of the
-10 -8 -6 -4 -2 0 2 4 6 8 10
16
17
18
19
20
Measurements
Model
Conductance (µS)
Gate Voltage (V)
-10 -8 -6 -4 -2 0 2 4 6 8 10
5
10
15
20
25
30
35
Measurement
Model
Conudctance (µS)
Gate Voltage (V)
-10 -8 -6 -4 -2 0 2 4 6 8 10
-0.6
-0.4
-0.2
0.0
0.2
0.4
Suspended
On substrate
Fermi Energy (eV)
Gate Voltage (V)
-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4
-0.2
-0.1
0.0
0.1
0.2
Energy (eV)
k (nm)
(a) (b)
(c)
Figure 5.3. The measured conductance (open blue circles) fitted to the Landauer model (red curve) for
(a) suspended and (b) on-substrate segments of the nanotube. (c) The relation between the Fermi energy
and gate voltage for the suspended and on-substrate segments. (d) Band structure of the suspended
metallic nanotube showing a 100 meV band gap.
58
suspended segment exhibits significant non-linear behavior due to its relatively large band gap
(E
g
=100 meV), while the on-substrate Fermi energy shows almost linear behavior, as expected
for a metallic nanotube with little or no band gap. In Table 5.1, we list the change in conductance
and band gaps of four samples measured using this approach.
We believe this reduction in the effective band gap is due to localized doping of the
nanotube by trapped charges in the substrate, which results in a spatially varying Fermi energy,
as illustrated schematically in Figure 5.4. This results in an inhomogeneous broadening of the
Fermi energy, as illustrated schematically in Figure 5.4. The spatial variation of the Fermi energy
in graphene on SiO
2
and hexagonal boron nitride has recently been mapped using scanning
tunneling microscopy (STM)[84]. On SiO
2
, the local Fermi energy was found to vary by as much
as 100 meV, which is consistent with our measurements on carbon nanotube devices. It is these
fluctuations in the Fermi energy which have made it difficult to observe the band gap in bilayer
graphene, unless it is deposited on h-BN[85]. The effective band gaps extracted from the
Landauer model are the result of the substrate obscuring the band gap rather than an inherent
modulation of the intrinsic band gap of the nanotube. The appropriate interpretation is that all
metallic carbon nanotubes have large band gaps that are typically obscured by the fluctuations in
the local Fermi energy when supported by a Si/SiO
2
substrate. The large effective band gaps
observed in the conductance of the suspended segment is the breaking of the crystal symmetry
due to curvature. Theoretically, the curvature induced band gap of a 1.3 nm diameter nanotube
has been predicted to lie between 26 and 35 meV [70, 86], which is 3-4 times smaller than the
band gaps reported in Table 5.1 for the suspended segment. This particular region may exhibit
59
curvature induced band gap as a secondary effect but there may be other phenomenon
contributing to the large band gaps, as described in the introduction of this paper.
Device Suspended band
gap (meV)
(ΔG/G
max
)
suspended
On substrate band
gap (meV)
(ΔG/G
max
)
substrate
Device 1 100 0.84 5 0.111
Device 2 90 0.76 14.3 0.28
Device 3 75 0.75 9.6 0.134
Device 4 90 0.82 5.1 0.158
5.4- Suspended nanotubes incased in ice:
Another way to reduce the observed mini gap in quasi-metallic nanotubes is by encasing
the suspended part with ice. This method will eliminate the observation of NDC while showing
current saturation in I-V
b
characteristics at high bias as investigated previously[22]. I was able to
Figure 5.4. Schematic diagram illustrating the spatial fluctuations of the energy bands due to the
trapped charges in the nanotube obscuring the mini-gap.
Table 5.1. The extracted band gap and conductivity modulation of the suspended and on substrate
regions for 4 different samples.
60
encase a quasi-metallic nanotube with ice during cryogenic temperature experiments by
condensing air moisture around the nanotube. Figure 5.5a is an optical image showing the
formation of ice on top of the chip. Figure 5.5b shows the I-V
b
of the nanotube at 300K without
any ice and at 77k when ice formed around the nanotube. As shown in figure 5.2a for substrate
supported devices, the ice encased I-V
b
shows current saturation instead of NDC, indicating the
relaxation of hot phonons caused by ice encapsulation which acts as a heat sink. Figure 5.5c
shows the I-V
gate
for both cases, with and without ice encasing at 77K and 300K, respectively. A
significant reduction to the measured conductrance of the nanotube occurred for the ice encased
case compared to the ice free case. This reduction is attributed to the alteration of the energy
band structure of the nanotube and hence, fluctuations in the Fermi energy. Therefore, I deduce
from these results that no matter what type of substrate the quasi-metallic nanotube is laying on,
an alteration to the nanotube’s band gap will occur. The origin of this reduction is the
modification of the energy band structure causing the effective band gap to reduce significantly.
61
5.5- Summary:
In conclusion, I have characterized carbon nanotube devices with one segment of the
nanotube suspended and the other segment lying on the substrate. The suspended segment shows
a significant change in the conductance (ΔG/G=0.84) as a function of gate voltage, while the on-
substrate segment shows a small change of ΔG/G=0.11. This reduction in band gap is also
observed for ice encased suspended metallic carbon nanotubes. A Landauer model is used to fit
the effective band gap of each segment, resulting in values that range between 75-100 meV for
0.0 0.4 0.8 1.2 1.6 2.0
0
4
8
12
16
20
Current ( A)
Bias Voltage (V)
-10 -5 0 5 10
0
4
8
12
16
20
24
T = 77K ice supported
T=300K freely suspended
Conductance (uS)
Gate Voltage (V)
Figure 5.5. (a) picture showing the formation of ice on the chip as seen from the optical window (b) I-
V
b
characteristics of the suspended quasi-metallic nanotube at 300K (red curve) with no ice and at 77K
(blue curve) when ice formed on the entire chip. (c) I-V
gate
characteristics of the nanotube before (red
curve) and after (blue dots) ice formation.
(a) (b)
(c)
62
the suspended segment and 5-14.3 meV for the on-substrate segment. This change in the effective
band gap is attributed to an alteration in the electronic properties of the nanotube. This effect is
believed to be associated with the trapped charges in the substrate, creating fluctuations in the
Fermi energy. Thus, metallic nanotubes which thought to have no band gap, have an intrinsic
band gap in their electronic properties which is screened out by the effect of the substrate.
63
Chapter 6
Band to Band Tunneling in Metallic Carbon Nanotube pn
devices
6.1- Introduction:
During the past few years, researchers have been trying to push the limits of Moore’s law
by applying different device concepts for optimal device performance. In order for these devices
to compete with the current state-of-the-art silicon technology, a transistor should have a room
temperature sub-threshold swing less than 60mV/decade, On-state current greater than 100mA,
switching voltage below 1.0V (and hence low power), and high I
on
/I
off
ratio with very low OFF-
state current [87]. Engineering such a device with all these requirements is a tremendous obstacle
and still an open area of research.
One proposed mechanism is tunneling field-effect- transistors (TFETs). In these devices,
electrons tunnel through a potential barrier, approximately equals the band gap of the material.
This effect is called Zener Tunneling. Figure 6.1a shows a qualitative comparison of I-V
gate
characteristics between different device mechanisms. In the figure, tunnel field-effect-transistors
show a sub-threshold swing less than 60mV/decade. The steepness in the drain current plotted in
figure 6.1a due to the exponential dependence of the tunneling coefficient on the electric field
according to
(
√
)
(6.1)
64
where the energy barrier is the band gap of the material (E
gap
),
is the Fermi velocity, and is
the applied electric field along the junction. This exponential increase in the current with the gate
voltage makes tunnel field-effect-transistors attractive candidates for the next generation of
devices.
A simple schematic representation of band-to-band tunneling is explained in figure 6.1b.
In this representation, a p-i-n junction is created and an electric field (and hence voltage) is
applied along the junction. At a certain voltage, the electrons start to tunnel through the intrinsic
region where they see the band gap as the potential barrier. The voltage at which electrons start
to tunnel is called zener breakdown voltage. It is worth mentioning that zener diodes exhibit this
effect which has many applications such as voltage reference [88], and temperature calibration
[89].
E
c
E
v
E
fp
eV
E
gap
x
eƐx
d
Figure 6.1. (a) Qualitative analysis of the drain current vs. gate voltage for various device structures.
The inset triangle shows a slope of 60mV/decade for comparison. (b) schematic representation of
band to band tunneling mechanism.
65
Due to their 1-D nature, carbon nanotube pn devices can exhibit ideal diode behavior
with various physical phenomena. The ability to make an electrostatically controllable pn
junction along the length of the nanotube has been studied by several groups [90, 91]. Lee et al.
has shown the first, nearly ideal, diode using suspended semiconducting single wall carbon
nanotube devices [92]. Bosnick et al. has shown avalanche breakdown mechanism for
semiconducting single wall carbon nanotubes [93]. Prior to the work presented in this chapter,
there have been no reports regarding metallic nanotube pn devices, mainly due to the shrinkage
of the band gap when the nanotube is in contact with the substrate as discussed in chapter 5.
