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Nanoscale Field Emission Devices for High-Temperature and High-Frequency Operation
Citation
De Rose, Lucía Belén
(2023)
Nanoscale Field Emission Devices for High-Temperature and High-Frequency Operation.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/8qa5-kn97.
Abstract
Field emission—the quantum-mechanical tunneling of electrons from the surface of a material into vacuum by means of a strong electric field—has been studied for over a century. However, the usage of devices based on this mechanism has been limited to a handful of niche applications such as high-power RF systems and field emission displays. The preference for solid-state devices relies on their low cost, long lifetimes, reduced power consumption, ease of integrability, and simple and scalable fabrication. Nonetheless, with the advent of modern fabrication techniques, it has been possible to build field emission devices with nanoscale dimensions that offer several advantages over traditional semiconductor devices. The use of vacuum allows ballistic transport with no lattice scattering. As device capacitance can be engineered by tuning the geometry, these devices are appealing for high-frequency operation. Vacuum is also inherently immune to harsh operating conditions such as high temperature and radiation, which is desirable for aerospace, nuclear, and military applications. In addition, even though field emission requires substantial electric fields, by exploiting the nanoscale gaps that can be easily fabricated with state-of-the-art lithographic capabilities, we can expect operating voltages comparable to CMOS. Thus, vacuum emission devices have the potential to greatly improve upon the limitations of current technologies.
In this work, we experimentally demonstrate various design paradigms to develop nanoscale field emission devices for high-temperature environments and high-frequency operation. First, we propose suspended lateral two- and four-terminal devices. By removing the underlying solid substrate, we aim to increase the resistance of the leakage current pathways that emerge at elevated temperatures. Tungsten is the chosen electrode material due to its low work function and ability to withstand high temperatures. Our next architecture consists of a multi-tip two-terminal array, which exclusively relies on the inherent fast response of field emission. Due to the strong non-linearity in the emission characteristic, frequency mixing is measured. Lastly, we combine field emission with plasmonics to conceive devices that can be modulated both electrically and optically at telecommunication wavelength. By taking advantage of the strong confinement and significant optical field enhancement of surface plasmon polaritons, we seek to minimize the applied voltages required for field emission as well as the necessary laser powers for photoemission towards the development of high-speed, low-power, nanoscale optoelectronic systems.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
Field electron emission, Fowler-Nordheim emission, Plasmonics
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Applied Physics
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Scherer, Axel
Thesis Committee:
Schwab, Keith C. (chair)
DeRose, Guy A.
Painter, Oskar J.
Scherer, Axel
Defense Date:
26 January 2023
Funders:
Funding Agency
Grant Number
NASA Goddard
80HQTR17C0011
Boeing Company
1516995
Record Number:
CaltechTHESIS:03312023-192646665
Persistent URL:
DOI:
10.7907/8qa5-kn97
Related URLs:
URL
URL Type
Description
DOI
Article adapted for Ch.3
ORCID:
Author
ORCID
De Rose, Lucía Belén
0000-0002-1432-8248
Default Usage Policy:
No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:
15126
Collection:
CaltechTHESIS
Deposited By:
Lucia De Rose
Deposited On:
14 Apr 2023 18:16
Last Modified:
21 Apr 2023 15:46
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Nanoscale Field Emission Devices for High-Temperature
and High-Frequency Operation

Thesis by

Lucía Belén De Rose

In Partial Fulfillment of the Requirements for the
Degree of
Doctor of Philosophy

CALIFORNIA INSTITUTE OF TECHNOLOGY
Pasadena, California

2023
Defended January 26th , 2023

Lucía Belén De Rose
ORCID: 0000-0002-1432-8248

iii

ACKNOWLEDGEMENTS
First and foremost, I would like to thank my advisor, Professor Axel Scherer, for
giving me the opportunity to join his research group without any prior experience
in nanofabrication. The freedom and trust he granted me from the start enabled me
to grow as an independent researcher.
Next, I would like to thank my thesis committee members: Professor Keith Schwab,
Professor Oskar Painter, and Dr. Guy DeRose. I would also like to extend special
thanks to Professor Stevan Nadj-Perge for serving on my candidacy committee.
I am deeply grateful to Dr. Max Jones (a.k.a. “Mini Boss” or “Mini Jefe”) for
his incredible mentorship. His patience, guidance, and encouragement have been
invaluable to me. It has been a privilege and honour to learn most of the fabrication
techniques used in this thesis from one of the best members of the KNI. I had a very
fun experience working with him and I could not have asked for a better mentor.
I would like to express my gratitude to my colleagues in the Scherer group for
the countless discussions, fruitful advice, and great help over the years: Christin
Ahlbrecht, Dr. Taeyoon Jeon, Amir Nateghi, Richard Smith, Dr. Dvin Adalian,
Changsoon Choi, Dominic Catanzaro, Musab Jilani, Xio Madero, Kaushal Shyamsundar, Samson Chen, Dr. William Fegadolli, and Tales de Barros Caldas. I would
also like to thank our admin, Kate Finigan, for taking care of all bookkeeping and
for her cheerful energy.
My work could not have been possible without all the wonderful staff at the KNI.
I would like to thank Dr. Guy DeRose for teaching me how to use the EBPGs
and providing support at critical moments even during weekends. Thanks to Alex
Wertheim for his patience in instructing me in all deposition equipment and for the
many relaxing conversations during process wait times. I would like to thank Dr.
Matt Hunt for training me in all microscopy tools, and Nathan Lee for always keeping
the etchers up and running. I would like to thank Bert Mendoza for providing very
useful suggestions and being willing to help with the wire bonder all the numerous
times it truly did not want to cooperate with me. I would also like to thank Dr. Lena
Wolff for teaching me so much about my favourite tool, the Orion. I would like to
express my gratitude to Barry Baker for his brief but memorable time with the KNI.
He always had a cheerful disposition that made my days better. And lastly, I would

