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Semiconductor devices for vacuum electronics, electrochemical reactions, and ultra-low power in-sensor computing
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Semiconductor devices for vacuum electronics, electrochemical reactions, and ultra-low power in-sensor computing
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Content
Semiconductor Devices for Vacuum Electronics, Electrochemical Reactions, and Ultra-low
Power In-sensor Computing
By
Ragib Ahsan
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfilment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
August 2023
© Copyright 2023 Ragib Ahsan
ii
To my family and friends
iii
Acknowledgements
Back in August 2018, when I first started as a PhD student, I had no idea what it would mean to
take the journey of PhD. I was here because nothing else was interesting enough for me at that
time and I needed to challenge myself with something new. And fast forward to 2023, this PhD
has challenged me in ways that I could not have perceived. The greatest accomplishment I have
had during my PhD journey is probably not any paper or any award, it is my ability to think
critically. And if I had to single out one person who played the most important role in this process,
it would be Professor Kapadia. His ideology about research has resonated with mine from the very
beginning and shaped mine in many ways. I think I learned a lot more disagreeing with him rather
than just blindly following his directions. At times, he would ask me to do things in a certain way
while I was hellbent on a different way. I would eventually realize why my way would not work
and why his was better. But I think what was important is the support I had from him while I was
figuring things out for myself. He has been a great mentor and advisor who entertained all my
stupid ideas until the law of large numbers kicked in and a good idea popped up eventually. This
whole process let me evolve as a researcher and shaped me into the person I am today. For that I
am eternally grateful to Professor Kapadia.
In addition to research, I would like to acknowledge three professors here at USC who I believe
had a big impact on how I think about problems. First, I would like to thank Professor AFJ Levi
for the quantum mechanics course (EE 539) that he taught. There are many different ways of
learning QM, but his was the one that helped me most as an electrical engineer. Second, I would
like to thank Professor Aluizio Prata for two electromagnetics courses (EE 470 and EE 570). EE
570 was the hardest course I have ever taken and I am proud that I could learn a little bit of EM in
this process. Third, I would like to thank Professor Armand Tanguay who taught the optics course
iv
(EE 529). I have had countless chats with him standing in the hallway of Seaver Science Center
5
th
floor. I hope all these professors keep me in their memory as the student who kept asking them
stupid questions all the time.
I want to acknowledge the wonderful professors with whom I have worked at USC: Professor
Michelle Povinelli, Professor Jayankanth Ravichandran, Professor Steve Cronin, Professor Joshua
Yang, Professor Peter Beerel, Professor Hossein Hashemi and all their students who helped me in
carrying out research. I am also grateful for the opportunity I had to work with different professors
outside of USC: Professor John Booske, Professor Siddharth Karkare, Professor Peng Zhang.
I have had an opportunity to work with many students in our research group and others over the
past years. Two people who have been the most inspiring and helped me the most would be Hyun
Uk Chae and Dr. Jun Tao. During the peak covid time, we were the only three students in the group
and they helped me through a lot of difficult times: professionally and emotionally. I would like to
thank Dr. Fatemeh Rezaeifar for being my first mentor from whom I learned a great deal of
experimental work. Looking back, Dr. Debarghya Sarkar was one of the most hardworking people
I know who taught me a good deal about how to be more professional with my work. I want to
thank my junior colleagues Atiyeh Abbasi, Juan Sanchez-Vazquez, Anika Tabassum Priyoti, Zezhi
Wu who all helped me do a lot of the work and helped me grow as a mentor.
Finally, I would like to thank my family members and my friends for all the support they showed
me over the years. Special thanks goes to my mother Ferdousi Begum and my wife Jaimun
Chowdhury who have been my rocks throughout the journey.
v
Table of contents
Dedication……………………………………………………………………………………..ii
Acknowledgements…………………………………………………………………………..iii
List of tables………………………………………………………………………………….ix
List of figures………………………………………………………………………………….x
Abstract……………………………………………………………………………………xxiii
1. Chapter 1: Introduction………………………………………………..…………………..1
1.1 Motivation……………………………………………………………………………..1
1.2 Electron emission devices……………………………………………………………..2
1.3 Electrochemical reactions with hot electrons………………………………………….3
1.4 Ultra-low power in-sensor computing with oscillators………………………………..3
2. Chapter 2: Waveguide integrated graphene photocathodes………………………………6
2.1 Introduction……………………………………………………………………………6
2.2 Hot electron emission processes in waveguide integrated graphene…………………...7
2.3 Waveguide integrated graphene photoemitter and experimental results………………8
2.4 Theoretical analysis of experimental results………………………………………….14
2.5 Comparison with literature…………………………………………………………...16
2.6 Methods: Fabrication and measurements…………………………………………….18
2.7 Electron emission calculations……………………………………………………….24
2.8 Monte Carlo simulation comparisons………………………………………………..36
vi
2.9 Heating of graphene………………………………………………………………….40
3. Chapter 3: Performance limits of graphene photoemitters………………………………..43
3.1 Introduction…………………………………………………………………………..43
3.2 Performance limits of hot electron emission from graphene…………………………43
3.3 Hot electron emission mechanisms in graphene……………………………………..45
3.4 Scattering and tunneling rates………………………………………………………..46
3.5 Results from MCBTE solver…………………………………………………………48
3.6 Emission current model………………………………………………………………49
3.7 Calculation and analysis……………………………………………………………...51
3.8 Experimental roadmap……………………………………………………………….56
3.9 Methods: Simulations………………………………………………………………...60
4. Chapter 4: Hot electron driven hydrogen evolution at gold surfaces……………………...69
4.1 Introduction……………………………………………………………………..........69
4.2 Hydrogen evolution cathode………………………………………………………….70
4.3 Experimental device and measurements……………………………………………...70
4.4 Tafel slope analysis…………………………………………………………………...75
4.5 Control measurements………………………………………………………………..78
4.6 Theoretical analysis…………………………………………………………………..85
4.7 Fabrication and measurement methods……………………………………………….88
4.8 Control devices……………………………………….……………………………..100
4.9 Monte Carlo simulation……………………………………………………………..109
5. Chapter 5: Hot electron driven hydrogen evolution at graphene surfaces……….............121
5.1 Introduction…………………………………………………………………………121
vii
5.2 Hydrogen evolution cathode…………………………………………………...........122
5.3 Device description and experimental results………………………………………..124
5.4 Theoretical analysis…………………………………………………………………135
5.5 Fabrication methods………………………………………………………………...139
5.6 Measurement details………………………………………………………………...140
5.7 Monte Carlo simulation……………………………………………………………..145
5.8 Quantum capacitance of graphene…………………………………………………..151
6. Chapter 6: Ultra-low power parallel computing with oscillatory retinal neurons……….156
6.1 Introduction…………………………………………………………………………156
6.2 Oscillatory retinal neurons…………………………………………………………..157
6.3 Photodetector with NDR…………………………………………………………....158
6.4 Frequency multiplexed computing with ORN………………………………………161
6.5 Experimental results on image processing………………………………………….163
6.6 Image classification with ORN……………………………………………………..168
6.7 Comparison with literature………………………………………………………….169
6.8 Methods: Fabrication and experiments……………………………………………...172
6.9 NDR mechanism…………………………………………………………………....174
6.10 Functions implemented by a single ORN………………………………………….183
viii
6.11 Comparison between different optical intensity ranges……………………………187
6.12 Processed images for a 10x10 kernel………………………………………………188
6.13 Readout layer………………………………………………………………………188
6.14 LSM details………………………………………………………………………..189
6.15 Energy calculation for peripheral circuit…………………………………………...191
ix
List of tables
4.1 Sheet Resistance (Rs) and Conductivity can be derived from measurement. Both
~12nm and ~100nm Au films show similar conductivity values……………………97
6.1 Comparison between different NPUs……………………………………………...170
6.2 Extended table for comparison between different NPUs in literature……………...195
x
List of figures
2.1 Device schematics and emission processes. Schematic of a, waveguide coupled graphene
photoemitter b, free space coupled graphene photoemitter, and c, measurement setup. d,
Graphene band structure illustrating band-to-band absorption process of relevance for the
photon energies used here. e, Hot electron after photon absorption and the subsequent
scattering processes. f, Illustration of the two emission processes—hot electron emission
before cooling and field emission of thermal electrons…………………………………..8
2.2 Waveguide integrated graphene device. a, Optical image of a waveguide integrated
graphene device. b1, SEM images of a U-groove, b2, plan view of silicon nitride
waveguide, and b3, cross-sectional view of a silicon nitride waveguide. c, Raman
spectrum of the graphene transferred to the waveguide. d, Normalized output power of
the waveguide before and after graphene transfer – this measurement enables extraction
of the optical absorption in the graphene layer. e, Excitation of higher order optical mode
inside waveguide. f, Absorption coefficient of the higher order mode to graphene layer
above the waveguide……………………………………………………………………10
2.3 Electron emission characterization. a, Current-Field characteristics of dark and light
emission of planar graphene with free space laser coupling. b, Current-Field
characteristics for waveguide coupled graphene. c, Photocurrent, defined as (ILight – IDark)
for both free-space and waveguide coupled emitters. I-time from integrated waveguide
assisted graphene emitter for different laser power. d, Responsivity of free space and
waveguide coupled cases……………………………………………………………….12
2.4 Hot Electron Scattering, Electron Emission, and Optical Absorption Simulation. a,
Simulated result of scattering rate vs hot electron energy above Dirac point for the
xi
scattering mechanisms considered here. b, Average loss of energy from the high energy
electron due to e-e scattering events. a. c, Trajectory of energy vs time for injected hot
electrons above 1.5eV from the Dirac point. d, Simulation results of tunneling rates along
the different hot electron energies above Dirac point. e, Electron-hole pair generation rate
in the graphene. Heat map shows generation rate across entire waveguide, and the plot
shows the graphene generation rate on the dashed line superimposed on the heat map. f,
Simulated hot-electron and field emission current as a function of applied electric
field……………………………………………………………………………………..14
2.5 Comparison with literature. a, Current vs average power density and b, current vs peak
power density…………………………………………………………………………...17
2.6 Schematic of waveguide integrated graphene emitter fabrication process……………...18
2.7 a) Optical image of U-groove with optical fiber and 632 nm light being pumped through
the fiber into the waveguide. Inset shows output from waveguide imaged with a camera.
b) Picture of an actual sample with optical fiber epoxied to a Si wafer with waveguide,
gold pads, and graphene. Entire sample plus optical fiber is then attached to another wafer
to ensure optical fiber does not break at attachment point………………………………20
2.8 a) Free space emitter I-E curves. b) Waveguide coupled I-E curve……………………...21
2.9 a) Schematic of graphene on Si3N4/SiO2 substrate, identical to the waveguide structure.
b) Current vs time for free space excitation under the same conditions as the free space
emitter shown in the main text (optical power = 190 mW)……………………………...22
2.10 Representative curve showing how devices respond to light. Initial overshoot is attributed
to laser power overshoot. Values reported for current vs. power curves were all reported
from stable region, not overshoot region………………………………………………..23
xii
2.11 a) Dark current measurement of graphene waveguide. b) Tunneling emission region
identification. c) Fit for field enhancement factor extraction…………………………...24
2.12 a) Field emission and hot electron emission current density vs local electric field for an
optical generation rate corresponding to an optical power density of S = 2.3×10
4
W/m
2
.
b) Same graph scaled for applied electric field using the field enhancement factor of…..35
2.13 Comparison of calculated optical phonon scattering rates with literature………………36
2.14 Steady state electronic temperature as a function of power density……………………..38
2.15 Evolution of electronic temperature with time………………………………………….39
2.16 Heating calculation geometry…………………………………………………………..40
3.1 Emission of photogenerated hot electrons from graphene while they go through the
scattering processes…………………………………………………………………….46
3.2 Simulation of hot electron scattering, electron emission and electronic temperature. a, hot
electron scattering rates for the major scattering mechanisms of graphene for electronic
temperature of 300K. b, total scattering rates for different electronic temperatures. c,
energy resolved tunneling rates for hot electrons in graphene. d, simulated time resolved
energy trajectory of hot electrons excited by different photon energies. e, average energy
lost by hot electrons due to e-e scattering. f, simulated electronic temperature of graphene
as a function of absorbed optical power density………………………………………...47
3.3 Electron emission current calculation for low power density photoexcitation. a, ratio of
TPA rate to SPA rate in graphene different absorbed power densities. b, simulated HE
and TFE current density for different photon energies at an absorbed power density of
10
4
W/m
2
(dots: SPA, connected lines: MPA). c, crossover electric field and current
xiii
densities as a function of photon energy. d, HE current density as a function of photon
energy for different electric fields………………………………………………………51
3.4 Electron emission current calculation for large power densities. a, calculated HE current
density for different photon energies at an electric field of 1.0 V/nm (dots: SPA,
connected lines: MPA). b, calculated TFE current density at 0.5 V/nm and 1.0 V/nm
fields. c, crossover between different emission mechanisms at different ranges of
absorbed power densities calculated at 1.6 V/nm for photoexcitation by 3 eV
photons............................................................................................................................53
3.5 Performance limits of the photoemitter. (a) Change in the electron emission mechanism
with increasing electric field for EPh = 4 eV, (b) QE for different photon energies and
power densities. Response time of the photoemitter in the (c) HE and (d) electronic
heating regimes…………………………………………………………………………55
3.6 Graphene density of states……………………………………………………………...60
3.7 Hot electron energy trajectories for electronic temperatures of (a) 400K, (b) 500K, (c)
600K, (d) 700K, (e) 800K and (f) for 4 eV photons at different temperatures…………..61
3.8 QE in the HE regime as a function of electric field for different photon energies………63
3.9 (a) Temporal evolution of electronic temperature, (b) Initial electronic temperature as a
function of absorbed pump fluence, and (c) change in current density with time……….64
4.1 Device schematics and hot electron injection process. (a) Schematic of the structure of
metal insulator semiconductor device used here. (b) Band diagram of the device and two
different paths for injected hot electrons into the Au region. (c) Current density vs applied
voltage for the Au/Al2O3/Si diode used here in both linear and log scale. (d) TCAD
xiv
Sentaurus simulations of surface electron concentration as a function of applied bias in
the Au/Al2O3/Si device…………………………………………………………………71
4.2 Linear sweep voltammetry (LSV) curves of 12nm Au MIS device. (a) Linear scale
solution current density vs applied Au-Solution voltage for varying Au-Si diode voltages
and (b) log scale of (a). (c) Solution current density vs applied Au-Si voltage for varying
Au-Solution voltages and (d) log scale of (c). (e) Tafel relation for the low VAu-Si and (f)
high VAu-Si………………………………………………………………………………73
4.3 Current flow mechanism and measurement result. (a) Schematic diagram of main current
components. Major currents are composed with several minor current components. (b)-
(d) Three major current measurements of the closed system, (i.e. ISi, IAu, and ISolution)
under different Au-Si voltages………………………………………………………….81
4.4 Hot electron measurement and characterization. (a) Current component ratio map along
the increase of Au-Si voltage. Portion of the hot electrons in total current keep increase
as Au-Si voltage increase. (b) Current density from direct injected electrons from Si to
electrolyte at different fixed VAu-Solution. (c) Quantum efficiency of hot electron device at
fixed 2.0V Au-Si voltage and (d) at fixed -0.8V Au-Solution voltage…………………..83
4.5 Hot electron simulations. (a) electron-electron and electron phonon scattering rates in
gold plotted as a function of energy above Fermi level. (b) Energy loss rate per fs,
obtained by multiplying scattering rate at a given energy by average energy loss per
scattering event. (c) Log scale attempt rate of electrons tunneling into gold/solution
interface plotted as a function of energy with and without hot electron injection. (d)
Linear scale attempt rate plot…………………………………………………………...84
xv
4.6 Current flow across the device and measurement set up. a, The directions of all the current
components. b, The schematic of measurement system connections…………………...90
4.7 Accurate fitting between the potentiostat and the voltage supplier of solution current at
fixed
. a, Measurement setup, b-d, Redox current density in
= 0.5V,1.0V,
and 1.5V………………………………………………………………………………..93
4.8 Effect of
without using the potentiostat system. a, Measurement setup, b, Solution
current density in different fixed
across
and c, log scale of b. solution
current at fixed VAu-Solution. a, -0.2V, b, -0.4V and c, -0.5V of VAu-Solution………………..94
4.9 Comparison between the potentiostat and a 1.5V battery connected to Au-Si junction. a,
Measurement setup, b, Solution current comparison in different biasing condition, c, log
scale of b………………………………………………………………………………..95
4.10 a, Schematic showing the effect of lateral resistance due to diode current. The voltage
drop depends on the resistance of the Au film. b, Schematic of a control device with
lithographically defined holes…………………………………………………………..96
4.11 Four-probe measurement of a, ~12nm Au film on SiO2 and b, ~100nm Au film on SiO2.
Both films were measured with 1mm spacing between four probes…………………….97
4.12 a, Fitting results of experiment and simulation diode curves. b, Sentaurus electrostatic
potential simulation with the silver ring contact modeled device………………………98
4.13 AFM analysis of the 12nm Au film. 12nm Au film evaporated with cryogenic
temperatures. The RMS roughness for this film was measured to be 0.71nm from the
AFM……………………………………………………………………………………99
4.14 Solution current measurement of control device with holes. Inset schematic shows the
structure………………………………………………………………………………...99
xvi
4.15 Control devices band diagram and measurements. a, Band diagram of MS device with
~12nm Au, b, with ~100nm Au and c, with heavily doped Si emitter. d, Solution current
result from device ‘a’, as injected current to base increased, it shows hot electron effect.
e, from device ‘b’, showing no hot electron effect due to thick Au region, and f, from
device ‘c’, no hot electrons generated from emitter region, due to narrow barrier..……101
4.16 Device stability measurement in before/after electrochemistry experiment. a, linear scale
of device current measurement before and after HER measurement. Note that
measurements were carried out about 1 year apart. Strongly indicating stability of device.
b, log scale of a. c, Redox current measured in fixed voltage condition for 1-hour…….102
4.17 Current stability measurement in different conditions along the time. Silicon, Au, and
Solution current at a,
= 1.0V,
= -0.2V, b,
=
2.0V,
= -0.2V, c,
= 1.0V,
= -0.4V, and d,
=
2.0V,
= -0.4V……………………………………………………………103
4.18 Three component currents in fixed VAu-Solution at a, 0V, b, -0.2V, c, -0.4V, and d, -
0.8V…………………………………………………………………………………...104
4.19 Quantum Efficiency of Device in different conditions. a, Quantum Efficiency vs
in different fixed
values., b, Quantum Efficiency vs
in
different fixed
values……………………………………………………105
4.20 Ohmic behavior of the back contact of device. The contact is one of the significant factors
in device measurement. To reduce the current loss in the contact region, Ag was
introduced as a contact material to n-type Si. Ag, which has work function ~4.7eV forms
the ohmic contact with n-type Si. We can see that in higher voltage regime, the resistivity
xvii
starts to increase due to the series resistivity. This behavior of back contact affects the
device measurement results…………………………………………………………...106
4.21 Accurate fitting between the potentiostat and the digital multimeter of solution current at
fixed
. a, -0.2V, b, -0.4V and c, -0.5V of
…………………...106
4.22 HER in D.I water condition. a, I - V measurement of solution current of linear scale and b,
log scale measured in different fixed
values. c, I - V measurement of solution
current of linear scale and d, log scale measured in different fixed
values………………………………………………………………………………….107
4.23 Gas formation at different biasing conditions. a, No reaction happens at non-biased
condition for both Au-Solution and Au-Si. b, Hydrogen generation happens at 2.0V Au-
Si biased condition without biasing Au-Solution voltage……………………………..108
4.24 Match between electron-electron scattering rates calculated by Ladstadter et. al. and this
paper…………………………………………………………………………………..111
4.25 a, Energy resolved attempt rates calculated at different electron injection energies b,
match between the electronic temperature profile calculated by Jiang et. al. from pump-
probe experiment and our MC simulations……………………………………………114
5.1 Device schematics, characterization, and hot electron transfer mechanism. (a) Schematic
of the structure of graphene insulator semiconductor device used here. (b) Current density
vs applied voltage for the graphene/Al2O3/Si diode used here in both linear and log scale.
(c) Raman spectroscopy of graphene layer transferred on top of the Al2O3/Si substrate.
(d) Electrochemical measurement set up for device characterization. (e) Band diagram of
device structure at the positively biased graphene-Si junction showing the injection of
hot electrons…………………………………………………………………………...122
xviii
5.2 Linear sweep voltammetry (LSV) curves of graphene SIG device and comparison
devices. (a) Linear scale solution current density vs applied Graphene-Solution voltage
for varying Graphene-Si diode voltages and (b) Solution current density vs applied
Graphene-Si voltage for stepping Graphene-Solution voltages. (c) Solution current
density comparison with the no-graphene device. (d) Solution current density of Pt and
Pd at the same scale of current density………………………………………………...125
5.3 Composition of current inside the device and system and measurement results. (a)
Schematic of current components flowing inside the system. Major currents (i.e. ISi,
IGraphene, and ISolution ) are composed with different minor current components. (b)-(e)
Measurement of three major currents of the closed system, under different Graphene-Si
voltages………………………………………………………………………………..130
5.4 Specific current component extracted from the major current. (a) Direct injection current
vs graphene-silicon voltage at different VGraphene-Solution (b) Normalized electron transfer
rate vs graphene-silicon at different voltage VGraphene-Solution. (c) Hot electron current vs
graphene-silicon voltage at different VGraphene-Solution. (d) Tafel slopes of different biased
conditions……………………………………………………………………………..132
5.5 Solving MCBTE for undoped graphene. (a) Attempt rate of electrons tunneling into the
graphene/electrolyte junction with 0.5 - 2.0 eV injection energy above the Dirac point.
(b) zoomed in version of (a) at higher electron energies……………………………….137
5.6 Current flow across the device and measurement set up. a, The directions of all the current
components. b, The schematic of measurement system connections………………….140
xix
5.7 Control device measurement. a, Device with small size graphene. b, Device with larger
size graphene. c-e, Current density vs applied VGraphene-Solution at different diode biased
conditions……………………………………………………………………………..143
5.8 Linear Voltage Sweep (LVS) in 0.1M KOH solution…………………………………144
5.9 Cyclic Voltammetry in 1mM Ferrocene + 1M KCl……………………………………144
5.10 a, Raman spectroscopy of 8 different spots after all the electrochemical measurements. b,
Optical images of the graphene layer with the 523nm laser spot………………………145
5.11 Attempt rates of p-doped Graphene…………………………………………………...147
5.12 Attempt rates of undoped Graphene…………………………………………………...149
5.13 Attempt rates of n-doped Graphene…………………………………………………...150
5.14 (a) Attempt rate of electrons tunneling into the graphene/electrolyte junction with 0.5eV
injection energy above the Dirac point. (b) - (d) with 1.0eV,1.5eV, and 2.0eV injection
energy…………………………………………………………………………………150
5.15 Circuit diagram of the system…………………………………………………………152
5.16 Graphene Fermi level shift due to VGraphene-Si and VGraphene-Solution……………………...153
6.1 ORN enabled by SGM photodetector. (a) Schematic of the SGM photodetector device.
(b) I-V curves measured at dark conditions and under uniform illumination (445 nm) in
linear and (c) log scale. (d) Schematic of a single unit of ORN. (e) V-t curves measured
at different optical intensities and (f) corresponding frequency spectrum. (g) spiking
frequency and amplitude as a function of optical intensity. (h) Experimental plot of
minimum optical power required for oscillation with neuron area. (i) Calculation of dark
current limited and LC limited Pop,min for oscillation without external electrical
power………………………………………………………………………………….159
xx
6.2 Frequency multiplexed computation with ORN. (a) Circuit schematic for two coupled
ORNs. (b) ORN voltage colormap showing nonlinear peak surfaces and their shift at
different center frequencies for LC = 10 mH and BW = 200 Hz. (c) ORN voltage colormap
showing different peak surface shapes for different LC values and their (d) analytical
approximations. (e) Original image and the scatter plot showing all the (P1,P2) pairs for
this image if it were input to a 1×2 convolutional kernel. (f-h) Image transformations
when the two coupled ORNs (LC = 10 mH) receive the (P1,P2) pairs as inputs similar to
a convolution operation and the corresponding scatter plots. The overlap between red and
blue scatter plots show how different subsets of inputs are thresholded by the network at
different center frequencies (BW = 200 Hz)…………………………………………..162
6.3 Image processing with coupled ORN network. (a) Circuit schematic for the ORN kernel
(b) I-V curves of all 9 SGM detectors in the network under same optical illumination. (c)
Oscillation V-t and (d) FFT curves at the output node when all ORNs are under uniform
illumination. (e) Frequency band filtered images showing edge detection, (f) intensity
filtering, (g) image sharpening, (h) object segmentation. (i) Original color image and
frequency domain images showing (j-m) image segmentation operation……………163
6.4 LSM implementation of ORN network for MNIST classification. (a) Image classification
pipeline of the LSM structure showing an original input image, structure of the liquid
layer, frequency sampled output images and further processing at the readout layer by
hidden ReLU units. (b) Training and testing accuracy of the readout layer for training
datasets corresponding to different frequency samples. (c) Classification accuracy of the
handwritten digits as a function of number of frequency samples for 7×7 pixels/image
and (d) for 21×21 pixels/sample………………………………………………………167
xxi
6.5 I-V characteristics of control devices. (a) I-V curves in dark and light conditions for a
device without graphene, (b) a device with graphene but without Ti in the metal, and (c)
a device with graphene and Ti/Au metal mesh but thick oxide underneath the metal
mesh…………………………………………………………………………………..174
6.6 Schematic of the NDR mechanism showing the competing transport channels for the
photogenerated carriers……………………………………………………………….175
6.7 (a) Optical micrograph of the grid in the device showing direction of position dependent
measurement. (b) Spatial dependence of current for focused beam measurements at 532
nm wavelength at a power of 12.6 mW. (c) I-V curves corresponding to the colormap
produced in (b). (d) I-V curves measured at different optical powers for beam position at
the midpoint of the diagonal. (e) Spatial dependence of peak and valley current and
PVCR…………………………………………………………………………………176
6.8 Temperature dependent I-V curves in (a) log and (b) linear scale……………………..177
6.9 Capacitance measurements of NDR device. Small signal capacitance-voltage
characteristics of NDR device at different power densities for (a) 1 KHz, (b) 10 KHz, (c)
100 KHz, and (d) 1 MHz. (e) Small signal capacitance measured at a power density of 57
mW/cm
2
and (f) dark conditions for different frequencies……………………………178
6.10 Sentaurus simulations of the NDR device. (a) Schematic of the simulated device (b)
Simulations showing the effect of charge traps and (c) carrier lifetime in determining
NDR behavior for a trap density of 10
12
cm
-2
. (d) Sentaurus simulation showing the
increased recombination at the trap states in the NDR regime for trap density of 10
12
cm
-
2
. (e) Modification of the valley current with barrier height (f) Position dependent
illumination and corresponding I-V sweeps (g) Change in VOC with n-Si doping (h)
xxii
Modification of NDR behavior as electron affinity of the graphene layer was changed, (i)
Scalability of the NDR device: I-V curve of a 1 µm device showing NDR behavior…180
6.11 Wavelength dependent responsivity measurements…………………………………..182
6.12 (a) Schematic of a single ORN (b) Power generated by ORN (c) Normalized fundamental
frequency of oscillation as a function of normalized optical power and applied voltage
(d) Normalized fundamental frequency and amplitude at Vapplied = 0V (e) Oscillation V-t
and (f) FFT curves for different values of normalized optical power. (g) ORN voltage
filtered at 28 KHz with different bandwidth and (h) filtered at different center frequencies
with a bandwidth of 200 Hz as a function of incident optical power. (i) Analytical
approximation of simulated behavior…………………………………………………183
6.13 Experimental results for images processed at different frequencies by the cascaded circuit
when pixel value = 1 corresponds to an optical power of (a-d) 2.75 mW and (e-h) 5.5
mW……………………………………………………………………………………183
6.14 Simulation results for a 10x10 kernel where only nearest neighbor oscillators are coupled
by an inductance of 5H………………………………………………………………...188
6.15 (a) Circuit schematic of ORN kernel and (b) current and voltage components………...191
6.16 Performance and maximum switching speed as a function of MOSFET VDD…………195
xxiii
Abstract
From high power microwave amplifiers to low power computing systems, semiconductors have
propelled the advancement of science and technology as we see them in the modern world. Large
abundance of silicon has enabled us in moving forward in this direction. In this thesis, we
demonstrate high efficiency realizations of silicon based electronic devices for three different
broad applications: (a) electron cathodes for vacuum electronics, (b) electron cathodes for
electrochemical reaction systems, and (c) in-sensor oscillator based computing system for ultra-
low power computing. Understanding the electron transport behavior in semiconductors and
engineering it for a particular application have been the proponent of these research thrusts.
First, we have integrated graphene, a 2D semimetal, to a photonic waveguide where it is forced to
absorb photons efficiently via evanescent coupling with electromagnetic fields. Improving the
optical absorption of graphene then allowed us to utilize it as an ultrathin hot electron emission
cathode. Through quantum mechanical understanding of hot electron scattering mechanisms in
graphene, we have then projected the performance limits of such a graphene photoemitter.
Second, we have taken advantage of a silicon/oxide/metal device structure that can catalyze
electrochemical reactions such as hydrogen evolution reaction by generating hot electrons that can
overcome the activation energy associated with the reaction. Such devices have been realized on
both graphene and gold based cathodes where they have demonstrated extraordinary quantum
efficiency and tunable reaction onset.
Third, we have engineered a novel silicon/graphene photodetector that shows negative differential
resistance under optical illumination and generates electrical voltage oscillations without external
electrical power. Then we have created a network of coupled oscillators that can take optical
xxiv
signals as input and modify the oscillatory outputs of the network through the coupling. We have
shown that such a network of oscillators encode different information about input signals in their
oscillation frequency bands and therefore enable frequency multiplexed, parallel computing.
Through theoretical projections, we show that such a computing architecture is capable of
performing computer vision tasks with an extraordinarily small energy cost of ~24 aJ/OP which
beats the state-of-the-art NVIDIA GPUs by a factor of 10
4
.
1
Chapter 1: Introduction
1.1 Motivation
Silicon based devices have been driving most of the innovations in the modern world. By
controlling the transport of electrons in a semiconductor such as silicon, we have been able to
achieve extreme computing abilities. Since its inception, silicon based industry has been focused
on a single goal: making the devices smaller, faster and cheaper. It has worked well for 5 decades
before hitting the ultimate limit: discreteness of atoms. While we still keep striving to go forward
with this goal, we have realized that such an advance has its limits and therefore alternate
approaches are necessary. It is time to invest efforts in innovating the ways we would use silicon.
From silicon photonics to optoelectronics, from power devices to logic devices, from digital
applications to analog, the potential is infinite.
In this thesis, we tap into that potential in three applications relevant to physics, chemistry and
mathematics. We leverage the electron transport in silicon-graphene based semiconductor devices
to achieve three different goals:
(1) Forcing non-equilibrium hot electrons to be emitted into vacuum for vacuum electronics
applications
(2) Driving electrochemical reactions with hot electrons for clean energy storage with hydrogen
(3) Performing parallel and ultra-low power computing with silicon-graphene based optoelectronic
oscillators for machine vision
2
1.2 Electron emission devices
Spontaneous electron emission from a material is prevented by the vacuum energy barrier. In order
for an electron to be emitted into vacuum, it needs to either gain enough energy to go above this
barrier or the barrier needs to be thinned down by an electric field so that it can tunnel through. In
a typical photoemitter, an electron gains excess energy from a photon to emit into vacuum.
However, this barrier is typically large (> 4 eV) and thus requires UV photons. In addition, the
photons are absorbed deep into a material and the photogenerated electrons need to transport
themselves to the emitting surface. Through this process, it is possible for them to lose significant
energy to different scattering mechanisms, eventually losing its ability to overcome the vacuum
barrier. For 2D materials such as graphene, electrons are always at the emitting surface and
therefore any requirement of a transport mechanism is eliminated. However, graphene cannot
absorb photons efficiently when they are incident normal to its surface. We have therefore adopted
an integrated photonics based approach where graphene sits on a waveguide and the photons
interact with graphene along its plane via the evanescent field of the waveguide, allowing graphene
to absorb photons efficiently. An electric field assists the hot electrons in graphene to be emitted
from its surface. We have further evaluated the theoretical performance limits of such an emitter
through detailed Monte Carlo Boltzmann Transport Equation (MCBTE) simulations. Our results
show extraordinary electron emission quantum efficiency in these devices. These efforts have been
published in Nature Photonics and Physical Review Applied back in 2019
1
and 2020
2
respectively.
I am indebted to my co-author, Fatemeh Rezaeifar, who contributed to half of the work published
in Nature Photonics. I am also grateful to all co-authors who have also granted me permission to
me to use the works as part of my dissertation.
3
1.3 Electrochemical reactions with hot electrons
Electrochemical redox reactions are driven by electron transfer between a source and an ion. Such
a reaction typically has an activation energy barrier that keeps the reactants at bay. Such an
activation barrier can be lowered by a traditional catalyst that modifies the adsorption of molecules
or ions on its surface and improves the kinetics of the reaction. However, designing a catalyst is
not an easy task and they need to be tailored for different reactions. We show a different approach
to solving this problem: driving electrochemical reactions with hot electrons. In a metal-insulator-
semiconductor device, an electron can be injected into the metal from the semiconductor by
applying a voltage. This electron tunnels through the oxide and gains energy from the electric field.
Such an electron arrives at the metal with higher energy than the thermal electrons and therefore
is called a non-equilibrium electron or a hot electron. This hot electron can transfer itself to an ion
by going over the activation energy barrier altogether. We show that a Si/Al2O3/Au and
Si/Al2O3/graphene hot electron cathode can efficiently drive electrochemical hydrogen evolution
reaction (HER) at the metallic surface by forcing hot electrons to be transferred into H
+
ions. This
approach to catalyzing electrochemical reactions with hot electrons can be adopted for any reaction
system. These works have been published in Nano Letters back in 2019
1
and 2020
2
. I am indebted
to my co-author, Hyun Uk Chae, who contributed to half of both Nano Letters papers. I am also
grateful to all co-authors who have also granted me permission to me to use the works as part of
my dissertation.