6.2- Band-to-Band (Zener) tunneling in small band gap carbon nanotubes:
Carbonaceous materials with a small band gaps such as carbon nanotubes and graphene
nanoribbons can show tunneling mechanism when a pn junction is created. To this end, let’s
discuss the theory of tunneling behind this junction. A schematic diagram of the pn junction
energy band is illustrated in figure 6.1b. By assuming a hyperbolic relationship for the first sub-
band in the energy band structure, the derived Wentzel-Kramer-Brillouin (WKB) band to band
tunneling (BTBT) probability is given by [24, 94]:
[
√
],
where E
gap
is the band gap energy, υ
F
is the Fermi velocity (8.4 × 10
5
m/s) , and Ɛ is the electric
field in the junction and is given by
,
(6.2)
(6.3)
66
where V
bi
is the built-in voltage of the junction, V is the applied bias voltage, and L is the width
of the intrinsic region. Assuming the tunneling current dominates the electron transport, we can
ignore the scattering effects in the channel, Using equation 3.2 along with g(E)∙v = 1/ħ, the
tunneling current is given by,
∫
[
]
,
where V is the applied bias voltage, and F
v
and F
c
are the Fermi Dirac distributions in the valence
and conduction bands, respectively. The term on the right side of equation 6.4 is the landauer
model equation and can be used whenever the applied voltage is larger than the thermal voltage.
6.3- Fabrication of suspended carbon nanotube pn devices:
There are different ways to create a suspended carbon nanotube with a split gate. Lee et
al. has shown embedded gates within the dielectric material, just underneath the source and drain
electrodes [43, 92, 95]. Other groups have a transfer method where, the suspended nanotube is
grown first on a trench, and then a contact mask aligner is used to transfer the suspended
segment to the desired pattern. Unfortunately, this method requires high accuracy of alignment
[96, 97]. Since the yield of suspended carbon nanotubes is low, we need a pattern that can be
fabricated using optical lithography techniques, just as fabricating suspended single walled
carbon nanotubes discussed in chapter 4.
The fabrication process to make pn devices is by first patterning the gate electrodes on
top of a SiO
2
/Si substrate. The separation between the gates varies between 200nm and 2µm. For
the 200nm gate separation, deep UV photolithography is used followed by metal deposition.
(6.4)
67
Then, a 500nm thick SiO
2
is grown followed by SiN growth (100nm thick) on top of the gates.
We then etch these 2 layers to expose the split gates and create the trench. Next, we pattern the
source and drain electrodes followed by metal deposition. The final step is opening catalyst
windows on top of the source and drain electrodes. Unlike the processes discussed above, this
process ensures that the nanotube growth is the last step in the lithography in order to produce
pristine suspended carbon nanotube pn devices. Figure 6.2 shows a step-by-step process
involved in fabricating a carbon nanotube pn device.
Figure 6.2. Fabrication processes involved in fabricating suspended carbon nanotube pn devices.
68
6.4- Band-to-Band (Zener) tunneling behavior in quasi-metallic nanotube pn devices
Due to the pre-existing small band gap in a metallic nanotube, all suspended metallic
nanotubes grown on a split gate structure can show tunneling behavior in the I-V
b
curves.
However, this behavior is only observed in cryogenic temperatures. In figure 6.3b, The
conductance-gate voltage characteristics taken with V
g1
=V
g2
(i.e., three-terminal device
configuration) exhibit a minimum conductance near zero gate voltage, at the charge neutrality
point, as shown in Figure 6.3b. This is typical of suspended quasi-metallic nanotubes and
indicates the presence of a quasi-metallic band gap. Under pn-gating conditions (i.e., V
g1
= -V
g2
)
at room temperature, the nanotube exhibits Ohmic behavior varying between 450.5.kΩ - 2.5MΩ,
as shown in Figure 6.3a. Figure 6.3c shows the current-voltage characteristics of the same quasi-
metallic nanotube gated in the pn-configuration at 4K, which shows rectifying behavior and
reverse breakdown at high negative bias voltages. The different data sets in the plot were taken
under different electrostatic gating conditions ranging from V
g1
=-V
g2
=1 to 5V. In the I-V
bias
curves shown in Figure 6.3c, the current saturation at high bias arises from the finite contact
resistance and optical phonon emission by hot electrons, discussed previously[56]. The reverse
breakdown voltage depends strongly on the applied gate potentials, as plotted in Figure 6.3d,
with the largest reverse breakdown occurring under the weakest gating conditions. Under heavy
gating, the insulating barrier region becomes smaller resulting in lower breakdown voltages. The
forward bias breakdown is also plotted in Figure 6.3d, which follows the same trend as the
reverse breakdown voltage, but is approximately 0.1V lower in magnitude. These reverse
breakdown voltages are much lower than those reported previously on semiconducting nanotube
pn-diodes, which have considerably larger band gaps (E
g
=0.6eV)[93]. Comparing the low bias
69
conductance under pp and pn gating conditions, we observe a 5 order of magnitude change from
6 x 10
-6
S to 3 x 10
-11
S, respectively.
1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0 Forward
Reverse
Breakdown Voltage (V)
V
gate1
= -V
gate2
(V)
-6 -4 -2 0 2 4 6
0
2
4
6
8
Conductance ( S)
V
gate1
= V
gate2
(V)
T=4K
T=300K
-0.4 -0.2 0.0 0.2 0.4
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Current (µA)
Bias Voltage (V)
T=300K
-0.8 -0.4 0.0 0.4 0.8
-2
-1
0
1
Current (µA)
Bias Voltage (V)
V
g1
= -V
g2
=1V
V
g1
=- V
g2
=5V
V
g1
= -V
g2
=1V
V
g1
=- V
g2
=5V
Figure 6.3. Current-bias voltage characteristics taken at (a) room temperature and (c) 4K with
the device gated in a pn configuration (i.e., V
g1
=-V
g2
). Here, no rectifying behavior is observed
at room temperure because of the small band gap. Rectifying behavior is observed at 4K with
tunable forward and reverse breakdown voltages. (b) Current-gate voltage characteristics at
300K showing a minimum near 0V. This dip in the conductance arises from the existence of a
band gap. (d) Forward and reverse bias breakdown voltages observed under different doping
conditions, demonstrating tunability between 1V and 0.2V.
.
(c)
(a)
(b)
(d)
70
In order to establish the breakdown mechanism, we measured the I-V characteristics by
sweeping the voltage in the forward and reverse directions, as shown in Figure 6.4b. Here, no
hysteresis is observed, indicating that this effect is caused by Zener tunneling in the junction
rather than avalanche breakdown, as observed in semiconducting nanotube pn-junctions[93]. A
schematic diagram of the Zener tunneling process is illustrated in the energy band diagram in
figure 6.4a (see section 6.2 for details), where electrons from the p-type valence band tunnel
across the insulating region to the n-type conduction band. Electrons tunneling across the i-
region see a potential barrier ~E
gap
in height. This mechanism is similar to the tunneling observed
in tunnel diodes, except that Zener tunneling occurs at higher bias voltages due to larger barrier
widths[98].
71
Figure 6.4c shows a fit using this Zener model to data taken under V
g1
=-V
g2
=3.5V gating
conditions showing excellent agreement with the experimental data. In our fits, the barrier height
(or band gap), the insulating region length (L), and the built-in voltage (V
bi
), are used as fitting
Figure 6.4. (a) Schematic diagram of the device geometry and energy band diagram illustrating
Zener tunneling (b) Forward and reverse sweeps for a quasi-metallic pn diode, showing no
hysteresis. (c) A fit of the measured rectifying behavior (black circles) to the Zener model (red
curve). (d) The extracted barrier width (L) and the built-in voltage used to fit the measured
rectifying I-V
bias
curves.
0 2 4 6
0.0
0.4
0.8
1.2
Barrier Width (µm)
Gate Voltage (V
g1
= -V
g2
)
0
10
20
30
40
50
Built-in Voltage (mV)
E
gap
= 53 meV
-0.4 -0.2 0.0 0.2 0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
Current (µA)
Bias Voltage (V)
V
g1
=-V
g2
=3.5V
p
n
E
g
SiO
2
Pt
Si
SiN
x
-1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0
-6
-4
-2
0
Current ( A)
Bias Voltage (V)
forward sweep
reverse sweep
(c)
(a) (b)
(d)
72
parameters. The tunnel barrier width and built-in potential from these fits for each of the I-V
bias
characteristics are plotted in Figure 6.4d using the curvature induced band gap of E
gap
=53.4meV
obtained from the identified chirality, as discussed in details in the next chapter. Here, the barrier
width decreases with increasing gate voltage while the built-in potential, correspondingly,
increases with increasing gating. It should be noted that these fits agree well with the
experimental data under high electrostatic doping conditions (i.e., |V
g
|>1V), but not very well
under low doping conditions (i.e., |V
g
|=1.5V, in figure 6.5), most likely due the Schottky barriers
at the electrical contacts, which can significantly affect the transport at low doping[3, 99].
Figure 6.5. Zener model fits for different electrostatic doping conditions (V
g1
=-V
g2
). (a) 1.5V, (b) 2V,
(c) 4V, and (d)5V.