iv
like to thank Tiffany Kimoto for always being very friendly and organizing great
KNI social hours.
I had an amazing time in California, and it would not have been possible without the
love and support of all the friends I made throughout graduate school. Thanks to
Stefan Lohaus for being an incredible best friend, housemate, and adventure buddy.
I would like to express my gratitude to my longest-standing friend here, Namita
Sarraf, for the meaningful conversations we have shared over these years and for
always being there during the ups and downs. I would like to thank Prachi Thureja for
being such a supportive friend and for the numerous entertaining outings. Thanks to
Michael Marshall for the countless amusing conversations during our Monday pizza
nights. Thanks to Andreas Bengtsson for all the fun times together and for keeping
me sane during the months of thesis writing. Thanks to Juan Pablo Cardenas for the
many adventures over the years. I would also like to thank Danilo Kusanovic for
always being willing to share an afternoon mate (Argentinian tea) or Thursday beer
with me. I could not have asked for better friends.
I would also like to acknowledge my friends from Argentina whom I have known
since I was a child and who have always kept me grounded: Cin Cernecca, Santi
Montoya, Lili Quiqueran, and Ceci Quiqueran. I am deeply thankful for their
friendship, which has been a source of strength and encouragement from afar.
Lastly, I would like to express my utmost gratitude to my parents, Gisela Krautwurst
and Jorge De Rose, for their unconditional love and for always stressing the importance of academic education. I would also like to thank my brother, Lucas De Rose
(a.k.a. “Monster”), for his unwavering support and encouragement. This journey
would not have been possible without them. Los quiero mucho.

ABSTRACT
Field emission—the quantum-mechanical tunneling of electrons from the surface
of a material into vacuum by means of a strong electric field—has been studied for
over a century. However, the usage of devices based on this mechanism has been
limited to a handful of niche applications such as high-power RF systems and field
emission displays. The preference for solid-state devices relies on their low cost,
long lifetimes, reduced power consumption, ease of integrability, and simple and
scalable fabrication. Nonetheless, with the advent of modern fabrication techniques,
it has been possible to build field emission devices with nanoscale dimensions that
offer several advantages over traditional semiconductor devices. The use of vacuum
allows ballistic transport with no lattice scattering. As device capacitance can be
engineered by tuning the geometry, these devices are appealing for high-frequency
operation. Vacuum is also inherently immune to harsh operating conditions such
as high temperature and radiation, which is desirable for aerospace, nuclear, and
military applications. In addition, even though field emission requires substantial
electric fields, by exploiting the nanoscale gaps that can be easily fabricated with
state-of-the-art lithographic capabilities, we can expect operating voltages comparable to CMOS. Thus, vacuum emission devices have the potential to greatly improve
upon the limitations of current technologies.
In this work, we experimentally demonstrate various design paradigms to develop
nanoscale field emission devices for high-temperature environments and highfrequency operation. First, we propose suspended lateral two- and four-terminal
devices. By removing the underlying solid substrate, we aim to increase the resistance of the leakage current pathways that emerge at elevated temperatures. Tungsten
is the chosen electrode material due to its low work function and ability to withstand
high temperatures. Our next architecture consists of a multi-tip two-terminal array,
which exclusively relies on the inherent fast response of field emission. Due to the
strong non-linearity in the emission characteristic, frequency mixing is measured.
Lastly, we combine field emission with plasmonics to conceive devices that can be
modulated both electrically and optically at telecommunication wavelength. By taking advantage of the strong confinement and significant optical field enhancement
of surface plasmon polaritons, we seek to minimize the applied voltages required
for field emission as well as the necessary laser powers for photoemission towards
the development of high-speed, low-power, nanoscale optoelectronic systems.

PUBLISHED CONTENT AND CONTRIBUTIONS

[1] L. B. De Rose, W. M. Jones, and A. Scherer. “Lateral nanoscale field emission
comb for frequency mixing.” [Manuscript submitted] (2023).
L.D. participated in the conception of the experiments. L.D. led the sample
fabrication, measurements, and writing of the manuscript.
[2] L. B. De Rose et al. “Effect of praseodymium coating on electron emission
from a nanoscale gold field emitter array.” [Manuscript submitted] (2023).
L.D. led the sample fabrication and participated in the measurements. L.D.
wrote the manuscript.
[3] S. M. Lewis et al. “Tuning the performance of negative tone electron beam
resists for the next generation lithography.” Advanced Functional Materials
32.32 (2022), p. 2202710. doi: 10.1002/adfm.202202710.
L.D. performed the tungsten etch.
[4] W. M. Jones, L. De Rose, and A. Scherer. “Waveguide integrated plasmon
assisted field emission detector.” US 11,009,658 B2 (Pasadena, CA). 2021.
L.D. participated in the sample fabrication and measurements.
[5] L. B. De Rose, A. Scherer, and W. M. Jones. “Suspended nanoscale field emitter devices for high-temperature operation.” IEEE Transactions on Electron
Devices 67.11 (2020), pp. 5125–5131. doi: 10.1109/TED.2020.3019765.
L.D. participated in the conception of the experiments. L.D. performed the
simulations, led the sample fabrication, and wrote the manuscript.
[6] S. M. Lewis et al. “Plasma-etched pattern transfer of sub-10 nm structures
using a metal–organic resist and helium ion beam lithography.” Nano Letters
19.9 (2019), pp. 6043–6048. doi: 10.1021/acs.nanolett.9b01911.
L.D. performed the tungsten etch.