1.4 Ultra-low power in-sensor computing with oscillators
The new age of artificial intelligence and computer vision is upon us. The emergence of GPUs has
propelled the advancement of machine learning related tasks significantly. However, it does come
at a significant cost as well: an extraordinary amount of energy consumption. While all humans in
4
the world spend ~20000 TWh of energy throughout a year, just machine learning tasks are costing
us ~1000 TWh, a stunning 5% of annual energy usage. With the projected growth of sensory nodes
across the world, this number will only go up. The main culprit behind such an enormous energy
cost is the von Neumann bottleneck. In a von Neumann computing architecture, the data is moved
back and forth between processor and memory many times costing an energy and time penalty.
Such a limitation can be avoided by adopting in-sensor and near-sensor computing approaches
where preprocessing of raw data is performed at the sensor to reduce transmission of any redundant
data. Taking inspiration from human retina where optical signals are converted to spiking
oscillations, we have proposed a novel computing architecture that houses a silicon/graphene based
optoelectronic spiking oscillator. Here, a silicon/graphene photodetector can generate spiking
oscillations when illuminated by light under certain circuit configurations. Such oscillators can
then be connected in a coupling network to allow information sharing between themselves. While
in a coupled network, the oscillation behavior of each oscillator is modified by the neighboring
oscillators. The power in different frequency bands of these oscillators then encode different
information about the input optical signal. We have shown through careful measurements and
detailed analysis that such a computing system is capable of performing frequency multiplexed
parallel processing of computer vision related tasks such as image processing and recognition with
an energy cost of 24 aJ/OP which is ~10000 times more efficient than the state-of-the-art NVIDIA
GPUs. I am also grateful to all co-authors who have granted me permission to me to use the works
as part of my dissertation.
5
Reference:
1. Rezaeifar, Fatemeh, Ragib Ahsan, Qingfeng Lin, Hyun Uk Chae, and Rehan Kapadia.
"Hot-electron emission processes in waveguide-integrated graphene." Nature
Photonics 13, no. 12 (2019): 843-848.
2. Ahsan, Ragib, Mashnoon Alam Sakib, Hyun Uk Chae, and Rehan Kapadia. "Performance
limits of graphene hot electron emission photoemitters." Physical Review Applied 13, no.
2 (2020): 024060.
3. Chae, Hyun Uk, Ragib Ahsan, Qingfeng Lin, Debarghya Sarkar, Fatemeh Rezaeifar,
Stephen B. Cronin, and Rehan Kapadia. "High quantum efficiency hot electron
electrochemistry." Nano letters 19, no. 9 (2019): 6227-6234.
4. Chae, Hyun Uk, Ragib Ahsan, Jun Tao, Stephen B. Cronin, and Rehan Kapadia. "Tunable
Onset of Hydrogen Evolution in Graphene with Hot Electrons." Nano letters 20, no. 3
(2020): 1791-1799.
6
Chapter 2: Waveguide integrated graphene photocathodes
2.1 Introduction
Photoemission plays a central role in a wide range of fields, from electronic structure
measurements to free electron laser sources. In metallic emitters, single-photon, multi-photon, or
strong-field emission processes are the three photoemission mechanisms. Photons with energy
lower than the material workfunction drive photoemission through multi-photon, or strong-field
processes, both of which require large optical powers, limiting the integration of photoemitters
with photonic integrated circuits. Using a 3.06 eV continuous wave (CW) laser, photoemission
from waveguide integrated graphene is observed to occur at peak power densities >5 orders of
magnitude lower than previous multi-photon and strong-field emission demonstrations, attributed
to the emission of hot electrons in graphene before thermalization. In metal tips this mechanism is
suppressed due to hot electron transport to the emitting surface and the large scattering rates,
significantly reducing the overall probability of hot electron emission into the vacuum. To
rigorously determine whether hot electron emission can explain the observed experimental
behavior, we simulate the absolute rates of (i) hot electron emission and (ii) field emission of
thermal electrons using the hot electron energy vs time trajectories, energy resolved emission rates
and thermal distribution of carriers. From both experiment and simulation, it seen that a critical
electric field exists, below which hot electron emission is dominant and above which field emission
of thermal electrons is dominant. Critically, without fitting parameters, simulations show an
expected cross over critical applied electric field of EC~3.9 V/µm and total current of IC~50 pA,
which semi-quantitatively reproduce both the experimentally observed values of EC~3.5 V/µm
and IC~130 pA. These results suggest that integrated photonics driven hot electron emission from
7
nanoscale materials provides a rich new area of exploration for both electron emitters and
integrated photonic devices.
2.2 Hot electron emission processes in waveguide integrated graphene
Metallic photoemission cathodes operate through three processes: (i) single photon excitation
1
,
where a single photon imparts enough energy to an electron to overcome the material workfunction
(ii) multi-photon emission
2-5
, where a high intensity of photons drive a single electron to undergo
multiple absorption events before scattering causes loss of energy, or (iii) strong-field emission
6-
10
, where the electric field of the photons themselves drive field emission. Multi-photon and strong-
field emission processes typically use photon energies which are below the metal workfunction,
but require high-power pulsed laser sources. In this work, we experimentally demonstrate that sub-
workfunction photons can be used at powers below the threshold for multi-photon emission or
strong-field emission to modulate graphene electron emission current through hot electron
emission. Monolayer graphene is chosen as a model material system due to the relatively low
optical powers needed to enable large non-equilibrium electron temperatures
11
, long scattering
times
12-14
, and the ultra-thin geometry, eliminating the need for hot electrons transport to emitting
surfaces. Integrated photonic circuits simultaneously enables us to eliminate the need for free-
space alignment, and overcome the absorption limitations of a single layer of graphene
15,16
. We
integrate monolayer graphene with silicon nitride waveguides on a silicon substrate. While single
devices are made here, an integrated photonics approach lays the foundation for on-chip arrays of
photoemitters where each element can be independently controlled.
8
2.3 Waveguide integrated graphene photoemitter and experimental results
Figure 2.1a schematically illustrates the structure of the waveguide-integrated graphene electron
emitter. A layer of graphene is transferred to a Si/SiO2 substrate with a silicon nitride waveguide
and gold contacts. Photons are coupled onto the chip via an optical fiber fixed to a U-groove etched
into silicon and aligned to the waveguide. Details of the fabrication procedures can be found in the
section 2.6. The free space coupled version of the emitter is shown in Figure 2.1b. The samples
are measured in vacuum using a high-voltage source to apply the extracting field, an optical fiber
for laser excitation, and an ammeter for current measurement (Fig. 2.1c). For these measurements,
the gold contacts are grounded, and the anode is held at high voltage (1-10kV). The optical
absorption of graphene in the ultraviolet-visible (UV-VIS) spectrum range is primarily from
Figure 2.1 | Device schematics and emission processes. Schematic of a, waveguide coupled graphene
photoemitter b, free space coupled graphene photoemitter, and c, measurement setup. d, Graphene band
structure illustrating band-to-band absorption process of relevance for the photon energies used here. e,
Hot electron after photon absorption and the subsequent scattering processes. f, Illustration of the two
emission processes—hot electron emission before cooling and field emission of thermal electrons.
9
interband transitions
15,16
(Fig. 2.1d), with electrons excited from ½ Eph below the Dirac point to ½
EPh above the Dirac point. While electrons can be excited by both single and multi-photon
absorption processes, only single photon absorption is considered here due to the low optical
excitation powers of <5 mW CW. In this work, 405 nm (3.06 eV) photons are used to excite the
graphene. These do not have enough energy to excite electrons above the graphene workfunction.
Thus, if the optical power is below the multiphoton emission threshold, there should be no
observed photocurrent unless the graphene is heated to the point that thermionic emission is
significant, or photoexcited electrons are emitted before relaxation.
However, photoexcited electrons will undergo both electron-electron scattering and electron-
phonon scattering, thermalizing on a time scale of less than a picosecond. Figure 2.1e
schematically represents the photoexcited electron and the subsequent energy loss through
scattering. In the presence of a vertical electric field, tunneling through the vacuum barrier offers
another possible pathway for the photoexcited electron. For monolayer graphene, the photoexcited
electrons will experience the tunneling potential over the entire cooling process. Thus, the energy
of the absorbed photon, the scattering rate, and the rate of tunneling into the vacuum will all
determine the pathway an excited electron takes. Since the photoexcited electrons experience a
smaller tunnel barrier as compared to the thermal population, hot electrons will dominate the
emission currents below a certain critical electric field while the large population of thermal
electrons will dominate emission above the critical field. Figure 2.1f shows the thermal electron
distribution of electrons and the hot electrons. This will then give rise to two distinct emission
behaviors: (i) emission of hot electrons before thermalization, which should be dependent on
10
photon absorption and dominant below some critical field, and (ii) field emission of the cold
electrons which will be independent of photon absorption and dominant above some critical field.
Figure 2.2a shows an optical image of a fabricated integrated photonics device, with the U-
groove, tapered Si3N4 waveguide, and monolayer graphene visible. Figures 2.2b1-b3 are scanning
electron microscope (SEM) images of the U-groove (Fig. 2.2b1), plan-view of a Si3N4 waveguide
(Fig. 2.2b2), and cross-sectional view of a Si3N4 waveguide (Fig. 2.2b3). To ensure that the
graphene was successfully transferred onto our waveguide, we carried out Raman spectroscopy
along multiple points on the waveguide. A representative Raman spectrum of graphene on the
optical waveguide is shown in Figure 2.2a with sharp 2D and G peaks labeled at 2689 cm
-1
and
Figure 2.2 | Waveguide integrated graphene device. a, Optical image of a waveguide integrated
graphene device. b1, SEM images of a U-groove, b2, plan view of silicon nitride waveguide, and b3,
cross-sectional view of a silicon nitride waveguide. c, Raman spectrum of the graphene transferred to
the waveguide. d, Normalized output power of the waveguide before and after graphene transfer – this
measurement enables extraction of the optical absorption in the graphene layer. e, Excitation of higher
order optical mode inside waveguide. f, Absorption coefficient of the higher order mode to graphene
layer above the waveguide.
11
1580 cm
-1
, respectively. The relative ratio of the measured I2D/IG peak intensity here is ~2.9 clearly
indicating monolayer graphene
17
. The fiber used here is a multi-mode fiber with a core diameter
of 200 µm, thus to maximize coupling, we use a relatively large multimode waveguide with 5 µm
thickness, 50 µm width, and a tapered end with a 200 µm width, which gives an expected power
coupling of ~0.024, using the area ratios.
As the relative distribution of modes inside the waveguide is not controlled in this experiment,
it is necessary to directly measure the absorption of the graphene layer. To do so, we first fabricated
a device without the graphene layer, pumped the waveguide with a 405 nm laser, and measured
the power output from a cleaved end of the on-chip waveguide with no graphene layer. Next, we
transferred the single layer graphene onto the waveguide and carried out the same measurement.
Figure 2.2d shows the normalized power output from the waveguide as a function of power emitted
from the end of the fiber attached to the U-groove. Using this data and the length of the graphene
on the waveguide, we measured an absorption of ~25 dB/cm for 405 nm light. To gain physical
insight into the absorption, we simulated the absorption in a layer of graphene on a Si3N4
waveguide using Lumerical FDTD
18
assuming all the light would be transported in a single mode
for modes from the 1
st
to the 20
th
. The schematic in Figure 2.2e shows the structure used for
simulation. The inset heat maps show representative mode electric field profiles for the 1
st
and 6
th
mode respectively. Figure 2.2f then shows the resulting simulated absorption in graphene vs mode
number. Using the combined experimental and simulation results, we determine that the results
observed here are due to a combination of multiple higher order modes, and cannot be explained
by the fundamental modes.
Field emission characteristics for the samples schematically represented in Figure 2.1a and
2.1b were measured with and without illumination from a 405 nm laser source with the samples at
12
room temperature and under a pressure of 5×10
-8
Torr. Current measurements were carried out
using a Keysight B2985A electrometer connected in series with our cathode to ground, and a high
voltage anode was used to apply the electric fields necessary to extract electrons from the graphene.
As a control sample, we characterized the electron emission from a free space laser coupled
graphene sheet transferred on an n-type silicon substrate with a doping level of ~10
19
cm
-3
. To
drive this sample optically, we illuminated the sample at an angle using the same 200 µm
multimode fiber and 405 nm laser source. Figure 2.3a shows the results for applied electric fields
Figure 2.3 | Electron emission characterization. a, Current-Field characteristics of dark and light
emission of planar graphene with free space laser coupling. b, Current-Field characteristics for waveguide
coupled graphene. c, Photocurrent, defined as (I Light – I Dark) for both free-space and waveguide coupled
emitters. I-time from integrated waveguide assisted graphene emitter for different laser power. d,
Responsivity of free space and waveguide coupled cases.
13
up to 3 V/µm. The power incident on the sample was measured to be 190 mW. Figure 2.3a shows
the I-E curves for graphene under free space illumination. We observed a clear, but small change
in the current with illumination. After an initial rise, the overall current level does not change
significantly with applied electric field. Next, we measured the I-E curves for waveguide integrated
graphene. As shown in Figure 2.3b, there is an initial ‘turn-on’ below ~0.5 V/µm, and then a steady
increase of the current under illumination. The current increases by ~50x from E = 0.5 V/µm to E
= 3.5 V/µm, in contrast to the free space illumination case. To understand the effect of illumination
for these two devices, we plot the photocurrent, defined as IPC = ILight – IDark, in Figure 2.3c. For
the free space case, the photocurrent is IPC = 1.05 pA while the photocurrent for the waveguide
integrated case is 129.3 pA for waveguide illumination. Critically, while the free space sample has
~190 mW of optical power incident upon it, the waveguide device only has ~4.6 mW of power
coupled into the waveguide due to the mismatch between the fiber core size and waveguide
dimensions. Using the power incident on the graphene, we plot the responsivity for the free space
and waveguide coupled graphene devices (Fig. 2.3d), with the linear curves shown in section 2.6.
Critically, the waveguide coupled sample demonstrates a responsivity ~5100x greater than the free
space sample from an unoptimized waveguide integrated device. As a control, we also
characterized the emission characteristics of a free space laser coupled graphene sheet on a flat
nitride and oxide substrate with no waveguide and two gold contacts, mimicking the graphene
structure in the waveguide surface. The results shown in Figure 2.9 indicate that the substrate is
not a major factor in the differences observed between the free-space and waveguide device.
14
2.4 Theoretical analysis of experimental results
To further understand the mechanism of emission, we compute the relative rates of electron
emission for hot electrons and thermal electrons for different local electric field strengths. First we
calculate the energy resolved scattering rates as shown in Figure 2.4a. We have considered three
scattering processes: i) electron-electron scattering, ii) longitudinal and transverse optical phonon
scattering, and iii) supercollision acoustic phonon (SC) scattering (Section 2.7). An ensemble
Monte Carlo Boltzmann Transport Equation (MCBTE) simulator is then used to emulate the
dynamics of the electrons in graphene (described in detail in the section 2.7). The scattering rates
used here are calibrated with prior published results (Figure 2.13), and it is shown that this
Figure 2.4 | Hot Electron Scattering, Electron Emission, and Optical Absorption Simulation. a,
Simulated result of scattering rate vs hot electron energy above Dirac point for the scattering
mechanisms considered here. b, Average loss of energy from the high energy electron due to e-e
scattering events. a. c, Trajectory of energy vs time for injected hot electrons above 1.5eV from the
Dirac point. d, Simulation results of tunneling rates along the different hot electron energies above Dirac
point. e, Electron-hole pair generation rate in the graphene. Heat map shows generation rate across entire
waveguide, and the plot shows the graphene generation rate on the dashed line superimposed on the
heat map. f, Simulated hot-electron and field emission current as a function of applied electric field.
15
simulator can reproduce published experimental pump-probe non-equilibrium electron
temperature profiles (Figure 2.14). Figure 2.4b shows the average energy loss due to electron-
electron scattering events as a function of hot electron energy. By injecting single particles at an
energy of 1.53 eV above the Dirac point and then tracking their energy vs time, we build up
statistics for the trajectory of hot electrons. Averaging the energy vs time plots of 50 particles, we
can see the effect of these scattering processes on the electrons photoexcited to 1.53 eV above the
Dirac point by a 3.06 eV photon. These electrons first go through a fast energy dissipation process,
largely due to optical phonon emission and electron-electron scattering. However, as the electron
energy reaches the optical phonon energy (~190 meV), the optical phonon scattering rates are
limited to absorption, and the energy loss per electron-electron scattering event decrease
significantly (Fig. 2.4b). Thus, at lower energies, the SC phonon emission dominates the energy
loss.
We have calculated the tunneling rate of the electrons at different energies by modeling
graphene as a finite quantum well, and then adjusting the barrier height and width to approximate
the pz orbital wavefunction decay into the vacuum
19
. Bardeen’s tunneling Hamiltonian approach
is then used to calculate the tunneling rate (section 2.7). The tunneling rate as a function of electron
energy above the Dirac point is shown in Figure 2.4d for an applied field of 3.2 V/µm, which
corresponds to a local field of 1.59 V/nm. The conversion from applied field to local field is
obtained by multiplying the applied field by the experimentally extracted field enhancement factor
of 498 (Figure 2.11). The optical generation rates are determined by combining optical absorption
measurements (Fig. 2.2d) with Lumerical FDTD to determine local generation rates, as shown in
Figure 2.4e. Using the energy trajectory (Fig 2.4c), tunneling rates (Fig 2.4d), and peak optical
generation rates (Fig 2.4e), the emission current due to the hot electrons is calculated. The details
16
of this calculation are given in section 2.7. Three current components are considered, (i) field
emission of the thermal electrons, (ii) tunneling of hot electrons before cooling, and (iii) a noise
floor component, which is the noise floor of our measurement system. We then calculated the
current vs applied electric field for the experimentally measured device geometry. These
simulations match two features of the experimental current vs field curves. First, the crossover
applied electric field is estimated to be ~3.9 V/µm using the experimentally extracted β=498,
which is close to our observed cross over of ~3.5 V/µm. Second, the current at the critical field is
calculated to be ~50 pA, which is also close to our experimentally observed current of ~130 pA as
the cross-over current between hot-electron and field emission current. The only parameters used
here were the device dimensions (50 µm × 4 mm), the extracted field enhancement factor (β=498),
and an assumed carrier density of 1.6×10
11
cm
-2
, which corresponds to the Fermi level at 4.5eV . It
should be noted that from this model we expect the behavior to be linear with optical power. From
our optical power vs current measurements (Figure 2.8), we find that at high fields (Eapplied=3.2
V/µm) the current is linear. However, at low fields, the current levels are super linear. Thus, our
present model appears to work well near the field emission threshold, but fails to capture the
behavior at low applied fields.
2.5 Comparison with literature
Finally, the waveguide integrated devices are compared to other published laser induced field
emission devices
6,20,21
which are driven by multi-photon or strong-field emission. As most multi-
photon and strong-field devices uses high peak-power pulsed lasers, we have normalized the
comparison by plotting the current in both peak power density and average power density. Figure
2.5a shows the current vs average power density. In this case, the waveguide integrated graphene
emitter gives dramatically higher current at a given average power density as compared to the
17
literature. When plotted vs peak power, the device here gives similar current to emitters driven
with 6 orders of magnitude higher peak power density. We attribute this dramatic reduction in
required both average and peak power to the use of graphene, which enables hot electrons to
remain at the emitting surface throughout the entire cooling trajectory (Fig. 2.4c) and the use of a
waveguide to efficiently excite the graphene. This is in direct contrast to metallic tips, which are
challenging to excite efficiently with free space optics, and where the hot electrons lose energies
before impinging on an emitting surface through the entire cooling period due to the 3-D structure.
In conclusion, a significant reduction in peak power power and average power densities required
for photoemission with sub-workfunction photon energy is achieved in waveguide integrated
graphene. Detailed hot-electron trajectory simulations and electron emission calculations show
semi-quantitative agreement between our experiments and simulation, providing strong evidence
that hot electron emission is responsible for the observed behavior. The materials properties which
enable this behavior in graphene are not present in the standard metallic or semiconducting electron
Figure 2.5 | Comparison with literature. a, Current vs average power density and b, current vs peak
power density
18
emitters which are used. However, this work suggests that other systems which exhibit these
properties, such as quantum dots, perovskites, and other 2-D materials may also exhibit efficient.
This work also represents the first time integrated photonic components, specifically waveguides,
have been used for the excitation of photoemitters, driven by the reduction in photon energy and
power needed. The combination of integrated photonics with these hot electron processes offer an
exciting platform for the creation of a class of integrated photoemitters where on-chip modulators,
waveguides, cavities, and photon sources could enable individually addressable arrays of electron
emitters.
2.6 Methods: Fabrication and measurements
2.6.1. Fabrication Method
The fabrication process of this device is summarized in Figure 2.6. We used <100> oriented P-
type lightly doped (1-10 Ω.cm) silicon substrate and deposited hard mask of SiO2 (4 µm on back
- 2 µm on front) and Si3N4 (0.5 µm on back - 12 nm on front) as a protection layer (Figure 2.6)
Figure 2.6: Schematic of waveguide integrated graphene emitter fabrication process.
19
against potassium hydroxide (KOH) etching of the substrate. Photoresist AZ5214 was spin coated
with 500 rpm for 5 s and 3000 rpm for 60 s and baked at 100 °C for 1 min. Prior to exposure, the
V-groove pattern should be aligned parallel to the primary flat of the <100> substrate. This step is
necessary for anisotropic etching of the silicon via KOH. After the exposure with a dose of 80
mJ/cm
2
and developing process (Figure 2.6b), the substrate was hard baked at 150ºC for 30 min
before wet etching of the hard mask layer to open the V-groove window. We used buffered oxide
etchant (BOE) 7:1 to etch the hard mask and opened the window above V-groove (Figure 2.6c). In
the next step, 30% KOH solution at 75º C was used to make the V-groove structure (Figure 2.6d).
V-groove is used for holding the optical fiber to couple the light from the optical fiber to the
waveguide. The SEM image of the V-groove is shown in Figure 2.7a. Alternatively, the groove
can be fabricated using dry etching, deep silicon etching through induced coupled plasma (ICP)
Bosch process to create U shape groove (U-groove). The advantage of using ICP is this technique
doesn’t require the alignment of groove pattern to the primary flat of the <1 0 0> substrate as well
as the substrate doesn’t go through destructive wet etching. Therefore, it can be done with hard
mask only on the front side and doesn’t require a thick hard mask on the back side. However, U-
groove requires monitoring the etching depth to get an accurate depth equal to optical fiber radius.
In addition, the flow rate of the passivation gas (C4F8) should be set at a very low level to protect
the photoresist during the deep etching process. After V-groove (U-groove) fabrication, we
deposited SiO2 (1 µm on the front side) and thick Si3N4 (5 µm on the front side) via PECVD
process as the clad and core of the optical waveguide respectively. For waveguide patterning, we
used photoresist AZ4620 that can let us have photoresist as thick as 10-12 µm which is necessary
for long Si3N4 RIE process. This photoresist was spin coated with 500 rpm for 15 s and 2000 rpm
for 25 s and baked at 100 °C for 2 min. After 2 hours of resting time for this photoresist, we aligned
20
the waveguide pattern on the mask with the V-groove (U-groove) and exposed it with a dose of
450 mJ/cm
2
followed by 4 min developing. After this step, the Si3N4 RIE process performed to etch
the Si3N4 and form the waveguide. For this process, we used CF4 and O2 with the ratio of 3:1 with
100 W of power under 50 mTorr pressure to etch the Si3N4.
The SEM image of the top and cross-section view of the final waveguide is shown in Figure 2.7.
The waveguide has a width of 50 µm and height of 5 µm as a multimode waveguide. After
waveguide fabrication, we evaporated Ti/Au (5/100 nm) on both sides of the waveguide as an
electrical contact. After metal evaporation, we transferred the CVD grown graphene on top of the
optical waveguide using wet transfer technique. After transfer, annealing performed using rapid
thermal annealing (RTA) at 450 ºC to remove the PMMA residue and assure an appropriate
adhesion of the graphene sheet to the optical waveguide for optimal evanescent optical absorption.
For this work, we used the fiber-coupled tunable CW laser source 405 nm with special fiber
provided for this wavelength with a metallic shield to reduce the optical loss. This fiber has a
diameter of 200 µm, and the last step was to align this fiber inside the V-groove (U-groove) for
Figure 2.7: a) Optical image of U-groove with optical fiber and 632 nm light being pumped through the
fiber into the waveguide. Inset shows output from waveguide imaged with a camera. b) Picture of an
actual sample with optical fiber epoxied to a Si wafer with waveguide, gold pads, and graphene. Entire
sample plus optical fiber is then attached to another wafer to ensure optical fiber does not break at
attachment point.
21
optical coupling. After alignment, we fixed the fiber using epoxy and cured it using a heat lamp.
The image of the alignment process as well as final emission device before loading to vacuum
chamber is shown in Figure 2.7.
2.6.2. Linear Current vs. Field Graphs for Free Space and Waveguide Samples
Figure 2.8: a) Free space emitter I-E curves. b) Waveguide coupled I-E curve.
5
4
3
2
1
0
Current (pA)
3.0 2.0 1.0 0.0
E(V/µm)
Light
Dark
140
120
100
80
60
40
20
0
Current (pA)
4 3 2 1 0
E(V/µm)
Light
Dark
22
2.6.3. Free-Space Excitation of Graphene on Si3N4/SiO2 Substrates
Using the same substrate structure as the silicon nitride waveguide, we have tested the free space
excitation of graphene. In this control experiment, we ensure that the results observed on the
waveguide case are not due to the difference in substrate between the waveguide (Si3N4/SiO2) and
free space (doped Si) considered in the paper. Here, using the same excitation power (190 mW),
we see that the current observed under two applied electric field conditions ranges from 500 fA to
~900 fA. This is a similar current level as observed from the graphene on silicon.
Figure 2.9: a) Schematic of graphene on Si 3N 4/SiO 2 substrate, identical to the waveguide structure. b)
Current vs time for free space excitation under the same conditions as the free space emitter shown in
the main text (optical power = 190 mW).
23
2.6.4. Photoresponse and Stability
2.6.5. Field Enhancement Calculations
The E-field enhancement factor of the waveguide is extracted from dark current measurement of
graphene above waveguide. The raw data of dark current and the corresponding Fowler-Nordheim
plot is shown below. This is extracted with a graphene work function of 4.5 eV which results in
β= 498 as the enhancement factor.
Figure 2.10: Representative curve showing how devices respond to light. Initial overshoot is
attributed to laser power overshoot. Values reported for current vs. power curves were all reported
from stable region, not overshoot region.
24
2.7. Electron Emission Calculations
2.7.1 General Approach:
We have used an open-source 2D Monte Carlo simulation package for semiconductor transport,
Archimedes. We have modified the codes of the simulator to accommodate the linear dispersion
relationship as well as for implementing the scattering mechanisms more rigorously. However,
the flow of the code and the basic framework have remained the same as original Archimedes.
Figure 2.11: a) Dark current measurement of graphene waveguide. b) Tunneling emission region
identification. c) Fit for field enhancement factor extraction.
25
2.7.2 Initializing the equilibrium carriers:
The linear dispersion relationship near Dirac point (approximately 2.5 eV above and below) gives
rise to a density of states that is also linear to energy. Restricting ourselves to the linear regime, we
initialize the equilibrium carriers in the valence band down to -2.5 eV where the Dirac point
denotes 0 eV . Depending on the carrier density, we choose the Fermi level for graphene. The
density of states for graphene reads
() =
ħ
(Eq. S1)
Where D(E) is the density of states in the units eV
-1
m
-2
and vF is the Fermi velocity of graphene
(10
6
ms
-1
). We initialize the electrons according to their density of states at each energy and fill the
states according to the Fermi distribution of the corresponding temperature. The valence and
conduction band electrons are identified by a specific variable that reads -1 and +1 for the valence
and conduction band respectively. The electrons are initialized in both K and K’ valleys and are
represented by a variable that has a value of 1 for K valley and -1 for K’ valley. Five million
particles are initialized, with each particle corresponding to an electron. This corresponds to a the
simulation of 1.25 µm
2
of a graphene monolayer in the energy range of interest, which is 2.5 eV
below the Dirac point and above in energy. At this stage, we also record the number of states at
each energy level as a reference so that we can accurately capture Pauli blocking once the
simulation progresses.
26
2.7.3 Scattering mechanisms
We have calculated the scattering rates for each mechanism using Fermi’s golden rule that is given
by
=
ℏ
∑ | (,
)|
(1 − (
))
,
(Eq. S2)
Where
is the scattering rate, (, ′) is the matrix element for the transition between the initial
state |⟩ to the final state |′⟩, f(k) is the Fermi-Dirac distribution, and
stands for the energy
conservation. Pauli blocking requires that one electron can only scatter into another state if the
second state is unoccupied. Since we track the electron distribution dynamically and always
calculate the (1 − (
)) term, we automatically ensure Pauli blocking. We numerically calculate
the scattering rates considering Pauli blocking before each scattering event. The scattering rates
for all the scattering mechanisms are then fed into the MC solver where the sum of the rates are
normalized to 1 and a random number between 0 to 1 is then used to determine the scattering
process the electron will go through. In the subsequent discussion, we will focus on the matrix
element for each scattering mechanism.
2.7.4 Electron-electron scattering
Electrons in a solid feel a coulombic potential that causes them to elastically scatter. The matrix
element for electron-electron scattering in graphene is given by
(
,
,
,
) =
+ 1
,
,
,
,
(Eq. S3)
Where |
⟩, |
⟩ are the initial states of the interacting electrons and |
⟩, |
⟩ are the final states
respectively, is the Lindhard dielectric function, =
−
=
−
is the change in
27
wavevector,
is the Bohr radius (0.0529 nm) and
is the effective atomic number for carbon
(4.6)
2
.
,
,
=
1 +
,
∗
(
)(
)
|(
)(
)|
1 +
,
∗
(
)(
)
|(
)(
)|
where
,
and
,
are 1 for
interband processes and -1 for intraband processes
2
. () is the tight-binding coefficient
considering three nearest neighbours. The Lindhard dielectric function ( ) has been extracted from
the previously published data. If graphene rests on a substrate with a dielectric constant of
, then
the effective dielectric function becomes
(
)
where
is the dielectric constant of air medium.
Before each scattering step in the simulation, a partner electron is chosen randomly from the Fermi
sea. For each pair of electrons, there are a range of final states available. We choose a pair of final
states from the available pairs randomly. Then the scattering rate is calculated for the pairs of initial
and final states using Fermi’s golden rule.
2.7.5 Electron-phonon scattering
There are two atoms in a unit cell of graphene and this allows graphene to have both acoustic and
optical phonon branches. There are six phonon branches: longitudinal optic (LO), transverse optic
(TO), out-of-plane optic (ZO), longitudinal acoustic (LA), transverse acoustic (TA), and out-of-
plane acoustic (ZA) phonons. However, among these phonons, the out-of-plane phonons do not
contribute to scattering significantly except for the case of freestanding graphene. The LO and TO
mode phonons actively participate in the initial cooling of the nonequilibrium carriers till they
have an energy above the phonon energies, 198 and 192 meV for LO and TO respectively. The
normal collision acoustic phonons have very small energy compared to the optical phonons and
do not contribute to the cooling of the nonequilibrium carriers effectively. However, one of the key
cooling mechanisms for graphene with nonequilibrium carrier distribution is the supercollision
acoustic phonon scattering. This supercollision scattering is caused by the disorder of the graphene
28
lattice due to defects and these disorders effectively relax the momentum conservation conditions
during acoustic phonon collisions. During supercollision scattering, it is possible for multiple
acoustic phonons to participate in a single scattering event
and the energy of a supercollision
phonon can be as large as the thermal energy (
) where
is the Boltzmann constant. Hence,
supercollision scattering process can cause a large energy dissipation and effectively cool the hot
electronic distribution. During our simulations, we consider the LO, TO and supercollision
acoustic phonon scatterings.
2.7.6 LO and TO phonons
For both LO and TO phonons, the matrix element squared is given by
| (,
)|
= 0.0405
[1 + cos ( + ′)]
+
±
(Eq. S4)
Here, and ′ are the angles the phonon wavevector makes with the initial state wavevector and
the final state wavevector of the electron respectively. is +1 for interband transitions in case of
LO phonons and -1 for the intraband ones whereas the situation is opposite for the TO phonons.
=
(
)/
is the phonon occupation probability calculated from the Bose-Einstein
distribution for the respective energies of phonons. For phonon emission, we consider the plus
sign, whereas the minus sign is considered during phonon absorption. During each scattering
event, a wavevector is chosen randomly for each optical phonon branch within an allowed range
obtained from the phonon dispersion relation and the corresponding final states for both absorption
and emission are calculated. The scattering rates are calculated from the pair of initial and final
states considering Pauli blocking.
29
2.7.7 Supercollision acoustic phonons
The supercollision acoustic phonon scattering has a matrix element squared
| (,
)|
=
+
±
(Eq. S5)
Here,
is the phonon wavevector,
is the phonon frequency, =
where is the
deformation potential (20 eV),
is the slope of LA phonon dispersion relation (2×10
4
ms
-1
), is
the mass density of graphene (7.6×10
-7
kgm
-2
), A is the area of graphene unit cell (0.051 nm
2
), and
L is the effective mean free path due to supercollision scattering
5
. We make a crude estimation of
= 20 as considered in the original supercollision theory for graphene
5
. Although accurate
determination of
requires the knowledge of the disorder concentration, when we use
=
20, we are able to reproduce experimentally measured dissipated power vs electronic temperature
relationship for graphene
4
. While choosing the final state, only energy conservation is considered
as disorder related processes relax the momentum conservation laws. Then the scattering rate is
calculated considering Pauli blocking.
2.7.8 Calculation of final states
Calculation of the final state is restricted by the energy and momentum conservation laws. During
an electron-electron scattering event between two electrons in the same band, both the scalar and
vector sums of the intial state wavevectors have to be equal to that of the final state wavevectors.
The scalar and vector sums represent the total energy and momentum of the states respectively.