-1.0 -0.5 0.0 0.5 1.0
-0.4
-0.2
0.0
0.2
0.4
Measured
Fit
V
g1
= -V
g2
= 1.5V
Current (µA)
Bias Voltage (V)
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
-0.4
-0.2
0.0
0.2
0.4
Measured
fits Current (µA)
Bias Voltage (V)
V
g1
= -V
g2
= 2V
-0.4 -0.2 0.0 0.2 0.4
-0.4
-0.2
0.0
0.2
0.4
V
g1
=-V
g2
= 4V
Measured
Fit
Current (µA)
Bias Voltage (V)
-0.4 -0.2 0.0 0.2 0.4
-0.4
-0.2
0.0
0.2
0.4
Measured
Fit
Current (µA)
Bias Voltage (V)
V
g1
= -V
g2
= 5V
(c)
(a)
(b)
(d)
73
6.5- Switching between ohmic behavior and rectifying behavior
Along with a tunable rectifying behavior, quasi- metallic nanotube pn devices can show
the transition between ohmic behavior and a rectifying behavior by changing the polarity of one
of the gates. In figure 6.6, the nanotube is gated at V
g1
=V
g2
=-1 V which shows ohmic behavior.
However, by changing the sign of one of the gates (pn junction), we can get a rectifying
behavior. In figure 6.6 a and b, the ratio of the ohmic conductance to the rectifying IV
conductance can reach 1.98 10
5
and 2.8 10
4
for device 1 and device 2, respectively. The
tunable characteristic of these devices can open new potential applications for nanotubes as
switches.
-1.0 -0.5 0.0 0.5 1.0
-1
0
1
2
Current (µA)
Bias Voltage (V)
V
g1
=V
g2
= -1V
V
g1
=-V
g2
= -1V
T=4K
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
-4
-2
0
2
4
V
g1
= -V
g2
= -8
V
g1
= V
g2
= -8
Current (µA)
Bias Voltage (V)
T=4K
4
10 8 . 2
rectifying
ohmic
G
G
5
10 981 . 1
rectifying
ohmic
G
G
Figure 6.6. Tunability between rectifying behavior and ohmic behavior for (a) device 1 and (b)
device 2.
74
6.6 – Anomalous tunable breakdown voltage behavior:
The breakdown voltage dependence on the pn junction has shown 2 opposite trends. One
trend is a decreasing breakdown voltage when the carrier concentration of the pn junction
1 2 3 4 5
0.00
0.02
0.04
0.06
0.08
0.10
0.12
Sample 1 L=4µm
Vbreakdown forward
Vbreakdown reverse
Breakdown Voltage (V)
V
gate1
= -V
gate2
(V)
0 1 2 3 4 5
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Sample 2 L=2.5 µm
Vbreakdown forward
Vbreakdown reverse
Breakdown Voltage (V)
V
gate1
= -V
gate2
(V)
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Breakdown Voltage (V)
V
gate1
= -V
gate2
(V)
Vbreakdown forward
Vbreakdown reverse
Sample 4 L=1.1µm
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
Sample 3 L=1.1µm
Vbreakdown forward
Vbreakdown reverse
Breakdown Voltage (V)
V
gate1
= -V
gate2
(V)
Figure 6.7. Zener breakdown for 4 different samples showing 2 opposite behaviors. Samples in
(a) and (b) exhibit a decrease in the breakdown voltage with increasing homogenous
electrostatic doping conditions, while samples in (c) and (d) show an increase in the zener
breakdown with increasing homogenous electrostatic doping conditions.
(c)
(a)
(b)
(d)
75
increases, just like the case described in the previous section. Figures 6.7a,b show 2 devices
exhibiting this phenomenon. While figures 6.7c,d, show the opposite trend for 2 different
devices. It should be noted that the first 2 devices exhibit different pn junction lengths, while the
ones shown in figure 6.7c,d, have a length of ~1.1µm. However, this may not be sufficient to
conclude that the length of the devices is the cause of these 2 different trends.
One possible reason is the schottky-to-ohmic crossover in the contacts. Briefly, this
model explains that the source exhaustion current, defined as the maximum attained current
which is set by the contacts doping can cause 2 different transitions in the electron transport of
the nanotube[100]. This source exhaustion current depends on the nanotube’s diameter and the
metal work function. However, this phenomenon requires a device with a high schottky barrier
as in the case of semiconducting nanotubes.
Another most likely scenario is that for each case, the nanotube’s energy band is aligned
differently with the metal work function, causing these 2 opposite behaviors to occur. However,
at much higher doping concentrations (V
g1
= -V
g2
>10V) the alignment of the bands for both
cases should show similar trend.
6.7 – Dependence of the breakdown voltage on the conductance band gap
Zener breakdown should strongly depend on the band gap energy, since the zener
transmission coefficient in equation 6.2 is strongly dependent on the band gap. Although the
breakdown voltage in metallic nanotube pn devices exhibits 2 opposite trends as a function of the
electrostatic doping, the maximum breakdown voltage for any given electrostatic doping should
increase with the band gap magnitude. Figure 6.8 shows this dependence where the maximum
76
breakdown voltage attained by any sample, for a given electrostatic doping, increases with the
band gap barrier. The band gap energy magnitude was extracted from the landauer model
described in chapter 3. This strong dependence of the breakdown voltage on the extracted band
gap is clear evidence that the breakdown mechanism is zener tunneling.
6.8- Room temperature carbon nanotube tunnel field-effect-transistor based on pn devices:
The carbon nanotube TFET discussed in section 6.3 operates in cryogenic temperatures
which hinders its integration for future electronic applications. In principle, TFETs should be
able to outperform silicon technology at room temperature. Engineering a carbon nanotube
TFET device with a tunable electrostatic pn junction requires a narrow band gap range. In figure
6.9a and 6.9b, one such device has been measured. This is the only device that can show
0.08 0.12 0.16 0.20 0.24
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Breakdown Voltage (V)
Effective Band Gap (eV)
Figure 6.8. Maximum breakdown voltage measured as a function of the extracted conductance
band gap for six different samples.
77
rectifying behavior at room temperature. What is interesting is the extracted conductance band
gap from fitting the conductance curve (inset of figure 6.9a) is found to be 240 meV.
-2 -1 0 1 2
-8
-6
-4
-2
0
2
4
6
8
10
Current (µA)
Bias Voltage (V)
-8 -4 0 4 8
0.0
0.2
0.4
0.6
0.8
1.0
Current(µA)
V
gate1
= V
gate2
(V)
-1.4 -0.7 0.0
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
Current (µA)
Bias Voltage (V)
-1.6 -1.2 -0.8 -0.4 0.0
1E-10
1E-9
1E-8
1E-7
1E-6
Current (µA)
Bias Voltage (V)
V
g1
= -V
g2
=1V
V
g1
= -V
g2
=9V
(a) (b)
(c) (d)
Figure 6.9. (a) Rectifying behavior observed at room temperature. (b) zoomed-in view of (a)
showing the reverse breakdown voltage. (c) log plot of the current showing regions with steep
slopes. (d) Extracted sub-threshold swing at different electrostatic pn doping concentrations.
0 2 4 6 8 10
0
20
40
60
80
100
120
S (mV/decade)
V
g1
= -V
g2
(V)
0.0
0.3
0.6
0.9
1.2
1.5
V
breakdown
(V)
78
In figure 6.9c and 6.9d, the log plot of the reverse bias and the sub-threshold swing are
shown, respectively. The low doping region is not really interesting since the turn on voltage is
almost zero. However, as the doping concentration increases, the sub-threshold swing decreases
and reaches 20mV/decade for V
g1
= -V
g2
= 9V. This is an improvement by at least 4 times
compared to the low doping sub-threshold swing. It should be noted that this data set was
observed only on one device which exhibits the largest quasi-metallic nanotube band gap
measured in this thesis. Thus, it is depicted that a nanotube with a band gap near 240 meV should
be a good candidate for room temperature TFETs operation.
6.9 – Summary
In conclusion, metallic nanotube pn devices exhibit ohmic behavior at room temperature
due to diffusive transport. However, at cryogenic temperatures (~4K), all metallic nanotube pn
devices show a tunable breakdown voltage. The forward and backward sweeps show that the
breakdown voltage overlap at a specific value, which suggests that the mechanism behind the
breakdown effect is band-to-band (zener) tunneling. By fitting the measured values to a zener
breakdown model, it is found that the built-in voltage increase and reaches values close to the
curvature-induced band gap energy. While the length of the insulating region decreases with
increasing electrostatic doping. Different metallic nanotube pn devices show 2 opposite tunable
breakdown voltage trends. Some samples show an increase in the breakdown voltage with
increasing electrostatic doping, while other samples show a decrease with increasing breakdown
voltage. Quasi-metallic carbon nanotubes with very large band gaps (E
gap
≥ 240meV) can show
79
rectifying behavior with zener breakdown mechanism at room temperature. Such nanotubes have
a sub-threshold swing as low as 20mV/decade which competes with state-of-the-art MOSFETs,
opening doors for future electronic applications.
80
Chapter 7
Photocurrent Generation and Probing the Excitonic
Transitions in Metallic Nanotube pn Devices
7.1- Introduction:
The ability to identify the precise chirality of carbon nanotubes optically has had a
tremendous impact in the field by enabling a direct comparison of theory and experiment[101].