vii

CONTENTS

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Published Content and Contributions . . . . . . . . . . . . . . . . . . . . . . vi
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii
List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
Chapter I: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Over a Century of Vacuum Tubes . . . . . . . . . . . . . . . . . . . 2
1.2 Dennard Scaling and Moore’s Law and the Future of Electronics . . . 4
1.3 The Emergence of Vacuum Micro and Nanoelectronics . . . . . . . . 9
1.4 Could Nothing Be Better Than Something? . . . . . . . . . . . . . . 11
1.5 Objective of This Work . . . . . . . . . . . . . . . . . . . . . . . . 14
Chapter II: Theoretical Background of Electron Emission . . . . . . . . . . . 19
2.1 Field Electron Emission . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Thermionic Emission . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3 Photoemission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4 Bulk Conduction in Dielectrics . . . . . . . . . . . . . . . . . . . . 35
2.5 Space Charge Effects . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Chapter III: Field Emission Devices for High-Temperature Operation . . . . . 45
3.1 General Design Paradigm . . . . . . . . . . . . . . . . . . . . . . . 46
3.2 Early Work on PECVD SiNx Substrate . . . . . . . . . . . . . . . . 50
3.3 Suspended Devices: Design and Fabrication . . . . . . . . . . . . . 58
3.4 Suspended Devices: Results and Discussion . . . . . . . . . . . . . 63
3.5 Challenges and Suggestions for Improvement . . . . . . . . . . . . . 73
3.6 An Attractive Material: Diamond . . . . . . . . . . . . . . . . . . . 79
Chapter IV: Field Emission Devices for High-Frequency Operation . . . . . . 91
4.1 Fundamentals of Frequency Multipliers and Mixers . . . . . . . . . 92
4.2 General Design Paradigm . . . . . . . . . . . . . . . . . . . . . . . 96
4.3 Selection of Physical Design Parameters . . . . . . . . . . . . . . . 97
4.4 Device Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.5 PCB Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.6 DC and AC Measurements . . . . . . . . . . . . . . . . . . . . . . . 110
4.7 Work Function Reduction . . . . . . . . . . . . . . . . . . . . . . . 122
4.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Chapter V: Plasmonically-Enhanced Field Emission . . . . . . . . . . . . . . 133
5.1 Plasmonics Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.2 The Hybrid Plasmonic Waveguide . . . . . . . . . . . . . . . . . . . 143
5.3 Field Emission Simulations . . . . . . . . . . . . . . . . . . . . . . 153

viii
5.4 Device Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
5.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
5.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Chapter VI: Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . 178

LIST OF FIGURES

Number
Page
1.1 Effect of reduced gate length and operating voltages: (a) relationship
between threshold voltage (𝑉𝑡ℎ ) and subthreshold leakage current
(𝐼𝑂𝐹𝐹 ) [14], (b) power density versus gate length [15], and (c) power
and delay as a function of threshold voltage (𝑉𝑡ℎ ) with 𝑉𝐷𝐷 = 0.5V
for 0.35 𝜇m process [16]. . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 42 years of microprocessor trend data [18]. . . . . . . . . . . . . . . 7
1.3 Metal and gate half pitch predictions (adapted from [22]). . . . . . . 9
1.4 Intrinsic carrier concentration as a function of temperature for various
semiconductors [34]. The shaded grey area corresponds to typical
doping range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1 The three main electron emission mechanisms from metal to vacuum:
(a) thermionic emission, (b) field emission, and (c) photoemission.
𝐸 𝐹 is the Fermi level, 𝜙 is the metal work function, 𝑈 is the vacuum
potential level, 𝐹 is an externally applied electric field, and 𝑓 (𝐸) is
the Fermi-Dirac distribution function. . . . . . . . . . . . . . . . . 20
2.2 Field emission model: FN (solid) and SN (dashed) barriers. . . . . . 22
2.3 Emission current density as (a) a function of electric field for various
work function values and (b) as a function of work function for various
electric field values. . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4 Emission current density as a function of temperature for various
field values and a representative work function of 4.5 eV. . . . . . . . 31
2.5 Electron emission processes from metal to vacuum under optical
illumination: (a) single photon photoemission (photoelectric effect),
(b) multi-photon emission and above-threshold photoemission, (c)
photo-assisted field emission, and (d) optical field emission. . . . . . 34
2.6 Schematic of FP emission: Coulombic trap potential at equilibrium
(grey) and under an external field (green). . . . . . . . . . . . . . . 36
3.1 Top-view of schematic for two types of proposed devices: (a) twoterminal diode-like device and (b) four-terminal triode-like device.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.2