On the other hand, for two electrons in opposite bands, the vector sum of the wavevectors and their
scalar difference need to be conserved. The possible final states for interaction between two
electrons in the same band lie on an ellipse. For interaction between two electrons in different
30
bands, the possible final states lie on a hyperbola. If the initial states have the wavevectors
,
and
,
, then the conic formed by them has one focus at the (0,0) point and
another one at
+
,
+
point. We rotate the conic to align its inclined axes to the
directions parallel to
and
axes to simplify the conic equation. However, we do not perform
any translation operation. Then the equation of the conic becomes
(
)
±
(
)
= 1 where
,
is the center of the conic which is the new coordinate of the point
,
after rotation. The plus and minus signs stand for the ellipse and the hyperbola respectively. The
constants and are determined using
,
and
,
from the standard mathematical
properties of the corresponding conics. Since we predetermine the energy of the final states, we
already know the magnitude of their wavevectors. If the magnitude of one final wavevector is |
|,
that final state will lie on the circle
+
= |
|
. Solving the equation of the conic and the
circle, we get the wavevector itself. However, we have to rotate it back to the original coordinate
system to get
,
. Subtracting
,
from
+
,
+
, we get the other
final state
,
.
The phonon density of states is maximum for an optical phonon branch at the wavevectors
where the slope of phonon dispersion relation becomes zero, i.e. at the extrema. Hence, most of
the phonons that interact with the electrons will have wavevectors corresponding to the extrema
of the phonon dispersion relation. For calculating the final state of an electron after optical phonon
scattering, we choose the magnitude of the phonon wavevector corresponding to the maxima of
that phonon branch. For LO and TO phonons, these magnitudes are ~2 nm
-1
and ~0.7 nm
-1
respectively corresponding to phonon energies of ~198 meV and ~192 meV respectively
2
. The
energy of the final state for the electron is then
±
where plus and minus signs
31
correspond to the absorption and emission of the phonon respectively. If the initial electron
wavevector is
,
and magnitude of phonon wavevector is
, the wavevector of the
final state will be
+
cos (),
+
sin () where is the phase of the phonon
wavevector that needs to be determined. Since we know the energy of the final state, magnitude
of the wavevector of final state |
| is already known and represents a circle,
+
= |
|
.
Therefore, the final wavevector should satisfy this equation,
+
cos ()
+
+
sin ()
= |
|
. From this equation, we solve for the only unknown and the wavevector
of the final state is obtained.
For supercollision scattering, we ignore momentum conservation. We consider a
supercollision phonon to have an energy equal to the thermal energy (
) and the energy of the
final state is then
±
. We randomize the wavevector of the final state for this energy
according to the dispersion relation of graphene.
2.7.9 Dynamic calculation of the electronic temperature
Heating of the electronic population of graphene is one of the most prominent features of the
nonequilibrium carrier dynamics of graphene. However, it is difficult to accurately calculate the
electronic temperature without analyzing and fitting the distribution itself as the system evolves.
We have dynamically calculated the electronic temperature without performing any fitting process.
A thermalized Fermi-Dirac distribution is related to its characteristic temperature by the relation
=
(
)/
(Eq. S6)
32
Differentiating the function with respect to , we get
= −
(
)/
. The
vs
plot has
a minima at =
with a value of
(.)
(
)/
=
.
. After passing our dynamically
calculated distribution function through a smoothing function to eliminate artifacts in minima, we
can calculate the electronic temperature from the minima situated at the Fermi level.
2.7.10 Modeling of emission current
The emission current directly depends on the tunneling rate of the electrons from graphene surface.
Following the tunneling Hamiltonian approach advocated by Bardeen, we calculate the tunneling
matrix element for graphene using WKB approximation similar to Harrison. For the tunneling
direction along z-axis, the tunneling matrix element squared then reads
| (
)|
=
(
ℏ
∫ (
)
.
)
(
)
(
)
(Eq.S7)
Here,
(
) and
(
) are the one-dimensional density of states available for tunneling for
graphene and vacuum respectively.
=
/ is the effective tunneling distance under the
triangular barrier as determined from the local electric field.
is the barrier seen by the electron
and we have considered graphene Dirac point to be 4.5 eV below the vacuum level. We consider
a model where in-plane momentum is not conserved
12,13
. Relaxing the momentum matching
condition is justified as the electric field does not terminate on the graphene sheet perpendicularly,
but rather is terminated at certain points, giving rise to an enhancement of the field. When
momentum is not conserved, the in-plane energy of the electrons also needs to be considered while
considering the effective barrier height. The one-dimensional density of states is given by
33
where is the length where the electrons are confined. For a quantum well, corresponds to the
width of the well and
ℏ
is the group velocity (
) of the electrons. Therefore, if we consider
graphene to be a finite rectangular quantum well with a barrier height of
and width of ,
(
)
=
ℏ
. The term
is called the attempt frequency of electrons in a quantum well which
is a quantitative measure of how frequently electrons are hitting the tunnel barrier. While
calculating the tunneling rate,
(
)
eventually cancels during the summation since summing
over the energy conserving delta function results in a
(
) term. Following the approach of
de Vega et. al., we use the barrier height and width to be free parameters so that the binding energy
of Dirac point of graphene becomes 4.5 eV and coincides with the first excited state of the quantum
well. The reason behind choosing the first excited state is to mimic the antisymmetric nature of the
2pz orbital of graphene. Solving the time independent Schrodinger equation,
= 45 and =
0.12 give us the desired behavior for the quantum well
14
. The eigenenergy of the first excited
state E1 then gives us the classical group velocity (
=
) of an electron in that state. Then
the ratio
gives us the attempt frequency (
~1.6 × 10
). The current density due to
field emission can be calculated from the equation
(, ) = ∫ () (, )()
(Eq. S8)
Where (, ) is the tunneling rate obtained from the tunneling matrix element and Fermi’s
golden rule as mentioned above. The equation for (, ) reads
(, ) =
2
ℏ
| (
)|
1 − (
)
,
34
=
2
ℏ
exp (−
2
ℏ
∫ (
− )
.
)
4
(
)
(
)
(1 − 0)
,
=
2
ℏ
exp (−
2
ℏ
∫ (
− )
.
)
4
2ℏ
(
)
(
)
(, ) = 2
exp (−
ℏ
∫ (
− )
.
) (Eq. S9)
Here, are the energy of the electron and the local electric field respectively. We have
considered all the final states in vacuum to be available and hence set (
) = 0. In addition to the
field emission current, we also consider the current due to the direct emission of electrons
generated because of the optical pumping from the CW laser at the energy
above Dirac
point. The direct emission current density is given by
(, ) = ∫ (,
) (( ), )
(Eq. S10)
Here, ( ) is the energy of the photoexcited electron as a function of time, with (0) =
,
and the time dependence is as shown in Figure 2.4c. (,
) is the generation rate. While
numerically evaluating the integral, we use the time dependent energy curve from Figure 4c
calculate the tunneling rates.
2.7.11 Emission current calculation
For our waveguide integrated graphene, the maximum power density is 2.3 × 10
W/m
2
from our
measurements and optical modeling. This is not large enough to cause any significant heating of
the electron population above the lattice temperature. Therefore, we consider an electronic
temperature of ~300K for the current calculations. In addition, we consider that graphene electron
density is 1.6 × 10
cm
-2
. Using the model described above, we then calculate the emission
35
current as we vary both the local electric field and the power density. The generation rate of the
electron-hole pairs is proportional to the power density as there is no significant multiphoton
absorption process in our power density regime. In the figure 2.4f, we can see a clear distinction
between two different emission processes: the field emission of the thermal electrons and the direct
emission of the photogenerated electrons. For small local fields, the direct emission process
dominates the emission current. As the local field increases, the contribution from the field
emission starts becoming significant and finally overwhelms the direct emission current (Figure
2.12a). The crossover between the field emission and direct emission happens at an applied field
of ~3.9 V/µm with a field enhancement factor of 498 (Figure 2.12b). This is in good agreement
with the experimental data where field emission becomes significant ~3.5 V/µm. To then calculate
the current, we estimate the emitting area in the device. To do this, we use the device area, which
is 50 µm × 4 mm, and then scale it by the extracted field enhancement factor of β=498, and assume
this is the emitting area. In our case, the emitting area is 402 µm
2
. This area is then multiplied by
the current densities obtained from the simulation to calculate the device current. At the crossover
Figure 2.12. a) Field emission and hot electron emission current density vs local electric field for an
optical generation rate corresponding to an optical power density of S = 2.3×10
4
W/m
2
. b) Same graph
scaled for applied electric field using the field enhancement factor of 498.
10
-13
10
-11
10
-9
10
-7
10
-5
10
-3
10
-1
10
1
10
3
Current Density (A/m
2
)
2000 1500
Local Electric Field (V/ m)
Field Emission
Hot Electron
Total
10
-13
10
-11
10
-9
10
-7
10
-5
10
-3
10
-1
10
1
10
3
Current Density (A/m
2
)
4.0 3.0 2.0
Electric Field (V/ m)
Field Emission
Hot Electron
Total
a
b
36
field, the total emission current from the model is found to be ~50 pA. This current is also in good
agreement with the experimentally measured current of at the cross over field of ~130 pA.
2.8 Monte Carlo simulation comparisons
2.8.1 Scattering rates
We have calculated the average scattering rates for different scattering mechanisms as mentioned
above. The calculated LO and TO phonon scattering rates are in good agreement with the ones
obtained from first principles calculation by Borysenko et. al and shown in Figure 2.13. Our
electron-electron scattering rates are also within the same order (~10
13
s
-1
) as predicted by the
hydrodynamic theory of graphene (
~
ℏ
= 3.9 × 10
)
16
. The electron-electron scattering
rate depends mainly on three factors: the electron concentration available for scattering, the
momentum exchanged between two electrons and the density of the available final states. Increase
in the later two factors have opposite effects on the net scattering rate. At lower energies, both the
momentum exchange and the density of available states are small whereas they tend to be larger
at higher energies. Because of these two opposing effects, the electron-electron scattering rates
Figure 2.13: Comparison of calculated optical phonon scattering rates with literature
37
first increase with electron energy when the effect of momentum exchange is overwhelmed by the
increase in the density of states. However, at higher energies, the increase in the momentum
exchange overrides and the overall electron-electron scattering rates start decreasing. At higher
electronic temperature, the concentration of electrons increases and consequently the number of
scattering events increases. This causes an increase in the scattering rates with increasing electronic
temperature.
2.8.2 Power density-electronic temperature relationship
The scattering rates are extremely important for estimating the electronic temperature for a certain
supplied power density. The photoexcited carriers lose the excess energy to the environment
through inelastic phonon scattering events. In the steady state, the power density supplied to
graphene must equal the energy lost due to these inelastic collisions.
= ∑
∫
(,)
∆
(, )()
(Eq. S11)
Here, is the supplied power density,
is the scattering rate for the
inelastic scattering process,
∆
is the change in energy during the scattering process (positive for absorption and negative for
emission processes). The scattering rate (
) of a specific mechanism corresponds to the number of
scattering events an electron goes through per unit time,
∆
(,)
corresponds to the total energy
change per unit time due to that scattering mechanism, and (, )() term gives the number
of available electrons within the energy interval per unit area. Therefore, the integration gives
us the total energy change per unit area per unit time, i.e., the power density change due to an
inelastic scattering mechanism. When we perform the sum over all the scattering mechanisms, we
get the total power density change by all the electrons in graphene at the temperature, T. Steady
38
state condition requires that this change in power density must be replenished by the supplied
power density. Hence, a certain supplied power density can support a unique electronic
temperature in steady state. The relevant inelastic scattering processes for graphene are
supercollision acoustic phonon scattering and optical phonon scattering (LO and TO). For optical
phonons, ∆
~ 190 and for supercollision acoustic phonons, ∆
~
. Putting in the
scattering rates obtained from matrix elements discussed above, we were able to reproduce the
relationship between and experimentally observed by Betz et. al
4
. From figure 2.14, we see
that the power density (>10
8
W/m
2
) required to initiate any electronic heating of the population in
graphene is larger than our experimental conditions. Thus we do not expect there to be any heating
of carriers over the lattice.
2.8.3 Reproducing published results with Monte Carlo simulations
To demonstrate the ability of the Monte Carlo simulator, we have simulated for the conditions of
a pump-probe experiment on graphene performed by Malic et. al. The published result analyzed
the experimental data using graphene Bloch equations and we have reproduced some of their
Figure 2.14: Steady state electronic temperature as a function of power density
39
relevant results using our Monte Carlo simulator. Following Malic et al, we have also considered
graphene on top of mica (
= 6) and a laser pulse of 0.3 mJ/cm
2
centered at 1.5 eV with a
temporal width of 10 fs. Here we have modeled the nonequilibrium distribution as an excited
population resulting from a Gaussian pump pulse with 10 fs temporal width. We converted the
pump fluence to the number of excited carriers within a spectral width (0.6 eV) corresponding to
the temporal width of the Gaussian pulse.
We have primarily been concerned with the evolution of the electronic temperature with
time. As shown in figure 2.15, our temperature evolution shows a good fit to the analysis performed
by Malic et al.
Figure 2.15: Evolution of electronic temperature with time
40
2.9 Heating of Graphene
To place an upper bound on the actual heating the graphene could experience due to absorbed flux,
we have carried out a simple calculation where we assumed that the silicon wafer acted as a heat
sink, and the silicon nitride combined with the silicon oxide were the thermal insulation. Using the
geometry shown in Figure 2.16, we have estimated that the maximum heating expected for 5 mW
of power absorbed case would be 0.7 K, and for 100 mW of absorbed power would be 14 K.
Figure 2.16: Heating calculation geometry
L = 1 mm
W = 50 m
t = 10 m
Thermal Conductivity
k=1.4 W/m-K
Graphene (Heat Source)
Silicon (Heat Sink)
41
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field photoemission. Physical review letters 105, 147601 (2010).
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of electrons from metallic nanostructures. Nature Photonics 8, 37 (2014).
8 Dombi, P. t. et al. Ultrafast strong-field photoemission from plasmonic nanoparticles.
Nano letters 13, 674-678 (2013).
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from sharp metal tips. Physical review letters 105, 257601 (2010).
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field-controlled photoemission from plasmonic nanoparticles. Nature Physics 13, 335
(2017).
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heterostructure. 12, 455 (2016).
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43
Chapter 3: Performance limits of graphene photoemitters
3.1 Introduction
Hot electron emission from waveguide integrated graphene has been recently shown to occur at
optical power densities multiple orders of magnitude lower than metal tips excited by sub-
workfunction photons. However, the experimentally observed electron emission currents were
small, limiting the practical uses of such a mechanism. Here, we explore the performance limits of
hot electron emission in graphene through experimentally calibrated simulations. Two regimes of
non-equilibrium emission in graphene are identified, (i) single particle hot electron emission,
where an electron is excited by a photon, and is emitted before losing significant energy through
scattering, and (ii) ensemble hot electron emission, where the photon source causes non-
equilibrium heating of the electron population beyond the electron lattice temperature. It is shown
that through appropriate selection of photon energy, optical power density, and applied electric
field hot electron emission can be used to create ultra-high current electron emitters with ultra-fast
temporal responses in both the single particle and ensemble heating regimes. These results suggest
that through appropriate design, hot electron emitters may overcome the limitations of thermionic
and field emitters.
3.2 Performance limits of hot electron emission from graphene
From modern electron microscopes to free electron lasers, electron emission devices play an
important role in a diverse range of applications
1-6
. Photoemitters constitute a class of electron
emitters that uses photons as the source of energy to produce the electron beam. Photoemission
occurs via three mechanisms, single photon emission, multi-photon emission, or strong-field
emission. Single photon emitters, where the incident photon has an energy greater than the
workfunction of the emitter are the most efficient and broadly used, but also require significant
44
infrastructure in terms of high photon energy lasers, or ultra-high vacuum chambers for negative
electron affinity emitters. Multi-photon and strong-field emitters allow the use of lower photon
energy lasers, potentially enabling the use of compact semiconductor lasers and integrated
photonics, but require high power densities (> 10
15
W/m
2
), which typically necessitate the use of
ultra-fast pulsed lasers
7-11
. Recently, it has been shown that hot electrons in graphene can mediate
photoemission from sub-workfunction photons at power densities over 5 orders of magnitude
lower than metal tips
12
.
In the previously explored structure, the graphene emitter sits on top of a waveguide that
evanescently couples the photons to the electrons. The thickness (~0.35 nm) of graphene directly
addresses the issue of long response time eliminating the need for the photoexcited electrons to be
transported to the emitting surface, as is necessary with standard metallic photoemitters. Favorable
scattering rates in graphene also allowed the photoexcited hot electrons to be emitted into vacuum
before thermalizing down to the Fermi level. Due to these features of graphene, it has been shown
that hot electron emission from waveguide integrated graphene using subworkfunction photons
can occur at power densities that are multiple orders of magnitude lower than metallic tips
emitters
12-15
. Previously, it was shown that an electron emission model obtained by solving the
nonequilibrium Monte Carlo Boltzmann transport equation (MCBTE) could quantitatively explain
the nature of the observed current density as a function of the applied electric field, optical power
density and photon energy
12,16
. In addition, there has been a number of theoretical studies on
graphene based Schottky barrier devices modeling the thermionic and photoexcited electron
emission of electrons over the barrier as well as on generalized 2D material based Schottky barrier
devices
17-20
. In this paper, we theoretically investigate the performance limits of electron emission
from graphene within a range of different subworkfunction photon energies, optical power
45
densities and electric fields, identifying experimental conditions under which high current density,
quantum efficiency, and ultrafast hot electron photoemitters could operate.
3.3 Hot electron emission mechanism in graphene
The unique linear band structure of graphene allows its electrons to be excited directly from the
valence band to the conduction band within photon energies ranging from far IR to UV . These
photoexcited electrons, referred to as “hot electrons,” in graphene are out of equilibrium compared
to the initial electron distribution. These nonequilibrium hot electrons therefore go through
different scattering mechanisms where they lose energy and thermalize. The most prominent
scattering mechanisms in graphene are: (1) electron-electron (e-e) scattering, (2) optical phonon
(OP) scattering, and (3) supercollision acoustic phonon (SC) scattering
12,21-28
. While e-e scattering
allows the hot electrons to elastically redistribute their excess energy among the “cold” electrons
in the Fermi sea, both OP and SC scattering cause them to lose energy to the lattice. When a vertical
electric field is applied to graphene, the vacuum barrier bends in response to the field and these
hot electrons can tunnel through the distorted vacuum barrier. In addition to the usual scattering
mechanisms, this tunneling mechanism provides another possible pathway for the hot electrons to
reach a different final state
12,21
. Probability rates of these mechanisms depend on the energy and
momenta of the involved electrons, phonons as well as the bandstructure of graphene and can be
46
quantitatively calculated using Fermi’s golden rule. Figure 3.1 summarizes the basic mechanism
of electron emission from graphene.
3.4 Scattering and tunneling rates
To quantitatively evaluate the electron emission current from graphene as a function of photon
energy, optical power density and electric field, it is important that we quantitatively determine the
rates of the scattering mechanisms and tunneling. Here, Fermi’s golden rule is used to calculate
the rates
12,29
:
=
ℏ
∑ | (,
)|
(1 − (
))
,
(1)
Figure 3.1: Emission of photogenerated hot electrons from graphene while they
go through the scattering processes
47
Here,
is the scattering rate, (, ′) is the matrix element for the transition between the initial
state |⟩ to the final state |′⟩, f(k) is the Fermi-Dirac distribution, and
ensures the energy
conservation. For different scattering mechanisms, the matrix element will be different and
therefore will lead to different scattering rates. Calculation of each of the scattering rates have been
carried out following the previous work
12
.
Figure 3.2a shows the scattering rates for all the scattering mechanisms as a function of electron
energy for an electronic temperature of 300K while figure 3.2b summarizes the total scattering
Figure 3.2: Simulation of hot electron scattering, electron emission and electronic
temperature. a, hot electron scattering rates for the major scattering mechanisms of graphene
for electronic temperature of 300K. b, total scattering rates for different electronic
temperatures. c, energy resolved tunneling rates for hot electrons in graphene. d, simulated
time resolved energy trajectory of hot electrons excited by different photon energies. e,
average energy lost by hot electrons due to e-e scattering. f, simulated electronic temperature
of graphene as a function of absorbed optical power density
48
rates for different electronic temperatures. Since increasing electronic temperature increases the
number of electrons in the Fermi sea, the e-e scattering increases significantly. This ultimately
leads to an increase in the overall scattering rates with increasing electronic temperature. The
tunneling rates for different electric fields are shown in figure 3.2c. Electrons with higher energy
see a smaller barrier and therefore have larger tunneling rates. On the other hand, when electric
field is increased, the nearly triangular vacuum barrier is further thinned and there is an exponential
increase in the tunneling rate. Therefore, an electron with higher energy will be able to tunnel the
barrier more frequently if a larger electric field is applied.
3.5 Results from MCBTE solver
The MCBTE simulation uses the calculated scattering rates to determine the energy-time trajectory
of the hot electrons. An open source Monte Carlo simulator, Archimedes, was modified to solve
the MCBTE for graphene
16
. The simulation is initialized with 5 million electrons which is
equivalent of simulating 0.5 μm
2
of graphene. Figure 3.2d shows the calculated trajectories for
four different photon energies when the electronic temperature is 300K. The trajectories have been
obtained by tracking the average energy of 50 photoexcited electrons during each simulation and
then averaging over 50 different simulations. The trajectory for 1 eV photons shows us three
distinct regions: (1) an initial drop in electron energy due to e-e scattering, (2) dissipation of energy
due to OP scattering until the electron energy goes below the OP energy (~190 meV), and (3) a
slower dissipation in energy due to SC scattering. Since e-e scattering rates are considerably
smaller than the OP scattering rates for higher energy electrons, the e-e scattering dominated initial
energy loss cannot be observed in the trajectories obtained for higher energy photons. Average
energy loss of hot electrons due to e-e scattering events has been shown in figure 3.2e. Figure 3.2f
shows the change in electronic temperature as a function of absorbed optical power density. Using
49
these scattering rates, the calculated electronic temperature profile is shown to match the
temperature experimentally observed by Betz et al
12,23
.
3.6 Emission current model
We have modeled the emission current using a quantum mechanical tunneling model
12,30-33
.
Throughout the paper, when we mention thermalized electrons, we refer to the electrons that follow
the Fermi-Dirac distribution with a well-defined electronic temperature. This temperature may be
that of the lattice, or under specific excitation conditions may be higher than the lattice temperature
itself. When these electrons are emitted out of the material over the vacuum barrier without any
influence of electric field, we define the current density due to this flux to be “thermionic emission”
current density. However, under the influence of electric field, there will be an increased flux of
emitted electrons as they have a finite rate of tunneling through the barrier as well. We define this
enhanced emission current density to be “thermionic field emission” (TFE) current density which
can be expressed as
12,17,34
(, ) = ∫ () (, )(, )
(2)
Here, is the electronic temperature, is the energy of the electron, is the electric field, is the
elementary charge, () is the density of states of graphene
35
, (, ) is the tunneling rate and
(, ) is the Fermi-Dirac distribution. This model for TFE current density was developed by
Sinha et. al.
34
and Ang et. al.
17
earlier while Rezaeifar et. al. redeveloped it with numerical
implementation
12
. For different optical power densities, we find the electronic temperature from
figure 2f and evaluate the integral numerically to calculate the current density due to the thermal
electrons.
50
In order to calculate the emission current due to photoexcited electrons, we consider the
possibility of multiphoton absorption (MPA)
36,37
so that every absorbed photon results in n
photoexcited electron-hole pairs for n photon absorption and therefore calculate the generation rate
from the relation, = ∑
(,
)
×
. Here, is the absorbed power density and
=
is the generation rate for the i-photon absorption process. Figure 3.3a shows the ratio of two
photon absorption (TPA) rate to single photon absorption (SPA) rate for different photon energies
and power densities. Now, we can calculate the emission current due to hot electrons (HE) from
the following relation
12
(, ) = ∑
∫
(,
) (( ), )
(3)
51
Here, ( ) is the energy of the hot electron as a function of time as shown in figure 3.2d where
(0) =
for n photon absorption.
3.7 Calculation and analysis
Using these relationships, we have calculated the current densities for four different photon
energies (1-4 eV) for a power density of 10
4
W/m
2
as we varied the electric field from 0.5 to 5
Figure 3.3: Electron emission current calculation for low power density
photoexcitation. a, ratio of TPA rate to SPA rate in graphene different absorbed
power densities. b, simulated HE and TFE current density for different photon
energies at an absorbed power density of 10
4
W/m
2
(dots: SPA, connected lines:
MPA). c, crossover electric field and current densities as a function of photon
energy. d, HE current density as a function of photon energy for different
electric fields
52
V/nm. The reason behind choosing 10
4
W/m
2
is to investigate the current density when there is no
significant heating of the electron population. We ignore electronic temperature deviation below a
power density of ~10
6
W/m
2
, as the electronic temperature does not deviate significantly. We have
considered MPA processes to order, = 3 for
= 1, 2 eV and = 2 for
= 3, 4 eV . Figure
3.3b shows the calculated hot electron current densities for different photon energies as well as the
TFE current density. At smaller electric fields, the thermal electrons see a wider and larger energy
barrier for tunneling whereas the high energy electrons see a narrower and smaller energy barrier.
Therefore, the hot electron component dominates at the smaller electric fields over the thermal
component as observed for the case of higher energy photons (>1 eV). At even smaller electric
fields, the MPA processes dominate over SPA for higher photon energies. There are two competing
factors that determine whether SPA or MPA process will dominate the observed current density:
(1) energy of the hot electron and (2) efficiency of the MPA process. The initial energy difference
between an electron that absorbed one photon and an electron that absorbed n photons is the energy
of (n-1) photons. The tunneling rate increases exponentially with the increase in electron energy
12
.
However, the magnitude of current density due to MPA at these conditions is below the threshold
current density likely to be observed in an experiment. From figure 3.3b, we can observe a clear
crossover between the hot electron dominated regime and the TFE dominated regime. However,
for 1 eV photons and below, the hot electron current is not significant enough within the electric
field range considered and no crossover can be observed. Figure 3.3c shows the crossover fields
and current densities as a function of photon energy. For higher photon energies, the crossover
field increases at a nearly linear rate and therefore the crossover current densities increase by
several orders of magnitude. Figure 3.3d shows the hot electron current density as a function of
photon energy for different electric fields. We can see an exponential increase in current density
53
with increasing photon energies. However, the increase is less steep for larger electric fields as the
barrier gets thinner and the difference in barrier heights play a less effective role in determining
the tunneling rates. For lower photon energies, the difference in barrier heights is even smaller and
the increase in HE current is even less prominent. The most significant observation from these
calculations is that there exists a distinct crossover field for every photon energy below which hot
electrons will dominate the emission current and for the same power density of different photon
energies and the same electric field below the crossover field, the efficiency of converting photons
to emitted electrons will be higher for higher photon energies.
For power densities >10
6
W/m
2
, the electron population will heat up to a temperature that
is significantly greater than the lattice temperature (300K). In addition to cold field emission and
single hot electron emission, this electronic heating leads to the emission of ensemble hot
electrons
38,39
. Figure 3.4a shows the calculated HE current densities for an electric field of 1 V/nm
considering the different hot electron trajectories obtained for the electronic temperatures produced
by the corresponding power densities. MPA processes exceed the SPA process only at higher power
Figure 3.4: Electron emission current calculation for large power densities. a, calculated HE
current density for different photon energies at an electric field of 1.0 V/nm (dots: SPA,
connected lines: MPA). b, calculated TFE current density at 0.5 V/nm and 1.0 V/nm fields. c,
crossover between different emission mechanisms at different ranges of absorbed power
densities calculated at 1.6 V/nm for photoexcitation by 3 eV photons.
54
densities. The corresponding TFE current densities due to ensemble carrier heating are shown in
Figure 3.4b. For power densities > 10
9
W/m
2
, the electronic temperature rises above 1000K and
the effect of increasing electric field becomes insignificant. Figure 3.4c shows the different
components of the total emission current density for
= 3 eV and = 1.6 V/nm. Here, we
can identify three different mechanisms of electron emission that dominate at different ranges of
power densities: (1) field emission at small power densities, (2) single hot electron emission at
intermediate power densities, and (3) ensemble hot electron emission at large power densities,
Since both hot electron generation rate and electronic heating are small at smaller power densities,
this regime is dominated by the tunneling of thermal electrons within few
(~26 ) of the
Fermi level, i.e., cold field emission. For intermediate power densities, electronic heating is still
insignificant whereas the generation rates increase proportionally and hence this regime is
dominated by the single hot electron emission. Beyond this regime, the electronic heating becomes
more significant and thermionic emission due to ensemble hot electrons dominates. Figure 3.4c
also shows the experimentally measured electron emission current from Fatemeh et. al. for the
same electric field and photon energy which shows a good agreement to our theoretical values
12
.
55
Figure 3.5a shows the individual emission components for EPh = 4 eV and different electric fields
from 2 to 5 V/nm to further elucidate how the electron emission mechanism changes between these
three regimes. The number of thermal electrons is very large compared to the number of hot
electrons before electronic heating kicks in. As a result, the increase in electric field favors field
emission more. This effect can very easily be seen in figure 3.5a as the HE regime is completely
overcome by the field emission regime at 5 V/nm. For the thermionic emission regime, the
increasing electric field does not change the emission current significantly as observed in figure
3.4b as well.
Figure 3.5: Performance limits of the photoemitter. (a) Change in the electron emission
mechanism with increasing electric field for EPh = 4 eV , (b) QE for different photon energies
and power densities. Response time of the photoemitter in the (c) HE and (d) electronic
heating regimes.
56
3.8 Experimental roadmap
Using the established tools, QE, response time, and current density are interrogated. Figure 3.5b
shows the QE of the graphene photoemitter as a function of absorbed power density for multiple
photon energies and an electric field of 2 V/nm. Photoemission QE is not a defined quantity in the
field emission dominated regime and therefore we have showed QE only for the single and
ensemble hot electron emission regimes. In the single hot electron regime, current density
increases linearly with absorbed power density and hence QE becomes constant over this range.
Photon energy determines the crossover power density between field emission and hot electron
regimes. While hot electron emission starts dominating at a power density of 10
2
W/m
2
for 4 eV
photons with a QE of ~10
-6
, 1 eV photons require a power density of 10
7
W/m
2
before moving on
to the hot electron regime with a significantly smaller QE of ~10
-11
. For increasing electric fields,
this constant QE in the HE regime increases and can exceed 100% for electric fields higher than
~4.8 V/nm for EPh = 4 eV as shown in Figure 3.8. For single photon photoemission or single photon
hot electron emission, it is not possible to get a QE exceeding 100%. However, when there is
ensemble carrier heating, the redistribution of excess energy between the photoexcited hot
electrons and the cold electrons via e-e scattering causes the sea of cold electrons to become hot
as well. As a result, energy of a single photon can potentially be transferred to many electrons
leading to a seemingly counter intuitive photoemission QE that exceeds 100%. However, it should
be noted that the power conversion efficiency will still be dramatically lower than 100%. In this
ensemble carrier heating regime, the true potential of graphene photoemitter is unleashed as QE
of the device goes above 100% at absorbed power densities above 10
11
W/m
2
irrespective of the
applied electric field. For typical bulk and even thin film metallic photoemitters, the
experimentally observed QE has always been well below 100% to the best of our knowledge
38,40-
57
46
. While theoretically it may be possible to achieve such high QE for metallic photoemitters, the
required power density to raise the electronic temperature would be orders of magnitude higher
compared to graphene primarily because achieving electronic heating in bulk metals requires large
amounts of energy deposited very quickly, and the resulting carriers quickly scatter down, reducing
the electronic temperature below the critical temperature which would allow a QE > 100%.
For pulsed photoexcitation, it is important for a photoemitter to provide an ultrafast response.
Response time (
) is defined as the time required for the photoemission current to drop down to
10% of its initial value
7,47
. However, this response time depends on the regime the photoemitter is
working on. For low energy pulses, there is no electronic heating and therefore HE process
dominates the emission current. As a result, the response time is determined by how fast the energy
of the photoexcited hot electron decays as well as the energy resolved tunneling rate of the
electrons. In figure 3.5c, we have used the energy trajectories (figure 3.2d) obtained from the
MCBTE solver and the energy resolved tunneling rates (figure 3.2c) to calculate
for HE
dominated regime for the graphene photoemitter. Higher photon energies result in larger tunneling
rates and therefore provide shorter response times. Larger electric fields increase the tunneling rate
for all energies and therefore the decay in emission current slows down resulting in an increase in
the response time. The negligible thickness of graphene ensures that the hot electrons are always
at the emitting surface thereby eliminating the transport time to the surface. This essentially
enables graphene to respond to the absorbed photons at a subpicosecond timescale going as short
as ~20 fs. However, for high energy pulses, there is a significant electronic heating which makes
thermionic emission the dominant emission mechanism. Using the energy dependent scattering
rates obtained from the MCBTE solver, we can calculate the temporal evolution of the electronic
temperature for a given absorbed pump fluence, i.e., energy density. From this electronic
58
temperature profile, we have calculated the time resolved current densities and therefore the
response time. Figure 3.5d shows the graphene photoemitter response times for the thermionic
emission dominated regime for different absorbed pump fluences. It is noteworthy to mention that
photon energy does not play a significant role in determining the response time in this regime since
the emission current is predominantly coming from the thermalized hot electrons. We can observe
two different regimes for the response time: (1) a drastic decrease in response time as absorbed
energy density increases in the lower energy density regime and (2) a slower increase in response
time as absorbed energy density increases in the higher energy density regime. There are two
competing mechanisms which cause this. First, there is an electronic temperature dependent
cooling rate, and second, when the energy dependence of tunneling rates increase, the time
dependence of current emission decreases. At low energy densities, electronic temperature rises
quickly with increasing energy density due to the small density of states available in graphene at
lower energies (Fig. 3.8b). Thus, the key mechanism leading to the initial decrease in response
time is the rapid increase in temperature leading to both increased cooling rates and larger changes
in current for the same temperature drop, due to the superlinear current-temperature relationship.