However, there is currently no comprehensive technique to identify the chirality of a nanotube in
a functional device (i.e., field-effect-transistor structures). For metallic nanotubes, Rayleigh
scattering and tunable Raman spectroscopy are the only optical methods able to unambiguously
establish nanotube chiralities. Tunable Raman spectroscopy is difficult to perform on individual
nanotubes, requiring lasers and notch filters to be tuned for each point in the spectrum[102]. This
technique is also limited by the range of the tunable laser, which typically only covers a small
portion of the Kataura plot. Rayleigh scattering requires that the nanotube be suspended over
several tens of microns, and cannot be performed on a nanotube in a field-effect-transistor (FET)
configuration[103, 104]. This has greatly limited our theoretical understanding of nanotube
device physics, particularly for devices that depend sensitively on nanotube chirality, as is the
case in quasi-metallic nanotube devices. For example, even the effect of electrostatic gating on
the optical transitions in metallic nanotubes (e.g.,
) has not been investigated. This work is
published in [105].
81
7.2 –Photocurrent generation in quasi-metallic nanotube pn devices:
Quasi-metallic nanotube pn-devices have the ability to produce a finite photocurrent at
room temperature, even though they do not exhibit rectifying behavior in this temperature range.
Figure 7.1 shows the short circuit current and the open circuit voltage of a 4µm long metallic
nanotube pn device at different incident optical power. A 633nm laser is used as the excitation
source and neutral density filters are inserted to attenuate the laser power. The photocurrent I-
V
bias
were taken in the middle of the nanotube to eliminate any photocurrent due to nanotube-
metal contacts.
-10 -8 -6 -4 -2 0 2 4 6 8 10
-150
-100
-50
0
50
100
150
Current (µA)
Bias Voltage (V)
Dark
0.206 mW
0.685 mW
1.4 mW
3.4 mW
6.9 mW
Vg1= +7V
Vg2= -7V
-10 -5 0 5 10
-150
-100
-50
0
50
100
150
Current (µA)
Bias Voltage (mV)
Dark
0.206 mW
1.4 mW
3.4 mW
6.9 mW
Vg1= -7V
Vg2= +7V
Figure 7.1. Measured current-bias voltage of a qausi-metallic carbon nanotube pn devices
for V
g1
= -V
g2
= 7 and (b) V
g1
= -V
g2
= -7. The nanotube exhibits increasing photocurrent
magnitude with increasing incident laser power.
(a)
(b)
82
Figure 7.2a plots the measured photocurrent at various laser power intensities. A striking
linear dependence of the photocurrent is observed. In order to show the photocurrent is generated
due to the pn junction, a spatial dependence of the photocurrent for a given electrostatic doping
is plotted in the inset of figure 7.2a. In this figure, the maximum photocurrent is detected in the
middle of the nanotnube, indicating a charge separation region.
In order to distinguish the behavior of the photocurrent, a photocurrent map is taken
under all possible electrostatic gating conditions as shown in figure 7.2b. The maximum
photocurrent is observed when the nanotube is doped in either a pn or np configuration (i.e.,
V
g1
=-V
g2
). Although there is some photocurrent in the pp and nn regions, which could be
attributed to photothermoelectric effect, the most dominant effect observed is photovoltaic effect.
These 2 different photocurrent mechanisms will be discussed thoroughly in the next chapter.
0 2 4 6 8
-150
-100
-50
0
50
100
150
PN (V
g1
= -V
g2
= -7V)
NP (V
g1
= -V
g2
= 7V) Photocurrent (nA)
Output Laser Power (mW)
0 1 2 3 4
-5
0
5
10
15
20
Current (nA)
Position (µm)
Figure 7.2. (a) Measured photocurrent as a function of the incident laser power for the
sample in figure 7.1. (b) measured photocurrent for different combinations of gate voltage
1 and gate voltage 2.
(a)
(b)
83
7.3 - Photocurrent spectroscopy and chirality assignment:
Probing the electronic transitions of carbon nanotubes pn devices has been recently
implemented by barkelid et al. They showed that by tuning the laser energy, 2 distinct peaks
appear in the photocurrent spectra which corresponds to the excitonic transitions in
semiconducting carbon nanotubes [40]. Lee et al. showed that the capture cross section and the
quantum efficiency of the nanotube can be calculated from the photocurrent measurements
[106]. Therefore, photocurrent spectroscopy has been an essential tool in characterizing
photodetectors.
Figure 7.3. Photocurrent spectroscopy setup using a lock-in technique.
Fianium
V
b
=0V
84
In this section, the photocurrent spectra were collected using a quasi-metallic carbon
nanotube pn device. The information gathered from the photocurrent spectra can shine the light
on some of the unknown features of this 1-D system. Figure 7.3 shows the photocurrent setup
used in this study. A lock-in technique is used to measure the generated photocurrent where a
Fianium supercontinuum white light laser is the light source in conjunction with a Princeton
Instruments double monochromater. The power spectral density was measured and compared
with the measured photocurrent in order to distinguish the nanotube’s peaks from the laser peaks
Figures 7.4a and 7.4b, under various pn-gating conditions (i.e., V
g1
=-V
g2
). A dominant peak is
observed at 2.14eV corresponding to the
optical transition of the nanotube. This nanotube
also exhibited a radial breathing mode (RBM) in its Raman spectrum at 215.7cm
-1
, which
corresponds to a diameter of 1.05nm by the relation
RBM
=227/d
t
[107]. Together, the nanotube
diameter and the
optical transition enable unambiguous identification of this nanotube
chirality to be (13,1), as shown in Figure 7.4c[108]. As the pn-gate potentials (V
g1
=-V
g2
) are
increased, the
peak shifts upward in energy and increases by a factor of 5 in intensity, as
shown in Figure 7.4d. This relatively small shift could either be due to electrostatic force-
induced strain[109] or band renormalization[110]. Tight binding predicts two
transitions in
non-armchair metallic nanotubes (i.e.,
and
), corresponding to different quantized
circumferential momenta in the zone folding scheme of carbon nanotubes. Here, however, we
only observe one peak at 2.14eV in the photocurrent spectrum, corresponding to
. The
absence of the corresponding
peak at 2.58eV from the photocurrent spectrum is interesting.
In previous tunable Raman studies, the
feature was also missing for small diameter
85
nanotubes d
t
< 1.3nm[108], and was attributed to the nodal nature of exciton-phonon coupling
[108].
T=300K
Photocurrent (pA)
1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
0
200
400
600
800
Photocurrent (pA)
Laser Energy (eV)
205 210 215 220
2.0
2.2
2.4
2.6
E
ii
(eV)
RBM Frequency (cm
-1
)
-4 -2 0 2 4
2.12
2.13
2.14
2.15
2.16
E
11
Energy (eV)
pn Gate Voltage (V
g1
=-V
g2
)
0
300
600
900
Photocurrent (pA)
(13,1)
(13,1)
(12,3)
(12,3)
(8,8)
215.7cm
-1
2.14eV
Figure 7.4. (a,b) Photocurrent spectra taken under different pn gating conditions showing the
evolution of a prominent excitonic peak corresponding to the
metallic transition. (c) Kataura
plot showing unique chiral identification based on the nanotube’s RBM at 215.7 cm
-1
and the
energy at 2.14eV. The intercept identifies a nanotube chirality of (13,1). (d) The
optical
transition energy (red) and photocurrent magnitude (blue) plotted at various electrostatic doping
conditions.
160 180 200 220 240 260 Intensity (a.u.)
Raman Shift (cm
-1
)
(c)
(a) (b)
(d)
86
Figure 7.5 shows additional photocurrent spectra taken from several quasi-metallic
carbon nanotube pn devices. The dominant peak corresponds to the excitonic transition E
ii
of the
nanotube, while the satellite peaks correspond to side phonon bands. It should be noted that the
FWHM of the excitonic transition energies are different for each device due to variations in the
fianium laser bandwidth from day to day. The chirality assignment follows the same procedure
discussed above where
is the only transition observed in the photocurrent spectroscopy
measurements. For nanotubes that did not show any RBM peaks, the expected diameter should
be larger than 1.5nm, and E
22
should fall in the measured wavelength range. For example,
devices in figures 7.5b,c and d have the same growth conditions which has shown to produce
large diameter nanotubes [31]. The observed excitonic transition energies are 2.18eV, 1.91eV,
and 2.24 eV, respectively. A quick check up of the Kataura plot reveals that these transitions
corresponds to large diameter nanotubes with chiral indices (22,13), (28,13), and (25,7),
respectively.
87
1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
-4
-2
0
2
4
800
800
400
0
200
600
V
g1
= -V
g2
(V)
Energy (eV)
800
600
400
200
0
Photocurrent (pA)
1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
0
100
200
300
400
Photocurrent (pA)
Energy (eV)
V
g1
=-V
g2
=1V
V
g1
=-V
g2
=3V
V
g1
=-V
g2
=5V
V
g1
=-V
g2
=7V
1.6 1.8 2.0 2.2 2.4
0.0
0.4
0.8
1.2
1.6
Photocurrent (nA)
Energy (eV)
V
g1
=-V
g2
= 1
V
g1
=-V
g2
= 3
V
g1
=-V
g2
= 5
V
g1
=-V
g2
= 7
800
400
0
200
600
Figure 7.5. (a) Photocurrent spectra map of the sample in figure 7.4 with additional doping
conditions showing a peak occurring at 2.14eV. Additional photocurrent spectra for (b) (22,13) (c)
(28,13), and (d) (25,7). The spectra show the evolution of prominent peaks which are attributed to
E
ii
excitonic transition.