3.3

3.4
3.5

3.6
3.7

3.8
3.9

3.10
3.11

Electric field norm and calculated field enhancement factor for various emitter radius of curvature: (a) 1 nm, (b) 5 nm, (c) 10 nm, and
(d) 20 nm. Field enhancement factor as a function of emitter radius
of curvature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulated electric field norm with streamlines (white lines) for a
general four-terminal device. The collector was grounded while the
emitter was biased negatively to induce electron emission. In (a) the
gates were biased negatively, and in (b) they were grounded. . . . . .
Emission and leakage current pathways for: (a) unetched substrate,
(b) deeply etched substrate. . . . . . . . . . . . . . . . . . . . . . .
Fabrication steps: (a) initial undoped Si substrate, (b) deposition
of 500 nm PECVD SiNx layer, (c) sputtering of 200 nm W, (d)
spin-coating of 100 nm 950 PMMA A2 e-beam resist, (e) EBL and
development, (f) evaporation of 35 nm Cr hard-mask, (g) lift-off, and
(h) dry etching in pseudo Bosch process. Note that the sketch is not
to scale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SEM of fabricated W triode-like device on SiNx : (a) top-view (b)
52◦ tilt, (c) 52◦ tilt and rotation. . . . . . . . . . . . . . . . . . . . .
IV characteristic for triode-like device on SiNx for various gate bias:
(a) both gates were grounded, (b) one gate we negatively biased to
repel electrons, (c) both gates were biased to steer electrons exclusively towards the collector, (d) both gates were biased to prevent
electron emission to the collector. In all cases, the collector was kept
grounded and the measurements were taken at room temperature. . .
Effect of temperature on electron emission: (a) IV characteristic, and
(b) FN plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fabrication steps for diode-like device: (a) initial Si3 N4 membrane,
(b) spin-coating of 1 µm 950 PMMA A8 electron beam resist, (c)
EBL and development, (d) sputtering of 150 nm of W, (e) lift-off, (f)
Ne focused ion beam milling. Note that the sketch is not to scale. . .
SEM of the two-terminal device after first lithography step. At this
point, the two terminals were connected. . . . . . . . . . . . . . . .
Various sputtering conditions on test samples: (a) RF power: 100
Watts; pressure: 2 mTorr, (b) RF power: 250 Watts; pressure: 3
mTorr, (c) RF power: 300 Watts; pressure: 40 mTorr. . . . . . . . . .

50
51

52
53

55
56

59
60

xi
3.12

3.13

3.14

3.15
3.16

3.17

3.18
3.19

3.20
3.21
3.22
3.23

4.1

Ion micrograph of suspended (a) two-terminal diode-like device and
(b) four-terminal triode-like device. In (a), the emitter-collector gap
measured 95 nm, and in (b) the emitter-collector gap measured 367 nm. 62
Photograph of (a) wire-bonded membrane, (b) membrane on ceramic
substrate sitting on top of heater with the heater off, (c) membrane
on ceramic substrate sitting on top of heater with the heater on, and
(d) testing setup at JPL. . . . . . . . . . . . . . . . . . . . . . . . . 64
Electrical measurements for the tow-terminal device as a function of
temperature: (a) IV characteristic removing the series resistance and
(b) its FN plot for currents over 15 nA for temperatures between 150
◦ C to 450 ◦ C. The lines correspond to the least-squares regression. . 65
Emission current in RD coordinates for various applied voltages. . . . 67
COMSOL simulation of the component of the electric field normal
to the emitting surface in V/m for the diode-like device. The emitter
was set to -10 V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Electrical measurements for triode-like device: (a) IV characteristic
at various gate bias at 150 ◦ C and (b) for 300 ◦ C, respectively. The
insets present the data in FN coordinates for currents over 15 nA.
(c) Summed emitter and collector currents to illustrate leakage to the
gate terminal for 150 ◦ C and (d) for 300 ◦ C. All legends indicate the
gate voltages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Calculated field factor for the four-terminal device as a function of
top gate voltage at 150 ◦ C and 300 ◦ C. . . . . . . . . . . . . . . . . . 71
Simulated IV characteristics for the current device geometry for the
various gate potential configurations experimentally tested at (a) 150
◦ C and at (b) 300 ◦ C. . . . . . . . . . . . . . . . . . . . . . . . . . . 72
SEM after testing for (a) diode-like and (b) triode-like devices. . . . . 74
SEM that shows device destruction due to electromigration that occurred during emission testing. . . . . . . . . . . . . . . . . . . . . . 75
Suspended device that broke during milling. . . . . . . . . . . . . . 77
Simplified band diagram illustrating the field electron emission mechanism from a metal cathode coated with n-type diamond with an effective NEA under forward bias. A depletion layer of width 𝑤 with
ionized donors forms at the metal-diamond interface. . . . . . . . . 81
Generalized FN emission IV characteristic and harmonic-rich resulting current due to the inherent non-linearity of the transfer function. . 92

xii
4.2

4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10

4.11

4.12

4.13

Generalized frequency mixer: (a) down-conversion, and (b) upconversion. Note that in (a) the product 𝜔 𝐿𝑂 + 𝜔 𝑅𝐹 also forms
but is not shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Simulation geometry: (a) top-view, and (b) cross-sectional view. . . . 98
Single-tip simulation: (a) overall geometry, (b) fine mesh box, and
(c) cut line (red line). . . . . . . . . . . . . . . . . . . . . . . . . . 98
Single-tip simulation results: (a) field enhancement factor and (b)
Maxwell capacitance as a function of tip length. . . . . . . . . . . . 99
Single-tip simulation results: (a) field enhancement factor and (b)
Maxwell capacitance as a function of tip base. . . . . . . . . . . . . 100
Single-tip simulation results: (a) field enhancement factor and (b)
Maxwell capacitance as a function of metal thickness. . . . . . . . . 101
Single-tip simulation results: (a) field enhancement factor and (b)
Maxwell capacitance as a function of substrate undercut. . . . . . . 102
Multi-tip simulation results: (a) field enhancement factor and (b)
Maxwell capacitance as a function of tip spacing. . . . . . . . . . . 103
General fabrication steps for field emitter multi-tip array: (a) initial
fused silica substrate, (b) evaporation of 25 nm Cr, (c) spin-coating
of 200 nm 950 PMMA A4 electron beam resist, (d) EBL and development, (e) Cr etch, (f) evaporation of 6 nm Ti, 60 nm Au, and 20
nm Ti, (g) lift-off, (h) residual Cr removal, (i) dry etching, and (j) wet
etching in BHF. Note that the sketch is not to scale. . . . . . . . . . 105
Images of representative devices after lift-off. (a) HIM of a device
with 40 tips. (b) SEM of a device with 10 tips and ground planes
in the vicinity. (c) and (d) are HIM of a device with 20 tips (same
device). Voltage contrast arises due to the difference in surface
potential between both tips once they were separated. . . . . . . . . . 106
HIMs of representative devices after dry etch: (a) 45 s etch (DC bias:
186 V) for a depth of ∼200 nm (image at 50◦ tilt), and (b) and (c) 40
s etch (DC bias: 206 V) for a depth of ∼120 nm (images at 52◦ tilt). . 107
HIMs of a finished field emission multi-tip arrays. (a) device with
ground planes at 45◦ tilt and rotation; (b) device as seen at 0◦ tilt and
(c) at 45◦ tilt. The undercut measured in average 130 nm in depth.
(d) Image at 52◦ tilt and rotation. On average, the gaps between the
two terminals measured 30 nm. . . . . . . . . . . . . . . . . . . . . 107