For higher energy densities, the increase in electronic temperature is significantly reduced, as
shown in figure 3.8b due to the larger graphene density of states. However, once at further
increased energy densities, thermionic emission becomes the dominant mechanism, which has a
reduced temperature dependence as compared to thermionic field emission. Thus, the response
times increase. As observed for HE regime response times, higher electric field results in longer
response times for thermionic emission dominated regime as well. In this regime, we observe a
subpicosecond response time within the range of 250 to 500 fs. Therefore, there exists a tradeoff
between maximum current and response time which forces us to choose whether to operate the
59
photoemitter in lower current and faster response HE regime or higher current and slower response
thermionic emission regime. Nevertheless, this opens the path to realizing ultrafast subpicosecond
photoemitters with extremely high current for commercial applications. Integrating optical cavities
such as ring resonators, Fabry-Perot resonators etc. with the graphene photoemitter as well as
engineering the field enhancement factor using nanoscale tips, we can achieve the high power
densities and electric fields to design arrays of commercially viable photoemitters
48,49
. Although
this work exclusively focuses on monolayer graphene photoemitters, it is possible to qualitatively
comment on the performance of few-layer graphene photoemitters as well from this study. While
an n-layer graphene (n > 1) potentially offers a greater higher optical absorption and carrier density
due to the extra layers, any photoexcited hot electron in the i-th layer from the bottom would be
required to transport to the top emitting surface layer (i = n). During this transport, we would
expect this hot electron to have (n-i) times the probability of getting scattered by optical phonons
and subsequently losing ~(n-i)×Eop energy where Eop ≈ 200 meV is the optical phonon energy in
graphene. Due to this additional loss in energy, the tunneling rate and consequently the emission
current will decrease. We believe that the monolayer nature of graphene which allows the hot
electrons to be at the emitting surface at all times plays a very significant role in exhibiting the
exceptionally good photoemission properties predicted by our study.
In conclusion, we have investigated the performance limits of a graphene photoemitter using an
MCBTE solving approach. Our theoretical calculations show that there are two key hot electron
emission mechanisms: single and ensemble hot electron emission. These two mechanisms can be
easily identified due to the existence of a critical optical power density (~10
9
W/m
2
) that clearly
distinguishes the emission current between two different regimes. Below the critical optical power
density, emission current is dominated by the emission of single hot electrons while above this
60
critical power density, significant electronic heating beyond the lattice temperature triggers the
ensemble hot electron emission. In the ensemble hot electron emission regime, it is possible to
obtain a photoemission QE > 100% as well as emission current density exceeding 100 mA/μm
2
.
These graphene photoemitters can be operated with ultra-fast subpicosecond response times while
maintaining an ultra-high emission current. We have further verified the accuracy of our
predictions showing good quantitative agreement between experimentally measured and
theoretically calculated current densities. This prediction provides an experimental roadmap
towards realizing the performance limits of graphene photoemitters and building next generation
electron emission sources that can address the limitations of present-day photoemitters.
3.9 Methods: Simulations
3.9.1. Graphene density of states:
In order to numerically calculate the thermionic field emission (TFE) current, we need to perform
the integral given by equation (2) from the main text. Performing the integral requires graphene’s
Figure 3.6: Graphene density of states
61
density of states
35
, (). Figure 3.6 shows the calculated () used throughout the paper for
calculating
.
3.9.2 Hot electron trajectories:
Figure 3.2d shows the hot electron energy trajectories for electronic temperature of 300K. We also
calculated the trajectories for temperatures upto 800K as shown in figure 3.7. These trajectories
were used to calculate
at different power densities.
Figure 3.7: Hot electron energy trajectories for electronic temperatures of (a) 400K, (b) 500K, (c)
600K, (d) 700K, (e) 800K and (f) for 4 eV photons at different temperatures
62
3.9.3 Multiphoton absorption rate calculation:
In addition to the single photon absorption (SPA) process, our current work considers multiphoton
processes as well. In general, multiphoton absorption (MPA) is a higher order process that becomes
significant only at large power densities. In order to study the MPA efficiency, we have calculated
the ratio of MPA rate to SPA rate of graphene using the theoretical approach outlined by Faisal
36,37
.
According to his approach, the absorption rate of n-photons for graphene is given by
= ∫
( )
(2
ℏ
cos )
() (Eq. S4)
Here,
is the n-photon absorption rate,
is the area of graphene unit cell (0.051 nm
2
),
is the
Fermi velocity of graphene (10
6
ms
-1
),
= ℏ is the single photon energy,
is the Bessel
function of the first kind of order n,
is the electric field of the electromagnetic wave, is the
angular difference between electron momentum and polarization direction of the electromagnetic
wave
12,36
. It is necessary to mention that Figure 3.3a shows the calculated ratio of the two photon
absorption (TPA) rate to SPA rate as a function of photon energy for different power densities.
Here, we can see that the efficiency of the TPA process increases by the same order of magnitude
compared to the order of magnitude increase in the power density. At very large power densities
(~10
13
W/m
2
), TPA becomes almost comparable to the SPA process (
~1) for lower photon
energies.
63
3.9.4 Quantum efficiency (QE) calculation for HE regime:
3.9.5 Response time calculation:
For response time calculation in thermionic emission regime, we calculate the energy loss rate at
different electronic temperature from the following relation
= ∑
∫
(,)
∆
(, )()
(Eq. S5)
Here,
is the energy loss rate, ∆
is the loss of energy during the scattering event, and
is
the probability rate for the
inelastic scattering process. After a time interval , the total energy
of the system goes down to
(, ) =
((0), 0) −
=
∫ (, ( ))()
.
((0), 0) is the total initial energy of the system for an initial
temperature of
= (0). Using these equations, we can calculate the temporal evolution of
electronic temperature as shown in figure 3.9a. Each of these temperatures can be translated to an
Figure 3.8: QE in the HE regime as a function of electric field
for different photon energies
64
absorbed pump fluence,
=
() −
(300) where
(300) is the energy
of the system before absorbing any energy at a lattice temperature of 300K. Figure 3.9b shows the
initial temperature of the system for different absorbed pump fluence. Then we calculate
as a
function of time as shown in figure 3.9c and identify the time intervals for the current to drop to
10% of the initial value, i.e., the response time.
Figure 3.9: (a) Temporal evolution of electronic temperature, (b) Initial electronic temperature
as a function of absorbed pump fluence, and (c) change in current density with time
65
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69
Chapter 4: Hot electron driven hydrogen evolution at gold surfaces
4.1 Introduction
Using hot electrons to drive electrochemical reactions has drawn considerable interest in driving
high-barrier reactions and enabling efficient solar to fuel conversion. However, the conversion
efficiency from hot electrons to electrochemical products is typically low due to high hot electron
scattering rates. Here, it is shown that the hydrogen evolution reaction (HER) in an acidic solution
can be efficiently modulated by hot electrons injected into a thin gold film by an Au-Al2O3-Si
metal-insulator-semiconductor (MIS) junction. Despite the large scattering rates in gold, it is
shown that the hot electron driven HER can reach quantum efficiencies as high as ~85% with a
shift in the onset of hydrogen evolution by ~0.6 V. By simultaneously measuring the currents from
the solution, gold, and silicon terminals during the experiments, we find that the HER rate can be
decomposed into three components: (i) thermal electron, corresponding to the thermal electron
distribution in gold (ii) hot electron, corresponding to electrons injected from silicon into gold
which drive the HER before fully thermalizing and (iii) silicon direct injection, corresponding to
electrons injected from Si into gold that drive the HER before electron-electron scattering occurs.
Through a series of control experiments, we eliminate the possibility of the observed HER rate
modulation coming from lateral resistivity of the thin gold film, pinholes in the gold, oxidation of
the MIS device, and measurement circuit artifacts. Next, we theoretically evaluate the feasibility
of hot electron injection modifying the available supply of electrons. Considering electron-electron
and electron-phonon scattering, we track how hot electrons injected at different energies interact
with the gold-solution interface as they scatter and thermalize. The simulator is first used to
reproduce other published experimental pump-probe hot electron measurements, and then simulate
the experimental conditions used here. These simulations predict that hot electron injection first
70
increases the supply of electrons to the gold-solution interface at higher energies by several orders
of magnitude and causes a peaked electron interaction with the gold-solution interface at the
electron injection energy. The first prediction corresponds to the observed hot electron
electrochemical current, while the second prediction corresponds to the observed silicon direct
injection current. These results indicate that MIS devices offer a versatile platform for hot electron
sources that can efficiently drive electrochemical reactions.
4.2 Hydrogen evolution cathode
Efficiently using hot electrons before thermalization has been an aim of fields such as hot-electron
transistors
1-4
, solar cells
5-7
, plasmonics
8-14
, photoemission
15,16
, memory
17,18
, and solar-to-fuel
19
devices. However, non-equilibrium electrons exhibit lifetimes of ~1-100 fs due to electron-
electron and electron-phonon interactions
20-22
. These ultra-short hot carrier lifetimes drive the
thermalization process to dominate over most other technologically relevant processes, causing
devices to generally have low hot-electron quantum efficiencies. Multiple strategies have been
explored to overcome these challenges, including engineering systems with low-electron densities
and weak electron-phonon coupling, such as quantum dots
23
, minimizing the transit length of hot
electrons, by creating devices using 2-D materials
1,24,25
, and the search for new materials with
naturally favorable scattering rates, such as perovskites
26
. However, the overall efficiency
27,28
of
these hot electron devices have mainly precluded their practical use, with photoemitters
29,30
and
Flash memory
31
as the two exceptions.
4.3 Experimental device and measurements
In this work, we use a metal-insulator-semiconductor junction to controllably create a hot electron
population via tunneling of electrons from the semiconductor conduction band into the metal and
then use that hot electron population to modulate the electrochemical reaction rate at a metal-
71
electrolyte junction. Figure 4.1a shows the basic device structure which consists of an n-type
silicon wafer, an aluminum oxide insulator layer, and a thin gold layer. The entire device is
encapsulated in an epoxy, leaving only the top gold layer exposed, and is immersed in a 0.5 M
H2SO4 solution. A cartoon schematic of the band diagram is shown in Figure 4.1b. MIS junctions
enable injection of the highest energy hot electrons when compared to both metal-insulator-metal
tunnel (MIM) junctions, or metal-semiconductor (MS) junctions. In MIM junctions, the large
density of states around the Fermi levels of the metals cause large currents to flow with relatively
smaller applied biases, limiting the energy at which hot electrons can be injected. For MS
junctions, the offset between the semiconductor conduction band and metal Fermi level are pinned
at the interface, and this causes the injected energy of the hot-electrons to be fixed by the Schottky
Figure 4.1. Device schematics and hot electron injection process. (a) Schematic of the structure of metal
insulator semiconductor device used here. (b) Band diagram of the device and two different paths for
injected hot electrons into the Au region. (c) Current density vs applied voltage for the Au/Al 2O 3/Si
diode used here in both linear and log scale. (d) TCAD Sentaurus simulations of surface electron
concentration as a function of applied bias in the Au/Al 2O 3/Si device.
72
barrier height. In this device, as the voltage across the MIS junction increases, there will be an
increase in both current and the energy at which the hot electrons are injected. This behavior occurs
due to the insulator layer depinning the semiconductor conduction band from metal Fermi level at
the junction. Thus the MIS structure is expected to generate the hottest electrons in the metal when
compared to MS or MIM structures.
Figure 4.1c shows the current density plotted as a function of applied bias for an Au/Al2O3/Si
device with a 12 nm thick gold layer, 6 nm thick Al2O3 layer, and a moderately doped n-type
(5×10
16
cm
-3
) Si wafer. From the device measurements, we see that the current increases
exponentially until VAu-Si~0.4V, and then increases linearly. To understand this behavior, we
simulate the device using a 2-D Technology computer-aided design (TCAD) Sentaurus simulation,
which self-consistently solves the drift-diffusion and Poisson equations. From this simulation, we
extract the silicon surface electron density, plotted in Figure 4.1d on both linear and log scales.
Importantly, the sheet charge density also shows a clear exponential and linear regime. These two
regimes occur depending on where the applied voltage is dropped. In the exponential regime (0 V
< VAu-Si < 0.4 V), the majority of the applied voltage is dropped across the semiconductor depletion
region, changing the semiconductor band bending and therefore surface charge density, but
without causing any significant change in the band offset between the metal Fermi level and
semiconductor conduction band. This occurs due to the oxide capacitance being much greater than
the semiconductor capacitance. Thus, although more electrons are injected from the semiconductor
into the metal in this regime, the relative energy at which they are injected does not significantly
change. Next, the linear charge density regime (0.4 V < VAu-Si) occurs when the majority of the
applied voltage is dropped across the oxide. In this regime there will be a nearly 1:1 ratio between
the applied bias and the change in the semiconductor conduction band edge position with respect
73
to the metal Fermi level. This regime occurs due to the semiconductor capacitance in accumulation
being much greater than the oxide capacitance. From these measurements and simulations, we
estimate that the initial 0.4 V applied bias does not change the offset between the silicon
conduction band and metal, but that for voltages above 0.5 V, the voltage is primarily dropped
across the oxide until the series resistance limits the current.
The electrochemical measurement was carried out using a potentiostat with two working
electrodes to apply independent bias voltages between the gold and solution terminals (VAu-Solution)
and the gold and silicon terminals (VAu-Si). We use a platinum wire as a counter electrode in the
Figure 4.2. Linear sweep voltammetry (LSV) curves of 12nm Au MIS device. (a) Linear scale solution
current density vs applied Au-Solution voltage for varying Au-Si diode voltages and (b) log scale of (a).
(c) Solution current density vs applied Au-Si voltage for varying Au-Solution voltages and (d) log scale
of (c). (e) Tafel relation for the low V Au-Si and (f) high V Au-Si.
a
b
c
d
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
10
1
J
Solution
(mA/cm
2
)
1.5 1.0 0.5
V
Au-Si (V)
V
Au-Solution
= -0.2V
V
Au-Solution
= -0.4V
V
Au-Solution
= -0.6V
V
Au-Solution
= -0.8V
20
18
16
14
12
10
8
6
4
2
0
J
Solution
(mA/cm
2
)
1.5 1.0 0.5
V
Au-Si (V)
V
Au-Solution
= -0.2V
V
Au-Solution
= -0.4V
V
Au-Solution
= -0.6V
V
Au-Solution
= -0.8V
Hot electron shift
50
45
40
35
30
25
20
15
10
5
0
J
Solution
(mA/cm
2
)
-1.0 0.0 1.0
V
Au-Solution
(V vs Ag/AgCl)
V
Au-Si
= 0V
V
Au-Si
= 0.5V
V
Au-Si
= 1.0V
V
Au-Si
= 1.5V
V
Au-Si
= 2.0V
Hot electron shift
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
10
1
J
Solution
(mA/cm
2
)
-1.0 0.0 1.0
V
Au-Solution
(V vs Ag/AgCl)
V
Au-Si
= 0V
V
Au-Si
= 0.5V
V
Au-Si
= 1.0V
V
Au-Si
= 1.5V
V
Au-Si
= 2.0V
e
f
2.8
2.4
2.0
1.6
1.2
0.8
0.4
0.0
Overpotential (η)
-5.0 -2.5 0.0
log j (mA/cm
2
)
V
Au-Si
= 0V
V
Au-Si
= 0.5V
127mV/dec
2.8
2.4
2.0
1.6
1.2
0.8
0.4
0.0
Overpotential (η)
-5.0 -2.5 0.0
log j (mA/cm
2
)
V
Au-Si
= 1.0V
V
Au-Si
= 1.5V
V
Au-Si
= 2.0V
i) 175mV/dec
ii) 190mV/dec
74
solution and an Ag/AgCl reference electrode. Unlike traditional electrochemical cells, where the
working electrode (WE) and the counter electrode (CE) are the primary current components
(ignoring current flow into the reference electrode), and are by definition equal in magnitude, in
this device there are three currents, the current leaving the silicon,
, the current leaving the gold,
, and the current leaving the counter electrode,
. In our MIS device, the current flow is
due primarily to electrons, and thus the electron flux directions are opposite to the current arrows.
To study the redox behavior of these devices, we carried out two types of ISolution measurements.
First, we sweep the voltage of the Au-Solution (VAu-Solution) junction and simultaneously step the
voltage of the Au-Silicon (VAu-Si) junction. Figures 4.2a-b plot the linear and log scale results of
these measurements, respectively. From the linear scale plot (Fig. 4.2a), as the voltage between
the Au-Silicon junction increases, the turn-on voltage for hydrogen reduction is reduced, and
current density increases. For an applied VAu-Solution = -1.5 V, the current increases from ~13
mA/cm
2
to ~42 mA/cm
2
when VAu-Si = 2 V. From the log-scale current plots (Fig 4.2b), we can
more clearly see the reduction curves shift as the VAu-Si voltage is increased. This shift to lower
voltages between the gold and solution is attributed to the increased flux of electrons impinging
on the gold solution surface, caused by the injection of hot electrons into the gold from the Si. To
understand the effect of the Au-Si junction voltage, we have swept VAu-Si while stepping VAu-Sol.
Figure 4.2c shows the results on a linear scale. In all cases of current vs VAu-Si, there is a turn-on
voltage, which becomes smaller as the VAu-Solution voltage is increased. This should occur as the
higher voltage will change both the concentration of [H
+
] at the gold/solution interface, and modify
the energy barrier. Figure 4.2d shows the same graphs on a log scale. At low diode voltages, the
solution current is nearly constant, limited by the thermal electrons in gold. Once VAu-Si becomes
75
sufficiently large, we see an exponential increase in the current until the linear regime shown in
Figure 4.2c. The initial exponential increase is attributed to the increase in energy of the electrons
injected into gold. Finally, there is a clear difference in the current levels at which the crossover
from exponential to linear occurs. These data show the electrochemical reaction rate on the gold
surface dramatically shifting due to the Au-Si junction.
4.4 Tafel slope analysis
To analyze the electrocatalytic activity and to elucidate the reaction mechanism of hot electron
devices, a Tafel analysis is introduced. In conventional electrochemistry, the Tafel equation is well
defined as:
(1) = +
where η is the overpotential, which is the difference between the electrode potential and the
standard electrode potential, =
.
(
) ,where R=8.314 Jmol
-1
K
-1
is the universal gas
constant, F= 96485.3 Cmol
-1
is the Faraday constant,
is the exchange current density, α is the
phenomenological charge transfer coefficient and =
.
is called the Tafel slope. For a single
electron transfer process, α is often found to be ~0.5 which leads the Tafel slope to be ~120
mV/dec. It is noteworthy that the Tafel equation originates from the Butler-Volmer equation:
(2)
=
∗ (
−
( )
)
where the second exponential term becomes negligible at large overpotential and reduces to the
simplified Tafel equation
32,33
. Figure 4.2e-f shows the Tafel slopes of different regions of the
solution current density at different VAu-Si conditions. As shown in the Figure 4.2e, when VAu-Si =
0 and 0.5V, which generates no or less hot electrons, the Tafel slope is ~127 mV/dec, which is
close to the often observed 120 mV/dec. This Tafel slope indicates that the hydrogen evolution
reaction happening at the electrode is predominantly limited the by single electron transfer step
76
which is popularly known as the Volmer reaction step (H
+
+ e
-
= Hads)
32-34
. With increasingly
negative overpotential, Tafel slope starts increasing and the solution current density starts getting
saturated. This saturation can be attributed to a number of factors: (i) as the current increases, the
reaction gets limited by the mass transport to and from electrode
32-34
, (ii) adsorption of reduced
hydrogen atoms at the electrode
32-34
, and (iii) deviation from the conventional Tafel equation at
higher overpotentials. The charge transfer coefficient, α=0.5 is generally not applicable at higher
overpotentials when the change in the activation energy of the redox reaction with overpotential
starts becoming non-linear
34
. It is hard to conclude which process is causing the saturation from
the Tafel plot alone as it is possible that all of these processes are contributing simultaneously.
Since our MIS device does not show any Tafel slope that is below 100 mV/dec, it is reasonable to
say that the reaction mechanism is not being limited by either the Heyrovsky step (H
+
+ Hads + e
-
=
H2, Tafel slope of 40 mV/dec) or the Tafel step (Hads + Hads = H2, Tafel slope of 30 mV/dec)
32-34
.
When there is a large positive VAu-Si, as shown in the Figure 4.2f, we can see that there are two
different regions with different Tafel slopes. We observe a Tafel slope of i) ~175 mV/dec, and ii)
~190 mV/dec at lower and higher overpotentials respectively. It would be erroneous to conclude
anything about the rate limiting step of the reaction from the Tafel slopes alone as the extent of the
Tafel slopes is not more than 2 orders of magnitude
33
. However, we can assume that the Heyrovsky
and Tafel steps are probably not the rate limiting steps as the Tafel slopes are way off the
conventional Tafel slopes for these steps. It is possible to observe a larger Tafel slope due to
increased surface coverage of adsorbed hydrogen atoms
32,34
. However, it is unlikely in the case of
gold electrode as gold is generally considered to be less capable of adsorption for both
chemisorption and physisorption. While the Tafel equation works reasonably for the lower VAu-Si
case, it deviates from the ideal form for hot electron cases. This deviation stems from the fact that
77
the derivation of Butler-Volmer equation considers electron flow from the Fermi level of the
electrode to the redox states
34
. Since the hot electrons have considerably higher energy than the
Fermi level, the conventional Tafel slopes do not manifest themselves in the higher VAu-Si cases.
For high VAu-Si, we attribute the Tafel slope (~175 mV/dec) at the lower overpotential to the hot
electrons being transmitted to the redox states with considerably larger transmission probability
than the thermal electrons in gold. With the increasing overpotential, the transmission probability
of the hot electrons does not increase considerably while the supply of the hot electrons remains
constant which leads to a saturation of the current followed by the first exponential increase. As
the overpotential increases further, the thermal electrons of gold also acquire a considerably large
transmission probability and we can see the second exponential increase in current with a different
Tafel slope (~190 mV/dec). While apparently it seems that the charge transfer efficiency (α~0.31)
has decreased compared to the VAu-Si = 0 case (α~0.47), it is noteworthy that the magnitude of
current density increased considerably. At this higher current density, the mass transport limitation,
ohmic losses and adsorption will also be higher which may collectively manifest as a larger Tafel
slope.
To make sure that the observed currents are not resulting from any experimental artifact, we
have carried out a set of control experiments. First, we have systematically modified the voltage
sources, to ensure that the result was not an artifact from the potentiostat. The key results show
that if Au-Si junction bias is carried out by an independent voltage source, the results are identical
to the two working electrodes based potentiostat measurement setup. After eliminating the
possibility of a measurement artifact, we studied whether the effect could be attributed to the lateral
resistivity of the gold film or pinholes in the gold film using control samples. First, Au film
resistivity measurement were carried out, with the measured resistivity used as an input to a 3-D
78
TCAD Sentaurus simulation which allowed us to accurately simulate the expected current density
and voltage drop across the gold films. The simulation results show that the lateral resistance of
the gold films only cause a maximum voltage drop of ~6 mV for a current density of 10 mA/cm
2
,
which is negligible with respect to the current and voltage shifts here. Once lateral resistivity was
eliminated as a potential source of the observed current shift, we studied the effect of pinholes in
the gold films on the current. It should be noted that from atomic microscope force (AFM)
measurements, the root mean square (RMS) roughness of the thin gold films are ~0.71 nm (Figure
4.13). To controllably test the effect of these holes, we fabricated a thick gold film (100 nm) with
lithographically defined holes (Figure 4.14). By then carrying out the same VAu-Si and VAu-Solution
sweeps, it can be determined if pinholes in the film could explain the results. However, Figure
4.14 shows that even with engineered holes, there is a small change in ISolution as a function of bias
between the silicon and gold, dramatically smaller than the experimental data. We have also
studied metal-semiconductor (MS) junctions, discussed in Section 4.8.1. The key results show that
an MS junction with 12 nm gold and moderately doped Si (5 × 10
16
cm
-3
) give similar overall
behavior, but with much lower current and voltage shifts (Figure 4.15a,d). As the thickness of the
gold is increased to 100 nm, the effect becomes negligible (Figure 4.15b,e). Furthermore, if a thin
gold layer is used with heavily doped Si, then the Schottky barrier becomes thin and turns into a
tunnel barrier, which causes electrons to be injected into the gold near the Fermi level, which also
eliminates the observed behavior (Figure 4.15c,f). These results also validate the idea that an MIS
junction will provide hotter electrons than an equivalent MS junction.
4.5 Control measurements
To determine if the oxide or silicon is degrading, causing current due to the dissolution of the
electrode, we carried out stability tests (Section 4.8.2). If the sample was attacked during the
79
electrochemical measurements, we expect the diode characteristics to change dramatically. Figures
4.16a,b show the I-V curve of the MIS diode when it was first fabricated, before any
electrochemical measurements were carried out, and after all the measurements in this paper were
carried out, with minimal difference. To highlight this measurement, the before and after curves
shown in Figure 4.16a,b were separated by about one year, highlighting the stability of the
Au/Al2O3/Si devices used here under our experimental conditions. Figure 4.16c shows the current
vs time curve for the MIS device, highlighting the stability. Figure 4.17 and 4.18 shows the three
current components for our MIS device vs time, to highlight the fact that the observed currents are
stable, and not time dependent or due to any kind of capacitive effects. These control experiments
shed light on the mechanism behind the observed behavior, and eliminate measurement error,
lateral resistivity, pinholes, or oxidation of the substrate itself as the possible cause of the observed
current behavior. Thus, we conclude that hot electrons injected into the gold are responsible for
the modulation of the reaction rate at gold/solution interface.
Next, we study how each of the three measured current components (ISolution, IAu, ISi) change as a
function of applied voltage. Figure 4.3a shows the measured current components, and the internal
current components which comprise them. The source of hot electrons in the gold is the electron
injection from the silicon conduction band. The electrochemical reduction current on the gold is
separated into two components, reduction due to the thermal electron population, IThermal Electron,
and reduction due to the hot-electron population, IHot Electron. Finally, there is a direct
electrochemical reduction component from the silicon to the solution, IDirect Injection. These
correspond to the measured components from the following relationships.
(1*) ISolution = -(IThermal Electron + IHot Electron+ IDirect Injection)
(2*) IAu = IThermal Electron + IHot Electron – IAu-Si
80
(3*) ISi = IAu-Si + IDirect Injection
From these relationships, we can see that when VAu-Si = 0 V, IAu-Si = 0 A, this becomes the
traditional 3-electrode measurement where the gold is the working electrode, and ISolution = -IAu.
Figure 4.3b shows the three measured current components during a VAu-Solution voltage sweep for
VAu-Si = 0 V. The observed behavior is as expected, with the IAu = -ISolution. Figure 4.3c,d show the
currents for VAu-Si = 0.5 V and VAu-Si = 1.5 V, respectively. Surprisingly, ISi increases with the
voltage applied between the solution and gold. Since the voltage between the gold and silicon is
fixed, and it was previously shown that the silicon does not directly inject current into the solution,
the current injected from the silicon into the gold should be constant with respect to VAu-Si.
However, as seen in Figure 4.3c,d, an increase in the measured current, ΔISi exists for both applied
voltages. This increase in ISi can be explained by four mechanisms, (i) a change in the gold
electrode voltage due to the lateral currents, (ii) holes in the gold which allow direct reduction of
hydrogen due to the potential of the silicon with respect to the solution, (iii) oxidation of the
silicon/Al2O3 substrate, or (iv) hydrogen reduction by injected elect a gold/hydrogen complex
which directly accepts electrons from the silicon, driving reduction without the need for a multistep
electron transfer to the ‘bulk’ gold and then to the solution. Our control experiments analyzing the
lateral gold potential drop, with lithographically defined holes, and stability measurements
eliminate mechanisms (i), (ii), and (iii). From this, we conclude that the increase in ISi is due to
81
direct injection of electrons into a species that is complexed with the gold. This is observable due
to the independent voltage control and current measurement of the gold and silicon terminals.
We note that since Fig. 3b-d are steady state measurements, for all cases, ISolution + IAu + ISi = 0.
Most importantly, from these graphs, we can quantify the three components of the electrochemical
reduction current, which are thermal electrons from the gold, hot electrons from the gold, and
direct injection from the silicon. Using Figure 4.3b, we can identify the contribution of the thermal
Figure 4.3. Current flow mechanism and measurement result. (a) Schematic diagram of main current
components. Major currents are composed with several minor current components. (b)-(d) Three major
current measurements of the closed system, (i.e. I Si, I Au, and I Solution) under different Au-Si voltages.
82
electrons in gold as a function of applied bias. At any given VAu-Solution, the thermal contribution
from the gold should stay constant. Thus, we can define the net change in solution current as:
(4*) ΔISolution = ISolution - ISolution(VAu-Si=0) = ΔISi + IHot Electron,
where ISolution(VAu-Si=0) refers to the current composed only with Au thermal electrons at non-
biased condition, ΔISi represents the increased amount of ISi due to the direct injected electrons
from the silicon except for the device diode current, and IHot Electron composed with hot electrons in
the Au regime. So, the net change of solution current shown in the equation (4*) can be explained
by analyzing the individual components which are presented in the equation (1*) – (3*).
83
From these curves, we can then extract the thermal, hot electron, and direct injection
components as a function of applied bias. Figure 4.4a shows the solution current density JSolution vs
VAu-Solution sweeps for five diode bias potentials (VAu-Si=0, 0.5, 1, 1.5, 2 V), with the total solution
current density separated into thermal electron, hot electron, and direct injection current density
components. When VAu-Si=0 V, all the measured current is due to the thermal electrons in the gold.
However, as the applied bias across the diode increases, both the direct injection, and hot electron
Figure 4.4. Hot electron measurement and characterization. (a) Current component ratio map along
the increase of Au-Si voltage. Portion of the hot electrons in total current keep increase as Au-Si voltage
increase. (b) Current density from direct injected electrons from Si to electrolyte at different fixed V Au-
Solution. (c) Quantum efficiency of hot electron device at fixed 2.0V Au-Si voltage and (d) at fixed -0.8V
Au-Solution voltage.
84
components increase. However, while the hot electron current increases monotonically, the direct
injection current appears to have a peak. Figure 4.4b plots the direct injection current density as a
function of Au-Si bias. At higher VAu-Solution, a clear peak is observed. We attribute this behavior
to the direct injection of carriers from the silicon into hydrogen ions on the surface of the gold,
with a well-defined energy state.
Figure 4.5. Hot electron simulations. (a) electron-electron and electron phonon scattering rates in gold
plotted as a function of energy above Fermi level. (b) Energy loss rate per fs, obtained by multiplying
scattering rate at a given energy by average energy loss per scattering event. (c) Log scale attempt rate
of electrons tunneling into gold/solution interface plotted as a function of energy with and without hot
electron injection. (d) Linear scale attempt rate plot.
85
Figure 4.4c shows the quantum efficiency of the hot electron reduction, defined as
J
/J
, where J is the current density as a function of VAu-Solution. Critically, it is seen that
the hot electron efficiency increases to ~85% before saturating at high solution potentials. This is
the highest quantum efficiency reported to date for a hot-electron mediated electrochemical
process. Furthermore, we also show the current density efficiency as a function of VAu-Si, and
demonstrate that at high diode biases the current efficiency is >50%. Figure 4.19 shows the overall
quantum efficiency in different biased conditions characterized in Figure 4.2. These efficiencies
suggest there is a clear path towards using MIS structures as efficient sources for hot electron
devices.
4.6 Theoretical analysis
To gain further insight into the hot electron dynamics in gold, we have carried out detailed
simulations using a modified 2D Monte Carlo simulation package for semiconductor transport,
Archimedes
35
. We have modified the simulator by implementing the gold density of states,
electron-electron (e-e), and electron-phonon (e-p) scattering. We describe the details of the
implementation in Section 4.19. Figure 4.5a shows the scattering rates for the e-e, e-p, and total
scattering as a function of energy above the Fermi level in gold. To verify the scattering rates used
here, we show that the electron-electron scattering rates used here match those published in
literature
36
(Figure 4.24). Furthermore, we show that the simulator used here can accurately
reproduce experimental electron temperature vs time profiles. While the e-p scattering rate is high
compared to the e-e scattering rate, due to the relatively small energy of acoustic phonons, at high
energy, the energy loss per fs for hot electrons is dominated by e-e scattering events (Figure 4.5b),
due to the relatively large average energy loss per scattering event for high energy electrons
86
interacting with electrons near the Fermi surface. Next, we carry out a simulation where we inject
electrons at varying energies above the gold Fermi level and track the decay.
From these results, the rate of attempts at the gold surface due to hot electrons is obtained as a
function of energy. Using the attempt rate enables us to account for the interactions of the electrons
in the gold with the surface. Essentially, this approach is analogous to the attempt frequency
approach used when calculating tunneling rates out of quantum wells, where the tunneling rate is
proportional to the rate at which electrons reflect off the quantum well barriers. Here we use the
attempt rate as an analog for the attempt rate for tunneling in quantum wells. This approach
simultaneously allows us to capture the rate of interactions between the hot electrons and the
gold/solution interface and normalize this rate accurately with the interaction rate between the
thermal electrons and the gold/solution interface. The rate of attempts at the gold surface due to
the thermal electrons in gold is also obtained from the simulation. By then normalizing these two
rates of attempts as described in Section 4.9.8, we plot the attempt rate for gold with no hot electron
injection, and gold with 26 mA/cm
2
of hot electrons injected 2 eV above the Fermi level. This is
the current density of our MIS device at VAu-Si = 2V. While many injection energies were simulated
(Figure 4.25a), we show the 2 eV injection result as it closely approximates the expected offset
given by considering the initial band offset between our n-doped Si and a gold electrode with a
workfunction of 5.1 eV, which is ~1eV, and then adding in the expected increase in energy due to
the applied voltage. While the applied voltage is 2V, the initial ~0.5 V can be assumed to drop
over the silicon depletion region, and the final ~0.5 V are expected to be limited by series
resistances, giving us an approximate injection energy of 2 V.
Figure 4.5c shows the results with the energy with respect to the gold Fermi-Level on the y-axis
and attempt rate on the x-axis in log scale, and Figure 4.5d shows a zoomed in view in linear scale.