(22,13) (13,1)
(c)
(a) (b)
1.8 1.9 2.0 2.1 2.2 2.3 2.4
0
50
100
150
200
250
Photocurrent (pA)
Energy (eV)
Vg1=-Vg2= 0V
Vg1=-Vg2= -1V
Vg1=-Vg2= -3V
Vg1=-Vg2= -5V
(25,7)
(28,13)
(d)
88
7.4- Summary:
Quasi-metallic carbon nanontube pn-devices produce a finite photocurrent at room
temperature. The generated photocurrent shows a strong dependence on the incident laser power
and the electrostatic doping concentration. The exciton dynamics in such a 1-D structure can be
probed by sweeping the incident laser energy, a dominant
peak is observed in the
photocurrent spectra while the
peak is absent, consistent with previous optical studies. The
electrostatic doping dependence of these photocurrent spectra show an increase in the
photocurrent intensity and a slight upshift of the
optical transition energy under heavily
doped conditions. By knowing the diameter of the nanotube, the chirality can be easily
determined unambiguously. These results demonstrate that quasi-metallic pn-devices may have a
broader impact in optoelectronic devices.
89
Chapter 8
Competing Photocurrent Mechanisms in Quasi-Metallic
Carbon Nanotube pn Devices
8.1- Introduction:
Carbon-based optoelectronic devices have demonstrated extraordinary properties. In
recent years, research has focused on engineering and designing optoelectronics with graphene
and carbon nanotubes devices [47, 91, 111-115]. Gabor et al. showed graphene with a double
gate structure exhibits a photocurrent caused by photothermoelectric effect, in which the optical
excitation creates a temperature gradient at the pn junction interface [116]. The thermoelectric
diffusion of carriers from the hot region to the cold region results in the measuremed
photovoltage/photocurrent. Extensive studies of semiconducting carbon nanotube pn devices
have been carried out, reporting multiple electron-hole pair generation[90], ideal diode behavior
[92], and photovoltaic effect [95].
As discussed in chapter 7, quasi-metallic carbon nanotube pn devices have been shown to
exhibit photocurrent [105]. This photocurrent is substantially large when the nanotube is gated in
a pn and np configurations. By tuning the laser energy, the measured photocurrent spectra reveal
a prominent peak that corresponds to an excitonic transition in quasi-metallic carbon nanotubes.
Barkelid et al. observed photothermoelectric effect in metallic carbon nanotube split
gates [117], where their photocurrent is a strong function of the nanotube’s thermoelectric
power. In the work presented here, we investigate the mechanisms underlying photocurrent
generation in quasi-metallic nanotubes with band gap magnitudes that cover a broad range. We
90
measure the photocurrent as a function of the electrostatic doping concentration. We compare the
measured photocurrent profile in a homogenous pn/np doping to the photothermoelectric model
and the photovoltaic model. We also correlate the photocurrent transport with the measured
conductance and the landauer model extracted band gap.
8.2 –Photothermoelectric effect and photovoltaic effect:
In carbon nanotube devices, there are 2 different photocurrent mechanisms that can
produce a finite photocurrent, photothermoelectric effect and photovoltaic effect.
Photothermoelectric effect occurs when photons excite electrons from the valance band to the
conduction band and then relax back to the Fermi energy in a time scale of picoseconds [118,
119]. The relaxation process is accompanied with phonon emission and causes a fermion
distribution that eventually leads the generated hot-free carriers to diffuse from the hot side to the
cold side (or from the lower density of states to the higher density of states as in the case of
monolayer graphene and bilayer graphene heterostructure [120]). In the case of pn devices, a
temperature gradient is created at the interface of the pn junction, causing carriers to move from
the hot side to the cold side. Figure 8.1a illustrates the process of photothermoelectric effect in
carbon nanotube pn devices. By creating an electrostatic pn junction in the middle segment of the
nanotube, hot and cold sides are created. Inducing optical excitation will lead to hot-free carrier
generation which will diffuse from the hot side to the cold side.
91
Photovoltaic effect arises from the existence of a charge separation in the intrinsic region.
A built-in electric field is set by the pn junction. This built-in electric field, if large enough, can
separate an electron-hole pair when an incident photon is absorbed in the intrinsic region. In 1-D
devices, due to the excitonic nature and the exciton binding energy in carbon nanotube devices,
photocurrent can be substantial whenever the incident photon energy matches an excitonic
transition. Figure 8.1b shows the schematic diagram of the electron-hole pair separation
mechanism. This mechanism has been observed in semiconducting nanotube pn devices [117,
121].
8.3 – Mechanism underlying the origin of the photocurrent in quasi-metallic nanotubes:
Figure 8.2a shows a schematic diagram of the device structure under investigation. The
experimental setup is shown in Figure 8.2b. A 633nm laser is focused in the middle portion of
the nanotube, where the pn junction is located. The photocurrent is measured at the drain
electrode. Figure 8.3a and b show photocurrent maps of 2 different 4µm long CNT devices for
all different gate voltages combinations. We observe 2 different trends. The first trend is shown
in figure 8.2c where the photocurrent magnitude reaches a maximum at low pn/np concentrations
Figure 8.1. (a) Schematic diagram illustration photothermoelectric in carbon nanotube pn
devices. Hot-free carriers diffuse from the hot side (right) to the cold side (left). (b)
Photovoltaic effect schematic showing electon-hole pair separation.
(a) (b)
92
and then decreases with increasing electrostatic doping. In this figure, we notice the 6 fold
pattern which is a clear characteristic of photothermoelectric effect. In figure8.2d, however, a
different trend is observed where the photocurrent reaches a maximum value and saturates with
increasing electrostatic doping. Although there are regions with small photocurrent magnitude
which could be due to the photothermoelectric effect, we attribute the photocurrent mechanism
in the pn and np regions to photoinduced electron-hole pair generation, where a built-in electric
field separates the electron-hole pair causing photocurrent to flow in the nanotube. These 2
different trends are illustrated in figure 8.4 where the photocurrent of a homogenous pn/np
doping is plotted for 4 different devices.
(a)
(b)
Figure 8.2.(a) Schematic diagram of the final device structure. (b) Experimental setup showing
the focused incident laser on the nanotube when it is biased in a pn configuration.
93
The photocurrent for devices 1 and 3 measured in figures 8.4a,c shows a profile similar to
the thermoelectric power profile. This profile is consistent at different optical powers as
illustrated in figure 8.5a. Under the photothermoelectric model, the photocurrent is expressed
as[120]
,
where is the thermoelectric power, is the difference in temperature between the doping
regions, and R is the resistance of the device. The thermoelectric power is given by the Mott
formula according to [122]:
;
where
is Boltzmann constant, T is the temperature, G is the nanotube’s conductance. The
term
is calculated from the measured conductance vs. gate voltage, while the term
is
Device 1
Device 2
(8.1)
(8.2)
Figure 8.3. Photocurrent maps for all different combinations of gate voltages 1 and 2 of (a)
device 1, and (b) device 2.
(a) (b)
94
extracted from the Fermi energy relation to the gate voltage from the Landauer model, which is
given by,
Here
eff
is the effective mean free path for a scattered electron in the system given by
Mathiessen’s rule [20, 56, 123]. The integral is taken over the density of states, which is given by
∑ |
|
,
where the derivative is taken over a hyperbolic dispersion relation with a small band gap. In
figure 8.c the thermoelectric power is plotted for device in figure 8.4c. The measured
photocurrent profile is in excellent agreement with the calculated thermoelectric power,
suggesting that the photocurrent generation is due to photothermoelectric effect.
dE
E
f
L T E
T E
h
e
R
G
eff
eff
CNT
CNT
) , (
) , (
4 1
2
(8.3)
(8.4)
95
-10 -5 0 5 10
-15
-10
-5
0
5
10
15
20
25
Photocurrent (nA)
V
g1
= -V
g2
(V)
-6 -4 -2 0 2 4 6
-20
-15
-10
-5
0
5
10
15
20
Photocurrent (nA)
V
g1
= -V
g2
(V)
-10 -5 0 5 10
-40
-20
0
20
40
Photocurrent (nA)
V
g1
=-V
g2
(V)
-6 -4 -2 0 2 4 6
-10
-8
-6
-4
-2
0
2
4
6
Photocurrent (nA)
V
g1
= -V
g2
(V)
-4 -2 0 2 4
0.0
0.6
1.2
1.8
2.4
3.0
G ( S)
Gate Voltage (V)
-10 -5 0 5 10
0
10
20
30
40
G ( S)
Gate Voltage (V)
-6 -4 -2 0 2 4 6
0
1
2
3
4
5
G (µS)
Gate Voltage (V)
-6 -4 -2 0 2 4 6
0
4
8
12
16
G (µS)
Gate Voltage (V)
Device 1 Device 2
Device 3
Device 4
Figure 8.4. Measured photocurrent at different homogeneous electrostatic pn doping
concentration of 4 different devices. The measured photocurrent shows a non-monotonic
profile for (a) device 1 and (b) device 3. The measured photocurrent saturates for with
increasing electrostatic doping for (b) device 2 and (b) device 4. The insets are the
measured conductance vs. gate voltage of each device.