xiii
4.14

4.15
4.16
4.17
4.18
4.19
4.20
4.21
4.22
4.23
4.24
4.25

4.26

4.27

4.28

4.29

Images of asymmetric devices. HIM of finished device with a blunt
multi-finger collector structure at (a) 0◦ tilt, and at (b) and (c) 45◦
tilt. HIM of a finished device with a block collector design at (d) 0◦
tilt and at (e) 52◦ tilt. (e) is a less-magnified SEM of the device after
lift-off. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Chip wire-bonded to signal lines and ground plane of custom PCB. . 109
Relevant PCB design dimensions. . . . . . . . . . . . . . . . . . . . 109
Photo of PCB with soldered SMA edge connectors and wire-bonded
chip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
PCB experimental data: (a) S-parameters and (b) calculated real
impedance using S11. . . . . . . . . . . . . . . . . . . . . . . . . . 111
Custom-built electrical feed-through for frequency measurements up
to 18 GHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Schematic diagram of the test circuitry. . . . . . . . . . . . . . . . . 112
Photos of the experimental setup: (a) vacuum chamber (front view)
and (b) electrical connections (back view). . . . . . . . . . . . . . . 113
IV curves for both asymmetric designs considered: (a) blunt multifinger collector structure and (b) block collector structure. . . . . . . 114
Electrical characterization as a function of the number of tips per
device: (a) IV characteristics and (b) FN plot. . . . . . . . . . . . . . 115
SPICE schematic for a 10 tip device. . . . . . . . . . . . . . . . . . . 117
Result of SPICE simulation illustrating effect of fractional change in
field enhancement factor for a single tip within an array in measured
total current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Electrical measurements before frequency mixing experiment: (a)
static characteristic, (b) corresponding FN plot, and (c) differential
conductance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
DC bias feedback loop to stabilize emission current for frequency
mixing measurements: (a) shows the DC current as a function of
experiment duration, and (b) illustrates how the voltage was adjusted
to maintain the current constant at some chosen level. . . . . . . . . . 120
Power spectra of the output signal. Each AC signal has an amplitude
of 1 V 𝑅𝑀𝑆 . (a) 𝑓1 = 35 MHz and 𝑓2 = 50 MHz with 350 nA DC
current, (b) 𝑓1 = 35 MHz and 𝑓2 = 45 MHz with 350 nA DC current,
and (c) 𝑓1 = 30 MHz and 𝑓2 = 35 MHz when the device is ‘off’ (0 nA).121
HIM (a) before and (b) after testing. . . . . . . . . . . . . . . . . . . 122

xiv
4.30
4.31

4.32
5.1

5.2

5.3

5.4
5.5

5.6
5.7

5.8

5.9

5.10

SPICE (a) circuit schematic and (b) IV characteristic simulation
showing the effect of reducing the work function by a factor 𝑐. . . . 124
Effect of Pr coating in field emission: (a) IV characteristics of Pr
coated and non-coated device and (b) FN plots. A dashed line at 10
nA is included in (a) to determine the turn-on voltage. . . . . . . . . 125
HIM of the device after a second layer of Pr was evaporated. . . . . . 127
Complex dielectric function of gold: (a) real and (b) imaginary components. A comparison between the Drude model (solid line) and
empirical data adapted from Johnson & Christy [4] is shown. . . . . . 135
Illustration of the SPP propagation along the 𝑥-axis. The evanescent
confinement on both sides of the interface is shown by the purple
exponential decay curves. . . . . . . . . . . . . . . . . . . . . . . . 136
Normalized SPP dispersion relation assuming Drude model with
negligible damping for propagation in air (blue) and SiO2 (red): (a)
real and (b) imaginary components. Note that the light lines (dashed
lines) with 𝜔 = 𝑐𝑘 are also included. . . . . . . . . . . . . . . . . . . 140
Field distribution of the fundamental mode for (a) MIM structure and
(b) all dielectric multilayer with 𝜖 𝑑1 > 𝜖 𝑑2 for comparison. . . . . . . 142
Normalized electric field of the fundamental mode for the MIM structure (blue) and all-dielectric geometry (red) for various slot widths:
(a) 𝜆/100, (b) 𝜆/10, and (c) 𝜆/2, where 𝜆 = 1550 nm. . . . . . . . . 143
Illustration of the cross-section of the hybrid plasmonic waveguide. . 144
Effect of metal loading a Si slab for both TE and TM polarizations.
(a) Shows a metal-loaded Si slab waveguide and (b) illustrates an
unloaded Si slab waveguide. . . . . . . . . . . . . . . . . . . . . . 144
Real component of 𝑛𝑒 𝑓 𝑓 for the bound TE mode of region II and
both TE and TM modes of region I as a function Si thickness and the
following spacer oxide thicknesses: (a) 20 nm, (b) 30 nm, (c) 40 nm,
and (d) 50 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Difference in the 𝑛𝑒 𝑓 𝑓 between the bound TE mode of the bare Si
slab waveguide of region II and the largest of either TE or TM modes
of the metal-loaded waveguide of regions I as a function of Si and
oxide thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
Simulation parameters: (a) two-dimensional geometry and (b) mesh
employed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