87
We immediately see that for high energies, there is significant increase in the hot-electron attempt
rate. Note that these results are in units of 1/cm
2
-s-eV, thus we can see that the injection of hot-
electrons at a rate of 26 mA/cm
2
creates an attempt rate on the order of ~10
18
/cm
2
-s-eV. While
these may seem high, they can be understood by considering the velocity of hot electrons in gold
to be vHE~10
8
cm/s, leading to a transit time across 10 nm thick gold of τAu ~10
-14
s. Considering
an energy loss rate of PHE~10meV/fs, an injected particle would lose 1 eV in τHE~100 fs, leading
to nrefl ~10 attempts/injected particle. A current level of 10 mA/cm
2
leads to a hot electron flux of
FHE~10
17
/cm
2
-s. Taking FHE× nrefl we get an interaction rate of ~10
18
/cm
2
-s-eV. This is a
significant interaction rate which allows us to explain why these devices exhibit such high
efficiencies with respect to hot electron driven electrochemistry—despite the high scattering rates,
there is still a significant number of interactions between the hot electron and the gold/solution
interface.
Finally, we also see a peak in the attempt rate (Fig. 4.5c) at the hot electron injection energy.
This occurs when electrons have been injected into the gold, but have not yet undergone e-e
scattering, as e-e scattering for electrons at 2 eV above the Fermi level would cause the loss of an
average of ~700 meV per scattering event, which is obtained by dividing the values in Figure 4.5a
and 4.5b. Before e-e scattering occurs, the injected electrons still have significant energy, and if
they are backscattered due to acoustic phonons, will have a non-zero chance of being injected back
to the Si. However, if the injected electrons are immediately transferred to the solution before e-e
scattering no current will flow in the gold due to this injected electron, and, simultaneously, the
net flux across the Si/Au interface will increase due to suppression of backscattering from the Au
into the Si. For our observed devices, we attribute the observed ΔISi, shown in Figure 4.3c,d to this
mechanism, and call it ‘direct injection current’ here. Furthermore, the peaked shape shown in
88
Figure 4.4b indicated the silicon direct injection current is related to a sharper feature in the
electron distribution, and not the hot electron tail which we see in Figure 4.5d.
In conclusion, we demonstrate that a MIS tunnel diode can act as a source of hot electrons for
efficiently driving electrochemical reductions, with efficiencies reaching ~85% for high biases.
This approach is general, and not limited to the Si/Al2O3/Au device with hydrogen reduction
shown here. Future experiments could explore hot holes for high-energy reduction reactions, other
redox reactions for carbon-to-fuel reactions, and other materials such as graphene and other 2-D
materials that transport electrons more efficiently to see if high efficiencies can be achieved at
lower voltages.
4.7 Fabrication and measurement methods
4.7.1 Fabrication methods
Moderately phosphorous doped (Nd = 5×10
16
cm
-3
) (100) and heavily phosphorous doped (Nd =
1×10
19
cm
-3
) (100) silicon wafer (MTI Corporation) were used as the substrate. Native SiO2 was
removed with 1:10 ratio of HF:H2O (Sigma Aldrich, 49% CMOS grade) etching for 1 minute.
After oxide etching, 1nm of titanium and 100nm of silver back contact metals were evaporated in
an electron beam evaporator (Temescal, SL1800). To prevent front side damage, a blank Si handle
wafer was used after an acetone, IPA, D.I water rinse. The metal insulator semiconductor (MIS)
structure was fabricated by depositing an aluminum oxide insulator layer with Atomic Layer
Deposition (Ultratech/Cambridge Savannah ALD) using Trimethyl aluminum (Aldrich,
1001278062) and water (Aldrich, W4502) precursors. Au films (10-100nm thick) were evaporated
under two different conditions. Room temperature Au film was deposited with Electron beam
evaporator (Temescal). Cryo (90K) temperature Au films were evaporated with thermal evaporator
89
(Denton Vacuum Inc, DV-502A). For the device reported in the main text, cryo evaporated Au
films were used. Image reversal photolithography was done for control device with holes. (Karl
Suss, 100UV030). For contact wire attachment, copper wire wrapped with aluminum foil at the
one end was used. Two wires are connected to front and back side of the devices each with fast
drying silver paint (Ted Pella Inc, 16040-30). A ring contact was drawn in the front side of device
in Au film region. For device encapsulation, a glass slide (VMR Micro slides) was used as a back
holder. Fabricated devices with contacts were placed on the glass with epoxy (Gorilla Epoxy clear)
to encapsulate the device while leaving the Au electrode surface exposed.
4.7.2 Electrical Measurements
All the electrochemical I-V measurements were done by using a potentiostat (Admiral Instrument,
Squidstat Prime). Two different channels were used to control separate voltages applied to the
system. Each channel has its own working, reference, and counter electrode. The first channel was
connected to the Au as the working electrode, a platinum wire as the counter electrode, and an
Ag/AgCl reference electrode; the second channel consists of Si emitter as the working electrode,
a platinum wire as the counter electrode, and Au as reference electrode to bias the Au-Si junction.
0.5M H2SO4 was used as the electrolyte solution. Schottky, Ohmic and four-probe I-V
measurement of devices were characterized by Semiconductor Parameter Analyzer (Keysight
B1500a). The roughness of the both Au film evaporated at 300 K and 90K substrate temperature
we characterized using an Atomic Force Microscope.
90
4.7.3 Current flow in device through measurement system
Figure 4.6a shows a schematic of the current flow map in our device. It notes the measured currents
(ISolution, IAu , ISi) and the internal currents components in the device. Specifically, we note that there
are 4 components we need to consider: (i) the diode current between Si and gold, (ii) the thermal
electron reduction current between the solution and gold, (iii) the hot electron reduction current
between the solution and gold, and finally (iv) the direct silicon injection current from the silicon
into the solution. Our measurement setup uses two working electrodes to simultaneously apply
bias between the gold/silicon and gold/solution. Thus, we have two sets of counter electrodes (CE
1 & CE 2), working electrodes (WE 1 & WE 2), and reference electrodes (RE 1 & RE 2). In a
potentiostat, current flows between the working electrode and the counter electrode, while the
reference electrode is used to set the voltage
1
. To apply voltage between the gold and solution, we
connect WE 1 to the gold, CE 1 to a platinum wire in the solution, and RE 1 to an Ag/AgCl as the
Figure 4.6. Current flow across the device and measurement set up. a, The directions of all the
current components. b, The schematic of measurement system connections.
a b
91
reference electrode also in the solution. To simultaneously apply voltage between the gold and
silicon, we connect the silicon to WE 2, the gold to RE 2, and the platinum wire to CE 2. This
allows us to control the voltage of these two junctions (Au/Si and Au/Solution) independently.
and
represent working electrode current in channel 1 and 2.
and
indicate
counter electrode current in channel 1 and 2, which are connected in series to a Keithly Multimeter
to measure the solution current more precisely. Figure 4.21 shows the accurate overlap between
the currents measured from the potentiostat and the multimeter.
Three terminal current measurement
Three different currents were measured to investigate the behavior of the MIS hot electron device
using the described measurement setup. The Si current and the Au current were measured through
the potentiostat and the solution current was measured using the digital multimeter (Figure 4.6).
The relationships between the different current components are as shown below:
=
= −
(1)
=
−
(2)
=
+
(3)
=
= −
(3)
=
+
(4)
92
=
+
= − (
−
) – (
+
)
= −
−
= − (
+
+
) (5)
Equations (1) and (3) represent the working electrodes connected to Au and Si, respectively. The
counter electrode current will be the negative value of working electrode since it has an opposite
direction to the working electrode in the closed potentiostat system. Equation (2) shows that the
measured gold current represents the hydrogen reduction current minus the diode current. We
claim that the hydrogen reduction current at the Au surface is composed of hot electrons and
thermal electrons. Equation (4) shows the components of Si current. Nominally, the Si current
should be the same whether the diode is in solution or out of solution, and is represented by the
diode current,
. However, our experiments show that there is an increase in the measured
silicon current without a commensurate increase in the gold current, suggesting that there are some
conditions under which electrons are directly injected into the solution from the silicon. This also
contribute to the Si current, which is what is described in equation 4. Finally, we can get the total
current by adding the current from both counter electrodes, shown in equation 5. When we add the
two together, we see that the measured counter electrode current,
, will be composed of
three different components,
,
, and
.
93
4.7.4. Modification of voltage sources in measurement system
In order to confirm that the measured results were not a circuit level effect, we used a 2 terminal
voltage source/multimeter to bias the Au/Si diode while keeping the Au/Solution potentiostat
connection. Figure 4.7a shows the measurement setup. Figure 4.7b-d shows the comparison results
using the voltage source plus a single potentiostat channel versus using two potentiostat channels
simultaneously. These results are nearly identical and show that this could not explain the results
Figure 4.7. Accurate fitting between the potentiostat and the voltage supplier of solution current at
fixed
. a, Measurement setup, b-d, Redox current density in
= 0.5V ,1.0V , and 1.5V.
b c d
a
20
18
16
14
12
10
8
6
4
2
0
J
Solution (mA/cm
2
)
-1.2 -0.8 -0.4 0.0 0.4 0.8
V
Au-Solution
(V vs Ag/AgCl)
V
Au-Si
= 0.5V
Voltage Supplier
Potentiostat
35
30
25
20
15
10
5
0
J
solution (mA/cm
2
)
-1.2 -0.8 -0.4 0.0 0.4 0.8
V
Au-Solution
(V vs Ag/AgCl)
V
Au-Si
= 1.0V
Voltage Supplier
Potentiostat
40
35
30
25
20
15
10
5
0
J
solution (mA/cm
2
)
-1.2 -0.8 -0.4 0.0 0.4 0.8
V
Au-Solution
(V vs Ag/AgCl)
V
Au-Si
= 1.5V
Voltage Supplier
Potentiostat
94
We also just used two voltage sources, one to bias the Au/Platinum and one to bias the Au/Si.
While this is a 2 terminal solution measurement with a thin Pt wire, we wanted to ensure that some
change was seen, to eliminate the complex circuitry of the potentiostat. Since there is no Ag/AgCl
reference electrode, the voltage drop across the electrolyte to the Pt counter electrode limits the
effect. However, the results show that as we increase the
, it clearly affects the solution
current.
Figure 4.8. Effect of
without using the potentiostat system. a, Measurement setup, b, Solution
current density in different fixed
across
and c, log scale of b. solution current at fixed
V Au-Solution. a, -0.2V , b, -0.4V and c, -0.5V of V Au-Solution.
a
b
c
c
50
45
40
35
30
25
20
15
10
5
0
J
Solution
(mA/cm
2
)
-4.0 -3.0 -2.0 -1.0 0.0
V
Au-Pt
(V)
V
Au-Si
= 0V
V
Au-Si
= 0.5V
V
Au-Si
= 1.0V
V
Au-Si
= 1.5V
V
Au-Si
= 2.0V
10
-4
10
-3
10
-2
10
-1
10
0
10
1
J
Solution
(mA/cm
2
)
-4.0 -3.0 -2.0 -1.0 0.0
V
Au-Pt
(V)
V
Au-Si
= 0V
V
Au-Si
= 0.5V
V
Au-Si
= 1.0V
V
Au-Si
= 1.5V
V
Au-Si
= 2.0V
95
Lastly, we also tested the biasing the
by using a 1.5V battery. The results do not exactly
overlap with the 1.5V applied using the potentiostat, however, this is due to the actual voltage
supplied by the battery not being exactly 1.5V.
4.7.5 Control Samples – Lateral Resistance and Pinholes in Gold Film
In order to ensure that lateral resistivity of the thin gold film (Figure 4.10a), or pinholes in the gold
film (Figure 4.10b) were not the cause of the observed effect, we carried out two sets of control
measurements and simulations. The first set of measurements was done to identify how much
Figure 4.9. Comparison between the potentiostat and a 1.5V battery connected to Au-Si junction.
a, Measurement setup, b, Solution current comparison in different biasing condition, c, log scale of b.
b c
a
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
10
1
J
Redox
(mA/cm
2
)
0.5 0.0 -0.5
V
Au-Solution
(V vs Ag/AgCl)
1.5V Battery
1.5V Potentiostat
24
20
16
12
8
4
0
J
Redox
(mA/cm
2
)
0.5 0.0 -0.5
V
Au-Solution
(V vs Ag/AgCl)
1.5V Battery
1.5V Potentiostat
96
voltage drop we might expect laterally across the gold film due to the current flow in the electrode.
The second, was a control sample with thick gold and lithographically defined holes in the gold to
simulate the effect of pinholes in a controlled fashion. Both of these effects will be influenced by
the surface roughness of the electrode, resistance of the gold electrode, and shape of contact
2, 3
.
First, we evaporated 12 nm and 100 nm gold films onto a 6nm Al2O3 deposited with an atomic
layer deposition (ALD) on Si/SiO2 handle substrate. By using a thick SiO2 layer of 2 µm, we
ensured that the Au was electrically isolated from the underlying Si. Next, we evaporated 4 bar
electrodes using of 100 nm silver through a shadow mask. We used the outer two bars to inject
current and the inner two bars to measure the voltage drop. Figure 4.11a-b show the measured
voltages on the two inner bars. The actual voltage drop across those two bars is then the subtraction
of the two lines shown in each graph. We carried these measurements out on both 100 nm thick
and 12 nm thick gold. From the measurements we were able to extract resistivity and sheet
resistance, as shown in Table 4.1. Importantly we got similar resistivity values for both 12 nm and
100 nm thick films, but with about a 10x difference in sheet resistance, which is expected. Using
Figure 4.10. a, Schematic showing the effect of lateral resistance due to diode current. The voltage drop
depends on the resistance of the Au film. b, Schematic of a control device with lithographically defined
holes.
.
97
this data, we could then carry out a full 3-D simulation of the diode with the gold contact using the
resistivity measured experimentally. By doing so, we could then identify what kind of voltage
variation we could expect across our gold film during diode operation.
Figure 4.11. Four-probe measurement of a, ~12nm Au film on SiO 2 and b, ~100nm Au film on SiO 2.
Both films were measured with 1mm spacing between four probes.
Table 4.1. Sheet Resistance (R s) and Conductivity can be derived from measurement. Both ~12nm
and ~100nm Au films show similar conductivity values.
98
To minimize the voltage distribution across the film, a silver paste rectangular ring shape contact
was used, as shown in the inset of Figure 4.12a. We then carried out a dry I-V measurement, and
carried out a 3-D TCAD Sentaurus simulation to match the simulation. Figure 4.12a shows the
overlap between our measured J-V curve and simulated J-V curve. We can see that the
characteristics are highly similar. Since we had already measured the resistivity of different
thickness of gold as shown in Figure 4.11 and Table 4.1, we simply used that value as an use as an
input parameter for Sentaurus simulations
4
. The important feature of these Sentaurus simulations
is that the current density from the device is accurate, and the size of the device simulated in
Sentaurus matched the real world size. Therefore, allows us to get a realistic map of the voltage
drop expected across the gold surface. Figure 4.12b shows a heat map of the potentials extracted
from the Sentaurus simulation for the potential in the gold laterally. This result was extracted at a
voltage which resulted in a current density of 10 mA/cm
2
results of the electrostatic potential
distribution on the thin gold surface from ring contact to center of the thin film. From the heatmap
of voltage distribution, we see that the difference of the highest electrostatic potential (0.3609V)
Figure 4.12. a, Fitting results of experiment and simulation diode curves. b, Sentaurus electrostatic
potential simulation with the silver ring contact modeled device
99
to the lowest point (0.3547V) is 0.0062V. Thus, we estimated that we get ~6 mV of lateral voltage
drop for every 10 mA/cm
2
flowing through the device. Since we worked between 0-30 mA/cm
2
,
we expect the overall lateral voltage drop to be negligible for the magnitude of the effect we see
here.
Controlling the surface roughness of thin Au film is also important, as there can be pinholes that
form in the gold, which will both increase resistivity, and cause the solution to contact the Si/Al2O3,
neither of which is desirable here. To minimize this, we carry out our gold film evaporation using
a thermal evaporator with the substrate held at ~90K. This low temperature minimized mobility of
Figure 4.14. Solution current measurement of control device with holes. Inset schematic shows the
structure.
10
-4
10
-3
10
-2
10
-1
10
0
J
Solution
(mA/cm
2
)
0.5 0.0 -0.5
V
Au-Solution
(V vs Ag/AgCl)
V
Au-Si = 0V
V
Au-Si = 1.0V
V
Au-Si = 2.0V
Figure 4.13. AFM analysis of the 12nm Au film. 12nm Au film evaporated with cryogenic
temperatures. The RMS roughness for this film was measured to be 0.71nm from the AFM.
100
the deposited gold atoms and enables highly smooth surfaces. Figure 4.13 shows AFM
measurements of the cryo evaporated 12 nm Au film. The RMS roughness extracted from this
AFM measurement is 0.71 nm, which is extremely smooth.
However, to test the effect of pinholes in the gold film, we fabricated a device which has a 100 nm
thick Au film with lithographically defined holes with 1 µm radius and a 30 µm pitch. These holes
are meant to simulate the effect of pinholes in our gold film. In Figure 4.14, we show the redox
measurements for applied diode biases of 0V, 1V, and 2V. Importantly we see minimal shift in the
resulting electrochemical J-V curves. This result shows that the magnitude of the observed
behavior cannot come purely from current being directly injected into the solution from Si.
4.8 Control devices
4.8.1 Metal-Semiconductor Hot Electron and Control Devices
In addition to the study of the lateral resistivity and pinholes, we created several metal
semiconductor devices to study this effect. Specifically, we create (i) thin gold/n-Si devices which
mirrored our MIS devices, but without the insulator layer, (ii) thick gold/n-Si devices, and (iii) thin
gold/n++-Si devices, where a heavily doped silicon wafer was used. Figure 4.15 shows the results
from these devices. First, Figure 4.15a shows the cartoon band diagram for the thin Au/moderately
doped Si device, and the corresponding measurements are shown in Figure 4.15d. We see that a
similar effect as previously observed for the MIS structure is observed. Next, Figure 4.15b shows
the cartoon band diagram for thick Au/moderately doped Si, and Figure 4.15e shows the
corresponding electrochemical measurements. As we see from the curves, there is essentially no
effect. Finally, Figure 4.15c shows the cartoon band diagram for thin gold/heavily doped Si. In
this device, since the electrons are injected at the Fermi level of the gold, it is not expected that
101
there will be any observed effect. Figure 4.15f shows the electrochemical current vs voltage curves
for the heavily doped gold device, again showing minimal effect. Thus, of the three samples, the
only device which showed a significant effect was the sample with thin gold and moderately doped
Si. For the thick gold device, we expect that the majority of the injected hot electrons will have
lost their energy by the time they reach the surface, so there is not going to be a significant
population of hot electrons. For the heavily doped Si device, the Schottky barrier width in the
silicon will be very small, which will cause electrons to directly tunnel into the gold, so even
though the gold film is thin, the injected electrons will not be hot.
Figure 4.15. Control devices band diagram and measurements. a, Band diagram of MS device with
~12nm Au, b, with ~100nm Au and c, with heavily doped Si emitter. d, Solution current result from
device ‘a’, as injected current to base increased, it shows hot electron effect. e, from device ‘b’, showing
no hot electron effect due to thick Au region, and f, from device ‘c’, no hot electrons generated from
emitter region, due to narrow barrier.
102
4.8.2 Device Stability measurement in different conditions
Stability tests were conducted to show our device is stable in a 0.5M H2SO4 solution under
measurement conditions. Figure 4.16a and b shows the comparison between diode I-V curves
before and after the electrochemical measurements were carried out in linear scale (Figure 4.16a)
and log scale (Figure 4.16b). The initial device current was measured before any electrochemical
measurement inside a 0.5M H2SO4 solution. After the electrochemical experiments included in
this paper were carried out, we remeasured the diode J-V characteristics again. It should be noted
that between the initial fabrication of the device, and the “post-electrochemical measurement”,
about 1 year elapsed. Additionally, a large number of measurements were carried out. As we see
from Figure 4.16a,b, there is almost no change in the device behavior. We use this data to show
that the MIS device is stable. Additionally, Figure 4.16c shows the device electrochemical current
when it is biased to VAu-Si=1 V and VAu-Solution=-0.8 V for 1 hour. While we see an initial drop, the
current is overall stable. The initial drop is attributed to some fraction of the surface being covered
by bubbles due to the HER.
Figure 4.16. Device stability measurement in before/after electrochemistry experiment. a, linear
scale of device current measurement before and after HER measurement. Note that measurements were
carried out about 1 year apart. Strongly indicating stability of device. b, log scale of a. c, Redox current
measured in fixed voltage condition for 1-hour.
103
4.8.3 Current Stability measurement in different conditions
Figure 4.17. Current stability measurement in different conditions along the time. Silicon, Au, and
Solution current at a,
= 1.0V ,
= -0.2V , b,
= 2.0V ,
= -0.2V , c,
= 1.0V ,
= -0.4V , and d,
= 2.0V ,
= -0.4V .
104
4.8.4 Device Quantum Efficiency
In this study, we present the device quantum efficiency to characterize how many hot electrons
can be extracted from the device. Quantum efficiency was calculated by dividing the hot electron
current density in solution (JHot Electron) current to the current density injected to the Au region from
the silicon/gold bias. Figure 4.19a shows the quantum efficiency of the device along the solution
voltage. It indicates that when
increases, the quantum efficiency increases
tremendously. It is noteworthy that at
= 2.0V and
= -1.5V point, quantum
efficiency reaches to ~85% and appears to saturate. Figure 4.19b shows the quantum efficiency of
Figure 4.18. Three component currents in fixed V Au-Solution at a, 0V, b, -0.2V, c, -0.4V, and d, -0.8V .
105
device as a function of the diode bias,
. It shows that at a fixed
bias, higher
improves the quantum efficiency.
Figure 4.19 Quantum Efficiency of Device in different conditions. a, Quantum Efficiency vs
in different fixed
values., b, Quantum Efficiency vs
in different fixed
values.
106
4.8.5. Analysis of series resistance of back contact of diode
4.8.6 Ensuring accuracy between potentiostat and multimeter measurements
Figure 4.20. Ohmic behavior of the back contact of device. The contact is one of the significant
factors in device measurement. To reduce the current loss in the contact region, Ag was introduced as a
contact material to n-type Si. Ag, which has work function ~4.7eV forms the ohmic contact with n-type
Si. We can see that in higher voltage regime, the resistivity starts to increase due to the series resistivity.
This behavior of back contact affects the device measurement results.
Figure 4.21. Accurate fitting between the potentiostat and the digital multimeter of solution
current at fixed
. a, -0.2V , b, -0.4V and c, -0.5V of
.
107
One challenge with the potentiostat is the relatively low resolution for the current measurement.
To enable measurements to lower current levels, we used an external multimeter connected in
series to the platinum electrode. Here, we show that for the high current measurements, the
measured currents are nearly identical for both the potentiostat and the multimeter. By using the
two channels of the potentiostat, we can measure two different currents (
and
) and
can be determined by adding two currents. Since
+
+
= 0, we can always know
the solution current from the measurements of the Si and Au currents. However, the limited
Figure 4.22. HER in D.I water condition. a, I-V measurement of solution current of linear scale and
b, log scale measured in different fixed
values. c, I-V measurement of solution current of linear
scale and d, log scale measured in different fixed
values.
108
resolution of the potentiostat limits the minimum current we can measure. We connected the
multimeter between the potentiostat and counter electrode to measure the Redox current more
precisely when chemical reactions happen. Figure. 4.21 shows accurately overlapped solution
current measured with the multimeter and the potentiostat, respectively.
4.8.7 Measurement in different pH medium
To show that our effects are not only coming from the acid medium, we measured the
sample in a neutral solution (pH = 7, 0.1M K2SO4). Figure 4.22 shows the solution current
measured with the same bias condition in the acid (pH = 0, 0.5M H2SO4) medium. We show that
for this, we also observe a similar change in current as a function of applied bias. However, we
note that it is dramatically smaller. The increase in current is from ~ 0.1mA/cm
2
to ~0.75mA/cm
2
as we modify the bias conditions. Our interpretation of these results center on the idea that the
lower [H
+
] concentration is responsible for a lower injection rate of hot electrons from the gold
into the solution, dramatically reducing the overall efficiency.
Figure 4.23. Gas formation at different biasing conditions. a, No reaction happens at non-biased
condition for both Au-Solution and Au-Si. b, Hydrogen generation happens at 2.0V Au-Si biased
condition without biasing Au-Solution voltage.
109
4.8.9 Bubbling at device surface
In Figure 4.23 we show two images, Figure 4.23a shows the device with both the Au-Solution and
Au-Si are biased to 0V. This gives us no current or hydrogen generation. Next, while keeping the
Au-Solution voltage at 0V, we turn on only the Au-Si voltage to 2V. At this point we see bubbling
that as the device turns on, we see bubble generation. At this bias condition, the solution current
is ~0.1-1 mA/cm
2
.
4.9. Monte Carlo Simulation
4.9.1 Monte Carlo simulation of the nonequilibrium carrier dynamics of gold
The dynamics of electrons injected into gold from silicon has been treated with the aid of an open-
source 2D ensemble Monte Carlo (MC) simulator, Archimedes
5
. We have modified the code to
incorporate the scattering mechanisms relevant to gold. We have considered a rectangular region
of gold with a width of 12 nm and a length of 300 nm. The shorter dimension corresponds to the
transport direction of the injected electrons. We have considered a parabolic dispersion
relationship for gold with an effective mass equal to that of free electrons. Since our simulation
takes only two dimensions into account, it is necessary to properly normalize the data with respect
to thermal electrons vs injected electrons. To do so, we initialize the simulation with 1 million
particles, which corresponds to a 3-D sample with a volume of 300 × 12 × 4.7 nm
3
, considering
the gold carrier density of 5.9 × 10
m
-3
for the conduction band. This depth factor then allows
us to properly normalize the effect of the injected electrons with the thermal electrons.
110
4.9.2 Initial equilibrium carrier distribution
We begin the simulation by initializing the equilibrium carrier distribution of gold according to
the temperature of the lattice (300K) and the density of states (DOS) of gold. The DOS used for
gold in this simulation has been extracted from the work of Ladstadter et. al.
6
, who used first-
principles based calculations to obtain the DOS. We only consider the conduction band of gold
where the Fermi level of gold lies 5.5 eV above the bottom of the conduction band
7
.
4.9.3 Scattering mechanisms
There are two major scattering mechanisms that affect the carrier dynamics of gold: (1) electron-
electron scattering and (2) electron-acoustic phonon scattering. Gold has no optical phonon branch
since it has only one atom per unit cell.
4.9.3.1 Electron-electron scattering
Electron-electron scattering rate in gold has been calculated using Fermi’s golden rule that is given
by
1
=
2
ℏ
| (
,
,
,
)|
(1 − (
)(1 − (
))
(
,
),(
,
)
Here,
is the electron-electron scattering rate, (
,
,
,
) is the matrix element for the
transition between the initial state |
,
⟩ to the final state |
,
⟩, () is the Fermi-Dirac
distribution, and
stands for the energy conservation. The matrix element for electron-electron
scattering in gold is given by
7-10
(
,
,
,
) =
()
1
||
+
,
,
111
Where =
−
=
−
is the change in wavevector,
is the Thomas-Fermi screening
momentum (
=
where
= 5.9 × 10
is the carrier density in gold,
= 5.5
is the Fermi level), () is the screened dielectric function ( () =
(1 +
)), and the delta
functions stand for the momentum conservation. Since we consider scattering due to coulombic
interaction between two electrons, we randomly choose an electron from the Fermi sea which acts
as a scattering partner for the electron that is being simulated before every scattering event. The
conduction electrons in gold are predominantly from 6sp orbital and they have a vanishing matrix
element while scattering with d-band electrons
6, 11
. Therefore, we excluded the d-band electrons
while choosing the partner electrons. The inclusion of (1 − (
)(1 − (
)) term ensures that
an electron cannot scatter into a state that is already occupied hence satisfying the Pauli blocking
principle. We dynamically track the energy resolved distribution of the electrons to take Pauli
blocking into consideration. Then we numerically calculate the scattering rate prior to every
scattering event. Using a free parameter, we have fit the electron-electron scattering rates to that
Figure 4.24: Match between electron-electron scattering rates calculated by Ladstadter et. al. and this
paper.
112
calculated by Ladstadter et. al
6
. as shown in Figure 4.24. Ladstadter et. al
6
used first principles
calculation approach to calculate the rates from the complete electronic band structure of gold.
4.9.3.2 Electron-acoustic phonon scattering
We have extracted the electron-acoustic phonon scattering rates from the work of Lugovskoy et.
al
10
as shown in figure 4.5a. These scattering rates were calculated using a pseudopotential
approach considering the phonon dispersion relationship as well as the band structure of gold
calculated in a first principles approach.
4.9.4 Calculation of final states
In order to calculate the final states after each electron-electron scattering event, we have
considered both the energy and momentum conservation laws. Let the initial wavevectors of the
two electrons be
,
,
,
and the final wavevectors be
,
,
,
. Then
the energy conservation requires
+
+
+
=
+
+
+
whereas momentum conservation requires
+
=
+
and
+
=
+
13,14
. If we do not have any further information, there are an infinite number of solutions for the
unknowns
,
and
,
. However, if we fix the energy of one final state hence
automatically fixing the energy of the other final state, the solution becomes unique. Therefore,
we check the energies of all the available final states and randomly choose the energy of one final
state. This is equivalent to choosing the values of both
+
and
+
. With these
new information, it is possible to find unique solutions for
,
and
,
. After
113
analytically solving the equations mentioned above, we update the wavevectors of both electrons
accordingly.
On the other hand, the phonon band structure of gold requires the acoustic phonon energy to be
between 0~3 meV
12, 13
. For electron-acoustic phonon scattering, we randomly choose an energy
between 0~3 meV for the phonon. Then we randomly assign the wavevectors of the final state so
that the energy of the final state equals the sum (difference) of the energy of the initial state and
the phonon for absorption (emission) of phonon.
4.9.5 Dynamic calculation of the electronic temperature
A thermalized distribution of electrons can be associated with an equivalent electronic temperature
following the Fermi-Dirac distribution
=
1
(
)/
+ 1
Here,
is the Boltzmann constant, is the electronic temperature, and
is the Fermi level.
From this equation, we can write
= −
(
)/
. At =
, = 0.5 and
=
−
(.)
=
.
. Therefore,
vs
plot will have a minima at =
from which we can
easily determine the electronic temperature, . We dynamically calculate the distribution and pass
it through a smoothing function so that the noise around the minima is greatly reduced. Then, we
calculate the electronic temperature by identifying the minima of the distribution at the Fermi level.
114
4.9.6 Monte Carlo simulation results - Attempt rates of hot electrons
To study the effects of the injected electrons, we have simulated for a situation where we inject 1
electron into gold every 5 fs whereas we start the simulation with 1 million electrons. The injected
electrons either transfer the energy to other electrons via e-e scattering or to the lattice via phonon
scattering. While going through these scattering processes, it travels inside gold with a group
velocity =
. As a result, these electrons bounce back and forth between the walls of the gold
region in the transport direction (12 nm apart). Here, we use the analog of the attempt rate in
tunneling theory to normalize the effect of the injected electrons to the thermal electrons. Thus, in
this formalism, each time an electron reflects off the gold solution interface, it attempts to tunnel
into the solution to drive the redox reaction. However, the actual probability of tunneling into the
solution is related to the specific redox reaction, the concentration of the reactant as the surface
etc. The number of reflections per unit time correspond to the attempt rate of the hot electrons
Figure 4.25: a, Energy resolved attempt rates calculated at different electron injection energies b,
match between the electronic temperature profile calculated by Jiang et. al. from pump-probe
experiment and our MC simulations.
115
which essentially gives us a quantitative understanding of how frequently the hot electrons are
attempting to interact with the gold-electrolyte interface. With that in mind, we calculated the
energy-resolved attempt rates of the hot electrons in gold for different injection energies as shown
in Figure 4.25a. The thermal electrons get accelerated when they gain energy from the injected
electrons and they tend to hit the gold-electrolyte interface more compared to the case where no
electron is injected. The injected electrons help populate the higher energy states and these states
also contribute to the total attempts. Some fraction of the injected electrons interacts with the gold-
solution interface without significant scattering, giving rise to a peak in the attempt rate at the
injection energy.
4.9.7 Calculation of the attempt rates
During the simulation, the i
th
electron has a momentum (
,
) and we have set the x-direction
as the transport direction. A positive (negative) value of
means the electron would move to the
+x (-x) direction. We consider that there is no electric field present inside gold and hence the
change in position of the electron is decided by the equation,
= ℏ
where is the change
in position in x-direction after a time , and
is the effective mass of an electron in gold which
we have assumed to be equal to the free electron mass as stated earlier. At the device transport
boundary (x=12 nm), we set a boundary condition such that if the final position of an electron at a
certain time were to exceed the boundary (x
= 12 + x
nm), the electron would be
elastically reflected (x
= 12 − x
nm). Then we obtain the energy resolved attempt rates by
registering the total number of attempts at hitting the boundary at different energies with an energy
bin size of 0.01 eV. In the steady state, the energy resolved attempt rates for the thermal electrons
follow the profile of the actual number of electrons available at each energy, hence follow the
116
()() profile. At energies higher than the Fermi level, the Fermi-Dirac distribution, () falls
exponentially and so does ()(). Since we simulate a finite number of electrons, the
simulation itself cannot capture such small numbers. Therefore, we extrapolate the energy resolved
attempt rates by fitting it to the numerically calculated × ()() profile where is a
constant. For the simulations that include the injection of hot electrons, we calculate the energy
resolved attempt rates in the same way. However, since we use a much higher injection current
density during the simulation compared to the real device, we need to normalize these rates to the
injection current density of the real device to get a quantitative understanding of the attempt rates.
The energy resolved attempt rate profile for hot electron injection has two components: (1)
attempts due to thermal electrons that follow the ()() profile and (2) attempts due to the hot
electrons. We subtract the thermal component from the overall energy resolved attempt rates and
that gives us the attempts due to the hot electrons only. We assume that the energy resolved attempt
rates due to the hot electrons is linearly related to the injection current density and therefore we
linearly scale the rates to the real injection current density. Since the number of thermal electrons
is much larger than the injected electrons, we can assume that the change in attempts due to the
thermal electrons is negligible as a function of injection current density. Following this
assumption, we sum the scaled energy resolved attempt rates due to hot electrons with the
× ()() profile calculated before and this sum gives us the overall energy resolved attempt
rates for hot electron injection normalized to the real injection current density.