(c)
(d)
(a) (b)
96
In contrast, figure 8.4b and d show the measured photocurrent for 2 different devices.
The photocurrent reaches a maximum and stays constant for a wide pn/np doping range. Figure
-6 -4 -2 0 2 4 6
-12
-10
-8
-6
-4
-2
0
2
4
Photocurrent (nA)
V
g1
= -V
g2
(V)
-10 -8 -6 -4 -2 0 2 4 6 8 10
-40
-20
0
20
40
Photocurrent (nA)
V
g1
= -V
g2
(V)
Figure 8.5. Photocurrent power dependence for homogeneous pn/np doping of (a) device 3,
and (b) device 4. For each case, the photocurrent reserves its profile for all incident laser
powers. The calculated thermoelectric power of (a) device 3 and (b) device 4. For device 3 the
thermoelectric power profile is in excellent agreement with the measured photocurrent profile.
While for device 4, the measured photocurrent profile does not follow the calculated
thermoelectric power profile,
(a) (b)
-10 -5 0 5 10
-100
-50
0
50
100
150
S ( V/K)
Gate Voltage (V)
-4 -2 0 2 4
-60
-30
0
30
60
90
S ( V/K)
Gate Voltage (V)
(c)
(d)
6.9µW
6.9mW
1.38mW
6.9mW
97
8.5b shows the power dependence of this photocurrent which shows saturation with increasing
pn/np doping concentration for 2 different laser powers. This photocurrent profile (device 4)
does not follow the extracted thermoelectric power plotted in figure 8.5. In fact, the photocurrent
profile is in good agreement with the photoinduced electron-hole pair separation model. This
effect has been observed earlier on suspended semiconducting carbon nanotube pn devices [117].
In this case, the photocurrent is proportional to the conductance of the nanotube according
to[124]
Where the conductivity of the nanotube,
is the nanotube’s cross-sectional area,
is the built-in electric field inside the junction and depends on the doping concentration,
and is the length of the nanotube. The conductance of the nanotube depends on the density of
states as discussed above. However, in a photovoltaic device, the density of states given in
equation 8.5 is also a function of the incident laser energy according to
(
)(
),
where is the quantum efficiency of the nanotube,
is the incident power of the
optical excitation, is the energy of the incident photon for a given wavelength ( ), and is the
carrier lifetime. According to this model, the generated photocurrent magnitude should exhibit
the same profile as the conductance of the nanotube. Since we can experimentally probe the first
sub-band in the density of states, we conclude that the predominant photocurrent mechanism for
a homogeneous pn/np doping is photovoltaic in origin.
(8.6)
(8.5)
98
8.4 – Conductance modulation and the associated mechanism behind the photocurrent:
In order to understand the different competing mechanisms behind the photocurrent
generation in quasi-metallic carbon nanotubes, we show the measured conductance of device 1
and device 2 in figure 8.6a. We notice a large modulation in the conductance of device 2
reaching 90% compared to device 1, which shows a change in conductance up to 30%.The
conductance modulation is strongly affected by the band gap of the nanotube [6, 56]. In this case,
device 2 exhibits a band gap that is 5 orders of magnitude larger than device 1. This anomalously
large band gap is the main reason behind the observation of 2 different photocurrent mechanisms
in quasi-metallic carbon nanotubes. Electron-hole separation requires a relatively large band gap,
in the order of 100meV, to generate enough carriers with a longer lifetime as explained in
equation 8.6. Table 8.1 shows 5 different devices with different band gaps and their associated
photocurrent mechanism observed. In that table, devices with band gaps larger than 75meV are
capable of showing photocurrent saturation with increasing pn/np doping concentrations. This
sets the band gap limit for which photovoltaic effect becomes the dominant photocurrent
mechanism for a homogenous pn/np doping in carbon nanotubes.
-6 -4 -2 0 2 4 6
2.8
3.2
3.6
4.0
4.4
G (µS)
Gate Voltage (V)
Device 1
-6 -4 -2 0 2 4 6
0
2
4
6
8
10
12
14
16
18
G (µS)
Gate Voltage (V)
Device 1
Device 2
Figure 8.6. (a) Measured conductance of device 1 and device 2.(b) a zoomed-in view of device 1
showing the conductance modulation is miniscule due to a small band.
(a)
(b)
99
Device band gap (meV) (ΔG/G
max
) photocurrent
mechanism observed
Device 1 170 0.90% El-hole Sep
Device 2 30 30% PTE
Device 3 180 97% El-hole Sep
Device 4 48 50% PTE
Device 5 75 73% El-hole Sep
8.5 - Summary
Quasi-metallic nanotube pn devices can show 2 different photocurrent trends. For devices
with a small conductance modulation, the photocurrent shows a non-monotonic function for a
homogeneous pn/np doping. The measured photocurrent profile agrees with the
photothermoelectric model as long as the device has a band gap E
gap
≤48 meV. Devices that show
a large conductance modulation, however, the photocurrent saturates to a certain value for a wide
range of pn/np doping concentrations. The associate photocurrent mechanism is photoinduced
electron-hole pair separation (photovoltaic effect), where the photocurrent is mainly dependent
on the nanotube’s density of states. This mechanism dominates the photocurrent transport for
quasi-metallic naontubes with band gaps E
gap
≥75 meV.
Table 8.1. The extracted band gap, conductivity modulation, and the photocurrent
mechanism observed for 5 different devices
100
Chapter 9
Photothermal Self-Oscillations in Suspended
Quasi-Metallic Carbon Nanotube Opto-
mechanical Systems
8.1- Introduction:
The small mass density (μ = 5 ag/μm) and high stiffness (Young’s modulus, E = 1 TPa)
of carbon nanotubes provide a nearly ideal system for high frequency mechanical resonators
[125, 126]. Since their first demonstration by Sazanova et al. in 2004 [126], the frequency and
quality factors of these devices has steadily risen [127-131]. These unique devices have enabled
interesting new phenomena to be studied. For example, Wang et al. were able to resolve subtle
differences in the structural phases of argon atoms adsorbed on the nanotube surface [132]. Also,
optical phonon emission by quasi-ballistic electrons was observed through abrupt changes in the
mechanical resonance frequency at high bias voltages [133]. These devices have demonstrated a
minimum mass resolution of 1.7×10
-24
grams [134, 135], which is several orders of magnitude
below other electromechanical systems. The loss (Q
-1
) in carbon nanotube resonators is
attributed to the scattering of phonons at the contact of the carbon nanotube and the metal
electrodes, which are minimized at low temperatures when there are almost no phonons
populated. High quality factors (~10
5
) have been achieved by exciting these devices with low
power (0.3nW) RF radiation and reading the devices out through Coulomb blockade [135, 136].
While optically driven graphene resonators have been studied since 2007[125], no previous
reports of optically driven CNT resonators has been given.
101
Coupling a mechanical resonator to an optically-resonant cavity can enable several useful
phenomena to be explored, such as self-oscillations, side-band cooling, and quantum zero-point
motion.[137] In fact, photothermal self-oscillations and laser cooling has been already been
achieved in graphene resonators [138]. However, no such functionality has been demonstrated in
CNTs.
In chapter 6, a rectifying behavior of quasi-metallic pn-junctions at cryogenic temperatures
has been demonstrated [139]. I showed that quasi-metallic nanotubes exhibit tunable breakdown
voltage at relatively low bias voltages. This mechanism behind this breakdown is found to be
zener tunneling where electrons tunnel from the pn junction while the nanotube’s band gap is the
tunneling potential.
(a)
(b)
(c)
Figure 9.1. (a) Schematic diagram
showing the metallic carbon nanotube
suspended over a trench. (b) SEM image
of the device structure. The nanotube
location is highlighted in red. (c) thermal
excitation experimental setup, The laser
power is large enough to induce heating
when the nanotube is gated in a pn
junction configuration.
102
9.2 –Oscillations in current-voltage characteristics of quasi-metallic nanotubes pn devices:
Optoelectronic measurements of quasi-metallic carbon nanotube pn devices were taken in
a high vacuum cryogenic chamber while the device temperature is 4K. Figure 9.1a and 9.1b
show a schematic diagram of the device geometry used in this study and the SEM image of the
final device structure, respectively. In the figures, the two gate electrodes are positioned beneath
an individual, suspended quasi-metallic carbon nanotube in order to electrostatically create p-
and n- regions. A 633nm laser is focused on the middle segment of the nanotube, where the pn
junction is located. The focused laser intensity is larger than 1mW in order to induce pressure
radiation force. Figure 9.1c shows a schematic of the experimental setup.
Figure 9.2 a and c show the I-V characteristics of a suspended quasi-metallic pn-junction
gated with V
g1
= -V
g2
= 9V. The dark I-V curve shows rectifying behavior with Zener breakdown
under a reverse bias of -1.2V, consistent with our previous work on Zener tunneling [139]. The
inset shows the I-V
g
characteristics taken with V
g1
=V
g2
showing a large modulation of the
conductance, indicating a relatively large band gap for this quasi-metallic nanotube [56]. The red
curve in Figures 9.2a and 9.2c show the I-V characteristics taken under illumination with 6.9mW
laser light focused to a 1µm spot. Under laser illumination, clear oscillations can be seen in the I-
V curve with a period of approximately 14mV. These oscillations were observed while sweeping
the bias voltage in short integration mode (~0.1538mV/msec), and correspond to a time-varying
oscillation rather than voltage-dependent oscillation (e.g., Coulomb blockade). Data from
another suspended CNT pn-device is shown in figure 9.2b and d. After considering several
schemes including Coulomb blockade and photo-assisted tunneling between n- and p-quantum
dots, I believe these oscillations arise from photothermal self-oscillations, which I am observing
in the I-V characteristics simply because we are sweeping the voltage at a constant rate.