xv
5.11
5.12

5.13
5.14
5.15
5.16

5.17
5.18
5.19
5.20
5.21
5.22

5.23

Complex 𝑛𝑒 𝑓 𝑓 for the proposed structure as a function of gap size:
(a) real and (b) imaginary components. . . . . . . . . . . . . . . . . 148
Electric field distribution as a function of gap width: (a) 10 nm gap,
(b) 30 nm gap, (c) 50 nm gap, and (d) 70 nm gap. Note that all figures
have the same intensity scale. . . . . . . . . . . . . . . . . . . . . . 148
Normalized field energy distribution along cut line as defined in Fig.
5.10 for various gap widths. . . . . . . . . . . . . . . . . . . . . . . 149
Percentage of time average energy density in metal tips and all gap
area as a function of gap width. . . . . . . . . . . . . . . . . . . . . 150
Propagation length as a function of gap size. . . . . . . . . . . . . . 151
Top-view of the hybrid plasmonic structure. A grating coupler was
used to couple free space light into the photonic mode of the waveguide, which was subsequently adiabatically converted into a plasmonic mode by means of an metallic taper. Simulations of the electric
field at various locations along the taper to depict mode hybridization
were also included. . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Computed Eikonal parameter as a function of gap width for a taper
angle of 45◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Cross-sectional view of the schematic for the proposed device with
electrical terminals. . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Electric field distribution (a) without and (b) with undercut. The
chosen gap was 30 nm. . . . . . . . . . . . . . . . . . . . . . . . . 154
Static field enhancement factor as a function of gap width. . . . . . . 155
Maximum electric field norm on the emitter tip as a function of gate
voltage for various emitter-to-collector gaps. . . . . . . . . . . . . . 155
Potential distribution for various gate bias: (a) 𝑉𝐺 = 𝑉𝐶 = 0 V, (b)
𝑉𝐺 = 𝑉𝐸 /2, (c) 𝑉𝐺 = 𝑉𝐸 , (d) 𝑉𝐺 = 1.5𝑉𝐸 , and (e) 𝑉𝐺 = 2𝑉𝐸 . The
red lines are streamlines illustrating the electron trajectory under the
specified bias. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
Main fabrication steps for plasmonically-enhanced field emission device: (a) initial SOI substrate, (b) doping of top Si layer, (c) Si
thinning via thermal oxidation and subsequent HF etch, (d) thermal
oxidation to grow spacer oxide layer, (e) EBL and development using
950 PMMA A8, (f) gold electron beam evaporation and lift-off, (g)
Ne focused ion beam milling, and (h) undercut in HF of cut area.
Note that the sketch is not to scale. . . . . . . . . . . . . . . . . . . . 159

xvi
5.24
5.25

5.26
5.27

5.28
5.29

5.30

5.31
5.32
5.33

SEM of device before milling the gap between the emitter and collector. Grating and focusing marks are also visible. . . . . . . . . . . 160
SEM of fabricated device: (a) top view of a device after milling
the plasmonic waveguide, (b) zoomed-in view of the gap region
illustrating the extent of the mill cut line, (c) side view at 52◦ of the
edge of the plasmonic waveguide before HF undercut, and (d) crosssectional view of the hybrid plasmonic waveguide of the finished
device. The separation between the emitter and collector measured
12.1 nm in its narrowest region. Pt was used to protect the top surface
of the device during ion cross-section milling. . . . . . . . . . . . . 162
Schematic of the measurement setup to electrically characterize the
devices. The collector was fixed at 0 V for all tests. . . . . . . . . . . 163
IV characteristic of a representative plasmonically-enhanced field
emission device during (a) forward and (b) reverse voltage sweeps.
The gate and collector were grounded. No leakage from the emitter
into the gates was measured. In (c), the data for both sweeps is
plotted in FN coordinates, indicating that field emission is the electron
transport mechanism, as evidenced by the straight line. . . . . . . . 165
IV characteristic for two different gate biases: 0 V and -0.5 V. No
significant leakage into the gate terminal was measured. . . . . . . . 165
Effect of applying a time-varying voltage signal on the electrical gate.
In (a), the signal applied to the gate and the measured currents in all
three terminals as a function of time are shown. In (b), the Fourier
transforms for all time-varying measured data were computed. . . . . 167
Schematic of the setup for optical measurements. The path of the
1550 nm free-space beam that is coupled to the device is shown in
red. For sample navigation, a white light source is also focused onto
the sample during measurement setup, as shown by the green line.
The dotted lines represent an elevation change in the beam. . . . . . 168
Photos of the (a) free-space optical setup and (b) electronic rack. . . . 169
Optical response of the field emission device to various EDFA output
powers as a function of emitter voltage. . . . . . . . . . . . . . . . . 170
NIR camera images of the input beam when coupling into the grating
is (a) minimized and (b) maximized via a 90◦ rotation of the half
wave-plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