4.9.8 Normalization of the attempt rates
In the real device, the injected current density is in the order of ~10
2
Am
-2
. However, such a small
injection current density would require us to simulate for several microseconds if we want to build
a good statistics of simulation results. Since the scattering processes have a lifetime in the order of
117
~0.1 fs, it would take a very long time to perform those simulations if we want to capture the
effects of the scattering events on the transport of the injected electrons which is not
computationally feasible. Therefore, we perform the simulations with a relatively high injection
rate of 0.2 electrons/fs which corresponds to an injection current density of 2.26 × 10
Am
-2
where the cross-section area of the device is 300 × 4.7 nm
2
(12 nm being the transport length). To
get a quantitative understanding of the simulation results, we need to normalize the attempt rates
to an injection current density that we observe in the real device (~260 Am
-2
). This can be achieved
by dividing the attempt rates by the ratio
.×
= 8.71 × 10
. Since we calculate the attempt
rates within an energy bin of 0.1 eV, the energy resolved attempt rates also need to be normalized
to the quantized energy bin size. This will give us the attempt rates in the units #attempts/(eV-fs).
Finally, we normalize this attempt rate to the cross-section area of the simulated device (300 × 4.7
nm
2
) which gives us the attempt rates in the units of # attempts/(eV-fs-cm
2
). The normalized
attempt rates obtained using this procedure have been shown in Figures 5c and 5d of the main text.
118
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Chapter 5: Hot electron driven hydrogen evolution at graphene
surface
5.1 Introduction
Here, we show that the turn on voltage for the hydrogen evolution reaction on a graphene surface
can be tuned in a semiconductor-insulator-graphene (SIG) device immersed in a solution.
Specifically, it is shown that the hydrogen evolution reaction (HER) onset for the graphene can
shift by > 0.8 V by application of a voltage across a graphene-Al2O3-silicon junction. We show
that this shift occurs due to the creation of a hot electron population in graphene due to tunneling
from the Si to graphene. Through control experiments, we show that the presence of the graphene
is necessary for this behavior. By analyzing the silicon, graphene, and solution current components
individually, we find an increase in the silicon current despite a fixed graphene-silicon voltage,
corresponding to an increase in the HER current. This additional silicon current appears to directly
drive the electrochemical reaction, without modifying the graphene current. We term this current
“direct injection current”, and hypothesize that this current occurs due to electrons injected from
the silicon into graphene that drives the HER before any electron-electron scattering occurs in the
graphene. To further determine whether hot electrons injected at different energies could explain
the observed total solution current, the non-equilibrium electron dynamics was studied using a 2D
ensemble Monte Carlo Boltzmann transport equation (MCBTE) solver. By rigorously considering
the key scattering mechanisms, we show that the injected hot electrons can significantly increase
the available electron flux at high energies. These results show that semiconductor-insulator-
graphene devices are a platform which can tune the electrochemical reaction rate via multiple
mechanisms.
122
5.2 Hydrogen evolution cathode
Electrocatalysis can be used to convert intermittent renewable energy generation into stored
chemical energy
1-5
. In general, these processes are an avenue towards creating fuels from abundant
molecules. Thus, design of electrocatalysts are of significant interest. However, the primary focus
of design efforts surrounds understanding and engineering the kinetic aspects of catalysts by
increasing density of active sites or intrinsic activity of catalysts
6-10
. Here, we show that through
controllable generation of hot electrons, we are able to electrically modulate the potential at which
the HER occurs on monolayer graphene. This potentially introduces another avenue through which
Figure 5.1. Device schematics, characterization, and hot electron transfer mechanism. (a) Schematic of
the structure of graphene insulator semiconductor device used here. (b) Current density vs applied
voltage for the graphene/Al 2O 3/Si diode used here in both linear and log scale. (c) Raman spectroscopy
of graphene layer transferred on top of the Al 2O 3/Si substrate. (d) Electrochemical measurement set up
for device characterization. (e) Band diagram of device structure at the positively biased graphene-Si
junction showing the injection of hot electrons.
a b
d
Si
Ti/Ag
Al
2
O
3
Graphene
Epoxy
Graphene n-Si Electrolyte
Donor (V
red
)
E
CB
Acceptor (V
ox
)
Direct electron
E
VB
G
2D
1000
900
800
700
600
500
400
300
200
100
Intensity (a.u.)
3000 2500 2000 1500
Raman Shift (cm
-1
)
e
c
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
10
1
Current Density (mA/cm
2
)
2.0 1.6 1.2 0.8 0.4 0.0
Graphene-Si (V)
50
40
30
20
10
0
Current Density (mA/cm
2
)
123
electrocatalysts may be engineered—through control over the electron distribution. Specifically,
we use a semiconductor-insulator-graphene (SIG) junction, whereby when a voltage is applied,
thermalized electrons from the semiconductor conduction band will tunnel across the insulator into
the graphene, where they will initially be out of equilibrium with respect to the Fermi-Dirac
distribution of the thermalized electrons in graphene. Regardless of the current limiting
mechanism, it is important to highlight that all electrons injected from the silicon into the graphene
will be hot electrons. Specifically, the thermal electrons in the silicon device will become hot
electrons in the graphene after injection. If there were no other terminals in this device, those
electrons would then cool to the graphene Fermi level, with the excess energy being dissipated as
heat
11
. However, in these devices, the graphene is also in contact with a solution, enabling electrons
in the graphene to drive electrochemical reactions. Thus, depending on the relative rates of cooling
and reaction, the injected hot electrons in graphene can traverse multiple pathways. We choose
graphene due to the low electron-phonon coupling and electron density when compared to metals
as well as the single layer physical structure
12,13
. The lower electron scattering rates are important
in reducing the hot electron cooling pathways, and the single layer structure enables every hot
electron to be at the surface, maximizing the probability of driving electrochemical reactions.
Recently, it was also shown that high quantum efficiency hot electron devices could be generated
with thin films of gold, suggesting that a material such as graphene, which has superior properties
from the perspective of hot electron devices could perform better
14
.
124
5.3 Device description and experimental results
In this work, we use a semiconductor-insulator-graphene junction to controllably create a hot
electron population via tunneling of electrons from the semiconductor conduction band into the
graphene layer and subsequently use the injected electron population to modulate the
electrochemical reaction rate between the graphene and an aqueous solution. Figure 5.1a shows a
schematic of the device structure which consists of a moderately doped n-type silicon wafer, an
aluminum oxide insulator layer, and a graphene layer. The device is encapsulated with the epoxy
to ensure only the graphene is in contact with the solution. After fabrication we carried out dry I-
V measurements to observe the diode behavior of the SIG device. Figure 5.1b shows the both
linear and log scale plots of the device I-V characteristic. As shown in the I-V curves, the diode
shows two exponential regions, with different slopes, which can be expected in a semiconductor-
insulator-metal device, as the current may be limited by (i) injection over the silicon depletion
region barrier, (ii) tunneling through the oxide, or (iii) parasitics. Here, the current appears to be
limited by silicon injection between the voltage region of 0 V – 0.4 V, and then appears to be
tunneling limited between 0.4 V – 1.9 V. To ensure that the graphene was successfully transferred
onto device, we carried out Raman spectroscopy on multiple points on the device surface. A
representative Raman spectrum of graphene on the aluminum oxide is shown in Figure 5.1c with
sharp 2D and G peaks labeled at 2680 cm
-1
and 1580 cm
-1
, respectively. The relative ratio of the
measured I2D/IG peak intensity is ~2, clearly identifying the monolayer graphene
15
. The
electrochemical measurement of this device was conducted by submerging into the 0.5M H2SO4,
which acts as the collector of hot electrons in this device. A potentiostat with two independent
channels is used for modulating i) a graphene-solution junction voltage (VGraphene-Solution) to control
the electrochemical reaction, and ii) a graphene-silicon voltage (VGraphene-Si) to control the injection
125
of high energy electrons from the silicon conduction band into the graphene. The schematic of the
device measurement set up is shown in the Figure 5.1c. To understand the measurement set-up,
details are presented in Figure 5.6. A schematic of the device and electrolyte band structure is
shown in the Figure 5.1e. One unique feature of this graphene-based device arises due to the small
Figure 5.2. Linear sweep voltammetry (LSV) curves of graphene SIG device and comparison devices.
(a) Linear scale solution current density vs applied Graphene-Solution voltage for varying Graphene-Si
diode voltages and (b) Solution current density vs applied Graphene-Si voltage for stepping Graphene-
Solution voltages. (c) Solution current density comparison with the no-graphene device. (d) Solution
current density of Pt and Pd at the same scale of current density.
100
90
80
70
60
50
40
30
20
10
0
J
Redox
(mA/cm
2
)
0.25 0.00 -0.25
E (V vs RHE)
Platinum
Palladium
Graphene
No Graphene
a b
c d
HER
Region
100
90
80
70
60
50
40
30
20
10
0
J
Redox
(mA/cm
2
)
0.6 0.4 0.2 0.0 -0.2 -0.4
E (V vs RHE)
100
90
80
70
60
50
40
30
20
10
0
J
Redox
(mA/cm
2
)
0.6 0.4 0.2 0.0 -0.2 -0.4
Graphene-Solution (V vs RHE)
V
Graphene-Si
= 0V
V
Graphene-Si
= 0.5V
V
Graphene-Si
= 1.0V
V
Graphene-Si
= 1.5V
V
Graphene-Si
= 2.0V
160
140
120
100
80
60
40
20
0
J
Redox
(mA/cm
2
)
1.6 1.2 0.8 0.4 0.0
V
Graphene-Si (V)
V
Graphene-Solution
= 0.2V
V
Graphene-Solution
= 0V
V
Graphene-Solution
= -0.2V
V
Graphene-Solution
= -0.4V
126
quantum capacitance of the graphene, allowing the Fermi level in the graphene to change as a
function of graphene-Si junction bias.
To study the redox behavior of graphene devices, we carried out two types of ISolution
measurements. The measured potentials here are rescaled to the RHE by using the equation ERHE
= EAg/AgCl + 0.197V + 0.0592V*pH. First, we carry our linear sweep voltammetry (LSV) of the
Graphene-Solution (VGraphene-Solution) junction while simultaneously stepping the voltage of the
Graphene-Silicon (VGraphene-Si) junction from 0V to 2V with 0.5V steps. Figures 6.2a shows the
plots of the LSV. As the voltage between the Graphene-Silicon junction increases, the turn-on
voltage for HER is reduced, and the current density at a given applied voltage increases.
Particularly interesting is the cases of VGraphene-Si =1.5 and 2.0 V. We see dramatic increases in the
current, with the largest currents observed >~100 mA/cm
2
. Figure 6.2b on the other hand shows
the plot of LSV of the Graphene-Silicon voltage while stepping with a fixed voltage across the
Graphene-Solution junction. There are two key factors that determine whether an electron will be
elastically transferred from graphene to a redox state, resulting in observed solution redox current:
i) the probability of redox states at the given energy being available and, ii) the probability that the
electron will be able to tunnel through the energy barrier posed by the electrochemical double layer
at the graphene-solution interface. There is an activation energy barrier (ΔGact) associated with the
electron transfer and the probability that an electron can overcome this barrier is dictated by
thermal fluctuations
16,17
. The probability of an electron being transferred into a redox state inside
the solution quantitatively differs from that of being transferred into an adsorbed intermediate.
According to the Anderson-Newns model of chemisorption on metal
18
, density of states of an
adsorbed atom will be shifted in energy as well as get broadened. This density of states is
proportional to the electron transfer probability. According to this model, both the energy shift and
127
broadening will have a complicated dependence on energy. Ignoring the energy dependence of the
shift and broadening, the density of states takes the form of a Lorentzian distribution. A full study
of such density of states requires considering the orbitals of the adsorbed atom and the orbitals of
the adsorbent. However, for electron transfer to redox states inside the solution, electron transfer
probability and redox density of states are different and can be obtained from Gerischer’s model
19
.
According to this model, if an electron in graphene has an energy ΔE in excess to the energy of
the redox state, the electron transfer probability is given by the Boltzmann term, e
|∆
∆|
where
kB is the Boltzmann constant
2020
. Within the harmonic oscillator approximation, this probability
distribution takes the Gaussian form,
(1) W
λ, ΔE, V
= (4πλk
T)
/
exp [−
(
)
]
Here, λ = 4∆G
is the reorganization energy of electron transfer where ∆G
is the activation energy
for ΔE = 0 and V
= 0.The term (4πλk
T)
/
normalizes the distribution. Since the
redox reaction happens at both redox species inside the solution and adsorbed to the electrode, ideally the
electron transfer probability should follow a combination of both the Lorentzian and Gaussian
distribution. However, since we are more interested in understanding the physical phenomena and not
performing a rigorous quantitative analysis, we can roughly approximate the Lorentzian distribution to a
Gaussian distribution. This way, we can use the Gerischer model as a proxy to the more involved
Anderson-Newns model for the sake of simplicity.
The probability that the electron can tunnel through the double layer barrier depends on the
specifics of the double layer structure itself
16
. To a first approximation, this probability should
continuously increase with increasingly negative
. When we approach more
negative
,
follows the Gaussian distribution and increases in the beginning.
128
Since typically takes a value between 1~3 eV, electron transfer probability will increase within
the
range of our concern (0.2 to -0.4V)
16
. In addition, tunneling probability also
increases. Increase in both of these probabilities manifest themselves as an increased amount of
current for increasingly negative
. When
becomes more positive,
the injection current as well as energy of the injected electron with respect to the graphene Dirac
point increases. This high energy electron follows one of three pathways: i) losing energy to other
low energy electrons in graphene via electron-electron (e-e) scattering, ii) losing energy to the
lattice through phonon scattering, or iii) transferring itself to the redox state and performing
reduction of the H
+
ion. In the steady state, this injection flux of electrons results in a distribution
of electrons differing from the Fermi distribution that have considerably higher energy compared
to the thermal electrons. These hot electrons with energy ∆ = −
(E = energy of electron
compared to Dirac point, ERedox = energy of standard redox state compared to Dirac point) will
have a higher electron transfer probability as ΔE − −
→ 0 limit. For an
injection energy exceeding or a
< −/, electron transfer probability will
start decreasing whereas tunneling probability should increase. However, the highest value
tunneling probability can attain is 1 and therefore the Gaussian distribution will be the limiting
factor in determining the success of an electron transfer.
To compare and analyze the source of these result, we carried out the identical experiment with
the device which does not have graphene on top of the insulator layer. Figure 2c shows the solution
current density vs Graphene-Solution voltage. Comparing the same amount of voltage, VWE-Si =
2V biased condition, which the working electrode represent graphene for the first device and
aluminum oxide for the second device, the no-graphene device shows less current with ~5mA/cm
2
at potential (V vs RHE) = - 0.3V, while the graphene device shows ~80mA/cm
2
, for which the
129
relative ratio is ~18. In addition, we measured the HER in same electrolyte by using the both
platinum and palladium electrode, which are excellent electrocatalysts due to their near ideal
positions on the volcano plots
21-23
. Figure 5.2d shows the measured current density of platinum
and palladium electrodes evaporated on top of the insulator layer as well. At VGraphene-Si = 2.0V,
the current density is ~2 times and ~4 times higher than the platinum and palladium, respectively.
This is noteworthy that none of the previous works have presented higher value than platinum in
both turn on voltage and current density at same voltage vs the reference electrode. To eliminate
the possibility of the effect of lateral voltage drop in graphene, we measured two different samples
with different ring electrode shapes and show that both devices demonstrate nearly identical
current densities (Figure 5.7). We also carried out the same measurement in different types of
electrolytes to verify the stability of our graphene device. Figure 5.9 shows the results of the cyclic
voltammetry in the 1mM Ferrocene + 1M KCl solution. Hot electron effect of the device can be
distinguished from the tail of the graph at the VGraphene-Si = 1.5V. Figure 5.8 also shows the results
of the LSV in alkaline condition by using the 0.1M KOH instead of 0.5M H2SO4. These devices
also show a similar hot electron effect in 0.1 M KOH solutions as well, but with lower current.
The reason the current level is reduced comes from the reduced availability of H
+
ions as well as
different mechanisms of the HER in the different pH of the electrolyte
24
. After the electrochemical
measurements, to ensure our physical stability of device, we carried out Raman spectroscopy to
ensure that the graphene layer was still present. Figure 5.10 shows the 8-points of Raman
spectroscopy results showing 2D and G peaks all labeled around at 2680 cm
-1
and 1580 cm
-1
,
130
respectively. The relative ratio of the measured I2D/IG peak intensity here is still around 2, it is
feasible to say that our device is stable even after several experimental runs.
Next, we analyze the current components that allow the graphene to have high currents by
studying each of the three measured current components (ISolution, IGraphene, ISi) from the potentiostat
system. Figure 5.3a shows the schematic of the measured current components, and the internal
current components which compose them. The source of hot electrons in the graphene is the
injection of electrons from the silicon conduction band tunneling through the oxide layer. In our
measurement, the total redox current is measured through the ISolution current component. The
Figure 5.3. Composition of current inside the device and system and measurement results. (a) Schematic
of current components flowing inside the system. Major currents (i.e. I Si, I Graphene, and I Solution ) are
composed with different minor current components. (b)-(e) Measurement of three major currents of the
closed system, under different Graphene-Si voltages.
a b
c d e
5
4
3
2
1
0
-1
-2
-3
Current (mA)
-0.4 -0.2 0.0 0.2
Graphene-Solution (V vs RHE)
V
Graphene-Si
= 1.0V
80
60
40
20
0
-20
Current (mA)
-0.4 -0.2 0.0 0.2 0.4
Graphene-Solution (V vs RHE)
V
Graphene-Si
= 1.5V 80
60
40
20
0
-20
-40
Current (mA)
-0.4 -0.2 0.0 0.2 0.4
Graphene-Solution (V vs RHE)
V
Graphene-Si
= 2.0V
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
Current (mA)
-0.50 0.00
Graphene-Solution (V vs RHE)
I
Graphene
I
Si
I
Solution
V
Graphene-Si
= 0V
131
platinum counter electrode is shared by two working electrodes (Graphene and Silicon), the total
current can be measured by collecting all the current components flow into Pt counter electrode.
The electrochemical reduction current on the graphene is separated into three components,
reduction due to the thermal electron population of graphene itself, IThermal Electron, reduction due to
the hot-electron population, IHot Electron, and a direct electrochemical reduction component from the
silicon to the solution, IDirect Injection, which is the most significant factor in this work. These
correspond to the measured components from the following relationships.
(2) ISolution = -(IGraphene + ISilicon)
(3) IGraphene = IThermal Electron + IHot Electron – IGraphene-Si
(4) ISi = IGraphene-Si + IDirect Injection
From these relationships, we can see that when VGraphene-Si = 0 V, IGraphene-Si = 0 A, since
none of the electron is tunneling from silicon conduction band. This shows the traditional 3-
electrode measurement where the graphene is the working electrode, and all the total solution
component comes from thermal electrons of graphene, which refers to the ISolution = -IGraphene in
Figure 5.3b. Unlike other metal electrodes, the amounts of thermal electrons from graphene is less
due to the low density of states. Figure 5.3c-f shows the three measured current components during
a VGraphene-Solution linear voltage sweep for VGraphene-Si from 0.5V to 2.0V. Since the voltage between
the graphene and silicon is fixed, the current injected from the silicon into the graphene should be
constant with respect to VGraphene-Si which indicated the device diode current. It can be noticed that
at positive VGraphene-Solution, the amount of ISi and IGraphene is identical for all the cases. This indicates
the current is looping inside the closed diode system without transfer of electrons from graphene
to the redox states. However, as seen in all the cases from Figure 5.3c to 5.3e, an increase in the
measured current, ΔISi exists as the VGraphene-Solution become more negative. This increase in ISi can
132
be explained by either of the mechanisms, (i) a change in the graphene electrode voltage due to
the lateral currents on top of the surface and (ii) hydrogen evolution reaction initiated by injected
electrons to a graphene/hydrogen complex which directly accepts electrons from the silicon,
driving hydrogen generation without the need for a multistep electron transfer without going
through any scattering mechanism. Our control experiments analyzing the lateral graphene
potential drop (Figure 5.7) enable us to eliminate the first mechanism. From this, we conclude that
Figure 5.4. Specific current component extracted from the major current. (a) Direct injection current vs
graphene-silicon voltage at different V Graphene-Solution (b) Normalized electron transfer rate vs graphene-
silicon at different voltage V Graphene-Solution. (c) Hot electron current vs graphene-silicon voltage at different
V Graphene-Solution. (d) Tafel slopes of different biased conditions.
133
the increase in ISi is due to direct injection of electrons from the Si, into graphene, and then
immediately transferred from the graphene into the solution before any electron-electron scattering
occurs in graphene. This is observable due to the independent voltage control and current
measurement of the graphene and silicon terminals. This effect is less prominent as we go to higher
VGraphene-Si, specially at VGraphene-Si = 2.0V, the ΔISi is almost zero. As stated earlier, increasing
VGraphene-Si also increases the energy of the injected electrons. When this energy increases beyond
a critical point so that ΔE − −
> 0, electron transfer probability for these
electrons decrease resulting in a decreased direct injection current. Instead of increase in ΔISi, we
could observe the amount of solution current increase coming from the change in graphene current,
ΔIGraphene. Since these high energy injected electrons cannot directly be transferred to the redox
states efficiently, they will scatter within the graphene, eventually giving the energy to the thermal
electrons and the lattice. This leads to an increase in the hot electron population and accounts for
the increase in IGraphene. However, it is important to mention that increasing VGraphene-Si also induces
a decrease in the Fermi level of graphene from the Dirac point due to its finite quantum
capacitance
25,26
. An increasingly negative VGraphene-Solution has the opposite effect and increases the
Fermi level of graphene. These two opposing effects can be explained considering the circuit
model shown in Figure 5.16. The voltage drop in graphene quantum capacitance, CGr is manifested
as the shift in graphene Fermi level from the Dirac point. Figure 5.17 shows a heatmap of the
Fermi level shift in graphene as a function of both VGraphene-Si and VGraphene-Solution for different
electrochemical double layer capacitance, CDL values (1, 50, 100, 200 μF/cm
2
). We consider a
range of CDL as it is expected to increase during the timespan of the measurement due to the added
pseudocapacitance of the adsorbed hydrogen. Previous investigations on graphene has showed that
CDL lies within the range of 1 to 10 μF/cm
2
27,28
. For such values of CDL, graphene is more likely
134
to be p-doped as observed in Figure 5.17.
This doped graphene has a different density of thermal
electrons compared to undoped graphene leading to a different thermal current.
To further get insight of this behavior, we have calculated both the direct injected current and
hot electron current, which can be extracted from the amount of change in ISi ( ISi) and IGraphene
( IGraphene) respectively by sweeping the VGraphene-Si. Since direct injection current originates from
the unscattered electrons in graphene, it has a very narrow energy distribution that can be
approximated to a weighted delta function where the weights are proportional to the diode current,
IGr-Si and injection energy is proportional to VGraphene-Si. As we change VGraphene-Solution from 0 V to
-0.4 V, we observe direct injection currents to be peaked at certain VGraphene-Si values (Figure 5.4a).
To further understand this behavior, we divide the direct injection current with IGr-Si which
disentangles the weights of the delta functions and gives us the true distribution of direct injection
current as a function of VGraphene-Si and therefore as a function of energy of the injected electrons.
This distribution is a composite of both electron transfer probability and the tunneling probability
of electrons at different injection energies. We call this quantity as electron transfer rate and
normalize its maximum to 1 for different VGraphene-Solution conditions (Figure 5.4b). We can clearly
observe a Gaussian behavior modulated by non-unity tunneling probability. When we analyze the
peaks of the modified Gaussian electron transfer rates shown in Figure 5.4b, we can observe a
negative shift (~ -0.2 V) in these peaks VGraphene-Solution changes by -0.2 V which is consistent with
equation (1).
Figure 5.4c shows the hot electron current extracted from the change of graphene current
ΔIGraphene. Hot electron in this work could be distinguished with the direct injected electrons as
electrons which have been scattered inside graphene yet have higher energy compared to the
135
thermal electrons. However, in this device, the majority of additional solution current occurs due
to direct injection. As shown in the Figure 5.4a and 5.4c, we can observe the transition of the
current components mainly from direct injection electrons to hot electrons. These results coincide
with our expectation that the lack of available redox states in the electrolyte limits the amount of
direct injection current and increases the hot electron current.
Figure 5.4d shows the Tafel plots for this device. The most striking feature of this plot is the
clear increase in exchange current density as a function of applied VGraphene-Si voltage. Here, we
propose that this clear increase as the graphene-silicon voltage is increased follows well with the
hot electron model of carrier injection from Si into graphene. Specifically, at higher biases, the
electrons injected into the graphene are injected at higher energies, due to the voltage drop across
the oxide. This in turn leads to the hot electrons interacting with the solution at a higher energy,
which mimics the effect of increasing the temperature of a reaction. However, the exchange current
density increases by nearly 2 orders of magnitude, which is unlikely to occur through simple
heating of the solution.
5.4 Theoretical analysis
To understand the behavior of the hot electrons inside the graphene layer, we have simulated the
non-equilibrium electron dynamics using a 2D ensemble Monte Carlo Boltzmann transport
equation (MCBTE) solver. Since electrons in graphene are confined in its 2D plane, we can model
graphene as a quantum well and calculate how frequently the confined electrons hit the energy
barriers, i.e., the attempt frequency (~16 fs
-1
). Combining this attempt frequency with the electron
distributions obtained from the simulations helps us quantify the interaction of graphene electrons
with the solution at the graphene-solution interface. Figure 5.5 shows the energy resolved attempt
136
rates of graphene for injection energies of 0.5 – 2.0 eV and an injection current of 1 mA/cm
2
for
undoped graphene. When there is no injection of hot electrons, attempt rate profile just follows the
graphene density of states and Fermi distribution. However, for a non-zero injection rate, the
attempt rates at higher energies are significantly higher compared to the zero-injection situation.
Figure 5.5b shows the attempt rates for higher energy electrons at different injection energies.
Here, we see that there is a clear increase in the attempt rate of electrons at higher energies which
implies greater rate of interaction between the high energy electrons and the surface. This increased
interaction at higher energies corresponds well to the increase in exchange current density for
higher graphene-silicon voltages where injection energy of electrons is higher.
For an injection current density of 1 mA/cm
2
, we have an injection flux of hot electrons (FHE)
= 6.25 electrons/(cm
2
.fs). For undoped graphene, an electron injected 1 eV above the Dirac point
has an energy loss rate of ~0.1 eV×10 ps
-1
= 1 meV/fs for e-e scattering and ~0.2 eV×50 ps
-1
= 10
meV/fs for optical phonon scattering
12
. Therefore, the electrons will lose 1 eV energy within τHE
≈ 100 fs. Within this 100 fs, an electron will have the opportunity to interact with the surface,
nattempt ≈ 100 fs×16 fs-1 = 1600 times. This leads to an attempt rate of FHE×nattempt ≈ 6.25×1600
attempts/(cm
2
.fs.eV) = 10
4
attempts/(cm
2
.fs.eV). From our simulations, we indeed see an attempt
rate of 10
4
~ 10
5
/(cm
2
.fs.eV) for electrons injected at 1 eV above the Dirac point for an injection
current of 1 mA/cm
2
for undoped graphene.
137
From Figure 5.11 to 5.14 shows the attempt rates for combinations of different injection energy
and different doping conditions of graphene. Since p-doped graphene has a very small e-e
scattering rate due to its small thermal electron density, the hot electrons do not redistribute their
energies with the thermal electrons as effectively and most of their energy decay is due to phonon
emission. The injected hot electrons can also gain some energy by absorbing phonons. Due to the
lack of redistribution in electron energies, we can observe a peak in the attempt rates near the
injection energy for p-doped graphene whereas for undoped and n-doped graphene, the attempt
rates monotonically decrease with increasing energy. When a positive voltage is applied between
graphene-silicon junction, graphene starts becoming p-doped as the Fermi level goes down. When
the electron is injected into graphene, there is a non-zero probability that it will be transferred
directly into the solution before getting backscattered by the phonons in graphene. The peak
observed in the attempt rates near the injection energy means that a major portion of these injected
electrons do not go through scattering in p-doped graphene. At the graphene/electrolyte interface,
transfer of electron from graphene to the H
+
ions depends on two important factors: i) the
Figure 5.5. Solving MCBTE for undoped graphene. (a) Attempt rate of electrons tunneling into the
graphene/electrolyte junction with 0.5 - 2.0 eV injection energy above the Dirac point. (b) zoomed in
version of (a) at higher electron energies.
138
probability of electrons tunneling through the double layer barrier and, ii) the probability of having
a redox state at the same energy due to thermal fluctuation induced broadening. The tunneling
probability exponentially increases with the increasing electron energy and the probability of
having a state in the same energy to facilitate the elastic tunneling depends on the applied VGraphene-
Si and temperature. The injected electrons that do not face any scattering upon injection have a
much higher tunneling probability compared to the thermal electrons. As a result, there is a finite
probability that these electrons can directly transfer to the H
+
ions while not bothering the rest of
the electrons in graphene. In our experiments, this registers as the direct injection current from
silicon to the solution. In a previous work, the same effect was observed for metal electrodes,
especially gold. However, for graphene, direct injection current constitutes a significantly larger
portion of the total solution current compared to gold because of this lack of e-e scattering in the
p-doped conditions, and single layer property.
In conclusion, we demonstrate that a graphene-based SIG diode can act as a source of hot electrons,
especially direct injected electrons for efficiently driving electrochemical reductions. By analyzing
the individual components, it is possible to not only discover the mechanism of the high energy
electron transfer but the characteristic of the graphene/electrolyte junction. Graphene- based hot
electron device is not confined to this certain structure, we could possibly get better results by
replacing each component with other materials. Future experiments could explore other redox
reactions for carbon dioxide reduction to useful materials, and other 2-D materials that transport
electrons more efficiently to see if high efficiencies can be achieved at lower voltages.
139
5.5 Fabrication methods
Moderately phosphorous doped (Nd = 5×10
16
cm
-3
) (100)) silicon wafer (MTI Corporation) was
used as the substrate. Native SiO2 was removed with 1:10 ratio of HF:H2O (Sigma Aldrich, 49%
CMOS grade) etching for 1 minute. After oxide etching, 1nm of titanium and 100nm of silver back
contact metals were evaporated in an electron beam evaporator (Temescal, SL1800). To prevent
front side damage, a blank Si handle wafer was used after an acetone, IPA, D.I water rinse. The
semiconductor-insulator-graphene (SIG) structure was fabricated by depositing an aluminum
oxide insulator layer with Atomic Layer Deposition (Ultratech/Cambridge Savannah ALD) using
Trimethyl aluminum (Aldrich, 1001278062) and water (Aldrich, W4502) precursors. Single layer
of graphene was grown on top of the copper foil by using chemical vapor deposition (CVD)
method by controlling the flow rate of hydrogen (H2) and methane (CH4). PMMA (A6495) is spin
coated on top of the graphene layer as an adhesion material to transfer the graphene. CVD grown
graphene was transferred on top of the aluminum oxide after the copper foil is etched, and PMMA
is removed by rising with the acetone. For contact wire attachment, copper wire wrapped with
aluminum foil at the one end was used. Two wires are connected to both front and back side of the
devices each with fast drying silver paint (Ted Pella Inc, 16040-30). A ring contact was drawn in
the front side of device in graphene layer region. For device encapsulation, a glass slide (VMR
Micro slides) was used as a back holder. Fabricated devices with contacts were placed on the glass
with epoxy (Gorilla Epoxy clear) to encapsulate the device while leaving the graphene electrode
surface exposed.
140
5.6 Measurement details
5.6.1 Measurement system
Figure 5.6 shows a schematic of the current flow map in our device measurement. Our potentiostat
measurement setup uses two working electrodes to apply bias between the graphene/silicon and
graphene/solution, respectively. Thus, we have two sets of counter electrodes (CE 1 & CE 2),
working electrodes (WE 1 & WE 2), and reference electrodes (RE 1 & RE 2). In a normal
potentiostat, current flows between the working electrode and the counter electrode, while the
reference electrode is used to set the voltage with working electrode
1
. First, to apply voltage
between the graphene and solution, which is the typical electrochemical measurement set up, we
connect WE 1 to the graphene, CE 1 to a platinum wire in the solution, and RE 1 to a 3M Ag/AgCl.
To apply voltage between the graphene and silicon at the same time, we connect the silicon to WE
2, the graphene to RE 2, and the platinum wire to CE 2. This allows us to control the two different
Figure 5.6. Current flow across the device and measurement set up. a, The directions of all the
current components. b, The schematic of measurement system connections.
141
voltage (VGraphene-Solution and VGraphene-Silicon) independently. By sharing the platinum for both CE1
and CE2, we are able to get the all the current source occurring inside the system.
and
represent working electrode current in channel 1 and 2.
and
indicate counter electrode
current in channel 1 and 2, which are connected in series to a Keithly Multimeter to measure the
total solution current more precisely since the current directly coming from potentiostat has low
resolution.
5.6.2 Three terminal current measurement
In this measurement set up, three different currents were measured to investigate the behavior of
the graphene based hot electron device. The silicon current and the graphene current were
measured through the potentiostat and the solution current was measured using the digital
multimeter (Figure 5.6). The relationships between the different current components are as shown
below:
For potentiostat channel 1;
=
= −
(1)
=
−
(2)
=
+
(3)
For potentiostat channel 2;
=
= −
(4)
=
+
(5)
For potentiostat channel 1&2 and multimeter;
142
=
+
= − (
−
) – (
+
)
= −
−
= − (
+
+
) (6)
Equations (1) - (3) represent the working electrode connected to graphene by using the channel
1, while equation (4) – (5) shows the channel 2, where the working electrode connected to silicon.