103
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2
-1.8
-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
dark
6.9mW
Current ( A)
Bias Voltage (V)
-1.2 -0.8 -0.4 0.0 0.4 0.8
-0.8
-0.4
0.0
0.4
0.8
Current ( A)
Bias Voltage (V)
dark
6.9mW
-10 -5 0 5 10
0.0
0.2
0.4
0.6
0.8
1.0
Current ( A)
V
gate1
=V
gate2
(V)
(a)
(c)
-120 -80 -40 0 40 80 120
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
Current (µA)
Bias Voltage (mV)
dark
6.9mW
V
g1
=-V
g2
= -2.5V
0 20 40 60 80 100
0
100
200
300
400
500
Current (nA)
Bias Voltage (mV)
dark
6.9mW
-10-8 -6 -4 -2 0 2 4 6 8 10
0.0
0.2
0.4
0.6
Current ( A)
V
gate1
= V
gate2
(V)
(b)
(d)
Figure 9.2. I-V
bias
of a quasi-metallic carbon nanotube with and without thermal
excitation for (a) device 1 (c) device 2. The inset shows the conductance of each device at
various gate voltages. A zoomed-in view of the induced current oscillations showing the
periodicity of the oscillations for (b) device 1 (d) device 2.
104
Figure 9.3a shows the time dependence of the electric current taken at a fixed bias
voltage of -1V. Here, a sinusoidal time varying signal can be seen with a period of oscillation of
628 msec, as determined by taking a Fourier transfer shown in Figure 9.3b. A low pass filter is
used to eliminate any high frequency noise. The measured time scale is consistent with the
scanning rate and periods observed in the voltage sweeps of Figure 9.2.
Figure 9.4a shows the temperature dependence of the I-V characteristics measured
without illumination. Here, the rectifying behavior subsides for temperatures above 10K. Figure
4b shows the I-V characteristics taken on the same sample with 6.9 and 17mW of laser power.
The striking similarity of these two datasets indicate that the the origin of these oscillations is
indeed, photothermal effect. Furthermore, 6.9mW is extremely high laser intensity, and causes
1 2 3 4 5
0
1
2
3
Amplitude
Frequency (Hz)
Figure 9.3. (a) Current dependence of the thermal oscillations as a function of time
showing a sinusoidal like wave. (b) Fast Fourier Transform of the data in (a) showing the
dominant peak happens at 1.59 Hz.
(a)
(b)
0 2 4 6 8 10
-0.35
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
Current (µA)
Time (s)
T= 4K V
b
=-1V
105
significant heating in the nanotube, which usually burns the nanotube at room temperature. It is,
therefore, inconceivable that substantial heating is not taking place in these devices. Figure 9.4c
shows the doping concentration dependence of the oscillations magnitude. As illustrated, the
oscillations magnitude becomes pronounced with increasing doping concentration.
-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15
-0.4
-0.2
0.0
0.2
0.4
Current (µA)
Bias Voltage (V)
Dark
6.9mW
17mW
-0.2 -0.1 0.0 0.1 0.2
-0.5
0.0
0.5
Current ( A)
Bias Voltage (V)
T=20K
T=10K
T=4K
T=300K
-100 -50 0 50 100
-0.5
0.0
0.5
Current (µA)
Bias Voltage (mV)
Vg1=-Vg2=-3 dark
Vg1=-Vg2=-3 6.9mW
Vg1=-Vg2=-2.5V dark
Vg1=-Vg2=-2.5V 6.9mW
(a)
(b)
Figure 9.4. (a) Temperature dependence of the I-V
bias
curves demonstrating zener tunneling is
very sensitive to temperature and occurs at T~ 4K. (b) I-V
bias
in dark and under thermal
excitations with 633nm laser. The measured laser power is 6.9mW (blue curve) and 17mW (red
curve).(c) gate voltage dependence of the oscillations showing change of magnitude of the
oscillations with the doping concentration. (d) Schematic diagram showing thermal self-
oscillations of the nanotube for node (red nanotube) and anti-node (blue nanotube).
(c) (d)
106
The photothermal self-oscillation mechanism proceeds as follows: The bottom of the
trench forms an optical cavity with an anti-node (maximum). Optical heating causes thermal
contraction (negative TEC), which in turn moves the CNT out of anti-node (maximum field
intensity). When the nanotube cools to a lower temperature, it expands and returns to the
maximum field intensity anti-node where it is optically heated once again, and so on. This is
depicted schematically in Figure 9.4c.
9.3 –Coupling of Zener tunneling model with thermal oscillations:
In order to further understand the underlying mechanism of these oscillations, we put
together a model that couples the heating effect with the zener tunneling model. Briefly, the
zener tunneling model occurs when electrons in the valence band of the p-type region tunnel
across the band gap (E
gap
) to the conduction band of the n-type region [105]. The WKB
tunneling probability is given by
[
√
],
where is the electric field in the junction which depends on built-in voltage and the tunneling
length. The I-V characteristic can be found by calculating the total current according to.
∫
[
]
,
where F is the Fermi Dirac distribution (temperature dependent) and V is the applied bias
voltage. Figure 9.5b shows the I-V curves for a nanotube that is thermally oscillating between
two different temperatures (200K and 350K) calculated using the Zener model. The result of
these calculations is in excellent agreement with the experimental data (figure 9.5a).
(9.1)
(9.2)
107
The acute temperature sensitivity of the Zener tunneling enables us to read out these
temperature oscillations electronically. However, it is not clear why the frequency of oscillation
so low. One possible reason is that the thermal time constant of these devices lies in the GHz-
THz frequency range, and the mechanical resonance frequency ranges between 10-100MHz for
1µm long suspended CNTs.[140] Here, we are clearly driving these oscillations off of resonance.
Similar slow periods of oscillation have been reported in optomechanial systems [141]. If our
resonator has a natural resonant frequency of 1MHz and a Q-factor of 10^6, the ring-up and ring-
down time scale would be on the order of a second [142].
While this argument is plausible, no Q-factors of 10
6
have ever been reported in CNT
resonators. Alternatively, these low frequency oscillations could be the result of opto-mechanical
mode mixing of the ground state and exited state modes. These modes are typically orthogonal in
frequency, however, due to their non-linear anhamonicity, they have slightly different
-100 -50 0 50 100
-0.5
0.0
0.5
Current (µA)
Bias Voltage (mV)
Vg1=-Vg2=-3 6.9mW
-0.3 -0.2 -0.1 0.0 0.1 0.2
-8
-6
-4
-2
0
2
4
6
8
Current (µA)
Bias Voltage (v)
Figure 9.5. (a) Measured current oscillations under 6.9mW of 633nm. (b) Zener tunneling
model I-V
bias
curves when the nanotube oscillates between 200K and 350K.
(b) (a)
108
frequencies, especially when driven strongly, resulting in beating at low frequency. Thi type of
beating could easily produce oscillations on the order of 1second.
9.4 – Summary:
Photothermal self-oscillations are observed in individual suspended quasi-metallic carbon
nanotubes (CNT) irradiated with intense focused CW light (6.9mW). The bottom of the trench
forms an optical cavity with an anti-node (maximum). Self-oscillations ensue from the optical
heating of the nanotube, which causes thermal contraction (negative TEC), which in turn moves
the CNT out of anti-node (maximum field intensity). When the nanotube cools to a lower
temperature, it expands and returns to the maximum field intensity anti-node where it is optically
heated once again, and so on. The oscillations in the nanotube temperature are observed in the I-
V characteristics of the CNT, which is electrostatically gated in a pn-junction configuration. Due
to the QM-CNTs small band gap, this pn-junction only shows rectifying behavior at low
temperatures near 4K. Upon heating, the I-V characteristics evolve from rectifying to “S” shape
curves. Here, oscillations in the electric current are observed due to the time varying optical
heating, which results in wiggles in the I-V characteristics of the CNT. Fixing the bias voltage at
-1V, I observe a time varying change in the electric current with a period of 628 msec.
109
Chapter 10
Conclusion and Future Outlook
10.1- Terahertz emission and detection with quasi-metallic carbon nanotube pn devices:
One of the advantages quasi-metallic carbon nanotube exhibit is this range of band gap
energies which can be used for optoelectronics in the terahertz/near infrared regimes. That is, the
band gap of quasi-metallic carbon nanotubes falls in the range of 10-240meV which corresponds
to a frequency range of (2.4 THz-58 THz). Quasi-metallic carbon nanotube pn devices offer the
advantage of detecting THz radiation that falls in that regime.
Careful engineering of a photodetector based on a pn junction requires band gap energies
less than the incident photons energy. In principle, quasi-metallic nanotube pn devices, if biased
under the right conditions, can emit THz-Far IR range. It would be interesting to fabricate and
test a device that is electrically biased and emits in the aforementioned range.