xvii
5.34

Optically-induced current measured by the lock-in amplifier as a function of emitter voltage when coupling into the grating is minimized
and maximized. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
5.35 SEM of the blown device after multiple continuous measurements. . 171

xviii

LIST OF TABLES
Number
Page
1.1 Basis of Dennard scaling for circuit performance (adapted from [12]). 4
1.2 Overall technology progression forecast (adapted from [22]). . . . . . 8
3.1 Device data as a function of temperature. . . . . . . . . . . . . . . . 57
3.2 Measured resistance values of membrane and ceramic pin grid array
package at low fields as a function of temperature. . . . . . . . . . . 63
3.3 Suspended two-terminal device data as a function of temperature. . . 67
4.1 Linear regression analysis data as a function of number of tips. . . . . 116
4.2 Measured power for all frequencies of interest shown in Fig. 4.28. . . 120
4.3 Expected and extracted FN parameters. . . . . . . . . . . . . . . . . 127
5.1 Drude model parameters, complex dielectric constant at 1550 nm,
and onset of interband transition for common noble metals. Adapted
from [5–7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

xix

LIST OF ABBREVIATIONS
BHF Buffered hydrofluoric acid
BS Beamsplitter
CCP Capacitively coupled plasma
CMOS Complementary metal–oxide–semiconductor
CNT Carbon nanotube
Cr Chrome
CVD Chemical vapour deposition
EBL Electron beam lithography
EDFA Erbium-doped fiber amplifier
FEA Field emitter array
FED Field emission display
FEM Finite element method
FET Field effect transistor
FFT Fast Fourier Transform
FIB Focused ion beam
FinFETs Fin field-effect transistors
FN Fowler-Nordheim
FP Frenkel-Poole
GAA Gate-all-around transistors
HF Hydrofluoric acid
HIM Helium ion micrographs
IC Integrated circuit
ICP Inductively coupled plasma
ICP-RIE Inductively-coupled plasma reactive-ion etcher
IF Intermediate frequency
IPA Isopropyl alcohol
IV Current-voltage
LO Local oscillator
MIBK Methyl isobutyl ketone
MIM Metal-insulator-metal
MOSFET Metal–oxide–semiconductor field-effect transistor
NEA Negative electron affinity
NIR Near-infrared
PCB Printed circuit board

xx
PEC Proximity effect correction
PECVD Plasma-enhanced chemical vapour deposition
PMMA Poly(methyl methacrylate)
Pr Praseodymium
RD Richardson-Dushman
RF Radio frequency
RIE Reactive-ion etching
SEM Scanning electron micrograph
Si Silicon
Si3 N4 Stoichiometric silicon nitride
SiNx Amorphous silicon nitride
SN Schottky-Nordheim
SOG Spin-on-glass
SOI Silicon-on-insulator
SPP Surface plasmon polariton
SSE Solid-state electronic
TE Transverse electric
Ti Titanium
TM Transverse magnetic
UHV Ultra-high vacuum
UNCD Ultrananocrystalline diamond
W Tungsten
WKB Wentzel-Kramers-Brillouin

Chapter 1

INTRODUCTION
Electronics constitutes the backbone of modern life. For the last 100 years, it has
transformed almost every aspect of society. It has facilitated global communication,
increased human lifespan, enabled space exploration, simplified trade, and improved
numerous areas such as defense, education, utilities, and food production and distribution to name a few. Due to its versatility, the applications of this technology
are so extensive that it is easier to think of where electronic devices are used than
where they are not. From phones and navigation devices, to heart-rate monitors and
chicken feeding systems, electronics has become an indispensable and ubiquitous
part of humankind, making it impossible to imagine a world without it.
In the first half of the twentieth century, all electronic devices used vacuum tubes in
their circuits. Some of the most important technological accomplishments attributed
to vacuum tubes include the development of the radio, television, radar equipment,
and long-distance telephone. Vacuum tubes were also a key component in the
world’s first electronic general-purpose programmable digital computer, the ENIAC
(more formally known as the Electronic Numerical Integrator And Computer). This
computer was built between 1943 and 1945 for the U.S. Army. It used almost 17,500
vacuum tubes, weighed 30 tons, covered around 170 square meters of floor space,
and consumed 150 kilowatts of electric power [1]. Due to its unprecedented ability
to be programmed to execute complex sequences of operations at electronic speed,
the ENIAC launched a new era: the Information Age.
However, the emergence of the transistor and later integrated circuit (IC) technology
quickly replaced vacuum tubes in almost all areas. Solid-state electronic (SSE)
devices were less fragile, more energy efficient, smaller, and, above all, able to
be mass-produced. Consequently, vacuum electronic devices based on thermionic
emission were displaced to a handful of niche applications such as microwave power
amplifiers, cathode ray tubes, and high-temperature and radiation environments.
Today, transistors are deeply embedded in almost all electronic devices. They can
be manufactured so small that billions of them can be packed into a single microprocessor. Yet, despite the apparent pushover of the transistor, vacuum technology did
not perish. Paradoxically, the same fabrication and processing tools developed to

reduce the size of solid-state ICs also enabled the miniaturization of vacuum technology, giving rise to the fields of vacuum micro and nanoelectronics. By reducing
their physical dimensions, vacuum devices can leverage some distinct inherent advantages including ballistic electron transport and resilience in harsh environments.
The resurgence of this technology appears to be timely, as SSEs seem to be reaching their technical limitations. The steady shrinkage of the transistor has become
detrimental, as issues related to heat dissipation and quantum effects are emerging.
In this chapter, we reference some key historical events to better understand the
context that brought about the electronics revolution of the last century, beginning
with the invention of the vacuum tube. We also discuss the current state of SSE
devices as well as their technical limits. Finally, we provide an overview of some
exciting prospects for vacuum nanoelectronics to help overcome these limitations.
1.1