The counter electrode current will be the negative value of working electrode for both cases since
it has an opposite direction to the working electrode in the closed potentiostat system. Equation
(2) shows that the measured graphene current represents the hydrogen reduction current minus the
diode current. We claim that the hydrogen reduction current at the graphene surface is composed
of either by hot electrons or thermal electrons or both. Equation (4) shows the components of
silicon current. The silicon current should be the same whether the diode is in solution or out of
solution, and is represented by the diode current,
. However, our experiments show
that there is an increase in the measured silicon current, suggesting that there are some conditions
under which electrons are directly injected into the solution from the silicon. This also contribute
to the silicon current, which is what is described in equation 4. Finally, we can get the total current
by adding the current from both counter electrodes, shown in equation (6). When we add the two
together, we see that the measured counter electrode current,
, will be composed of three
different components,
,
, and
.
143
5.6.3 Investigation on voltage drop on graphene surface
To minimize the voltage distribution across the graphene film, a silver paste rectangular ring shape
contact was used instead of single dot contact. In order to ensure that lateral resistivity of the
graphene layer is not the cause of the observed hot electron effect, we carried out experiments with
different sizes of ring contact. The measurement was done to identify how much voltage drop we
might expect laterally across the graphene layer due to the current flow in the electrode.
Figure 5.7 shows the two different sizes of measured devices and their current density at same
biased conditions. Normalized current density were presented. Even though at lower VGraphene-Silicon
,current density does not match, however, this difference comes from the fact that the difference
in the graphene surface active site. When we inject high current by applying large VGraphene-Silicon,
it shows that both devices demonstrate nearly identical current densities. By doing so, we could
identify that our effect coming from voltage drop is negligible during diode operation.
Figure 5.7. Control device measurement. a, Device with small size graphene. b, Device with larger
size graphene. c-e, Current density vs applied V Graphene-Solution at different diode biased conditions.
144
5.6.4 Device Stability measurement in different conditions
Stability tests were conducted to show our device, mainly the graphene monolayer is stable not
only in a 0.5M H2SO4 solution condition. Figure 5.8 shows the results of the J-V in 0.1M KOH
condition.
Figure 5.8. Linear V oltage Sweep (LVS) in 0.1M KOH solution.
Figure 5.9. Cyclic V oltammetry in 1mM Ferrocene + 1M KCl
145
Not just for the hydrogen evolution reaction, we characterized by using standard ferricyanide
system. The supporting electrolyte used for the potassium ferricyanide was 1M KCl. We can
observe the hot electron effect clearly as the reduction current tail goes down when we increase
the VGraphene-Si from 0V to 1.5V. It clearly indicates that not just for hydrogen evolution reaction,
the hot electron can be used in the other redox couple condition as well.
5.7 Monte Carlo simulation
We have studied the non-equilibrium dynamics of hot electrons in graphene using Archimedes, an
open-source 2D ensemble Monte Carlo (MC) simulator
2
. We have accounted for the linear band
structure and all the prominent scattering mechanisms of graphene. In our previous work, we have
extensively explained the working theory behind the MC simulator specific to graphene and will
not repeat the details here. We have initialized the simulation with 1.25 million electrons within
Figure 5.10. a, Raman spectroscopy of 8 different spots after all the electrochemical measurements. b,
Optical images of the graphene layer with the 523nm laser spot.
1800
1600
1400
1200
1000
800
600
400
200
Intensity (a.b.u)
2800 2400 2000 1600 1200
Raman Shift (cm
-1
)
Point1 Point5
Point2 Point6
Point3 Point7
Point4 Point8
a b
146
the energy range of -2.5 eV to 2.5 eV where the Dirac point lies at 0 eV. Graphene has a carrier
density of 9.18×10
18
m
-2
within this energy range. Therefore, simulating 1.25 million electrons is
equivalent to simulating 0.136 μm
2
of actual graphene. Since graphene can become
electrostatically doped due to its finite quantum capacitance when the graphene-silicon junction is
biased, it is also important to understand the behavior of hot electrons in the doped conditions.
Hence, we have simulated the dynamics of hot electrons injected into graphene at different
energies and doping conditions to estimate the distribution of the hot electrons.
5.7.1 Monte Carlo simulation results - Attempt rates of hot electrons
In order to understand the dynamics of the injected hot electrons, we have injected 1 electron per
5 fs at a specific energy. These electrons are hot compared to the thermal electrons in graphene
and will scatter through different mechanisms to thermalize to the lattice. We have considered four
important scattering mechanisms: electron-electron (e-e) scattering, longitudinal optical (LO)
phonon scattering, transverse optical (TO) phonon scattering, and supercollision acoustic (SC)
phonon scattering. As these electrons interact with the thermal electrons, there is a redistribution
of energy between these electrons due to e-e scattering which allows the hotter electron to lose
some energy and the lower energy electron to gain the lost energy. It is also possible that the lower
energy electron will lose energy to make the hot electron even hotter. However, this is less likely
to happen as this often requires the lower energy electron to make an interband transition from the
conduction band to valence band which is only possible when both electrons have momentum
collinear to the Dirac cone. As a result, on an average we observe an energy loss from the hot
electron due to e-e scattering events. For undoped graphene, both the scattering rate and average
energy loss for e-e, LO, TO phonon scattering are of the same order
3
. This causes a fast decay in
energy of the hot electron. However, as the energy of the electron decreases, average energy loss
147
for e-e scattering goes down and optical phonon scattering rates go down dramatically when the
electron energy is below the optical phonon energy (~190 meV)
3
. At this point, the only dominant
scattering mechanism is the SC phonon scattering
3
. However, average energy loss due to SC
phonons is small compared to e-e and optical phonon scattering which leads to a slow decay in
energy
3
. For a p-doped graphene, the number of thermal electrons is small while the opposite holds
for n-doped graphene. Since the hot electrons partner up with the thermal electrons to go through
the e-e scattering events, e-e scattering rates are smaller (larger) for p-doped (n-doped) graphene
compared to the undoped one. Therefore, the population of hot electrons is affected greatly by the
doping condition in graphene, i.e., the applied voltages to the graphene-silicon and the graphene-
solution junctions.
When we keep injecting these electrons at a certain rate at a specific energy, they scatter with
other electrons and phonons and reach a steady state energy distribution that is not the same as the
Fermi distribution. All these electrons are confined within the 2D layer of graphene which is
equivalent to a quantum well. We have used a quantum well model for graphene to calculate the
attempt frequency (
) of the electrons. Each time an electron hits the graphene surface, it is
considered as an attempt to tunnel through the electrolytic double layer barrier that holds the
electron back from transferring into the H
+
ions. The probability of an electron tunneling into the
ion depends on the specifics of the double layer barrier, the concentration of H
+
ions, workfunction
of graphene, redox potential of hydrogen reduction reaction etc. The distribution of electrons, in
conjunction with graphene’s density of states, tells us the actual density of electrons at any energy.
In our simulation, we calculate the number of total electrons at every energy bin. Multiplying this
energy resolved number of electrons with the attempt frequency,
gives us the attempt rate in the
units of #attempts/time. Normalizing this attempt rate with the area of graphene and the energy
148
bin size gives us the attempt rate in the units of #attempts/(area.time.energy). This attempt rate
tells us how frequently and how many electrons at any specific energy are going to attempt to
penetrate the double layer.
5.7.2 Calculation of different components of attempt rates:
The steady state attempt rate of the thermal electrons follows the ()()
profile where ()
is the graphene density of states and () is the Fermi distribution. Since our simulation includes
a small number of electrons compared to actual device, it is not possible to capture the tail of the
Fermi distribution. Hence, we perform an extrapolation of the energy resolved attempt rates by
calculating theoretical ()()
for thermal electrons and fitting this result to the result
obtained from simulation. This attempt rate due to thermal electrons provide us a reference to
compare the hot electron attempt rates. For our simulations, we use an injection current density
which is very large compared to the actual injection current density in a real device. This requires
us to normalize our results to an injection current density observed in a real device. Such a
normalization will allow us to quantitatively understand how the hot electrons interact with the
graphene-solution interface.
There are two components that constitute the energy resolved attempt rate profile for hot
electron injection: (1) the thermal component that follows the ()()
profile and (2) the hot
electron component. We can isolate the two components by subtracting the theoretically calculated
thermal component from the attempt rate profile containing both components and this will give us
the hot electron attempt rates. We make an assumption that hot electron attempt rates are linearly
dependent on the injection current density. This assumption is reasonable since the number of
149
injected electrons are negligible compared to the number of thermal electrons and therefore the
injection current density does not have any significant effect on the thermal component of the
attempt rate
4
. Therefore, we can scale the hot electron attempt rates to a realistic injection current
density. Then we combine the two components again and this gives us a normalized energy
resolved attempt rate for a specific injection current density for a specific injection energy. Figures
5.11-5.14 show the attempt rates for graphene in different doping conditions. Figure 5.11-5.14
shows the overall attempt rates for graphene in different doping conditions at same fixed injected
energies.
Figure 5.11. Attempt rates of p-doped Graphene
Figure 5.12. Attempt rates of undoped Graphene
150
Figure 5.14. (a) Attempt rate of electrons tunneling into the graphene/electrolyte junction with 0.5eV
injection energy above the Dirac point. (b) - (d) with 1.0eV ,1.5eV , and 2.0eV injection energy.
10
1
10
3
10
5
10
7
10
9
10
11
10
13
10
15
Attempt rates (cm
-2
fs
-1
eV
-1
)
2.0 1.5 1.0 0.5 0.0
Energy above Dirac point (eV)
E
F
= -0.2 eV
E
F
= -0.1 eV
E
F
= 0.0 eV
E
F
= +0.1 eV
E
F
= +0.2 eV
Injection Energy = 1.5eV
10
-1
10
1
10
3
10
5
10
7
10
9
10
11
10
13
10
15
Attempt rates (cm
-2
fs
-1
eV
-1
)
2.0 1.5 1.0 0.5 0.0
Energy above Dirac point (eV)
E
F
= -0.2 eV
E
F
= -0.1 eV
E
F
= 0.0 eV
E
F
= +0.1 eV
E
F
= +0.2 eV
Injection Energy = 1.0eV
10
-1
10
1
10
3
10
5
10
7
10
9
10
11
10
13
10
15
Attempt rates (cm
-2
fs
-1
eV
-1
)
2.0 1.5 1.0 0.5 0.0
Energy above Dirac point (eV)
E
F
= -0.2 eV
E
F
= -0.1 eV
E
F
= 0.0 eV
E
F
= +0.1 eV
E
F
= +0.2 eV
Injection Energy = 0.5eV
10
1
10
3
10
5
10
7
10
9
10
11
10
13
10
15
Attempt rates (cm
-2
fs
-1
eV
-1
)
2.5 2.0 1.5 1.0 0.5 0.0
Energy above Dirac point (eV)
E
F
= -0.2 eV
E
F
= -0.1 eV
E
F
= 0.0 eV
E
F
= +0.1 eV
E
F
= +0.2 eV
Injection Energy = 2.0eV
a b
c d
Figure 5.13. Attempt rates of n-doped Graphene
151
5.7.3 Normalization of the attempt rates
In our real devices, the injection current density is actually the current density measured at the
graphene-silicon junction. This current density is of the order of ~10 mA/cm
2
. If we want to
simulate such a small injection rate, the simulation would require several microseconds. The
scattering rates in graphene are of the order of ~0.1 fs
-1
and a microsecond of simulation would
require several days to complete if we want to build a good statistics from the result. Given the
restraints in our computing abilities, we simulate for a much higher injection rate of 0.2 electrons/fs
which makes our simulation tractable. An injection rate of 0.2 electrons/fs is equivalent to
2.35×10
7
mA/cm
2
injection current density considering a graphene area of 0.136 μm
2
. We
normalize our results to an injection current density of 1 mA/cm
2
by dividing the hot electron
component of the attempt rate by the ratio
.×
= 2.35 × 10
. We have considered an energy
bin size of 0.01 eV to calculate the density of states and electron distribution. Therefore, we divide
the attempt rates by the bin size of 0.01 eV to get the attempt rates in the units of #attempts/(fs-
eV). In order to normalize the attempt rate to the graphene area, we further divide it by 0.136 μm
2
= 1.36×10
-9
cm
2
and this gives us the attempt rates in the units of #attempts/(cm
2
.fs.eV).
5.8 Quantum capacitance of graphene
Figure 5.15 shows the equivalent circuit diagram of our device where CDL is the electrochemical
double layer capacitance between graphene electrode and electrolyte, CGr is the quantum
capacitance of graphene, COx is the capacitance of the Al2O3 layer and CSi is the capacitance of the
depletion/accumulation region of silicon. We have calculated CGr from the density of states of
graphene
5, 6
and considered typical values of CDL and then calculated the voltage drop across the
CGr capacitance as shown in Figure 5.16. This voltage drop is the change in Fermi level in graphene
152
due to different applied voltages. Since CSi becomes very large in the accumulation region, COx
becomes the effective capacitance of the series combination. COx for a 6 nm Al2O3 layer is ~1.5
μF/cm
2
and CDL is typically within 1-10 μF/cm
2
for graphene-acid double layer. The Fermi level
shift is therefore directly dependent on the relative values of COx and CDL compared to CGr. For
smaller CDL, both positive and negative shifts in Fermi level are small as both CDL and COx are
comparable to CGr. When CDL becomes much larger compared to CGr, positive shift becomes more
pronounced compared to negative shift. However, CGr itself changes as a function of the voltage
drop across it. As voltage drop across CGr increases, the increased density of states causes CGr to
increase as well. As a result, CGr can become comparable to or larger than both CDL and COx and
therefore no appreciable doping effect can be observed even when the applied voltages are large.
Figure 5.15. Circuit diagram of the system
153
Figure 5.16. Graphene Fermi level shift due to V Graphene-Si and V Graphene-Solution
C
DL
= 1 μF/cm
2
C
DL
= 100 μF/cm
2
C
DL
= 200 μF/cm
2
C
DL
= 10 μF/cm
2
a b
c d
154
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156
Chapter 6: Ultra-low power parallel computing with oscillatory
retinal neurons
6.1. Introduction
In-sensor and near-sensor computing architectures enable multiply-accumulate operations to be
carried out directly at the point of sensing. In-sensor architectures offer dramatic power and speed
improvements over traditional von Neumann architectures by eliminating multiple analog-to-
digital conversions, data storage, and data movement operations. Current in-sensor processing
approaches rely on tunable sensors or additional weighting elements to perform linear functions
such as multiply-accumulate operations as the sensor acquires data. We implement in-sensor
computing with an oscillatory retinal neuron device that converts incident optical signals into
voltage oscillations. We introduce a computing scheme based on the frequency shift of coupled
oscillators that enables parallel, frequency multiplexed, non-linear operations on the inputs.
Simulation elucidates how this computing occurs. We experimentally implement a 3×3 focal plane
array of coupled neurons and show that functions approximating edge detection, thresholding, and
segmentation occur in parallel. An example of inference on handwritten digits from the MNIST
database is also experimentally demonstrated with a 3×3 array of coupled neurons feeding into a
single hidden layer neural network, approximating a liquid state machine. This network
demonstrated a 14.8% reduction in classification error from 2.16% to 1.84% compared to the same
neural network with standard photodetector inputs. Finally, the equivalent energy consumption to
carry out image processing operations, including peripherals such as the Fourier transform circuits,
is projected to be ~24 aJ/OP.
157
6.2 Oscillatory retinal neurons
In-sensor computing has emerged as a promising approach to improve computational speed and
reduce energy consumption
1-15
. Local weighting devices or tunable responsivity sensors enable in-
sensor architectures, where the input signal is multiplied by a weight at the point of sensing,
resulting in local multiply-accumulate (MAC) operations on the inputs. By eliminating the initial
data conversion, storage, and transmission, in-sensor architectures offer dramatically higher speed
and lower power consumption when compared to traditional von Neumann architectures. A wide
variety of modalities, including auditory
10,17-22
, olfactory
19
, tactile
24-26
and vision
6,7,9,11-13,15,27
sensors, benefit from the improved performance. However, these approaches generally execute a
single MAC operation on the input data
1,14,15,28-30
. Furthermore, parallel operations require scaling
the number of weighting devices connected to each sensor, which can be costly from an area and
power perspective.
We introduce an in-sensor computing approach where a coupled photosensor array carries
out parallel computation on the input image. Each pixel in the array acts as an oscillator, generating
an optical power-dependent frequency spectrum. When coupled, neighboring pixels also affect
each pixel's frequency spectrum. The power in a frequency band then becomes a non-linear
function of the inputs. Separate frequency bands, therefore, encode separate non-linear functions
of the inputs in parallel. Here, each pixel is an oscillatory retinal neuron (ORN) that directly
converts the input optical signal into voltage oscillations. We show through simulation and
experiment that coupled ORN networks carry out approximations of both basic and advanced
image processing functions, such as edge detection and image segmentation directly in the sensor,
encoded by choice of frequency and bandwidth of the output filter. Notably, the ORNs do not
require external electrical power, and when considering peripheral circuits such as buffers, selector
158
circuits, and analog fast Fourier transform circuits, the equivalent energy per operation can be as
low as 24 aJ/OP. Using the change in frequency spectrum instead of the phase dramatically relaxes
the fabrication tolerance requirements compared to other approaches that rely on synchronization
of oscillators, such as Ising machines
33-39
, leading to considerably greater scalability.
6.3 Photodetector with NDR
The ORNs are composed of two elements, (i) a photodetector that exhibits voltage-controlled
negative differential resistance (NDR) under illumination and (ii) an inductive element that can
drive an electrical oscillation by taking advantage of the instability of the NDR behavior. A
semiconductor-graphene-metal (SGM) photodetector, schematically shown in Figure 6.1a,
exhibits NDR in the detector’s power generation regime. The device comprises a p-type silicon
substrate, a Ti/Au (5 nm/100 nm) metal grid, and a graphene layer. Linear scale I-V measurements
of a 1 mm ×1 mm device under dark and uniform optical illumination are shown in Figure 6.1b.
In the dark, the device exhibits Schottky-diode behavior, while exhibiting NDR under illumination.
Figure 6.1c shows the log-scale I-V curves, highlighting that the NDR is only observed under
159
illumination. Section 6.9 and Figures 6.5-6.11 discuss the device-level behaviors in detail.
Connecting this device with an inductive element under appropriate bias conditions generates
optical intensity dependent oscillations, as shown schematically in Figure 6.1d. An active inductive
element, the Hara inductor, comprising a single MOSFET and a resistor, enables the scalability of
Figure 6.1: ORN enabled by SGM photodetector. (a) Schematic of the SGM photodetector device.
(b) I-V curves measured at dark conditions and under uniform illumination (445 nm) in linear and (c)
log scale. (d) Schematic of a single unit of ORN. (e) V-t curves measured at different optical intensities
and (f) corresponding frequency spectrum. (g) spiking frequency and amplitude as a function of optical
intensity. (h) Experimental plot of minimum optical power required for oscillation with neuron area. (i)
Calculation of dark current limited and LC limited P op,min for oscillation without external electrical
power.
160
the ORN. The observed oscillations are analogous to classical Van der Pol oscillators and the
Fitzhugh-Nagumo model of neurons
41-44
.
Other graphene-based photodetectors have exhibited NDR behavior, but all at a forward
diode bias
45-51
. However, this device generates an open-circuit voltage and exhibits NDR at
negative and zero applied voltages. This critical distinction allows oscillations at V
≤ 0V ,
which enables operation without external electrical power. Figure 6.1e shows experimental V-t
curves for a photodetector with an active area of 1 cm
2
. Figure 6.1f shows the corresponding
frequency spectra, illustrating the change as a function of the optical intensity. Figure 6.1g shows
the oscillation frequency and amplitude as a function of incident optical intensity, where we
observe that a minimum optical intensity is required to trigger oscillations in this ORN circuit.
These measurements were all performed at Vapplied = 0V .
To explore the scaling behavior of ORNs, photodetectors with areas between 600 µm
2
and
1 cm
2
have been fabricated and tested. The minimum optical power required for oscillation without
external electrical power scales linearly with the device area, as shown in Figure 6.1h. Two
parameters limit the oscillation dynamics of ORNs, the dark current and the capacitance. First, the
dark current does not exhibit NDR and adds with the light current. Second, the photon flux should
generate sufficient light current so that the valley of the NDR is greater than the dark current. There
must also be sufficient photocurrent to charge and discharge the capacitance at timescales of the
oscillation frequency. The addition of external power can mitigate this limitation. For a moderately
doped p-Si substrate, the depletion capacitance at the graphene-silicon junction is ~0.1 fF/µm
2
.
Figure 6.1i shows the minimum optical intensity for oscillation assuming a device capacitance of
0.1 fF/µm
2
as a function of device dark current density. We can see a crossover between two
different regimes: (1) inductance-capacitance (LC) limited regime at smaller dark currents and (2)
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dark current limited regime at larger dark currents. For our photodetectors, the Schottky nature of
the junction results in a larger dark current, limiting the threshold optical intensity to ~400 W/m
2
.
At smaller dark current densities, it is possible to decrease this threshold to below 2 mW/m
2
.
6.4 Frequency multiplexed computing with ORN
Next, we present a simple demonstration of how these coupled oscillators carry out computation.
We use simulations of ORN circuits connected to bandpass filters to elucidate the behavior of
coupled ORNs and how image processing occurs. We considered an ORN comprising a
photodetector with an active area of 1 mm
2
connected to an external inductor (L = 10 mH) with
Vapplied = 0V . We simulated the V-t curves of the ORN using the experimental photodetector
capacitance and J-V values. The V-t output of the simulation is filtered with varying center
frequencies (f) and bandwidths (BW) representing different bandpass filters. Section 6.10 and
Figure 6.12 show through simulation and analysis that each bandpass filtered output of a single
ORN can be analytically approximated with Lorentzians. Figure 6.2a shows the schematic of two
ORNs with inductive coupling, LC = 10 mH. Figure 6.2b plots the bandpass filtered Vosc1
magnitude as a function of P1 and P2 for varying center frequencies f = 28.4, 28, and 27.6 KHz
with BW = 200 Hz. The results show that two coupled oscillators define a curved subspace of the
input. Figure 6.2c shows the simulation results for a fixed filter with f = 28.4 KHz and BW = 200
Hz and varying coupling impedance. This results in subspaces of varying shapes. While accurate
solutions of the oscillator-coupled non-linear differential equations require numerical solutions,
we can analytically approximate the subspace by reducing the two oscillator problem to a single
oscillator problem by introducing a new quantity
=
+
+ (
+
) +
+
which nonlinearly combines P1 and P2. The coupled oscillator result then becomes
(
, , ) =
(
)
(∆)
, which can be fit to approximate the result from Figure 6.2c
162
as shown in Figure 6.2d. Here, P00 is a function of the center frequency f and ∆ is a function of
the filter bandwidth, BW.
To obtain a visual representation of how an image is processed in this scheme, we have
treated the 2-ORN circuit as a 1×2 convolutional kernel and processed a grayscale image of a cat
(Fig. 6.2e, top panel) with 250×240 pixels. The bottom panel of Figure 6.2e shows the (P1, P2)
pixel pairs, which serve as inputs to the 1×2 convolution kernel. The top panels in Figures 6.2f-h
show the filtered output images for f = 28.4, 28.6 and 28.8 KHz and BW = 200 Hz. Clearly, the
original image has been mapped to multiple processed images, indexed by the filter's center
Figure 6.2: Frequency multiplexed computation with ORN. (a) Circuit schematic for two coupled
ORNs. (b) ORN voltage colormap showing nonlinear peak surfaces and their shift at different center
frequencies for L C = 10 mH and BW = 200 Hz. (c) ORN voltage colormap showing different peak
surface shapes for different L C values and their (d) analytical approximations. (e) Original image and
the scatter plot showing all the (P 1,P 2) pairs for this image if it were input to a 1×2 convolutional kernel.
(f-h) Image transformations when the two coupled ORNs (L C = 10 mH) receive the (P 1,P 2) pairs as
inputs similar to a convolution operation and the corresponding scatter plots. The overlap between red
and blue scatter plots show how different subsets of inputs are thresholded by the network at different
center frequencies (BW = 200 Hz).
163
frequency. The bottom panels of Figures 6.2f-h show how the subspaces, defined by the ORN
coupling, filter center frequency (f), and bandwidth (BW), overlap with the (P1, P2) pixel pairs of
the original image. The coupled ORNs select the subset of the pixels that overlap with the defined
subspace. These results on a toy problem visually show how non-linear computations are
performed using coupled ORN oscillators.
6.5 Experimental results on image processing
Figure 6.3: Image processing with coupled ORN network. (a) Circuit schematic for the ORN kernel (b)
I-V curves of all 9 SGM detectors in the network under same optical illumination. (c) Oscillation V-t
and (d) FFT curves at the output node when all ORNs are under uniform illumination. (e) Frequency
band filtered images showing edge detection, (f) intensity filtering, (g) image sharpening, (h) object
segmentation. (i) Original color image and frequency domain images showing (j-m) image segmentation
operation.
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To experimentally demonstrate how coupled ORNs carry out more useful and complex image
processing functions, from edge detection to image sharpening, we have experimentally fabricated
a 3×3 ORN focal plane array with a cascaded connection, as shown in Figure 6.3a. We use this as
a kernel that slides across an image in the same manner as a convolution operation in a
convolutional neural network (CNN). A digital projector and external lens form the desired 3×3
segment of an image on the ORN focal plane array. An oscilloscope measures the output V-t signal
from a single node of the array, marked by Vout in Figure 6.3a. The output spectrum is then
processed in software to obtain the FFT and filtered outputs. Figure 6.3b shows the I-V curves of
all the SGM photodetectors in the experimental array under the same optical intensity (3
mW/mm
2
). Figure 6.3c shows a representative V-t curve obtained from the 3×3 array when all the
pixels are illuminated with uniform intensity. Figure 6.3d shows the frequency spectrum of the V-
t curve of Figure 6.3c.
We then took the digital grayscale image of a cat (Fig. 6.2e) and projected it on the 3×3
ORN focal plane array, using the array as a convolution kernel with a stride of one (pixel intensity
of 1 refers to 5.5 mW incident optical power). Figures 6.3e-h show the images obtained at 4 KHz
(BW = 100 Hz), 2.8 KHz (BW = 200 Hz), 2.4 KHz (BW = 800 Hz), and 3.2 KHz (BW = 1.6 KHz),
respectively. These filtered images demonstrate edge detection, intensity filtering, image
sharpening and object segmentation operations. The circuit topology of this ORN kernel performs
a multi-thresholding operation where the nonlinearly averaged intensity (
) of the 3×3 pixels cell
is mapped to a high value if
<
<
and to a low value if
<
or
>
where
and
changes with center frequency and bandwidth. As the bandwidth increases,
|
−
| becomes larger and can cover a larger range of pixel intensities. Therefore, at
different frequencies, the ORN kernel thresholds the image within different pixel intensity ranges
165
and the images shown in Figure 6.3e-h result from these different non-linear operations. As we
increase the bandwidth from Figure 6.3e to 6.3h, we observe a larger image region thresholded to
bright pixels. In this way, smaller bandwidth filters enable lower-level feature extraction, such as
edges, while high bandwidth filters lead to higher level feature extraction, such as object
segmentation. Figure 6.13 shows the processed images when the image is projected at different
optical power ranges. When the incident optical power range is lower, similar image processing
can be obtained at higher center frequencies. This result shows that the choice of optical power
range is not very critical if appropriate center frequencies are chosen.
Next, we have investigated whether the same 3×3 ORN focal plane array can perform
image segmentation from an image with multiple objects. A color image of size 180×156 pixels
(Figure 6.3i) that features a Christmas tree, two dogs and a cat was selected. The image is split into
three different grayscale images according to the pixel intensities of the color channels (R-channel,
G-channel, and B-channel). Only pixels of the same color were coupled together. Therefore, each
bandpass filter used had three different output images, one for each color channel. Figure 6.3j-m
shows the images filtered at 3.0 KHz (B-channel), 3.5 KHz (B-channel), 4.0 KHz (B-channel),
and 4.5 KHz (G-channel), respectively. The bandwidth used for each center frequency is 1 KHz.
At 3.0 KHz (B-channel), the bright background emerges as white and rest of the image is
thresholded to black, effectively segmenting the background. The images filtered at 3.5 KHz (B-
channel) and 4 KHz (B-channel) segment the dog on the left and the cat, respectively. On the other
hand, when filtered at 4.5 KHz (G-channel), the tree and the dog in the middle are detected. It is
important to note that we have only used a single bandpass filter to segment an entire object in this
case. Improved segmentation quality is expected when a linear combination of multiple
166
frequencies is used. These results clearly illustrate how the ORN kernel can perform parallel,
frequency multiplexed image processing and segmentation tasks.
These results show us two essential properties of this architecture: (1) the absence of any
encoding or preprocessing for input, and (2) the ability to perform parallel computation at different
frequencies. Since the projection of image and data acquisition are both performed in analog
domain, inevitably noise is added to both the input and output of the system but can still obtain
excellent results. It is also important to note that the circuit configuration used here to couple the
167
oscillators is not unique. Figure 6.14 shows image processing results obtained using a 10×10
coupled oscillator array kernel where the ORNs are connected to their nearest neighbors with a
coupling inductance of 5 H. Engineering the circuit configurations allows the implementation of a
variety of image processing functions.
Figure 6.4: LSM implementation of ORN network for MNIST classification. (a) Image classification
pipeline of the LSM structure showing an original input image, structure of the liquid layer, frequency
sampled output images and further processing at the readout layer by hidden ReLU units. (b) Training
and testing accuracy of the readout layer for training datasets corresponding to different frequency
samples. (c) Classification accuracy of the handwritten digits as a function of number of frequency
samples for 7×7 pixels/image and (d) for 21×21 pixels/sample.
168
6.6 Image classification with ORN
Inference is carried out by using a 3×3 pixel coupled oscillator network to act as a liquid layer to
construct a liquid state machine (LSM). Images from the MNIST database scaled to 21×21 pixels
were serially projected on the 3×3 array with a stride of 3, while output signals were acquired from
a single pixel. This data acquisition mode converts 21×21 images into 7×7×n datapoints where n
is the number of frequency samples considered. Each frequency sample corresponds to a bandpass
filtered output at a given center frequency and a bandwidth of 1 KHz. Ten thousand images from
the MNIST database were projected on the array, and the output data was collected and fed into a
readout layer consisting of a single hidden layer with 100 nodes followed by a 10-node output
layer. The hidden layer used a ReLU activation function, and the output layer used a softmax
activation function. We use backpropagation to train only the readout layer while keeping the liquid
layer connections untouched. Section 6.13 summarizes the implementation of the readout layer.
Figure 6.4a shows the LSM schematic. Figure 6.4b plots the accuracy obtained at the 50
th
epoch
if only a single frequency from each coupled array is fed into the hidden layer.
As expected, the single-frequency results show that the resulting accuracy varies by filter
frequency. Feeding multiple frequency samples per pixel to the hidden layer is expected to
augment the accuracy of the network. Figure 6.4c shows how feeding multiple frequencies into
the hidden network modifies the testing accuracies obtained at the 200
th
epoch. We have done this
for both experimental and simulated ORN arrays. The experiments were carried out on 10,000
images, limited by the speed of our data acquisition and projection setup. We observed a peak
accuracy of 92.51% with 7 frequencies sampled per pixel. To evaluate the potential of this result
if the full dataset of 70,000 images were used, a simulated version of the same 3×3 ORN focal
plane array was also carried out. We see the resulting accuracy for the experimental and simulation
169
cases with 10,000 images are very similar. As the simulation uses the experimental device I-V
curves, discrepancies between the simulation and experiment are attributed to the additional noise
introduced by our image projection and data collection setup. The experimental data acquisition
and simulation details are discussed in section 6.14. The in-sensor processed image performs better
than the equivalent 7×7 input directly fed to the hidden layer without the liquid layer, which results
in 90.06% accuracy. Similarly, through simulation we see that for all 70,000 images the accuracy
reaches 97.21% with multiple frequencies, which is higher than the corresponding direct 7×7 data
input (94.11%) into the neural network. Critically, if the 3×3 array is used as a convolution kernel
with a stride of 1, a peak accuracy of 98.16% is achieved for 11 frequency samples per pixel, as
shown in Figure 6.4d. This is higher than a standard imager directly inputting the 21×21 data
(97.85%) into the neural network, showing improvement using this hardware over a purely
software-defined approach. These results show that the parallel processing performed at different
frequencies improves the network and that the coupling between pixels in the 3×3 array allows
down-sampling of the number of outputs to the hidden layers of the fully connected neural
network. In addition, the LSM architecture does not require the training of liquid layer
interconnections, which significantly reduces the complexity and computational cost of the
training.
6.7 Comparison with literature
While an ORN array does not require any external electrical power to drive the oscillations, the
system requires peripheral circuitry to read the voltages and perform bandpass filtering operations.
A charge domain on-chip FFT processor
55
can perform such operations with a low energy cost. As
discussed in section 6.15, an ORN array can perform convolution equivalent tasks with a
170
performance of 42211 TOPS/W, which translates to an energy cost of 24 aJ/OP with a precision
equivalent to 8-bit integer operations in digital systems. These projections clearly show that
frequency multiplexed computing using coupled ORN array has the potential to completely replace
the energy-expensive convolutional layers in CNN for deep learning applications.
NPU
application
Type Comment bits
Reported
TOPS/W
Normalized
TOPS/W (8
bits)
Analog to
information
conversion
1
Analog In-sensor NN 8 43.5 43.5
VMM
2
Digital SRAM 4 351 87.75
MAC
macro
16
Analog DRAM 4 217 54.25
VMM
23
Digital
DNN learning
processor
8 146.52 146.52
Arithmetic
logic
31
Digital
Superconducting
logic devices
8 120 120
VMM
32
Analog
Si-
CMOS/CAAC-
IGZO based
memory
6 210 118.13
VMM
40
Digital
Stochastic NN
accelerator
8 75 75
MAC
macro
52
Digital SRAM 8 63 63
MAC
macro
53
Analog
SONOS
memory
8 100 100
MAC
macro
54
Digital SRAM 1 20943 327.23
General
purpose
Digital NVIDIA A100 8 4.992 4.992
General
purpose
Digital
Apple a16
Bionic
8 2.67 2.67
General
purpose
Digital
Qualcomm
Snapdragon 865
8 4.5 4.5
Nonlinear
convolution
(3×3 kernel)
(This work)
Analog ORN 8 42211 42211
Table 6.1: Comparison between different NPUs
171
Table 6.1 shows the performance comparison between different neural processing units
(NPU) for deep learning. Different NPUs operate at different bit resolutions and therefore an n-bit
performance was scaled by a factor of
to get a normalized 8-bit performance. Such a scaling
is reasonable
56,57
since number of transistors in digital logic typically scales as ~n
2
.