Figure 10.1 (a) Suspended carbon nanotube pn device structure, and (b) schematic diagram of
the light emission process of a suspended CNT pn-junction device.
S D
n p
e
+
e
-
ħω
(a) (b)
110
10.2- Near infrared (IR) photocurrent spectroscopy:
Although in this thesis, the photocurrent spectroscopy is discussed, the near IR
measurements show interesting peaks that still unidentified. In figure 10.2a, the photocurrent
measurements in the near IR for the nanotube in figure 10.2b is shown. After normalizing the
photocurrent magnitude to the fianium laser spectral curve, 2 distinct peaks arise from the
nanotube. These peaks exhibit photocurrent magnitude less than the main excitonic transition
E
11
. It would be interesting to identify the origin of these peaks and what they could correspond
to.
10.3- high frequency NDC based oscillator:
The negative differential conductance can be used to engineer a circuit that outputs an ac-signal
by canceling output impedance of the nanotube device. That is, the negative resistance needs to
0.8 1.0 1.2 1.4
0.0
0.5
1.0
1.5
2.0
2.5
Normalized Photocurrent(nA) / photon
Energy (eV)
0.8 1.0 1.2 1.4
0
70
140
Fianium
CNT
Photocurrent (pA)
Energy (eV)
Vg1=-Vg2=-5V
Vg1=-Vg2=-4.5V
Vg1=-Vg2=-4V
Vg1=-Vg2=-3.5V
Vg1=-Vg2=-3V
Vg1=-Vg2=-2.5V
Vg1=-Vg2=-2V
Vg1=-Vg2=-1.5V
Vg1=-Vg2=-1V
Vg1=-Vg2=-0.5V
Vg1=-Vg2=0V
CNT
0.0
0.1
0.2
0.3
Fianium PSD
Figure 10.2. (a) Measured photocurrent and (b) normalized photocurrent in the near infrared
regime for (13,1) nanotube shown in figure 7.5a.
(a) (b)
111
be canceled out as well as the imaginary part of the output impedance by appropriately designing
and optimizing the parameters of the circuit. It is a challenging experiment to perform since
suspended carbon nanotube field-effect-transistors exhibit different negative resistance values,
which makes it hard to fabricate such a device.
To this end, an accurate model of the nanotube device is essential. One possible approach
is to use high frequency suspended carbon nanotube devices investigated by Tuo and Amer et al
[15]. The device structure is shown in figure 10.4a where the nanotube is impedance matched
using a tapered transmission line fixture on a high resistivity silicon substrate. The circuit
diagram is shown in figure 10.4b. One can find the input resistance and calculate the gain of the
circuit in order to manipulate the circuit by adding the appropriate elements for AC oscillation.
Figure 10.3. Schematic diagram of self-sustaining oscillator.
Figure 10.4. (a)Schematic diagram of a tapered transmission line fixture. (b) Circuit model of
the nanotube device.
(a) (b)
112
10.4- Conclusion and final remarks:
Quasi-metallic carbon nanotubes are one of the few materials that has potential future
applications. The high electronic performance and the different types of phenomena, which
quasi-metallic nanotubes exhibit, promise a near future implementation in various applications.
The negative differential conductance and the high mobility are one of those properties needed to
enhance the performance of current integrated electronics, which has potential applications in
nano-electronics.
In light of this thesis, a sudden drop in current (kink) is observed in the current-voltage
characteristics of suspended carbon nanotube devices. The kink in the I-V
bias
is one of the clear
indications of the qausi-ballistic electron transport nature in a 1-D device. This kink is found to
be the threshold of the optical phonon emission. The kink dynamics changes with different
ambient gases. That is, the kink magnitude changes with different gases due to how gas
molecules interact with the nanotube’s optical phonons.
Although quasi-metallic carbon nanotubes have a mini-gap which is observed by the
modulation of the nanotube’s conductance, it is affected once the nanotube is in contact with a
substrate. Suspended devices show a large modulation in the conductance compared to devices
that are in contact with the substrate. The trapped charges in the oxide causes the diminishing of
the intrinsic band gap by creating puddles of n and p type charges along the length of the
nanotube, causing a miniscule modulation in the conductance for on-substrate devices. Thus,
nanotubes are extremely sensitive to the surrounding environment. Careful considerations should
be given in order to account for the environmental effects that may significantly alter the
expected performance.
113
Creating a pn junction along the length of the nanotube has been a challenge. However,
the benefits from an electrostatically tunable carbon nanotube pn junction are tremendous due to
their 1-D nature and the excitonic nature of optoelectronics based on carbon nanotubes. In this
thesis, quasi-metallic carbon nanotube pn devices are fabricated. When biased in a pn
configuration, no rectifying behavior is observed at room temperature. However, at cryogenic
temperatures, the nanotube shows a striking rectifying behavior with a sub-threshold swing in the
order of 1mV/decade and a tunable breakdown voltage at various electrostatic doping
concentrations. The mechanism behind the breakdown voltage is zener tunneling breakdown
where electrons tunnel through a potential barrier set by the nanotube’s band gap. The
breakdown voltage is strongly dependent on the nanotube’s band gap, which is clear evidence
that the mechanism behind the breakdown voltage is zener tunneling. The extracted band gap
from the zener tunneling fits agrees with the curvature induced band gap while the extracted
band gap from the conductance fit over estimates the nanotube’s band gap. The reason behind
this discrepancy is still a subject of research but a possible reason is the existence of a Mott state
in carbon nanotubes.
Optoelectronics based on quasi-metallic carbon nanotubes have shown interesting results.
These devices can generate photocurrent at room temperature once excited with an optical
source. Photocurrent spectroscopy reveals a prominent peak which corresponds to E
ii
excitonic
transition. Diameter information such as RBM peak can provide the exact chirality of the
nanotube. Under the work of this thesis, I have found a technique that determines the chirality of
the nanotube unambiguously at room temperature in a functional device for the first time. The
fundamental origin of the generated photocurrent in these devices has shown 2 competing
mechanisms, devices with a band gap less than 48 meV can show photo-thermoelectric effect,
114
where most of the generated photocurrent is caused by the difference in the seebeck coefficient
between the p and n regions. However, devices with a band gap close to or larger than 75meV
show a photovoltaic effect, where most of the generated photocurrent is due to photo-induced
electron-hole pair separation due to the built-in electric field in the junction. Finally, the opto-
mechanical action of carbon nanotubes is a hot topic for the last few years. The ability to drive
the nanotube’s resonance frequency optically has been a challenging task. However, coupling the
zener effect with the opto-mechanical system, where the nanotube is suspended over an optical
cavity, shows oscillations in the order of milliseconds. The reason behind the low frequency
oscillation is still unclear. Therefore, further high frequency investigation is required in order to
understand the physical properties behind this opto-mechanical system.
115
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Abstract (if available)
Abstract
Electronic devices have become the backbone of our daily life usage. In recent years, new types of electronics have emerged such as wearable electronics, flexible electronics, and optoelectronics. In particular, the idea of converting light into electricity with high efficiency, by carefully engineering the device structure, has become an active area of research. In this thesis, carbon nanotube electronic and optoelectronic devices are investigated which are based on suspended quasi‐metallic carbon nanotubes. These quasi‐metallic nanotube electronics exhibit semi‐ballistic electron transport at room temperature, which gives them high sensitivity to gaseous environment. Once the nanotube is in contact with a substrate, the mini‐gap in their energy band structure diminishes due to fixed charges in the oxide. Moreover, quasi‐metallic carbon nanotube tunnel field‐effect‐transistors (TFETs) using an electrostatically tunable pn junction are engineered and studied. Although these devices do not show any diode behavior at room temperature, they show a finite photocurrent due to the existence of a space charge region. At cryogenic temperatures, these transistors show a tunable band‐to‐band (zener) tunneling with sub‐threshold swing ~1mV/decade. At room temperature, these devices can produce photocurrent upon light exposure. The mechanism underlying the generated photocurrent in these devices reveals two different mechanisms. Devices with small band gaps (Egap < 75meV) exhibit photothermoelectric effect, while devices with larger band gaps, photo‐induced electron hole separation by a built‐in electric field (photovoltaic effect) dominates the photocurrent transport. Upon photothermal heating of these devices at cryogenic temperatures, an oscillatory behavior occurs in the current‐voltage characteristics with a very low frequency of oscillation. This oscillatory behavior is found to be caused by opto‐mechanical action where the nanotube is thermally coupled to an optical cavity.
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Creator
Amer, Mohammed Reda
(author)
Core Title
Electronic and optoelectronic devices based on quasi-metallic carbon nanotubes
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Electrical Engineering
Publication Date
08/18/2014
Defense Date
08/11/2014
Publisher
University of Southern California
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Tag
band gap energy,carbon nanotube,carbon nanotube field‐effect transistor,carbon nanotube resonator,electron transport,metallic,OAI-PMH Harvest,photocurrent,photothermal oscillations,photothermoelectric effect,photovoltaic effect,pn junction,semiconducting,thermoelectric transport
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), Zhou, Chongwu (
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Tags
band gap energy
carbon nanotube
carbon nanotube field‐effect transistor
carbon nanotube resonator
electron transport
metallic
photocurrent
photothermal oscillations
photothermoelectric effect
photovoltaic effect
pn junction
semiconducting
thermoelectric transport