In conclusion, we have introduced in-sensor neuronal computing as an alternative to in-
sensor synaptic computing. We demonstrated that coupled ORNs enable highly parallel, frequency
multiplexed computation on input images without data conversion, storage, or transmission
penalties. Experimental implementations using 3×3 arrays of coupled ORNs show parallel image
processing on projected images. These include edge detection, intensity filtering, and object
segmentation as examples of image processing tasks carried out at the detector array. We have also
demonstrated that inference with these devices performs handwritten digit classification from the
MNIST database with higher accuracy than traditional photodetectors. While we have focused on
image classification and image processing applications, we expect this computational approach to
be general. Most importantly, ORN-based computation is extremely energy efficient with an
estimated performance of ~42211 TOPS/W considering the energy cost of the peripheral circuits,
laying the framework for a general, ultralow power, variation tolerant approach to oscillator-
computing.
172
6.8 Methods: Fabrication and experiments
6.8.1 Fabrication methods
Moderately boron doped (Na = 5×10
15
cm
-3
) silicon (100) wafer was used as the semiconductor
substrate. A 5 nm Ti/60 nm Au mesh is photolithographically defined and deposited by electron
beam evaporation. A monolayer of CVD grown graphene is transferred on top of the metal mesh
via wet transfer method
58
. A 100 nm aluminum film sputtered at the back side of the substrate acts
as the contact to silicon.
CVD graphene was grown on a Cu foil by using low pressure CVD. Cu foil was etched inside
FeCl3 copper etchant for 30 seconds before the graphene growth. Cu foil was annealed in a quartz
tube furnace at 1000°C for 30 min with 50 standard cubic centimeters per minute (sccm) hydrogen
(H2) flow rate. Graphene was synthesized under 7 sccm of methane (CH4) and 50 sccm of
hydrogen (H2) for 40 min. For transfer, Poly(methyl methacrylate) (PMMA A6495) was spin-
coated on top of Cu foil at 2000 rpm for 60 sec and baked for 5 min under 170 °C. PMMA spin-
coated Cu foil was etched using FeCl3 copper etchant graphene to remove the Cu while the
remaining PMMA/Graphene floats to the top. The stacked layer was cleaned with D.I water and
transferred to 10% hydrochloric acid solution to remove the remaining Cu etchants. After cleaning
with D.I water once more, PMMA/Graphene was transferred on top of the oxide/semiconductor
substrate. The substrate was dried in the air overnight followed by 90°C for 15min, 150°C for
30min, and 90°C for 15min to ensure the adhesion between the graphene and the substrate. Finally,
the substrate was immersed in acetone for 12 hours to remove the PMMA. CVD grown monolayer
graphene transferred on the substrate was analyzed by Raman spectroscopy. Raman spectra were
collected with Renishaw spectrometer with a 532-nm laser focused in a 0.5-μm spot through a
Leica microscope with a 100x objective lens.
173
6.8.2 Wavelength dependent measurements
A supercontinuum laser with grating monochromator was used to illuminate the SGM
photodetector with lights of different wavelengths between 400 and 1100 nm. Applied voltage was
stepped while light and dark current measurements were performed. The difference between these
two current measurements, i.e., the photocurrent was then used to measure the responsivity of the
device.
6.8.3 ORN measurements
A 5×5 array of SGM photodetectors was fabricated and individual devices were wirebonded to a
PCB. The devices were electrically connected to the inductors (all 10 mH) on a breadboard to form
the ORN kernel. A digital projector was used to project the patterns on the device array (a 3×3
array from the 5×5 array) and an oscilloscope was used to record the oscillation waveforms. The
whole process was automated using MATLAB environment.
174
6.9 NDR mechanism
6.9.1 Control devices
To elucidate the mechanism of NDR, we have performed I-V measurements on three different
control devices: (1) a silicon-Ti/Au grid device without graphene, (2) a silicon-Au grid-graphene
device, and (3) a silicon-Ti/Au grid-graphene device with 200 nm thick PECVD SiO2 under the
Ti/Au mesh only. Figure 6.5 shows the I-V curves of these three devices, where we observe that
the NDR behavior is absent for all three. The device without graphene operates only in the
photovoltaic regime, while the device without Ti and the device with thick oxide under metal do
not operate in the photovoltaic regime. These behaviors indicate that photovoltaic regime of
operation is directly coming from the collection of charge carriers by the metal mesh itself and the
Ti/Si Schottky barrier is crucial to the device operation. The graphene generates the NDR, which
is responsible for the decrease in the collected photocurrent as a function of applied bias.
Figure 6.5: I-V characteristics of control devices. (a) I-V curves in dark and light conditions for a device
without graphene, (b) a device with graphene but without Ti in the metal, and (c) a device with graphene
and Ti/Au metal mesh but thick oxide underneath the metal mesh.
175
6.9.2 NDR Model
Figure 6.6 shows the schematic for our proposed model for the observed NDR behavior in this
device. Two possible channels can collect the photogenerated electrons: (1) lateral diffusion in the
plane of the silicon surface to reach the Ti/Au contact or (2) collection into graphene through the
thin native oxide barrier. These two collection channels compete with recombination processes at
the Si/graphene interface and bulk. The Ti/Au contact region collects the majority of electrons at
lower voltages when the native oxide barrier is opaque. When the voltage is increased, the barrier
between the graphene and native oxide barrier becomes less opaque, collecting more
photogenerated electrons in the graphene. However, the surface Fermi level will also move,
modifying the density of unoccupied interface defect states, which modifies the interfacial
recombination rates. Further increasing the voltage causes the native oxide barrier to become
transparent and the defect states to fill. The electrons tunnel into graphene and overall
recombination reduces(photoconductive regime).
Figure 6.6: Schematic of the NDR mechanism showing the competing transport channels for
the photogenerated carriers.
176
6.9.3. Position and temperature dependent measurements
To verify the proposed mechanism, we have performed a position dependent I-V measurement on
the device using a focused laser beam of 532 nm wavelength with a spot size of ~100 µm
2
and
power of 12.6 mW. We have scanned the beam through the diagonal of a single mesh square, as
shown in Figure 6.7a. The device has a square mesh with 20 um width and 1 mm pitch. The beam
was first positioned at one of the intersections of the mesh and then moved through the diagonal.
Since each square has 1 mm sides, the diagonal length is 1.414 mm. As the beam moves through
Figure 6.7: (a) Optical micrograph of the grid in the device showing direction of position
dependent measurement. (b) Spatial dependence of current for focused beam measurements at
532 nm wavelength at a power of 12.6 mW. (c) I-V curves corresponding to the colormap
produced in (b). (d) I-V curves measured at different optical powers for beam position at the
midpoint of the diagonal. (e) Spatial dependence of peak and valley current and PVCR.
177
the diagonal, it reaches the maximum distance from the metal mesh when it reaches the midpoint
of the square diagonal, i.e., 0.707 mm from the intersection. We observe a change in I-V
characteristics as a function of the distance between the beam and the metal grid. Due to the square
geometry of the mesh, the distance from the contacts is maximum when the beam is at the midpoint
of the diagonal. Figure 6.7b shows a colormap of the current magnitude in as we sweep the voltage
and the distance along the mesh diagonal. For VGr-Si < 1 V , the current varies with distance along
the diagonal. The I-V curves used to produce this colormap is shown in Figure 6.7c. Figure 6.7d
shows the I-V curves measured at the midpoint of the mesh diagonal for different optical power
densities where we can observe a threshold optical power required to obtain the NDR behavior.
Figure 6.7e shows a line plot of the peak, valley, and peak-to-valley current ratio (PVCR) as a
function of the distance along the mesh diagonal. The peak PVCR occurs when light is incident in
the middle of the diagonal because of the large relative change in valley current.
Figure 6.8: Temperature dependent I-V curves in (a) log and (b) linear scale.
(a)
(b)
178
Temperature dependent measurements were performed on the device with a diffused laser beam
of 635 nm wavelength at 40 mW optical power. Temperature of the device was varied from 80K
to 300K. The temperature dependent I-V curves (Figure 6.8) show that the NDR behavior does not
have a significant dependence on temperature, consistent with the proposed model.
6.9.4. Capacitance measurements
Capacitance of the device has been measured under both dark and illumination conditions using a
capacitance measurement unit of Keysight B1500a semiconductor parameter analyzer. The
measurements were performed under different optical power densities at 445 nm wavelength and
for different measurement frequencies (1 KHz, 10 KHz, 100 KHz and 1 MHz). Figure 6.9a shows
the C-V curves for the device measured at a small signal frequency of 1 kHz under uniform optical
illumination with varied power densities at 445 nm wavelength. The dark C-V curve shows an
Figure 6.9: Capacitance measurements of NDR device. Small signal capacitance-voltage characteristics
of NDR device at different power densities for (a) 1 KHz, (b) 10 KHz, (c) 100 KHz, and (d) 1 MHz. (e)
Small signal capacitance measured at a power density of 57 mW/cm
2
and (f) dark conditions for different
frequencies
179
initial increase in capacitance due to formation of a depletion region and then a decrease in the
capacitance as the width of depletion region increases with increasing reverse bias voltage. The C-
V behavior under illumination shows a larger initial capacitance followed by a sharper decrease in
capacitance for lower voltages. The larger capacitance under illumination can be attributed to the
increase in charge in the depletion region due to photogenerated carriers while the sharp decrease
can be attributed to the presence of a recombination process that annihilates these photogenerated
carriers. When the voltage is increased further, we see another slow increase followed by a slow
decrease in capacitance unlike the dark measurements. When we compare these C-V
measurements with the higher frequency C-V measurements (Figure 6.9b-f), we observe that the
second increase in the capacitance disappears at the higher frequencies. This frequency dependent
behavior supports the hypothesis that charges responsible for the second increase in capacitance
are due to slow charge trapping centers in the device. These experimental results agree with the
mechanism proposed in Figure 6.6.
6.9.5 Sentaurus simulations
To further validate the proposed mechanism, we have performed TCAD Sentaurus simulations of
the device. We have simulated the carrier transport characteristics of the device using a drift-
diffusion model in Sentaurus TCAD. For the simulations, we have considered a 2D device with
100 um width instead of the 1 mm width of the real device to save simulation resources. Figure
6.10a shows a schematic of the simulated device. The device has 100 um thick 5e15 cm
-3
boron
doped p-Si as substrate and a 3 nm thick layer of SiO2 on top of silicon. We have used a 1e17 cm
-
3
phosphorous doped n-Si as proxy to the TiOx layer underneath the metal mesh. Then we have
used a 1 nm thick semiconductor with 0.01 eV bandgap and an electron affinity of 4.5 eV as a
180
proxy to graphene layer. We have considered a direct tunneling mechanism between silicon and
graphene with adjustable tunnel barrier height. Figure 6.10b shows the J-V curves calculated for
different electron trap densities under illumination of a power density of 65 mW/cm
2
at 445 nm
wavelength. Tunnel barrier was fixed at 50 meV for these calculations. As the trap density is
increased, we can see the emergence of NDR behavior which again vanishes when the trap density
becomes too large. Figure 6.10c shows the effect of bulk electron lifetime in silicon on the NDR
behavior for a trap density of 10
12
cm
-2
. When the lifetime is short (10 ns), the bulk recombination
Figure 6.10: Sentaurus simulations of the NDR device. (a) Schematic of the simulated device (b)
Simulations showing the effect of charge traps and (c) carrier lifetime in determining NDR behavior for
a trap density of 10
12
cm
-2
. (d) Sentaurus simulation showing the increased recombination at the trap
states in the NDR regime for trap density of 10
12
cm
-2
. (e) Modification of the valley current with barrier
height (f) Position dependent illumination and corresponding I-V sweeps (g) Change in V OC with n-Si
doping (h) Modification of NDR behavior as electron affinity of the graphene layer was changed, (i)
Scalability of the NDR device: I-V curve of a 1 µm device showing NDR behavior.
181
dominates over the interfacial recombination, and therefore no NDR is observed. However, NDR
is observed when carriers have a long lifetime (>100 ms) in the bulk and interfacial recombination
becomes more prominent. Figure 6.10d shows the recombination rate at the electron trap states for
a trap density of 10
12
cm
-2
as well as the J-V curve. We can clearly see increase in recombination
rate at the trap states when the NDR regime starts and then we see a subsequent decrease in
recombination rate as NDR regime ends and current starts to increase.
Then we have fixed the electron trap density at 10
12
cm
-2
and varied the tunnel barrier height as
shown in Figure 6.10e. We can clearly observe the increasing sharpness of the I-V curves as the
tunnel barrier is increased. Then we have simulated for position dependent illumination with 10
um spot width (Figure 6.10f). When the light is shined on the n-Si region (0-10 um), we cannot
observe any NDR behavior. This is consistent with what we observe experimentally where we also
do not observe NDR when light is shined very close to the metal mesh. As we move further from
the n-Si region, we see a decrease in the current which is also consistent with experimental
observations. Since n-Si is used as a proxy to the TiOx layer, we have varied the doping in n-Si to
investigate how that affects the behavior of the device as shown in Figure 6.10g. When the doping
is increased, there is an increased electric field at the junction which causes more electrons to be
collected and increases the open circuit voltage of the device. We have also varied the electron
affinity of the graphene layer to see how it affects the NDR behavior as shown in Figure 6.10h. An
increasing electron affinity causes an increased electric field at the depletion region at the
silicon/native oxide/graphene interface due to larger difference in electron affinity of silicon and
graphene. As a result, the collection of electrons at the depletion region improves and current
increases in photovoltaic regime. However, when the depletion region has a strong electric field,
there is a strong pull on the electrons toward the n-Si region which causes the NDR regime to
182
occur at even higher voltages. In order to investigate the scalability of the device, we have
performed simulation on a device with 1 um width as well. As shown in Figure 6.10i, the 1 um
device also shows NDR behavior when illuminated with 65 mW/cm
2
optical power density at 445
nm wavelength. However, it will be impractical to scale the devices below 1 um because of
diffraction. While our experimental results show that the charge trapping states at the silicon/oxide
interface are responsible for the NDR behavior, the TCAD simulations help us quantitatively verify
the validity of the proposed mechanism.
6.9.6. Responsivity measurements
Figure 6.11: Wavelength dependent responsivity measurements
183
6.10 Functions implemented by a single ORN
Figure 6.12a shows the schematic of an ORN circuit. The inductor and the intrinsic capacitance of
the photodetector creates an LC tank circuit that can be forced into relaxation oscillation by the
Figure 6.12: (a) Schematic of a single ORN (b) Power generated by ORN (c) Normalized fundamental
frequency of oscillation as a function of normalized optical power and applied voltage (d) Normalized
fundamental frequency and amplitude at V applied = 0V (e) Oscillation V-t and (f) FFT curves for different
values of normalized optical power. (g) ORN voltage filtered at 28 KHz with different bandwidth and
(h) filtered at different center frequencies with a bandwidth of 200 Hz as a function of incident optical
power. (i) Analytical approximation of simulated behavior.
184
NDR characteristic of the photodetector. The following differential equation governs the
oscillation behavior of the circuit.
+ (
, )
+
=
√
+
(
,
)
+
√
=
√
Here, (
, ) is the negative differential conductance (NDC) of the photodetector which is
nonlinear to Vosc and can be approximated linear to via this relation, (
, ) =
(
,
). This linear dependence on P holds as long as P ≥ PNDR, min where PNDR, min is the
smallest optical power that allows the device to exhibit NDR behavior. It is noteworthy that choice
of P0 is arbitrary since it does not affect the absolute value of (
, ). The equation resembles
that of a generalized Van der Pol relaxation oscillator. Such a nonlinear differential equation does
not have any analytical solution. For an SGM photodetector, (
,
) and C are both known
quantities as obtained from experimental measurements. An external inductor (L), the incident
optical power (P), and the applied voltage (Vapplied) then determine the oscillation behavior. Figure
6.12b shows the colormap of power generated (
=
∫
) at the voltage source,
Vapplied, due to the photovoltaic regime of operation as a function of Vapplied and P (assuming C = 1
nF and L = 100 mH). Since the photodetector shows NDR behavior only within -100 mV and 80
mV , the circuit does not show any oscillation at Vapplied < -100 mV and Vapplied > 80 mV . There is a
net generation of electrical power (Pgen > 0) at -100 mV < Vapplied < 0 mV and a net consumption
(Pgen < 0) at 0 mV < Vapplied < 80 mV . This is a unique characteristic of SGM photodetector which
185
separates it from other photoactivated NDR devices where absence of the open circuit voltage
prevents any electrical power generation from optical power.
While the equation can be solved for individual values of P, L, and C, it is of great benefit to find
a normalized solution to the equation in order to better understand the oscillation behavior of the
ORN circuit. A normalized quantity
absorbs the change in P, L, C and therefore leads to a
normalized solution. Figure 6.12c shows the colormap of fundamental oscillation frequency
(fpeak,1) as a function of Vapplied and
where we have considered P0 = 1 mW. For Vapplied = 0V ,
Figure 6.12d shows the change in fpeak,1 and oscillation amplitude as a function of
. With
increasing
, we observe a decrease in fpeak,1 from its pristine harmonic oscillation frequency
of
=
√
. This decrease can approximately be modeled as
,
=
1 −
=
(1 − ). For
≈ 400 , there is a drastic increase in oscillation amplitude marking the
onset of the relaxation oscillation. This normalized threshold for oscillation helps us predict the
oscillation behavior for extreme scaling of device area or optical power. When the device is scaled
down to a smaller area, there is a decrease in both P and C for the same optical intensity. Such a
change can be compensated directly by increasing L if P ≥ PNDR, min. Similarly, when a device
operates at a smaller optical intensity and hence a smaller P (≥ PNDR, min) for the same device area,
L can be increased accordingly to ascertain oscillation from the circuit. It is also important to note
that these equations do not consider the effect of parasitic series resistance in the circuit. When P
increases significantly so that the series resistance is smaller compared to the resistance of the
photodetector, the resistive losses in the circuit may prevent the oscillation from starting.
186
Therefore, the dynamic range for an ORN is determined by the lowest power at which we observe
NDR (PNDR, min) and the highest power at which the losses from the series resistance become too
large.
The origin of these results can be understood through analytical modeling of the oscillation
frequency spectra of an ORN. As observed from Figure 6.12f, frequency spectrum of a single ORN
can be expressed as a sum of all the frequency peaks, including the fundamental and the harmonics.
We can model these peaks as Lorentzian peaks centered at
,
and of width ∆
.
(, ) =
( −
,
)
+ (∆
)
A bandpass filtering operation at center frequency f with bandwidth BW gives us the integrated
amplitude contribution.
(, , ) =
( −
,
)
+ (∆
)
/
/
(, , ) =
( −
,
)
+ (∆
)
/
/
(, , ) =
∆
+ /2 −
,
∆
−
− /2 −
,
∆
(, , ) =
∆
. ∆
(∆
)
+ ( −
,
)
+ ( )
/4
For small arguments of arctan function,
(, , ) ≈
.
(∆
)
+ ( −
,
)
+ ( )
/4
187
(, , ) =
.
(∆
)
+ ( − .
(1 − ))
+ ( )
/4
(, , ) =
.
(∆
)
+ ( . .
)
−
−
. .
+ ( )
/4
(, , ) =
(∆
)
+ ( −
)
Here,
=
.
( ..
)
, ∆
=
(∆
)
( )
( ..
)
, and
=
..
. The final equation shows that the
amplitude contribution at each center frequency is also a sum of Lorentzian peaks. In addition,
increasing filter bandwidth causes an increase in the peak width (∆
) and increasing the center
frequency causes a shift in these peaks (
) towards smaller optical powers.
6.11 Comparison between different optical intensity ranges
Figure 6.13: Experimental results for images processed at different frequencies by the cascaded circuit
when pixel value = 1 corresponds to an optical power of (a-d) 2.75 mW and (e-h) 5.5 mW.
188
6.12 Processed images for a 10x10 kernel
6.13 Readout layer:
A three-layer simple neural network is constructed for the training and testing. The input layer
contains 49×k neurons where k is the number of frequency samples considered. The hidden layer
consists of 100 neurons with ReLU activation function and output layer consists of 10 neurons,
each of which indicates the possibility of corresponding classes. The three layers here are fully
connected, suggesting 49000×k synapses or weight values need to be trained for good
classification. In each training epoch, 8571 input images are used as training images, the other
1429 are used as test images. In the supervised training process, one-hot encoding and the softmax
activation function :
( ) =
∑
are used, here is a scaling factor. And the loss
(or cost) that need to be minimized is calculated by the cross-entropy function: =
−
∑
log [
( )]
, where
is the label of the input image, = 10 is the number of
Figure 6.14: Simulation results for a 10x10 kernel where only nearest neighbor oscillators are coupled
by an inductance of 5H
189
classes. The values of the weight are initially randomly generated from a Gaussian distribution,
then updated by gradient descent and backpropagation: = −
, here the learning rate
= 0.2. In images testing, the most activated neuron (with the highest output value) is compared
with the label, and the accuracy is calculated by dividing the matched images number with the
testing image number.
6.14 LSM details
6.14.1 LSM experiments and data handling:
These experiments use an inductively cascaded array of 9 ORNs as the liquid layer. An MNIST
image is typically 28×28 pixels. We truncate the image to 21×21 pixels and then divide it into a
7×7 cell matrix of 3×3 pixels. This is similar to sweeping the image with a 3×3 convolutional
kernel with a stride of 3. Then each of these 3×3 pixels cell is physically projected onto the liquid
layer. Oscillation V-t time series is then collected from one of the pixels (7th oscillator of the array
in these experiments) using an oscilloscope. The acquired time series is then transformed to a
frequency spectrum via FFT. The FFT operation is equivalent to performing a bandpass filtering
operation at different frequencies. For these measurements, we chose 1 KHz bandwidth for the
bandpass filter and performed this operation for 100 different frequency bands up to 100 KHz.
Therefore, we get a 7×7 data for every frequency sample, a 7×7×100 data per image, and a total
dataset of size 7×7×100×10000. Then 6/7 part (~86%) of the data was separated as the training
dataset (7×7×100×8571) and the rest 1/7 part (~14%) was separated as the testing dataset
(7×7×100×1429). We have then trained the readout network using 100 different 7×7×8571 datasets
and tested them with the corresponding testing datasets.
190
6.14.2 Simulation of the LSM:
Simulation of the LSM requires us to solve the equations governing the dynamics of all oscillators
in the ORN kernel simultaneously. Let
be the instantaneous voltage across the k
th
SGM
photodetector device. Then
is updated at each time step using the following equations:
(+ ∆ ) =
( ) +
( ) × ∆
,
(+ ∆ ) =
,
( ) +
,
( ) × ∆
( ) =
,
( )
,
( ) =
( ) −
( )
,
( ) +
,
( ) +
,
( ) =
,
( )
,
( ) = (
( ))
Here,
,
,
,
,
,
are the currents through the k
th
inductor, capacitor, and photodetector.
,
is
obtained from a lookup table containing the experimental I-V data for our devices. In addition,
(0) = 0 and
(0) = 0 for all k, and
( ) = 0 and
,
( ) = 0 for all t. In order to make
sure that the solution is not diverging, we need to consider small enough ∆ appropriate for the
problem at hand. Figure 6.15 shows the circuit schematic for this kernel. Every time a new 3 × 3
pattern is introduced to the kernel, this system of equations is solved simultaneously, and the
corresponding time series and frequency spectrum is stored.
191
6.15 Energy calculation for peripheral circuit
An ORN array requires peripheral circuitry to read the oscillating voltage signals and filter
them into different frequency bands. Power (voltage) in each frequency band mapped across the
ORN array then represents a single feature of the image. There are 3 key components to the
peripheral circuit: (1) amplifiers to isolate the oscillators from the readout circuit and provide
necessary electrical energy to sampler (2) sample and hold circuit consisting of sampling switches
and capacitors and (3) an DFT (discrete Fourier transform) processor that filters the input signal
into frequency bands. An on-chip analog DFT processor can be designed using the radix-2
decimation in time (DIT) FFT algorithm. The radix-2 algorithm can be implemented in voltage,
current or charge domain. However, the charge domain approach has been the most promising one
in terms of energy efficiency of FFT operation. There has been a demonstration of an analog FFT
processor fabricated with CMOS 65 nm technology using charge domain approach that can
perform a 16 point FFT with an energy cost of 12.2 pJ at a sampling speed of 5 GHz
1
. We can scale
Figure 6.15: (a)Circuit schematic of ORN kernel and (b) current and voltage components
192
this approach for 128-point FFT so that the ORN array oscillating signals can be filtered into 64
unique frequency bands and therefore generates 64 different features per oscillator.
A k-point implementation of radix-2 algorithm has
butterfly operations and each butterfly
operation requires 10 scalar operations. Therefore, the total number of operations in a k-point FFT
is 5
. Scaling a 16-point FFT architecture to a 128-point architecture therefore increases the
scalar operations by 14x. If we use the same design architecture as Ref X, the number of transistor
switches and total switching energy consumption in the processor would then increase by 14x. On
the other hand, the total number of sampling capacitors increases linearly from 256 to 2048. It is
noteworthy that the destructive nature of passive computing requires multiple copies of the same
sample. This implementation requires 2 copies per butterfly, 2 copies for complex math, 2 copies
for differential input, and 2 copies for quadrature (I/Q) input which makes the total number of
capacitors 2×2×2×2=16 times larger than the FFT points. However, since our signals are real
valued, we can multiplex signals from two oscillators into the same FFT architecture which
effectively reduces the number of sampling capacitors and switches by 2x per oscillator. In
addition, since the quadrature inputs are not available for our signals, we can reduce the number
of sampling capacitors and switches by another 2x per oscillator. However, this also reduces the
number of useful frequency bins by 2x. Therefore, the 128-point FFT would have 512 sampling
capacitors and have a 3.5x larger energy consumption compared to 16 point FFT and bin the signal
to 64 frequency bands.
The choice of sampling capacitor directly depends on the maximum SNR we expect at full scale
(VFS). Our ORN arrays typically have a maximum rms voltage of 0.3V (= VFS) and the output
reflected noise power contribution for this FFT architecture is ~0.26
where C is the value of the
193
sampling capacitance. In order to compare our results to that of a digital processor, we choose an
SNR of 49.92 dB which is equivalent to the SNR of an 8 bit ADC ( =
.
.
). Then the
sampling capacitance C is given by
= 10
×
0.26
= 0.3976 × 4
×
= 1.2
Since the energy consumption of 16 point FFT processor is 12.2 pJ/FFT, the total capacitance of
the switching transistors is
×.×
.
= 17 where VDD = 1.2V is the supply voltage for the
transistors. The number of transistors for 16 point FFT is ~5120 and therefore the gate capacitance
of each transistor is 3.31 fF. However, the on resistance of the transistors is given by
~
(
)
and therefore the maximum switching frequency is ~
(
)
.
.
Numerical calculations (Figure 6.16) show that the capacitor voltage can settle to 2% of the final
voltage within the half cycle of 1 GHz clock for a
−
= 0.16 even for the worst case
scenario where the voltage rises from 0V to VFS = 0.3V . Since Vth ≈ 0.3V for NMOS switches, we
can choose a reduced VDD = 0.46V with a switching transistor gate capacitance of CSW =
CoxA=0.05 fF for W = L = 65 nm. For 128-point FFT, the number of transistors would be 3.5×5120
= 17920 and the total switching energy consumption will be 17920 ×
× 5 × 10
× 0.46
J =
47.17 fJ.
On the other hand, each signal needs to be sampled 128 times using a pseudo-differential sampler
that has 4 transistors. For the same CSW, the switching energy for the sampler is
4 × 128 ×
× 5 × 10
× 0.46
J = 2.7 fJ.
194
The sampling capacitors in the FFT processor have to be charged by the oscillator output and this
charging costs an energy of 4 × 128 ×
× 1.2 × 10
× 0.15
J = 6.9 fJ. Since the oscillators
can have any instantaneous voltage between 0 and 0.3V , an averaged 0.15V was considered for
this calculation.
This brings the total energy consumption of the peripheral circuit to 56.8 fJ. Since the FFT
processor generates 64 outputs and each convolution operation for a 3x3 kernel is equivalent to 17
operations, the energy cost becomes 56.8/(64x17) fJ/OP= 0.0522 fJ/OP and the processor
performance is 1/0.0522 Ops/J = 19159 TOPS/W. Figure 6.16 shows the processor performance
and switching speed as a function of VDD in the switching MOSFETs. At a reduced operation
frequency of 1 MHz, the projected performance increases to 42211 TOPS/W.
195
Table 6.2 shows the performance comparison between different NPUs and general purpose neural
engines.
NPU
application
Type Comment bits
Reported
TOPS/W
Normalized
TOPS/W (8
bits)
VMM
2
Digital NN accelerator 8 1.7 1.7
MAC macro
3
Digital Mobile SoC 8 11.5 11.5
VMM
4
Analog RRAM 6 9 5.06
VMM
5
Digital 3D-RRAM 8 8.32 8.32
Figure 6.16: Performance and maximum switching speed as a function of MOSFET V DD.
196
VMM
6
Digital RRAM 4 36.61 9.15
VMM
7
Analog
Magnetic
RRAM
1 405 6.33
Logic gate
8
Digital 2D neuristor 1 622.35 9.72
Analog to
information
conversion
9
Analog In-sensor NN 8 43.5 43.5
VMM
10
Digital SRAM 4 351 87.75
VMM
11
Analog RRAM 1 78.4 1.23
MAC macro
12
Analog DRAM 4 217 54.25
VMM
13
Digital SRAM 1 885.86 13.84
VMM
14
Digital BNN accelerator 1 223 3.48
ReRAM
write
15
Analog RRAM 4 66.5 16.63
VMM
16
Digital
DNN learning
processor
8 146.52 146.52
Arithmetic
logic
17
Digital
Superconducting
logic devices
8 120 120
VMM
18
Mixed NN accelerator 4 161.6 40.4
VMM
19
Analog
Si-
CMOS/CAAC-
IGZO based
memory
6 210 118.13
197
VMM
20
Digital
Stochastic NN
accelerator
8 75 75
VMM
21
Digital BNN accelerator 1 617 9.64
VMM
22
Digital BNN accelerator 2 198.9 12.43
SNN
23
Mixed
Mixed mode
spiking neuron
4 124.2 31.05
Combinatorial
problem
solving
24
Analog Binary RRAM 1 2000 31.25
MAC macro
25
Digital SRAM 8 63 63
MAC macro
26
Analog
SONOS
memory
8 100 100
MAC macro
27
Analog SRAM 4 177 44.25
MAC macro
28
Digital SRAM+DRAM 1 1220 19.06
Image
denoising
29
Digital SRAM 1 51.3 0.8
Image
filtering
30
Digital SRAM 1 389 6.08
MAC macro
31
Digital SRAM 8 30.3 30.3
Data
buffering
macro
32
Digital SRAM 4 43 10.75
MAC macro
33
Digital SRAM 1 20943 327.23
198
VMM
34
Analog
Ferroelectric
tunnel junction
memristors
4 100 25
General
purpose
Digital NVIDIA A100 8 4.992 4.992
General
purpose
Digital Google TPUv4 8 1.432 1.432
General
purpose
Digital
Apple a16
Bionic
8 2.67 2.67
General
purpose
Digital
Huawei Da
Vinci Ascend
310
8 2 2
General
purpose
Digital
Qualcomm
Snapdragon 865
8 4.5 4.5
Nonlinear
convolution
(3x3 kernel)
(This work)
Analog ORN 8 42211 42211
Table 6.2: Extended table for comparison between different NPUs in literature
199
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Abstract (if available)
Abstract
From high power microwave amplifiers to low power computing systems, semiconductors have propelled the advancement of science and technology as we see them in the modern world. In this thesis, we demonstrate high efficiency realizations of silicon based electronic devices for three different broad applications: (a) electron cathodes for vacuum electronics, (b) electron cathodes for electrochemical reaction systems, and (c) in-sensor oscillator based computing system for ultra-low power computing.
First, we have integrated graphene to a photonic waveguide where it is forced to absorb photons efficiently via evanescent coupling with electromagnetic fields. Improving the optical absorption of graphene then allowed us to utilize it as an ultrathin hot electron emission cathode.
Second, we have taken advantage of a silicon/oxide/metal device structure that can catalyze electrochemical reactions such as hydrogen evolution reaction by generating hot electrons that can overcome the activation energy associated with the reaction. Such devices have been realized on both graphene and gold based cathodes where they have demonstrated extraordinary quantum efficiency and tunable reaction onset.
Third, we have engineered a novel silicon/graphene photodetector that shows negative differential resistance under optical illumination and generates electrical voltage oscillations without external electrical power. We have shown that such a network of oscillators encodes different information about input signals in their oscillation frequency bands and therefore enable frequency multiplexed, parallel computing. Through theoretical projections, we show that such a computing architecture is capable of performing computer vision tasks with an extraordinarily small energy cost of ~24 aJ/OP.
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University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Ahsan, Ragib
(author)
Core Title
Semiconductor devices for vacuum electronics, electrochemical reactions, and ultra-low power in-sensor computing
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Electrical Engineering
Degree Conferral Date
2023-08
Publication Date
07/11/2023
Defense Date
06/12/2023
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
cathode,electrochemistry,electron emission,hydrogen evolution,neuromorphic computing,OAI-PMH Harvest,oscillator based computing,semiconductor
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theses
(aat)
Language
English
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Electronically uploaded by the author
(provenance)
Advisor
Kapadia, Rehan (
committee chair
), Ravichandran, Jayakanth (
committee member
), Wu, Wei (
committee member
), Yang, Joshua (
committee member
)
Creator Email
ragib.ahsan014@gmail.com,ragibahs@usc.edu
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theses (aat)
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Ahsan, Ragib
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Tags
cathode
electrochemistry
electron emission
hydrogen evolution
neuromorphic computing
oscillator based computing
semiconductor