Over a Century of Vacuum Tubes

The first measurement of atmospheric pressure has been attributed to E. Torricelli in
1643. He carried out his famous experiment with a mercury-filled tube, becoming
the first person to successfully produce a vacuum. A couple of years later, O.
von Guericke made the first functional piston pump, the precursor of all vacuum
technologies. While some improvements were made, the design of the solid-piston
pump remained unchanged for about 200 years. Yet, the second half of the 19th
century saw an accelerated development of vacuum pumps and pressure gauges,
as well as advancements in seal technology, largely fueled by the demands of the
growing incandescent lamp industry. Two of the most important inventions include
the mercury-piston pump as well as the McLeod gauge [2].
In 1883, T. Edison was studying the cause of uneven blackening inside his carbon
filament incandescent lamp that affected the efficiency and lifetime of the bulb. He
experimented by adding an extra electrode to the setup, observing that current would
only flow to it when it was positively biased. This observation became known as
the “Edison effect” and is regarded as one of the most important experiments in
thermionic emission. However, unable to satisfactorily explain his discovery, he
did not conduct further research on this topic. In 1904, J. Fleming used Edison’s
findings to develop the first practical vacuum tube device, the thermionic diode.
It consisted of an evacuated glass bulb with two terminals: an electron-emitting
cathode and an anode. Current would flow through the cathode electrode causing
it to heat, leading to some electrons gaining enough kinetic energy to escape via

thermionic emission. The anode electrode would be positively biased to collect
these emitted electrons. However, if a negative voltage was applied, no current
would flow through the anode. This unidirectional behaviour was then used to
rectify high-frequency electromagnetic waves, which became particularly useful
in telegraph-receiving stations to detect radio signals. Because of this invention,
Fleming is considered by many to be the “father of electronics” [3, 4].
In the years that followed, significant progress was made to the diode. In 1906,
L. De Forest added a wire grid between the anode and the cathode, known as the
control grid, and invented the triode. By adjusting the grid voltage, the electron
current between the other two terminals was controlled, thus enabling signal amplification, which was crucial for long-distance radio and telephone communication
[5]. A fourth grid, known as the screen grid, was added between the control grid
and the anode to reduce the capacitance between these two terminals caused by
the Miller effect [6]. An additional grid, called the suppressor grid, was placed
closer to the anode to prevent secondary electron emission from the anode to the
screen, which caused instability. These devices became known as the tetrode and the
pentode, respectively. Further improvements to vacuum tubes included the replacement of carbon filaments with tungsten filaments and later by thoriated tungsten
and oxide-coated filaments, which increased the emission efficiency as well as the
lifetime. Moreover, multiple advances in vacuum techniques were made, including
the invention of the rotary oil pump, the molecular drag pump, and the mercury
diffusion pump, as well as the introduction of getters [7, 8].
The hegemony of the vacuum tube lasted almost half a century. The urge to
operate at higher frequencies than those attainable with vacuum tubes, as well as the
significant advancements made in quantum mechanics during the 1920s, especially
the development of electronic band structure, encouraged the research in SSEs. In
1947, J. Bardeen, W. Brattain, and W. Shockley demonstrated the first working
point-contact transistor at Bell Labs. A year later, Shockley also developed the
junction transistor. Two other breakthroughs in SSE technology came with the
invention of the metal-oxide-semiconductor field-effect transistor (MOSFET) by D.
Kahng and M. Atalla, and the introduction of the IC by J. Kilby [9]. Due to their
smaller size, higher efficiency, longer lifetimes, ability to be mass-produced, and
ease of integration, transistors quickly displaced the bulky vacuum tubes. Only in a
handful of niche applications did vacuum technology still prevail, such as microwave
power amplifiers and X-ray tubes.

1.2

Dennard Scaling and Moore’s Law and the Future of Electronics

For more than 50 years, the semiconductor industry has followed Moore’s law, which
states that the number of transistors per die doubles approximately every two years.
This prediction was originally proposed by G. Moore in 1965 and has since been
the operating principle at the forefront of microchip development, as it describes a
commitment of developers to continuously advance the performance of ICs. Owing
to the exponential improvement outlined in Moore’s law, the primitive and exclusive
personal computers manufactured in the 70s quickly gave rise to the advanced and
ubiquitous smartphones available today [10, 11].
The success of Moore’s law can be greatly attributed to the ability to shrink solidstate devices. The basic principle of geometric scaling was originally proposed by
R. Dennard in 1975, and it is commonly referred to as Dennard scaling. A summary
of Dennard scaling is outlined in Table 1.1 where 𝜅 is a unitless scaling factor. The
core concept consists in simultaneously scaling three variables of a device, namely
its physical dimensions, doping concentration, and voltage. All linear dimensions
are reduced by the common factor 𝜅. This includes horizontal dimensions such
as channel length and width, as well as vertical dimensions such as gate insulator
thickness. In addition, the substrate doping concentration is increased by 𝜅, and
the voltages applied are reduced by 𝜅. As a consequence, the electric field of the
scaled device remains constant, which is vital to maintaining reliability in terms
of hot-carrier injection. Additionally, both the current and capacitance decrease
by 𝜅, which in turn decreases the circuit delay by 𝜅 and the power dissipation
by 𝜅 2 . Ultimately, this results in the power per unit area, i.e., the power density,
Device or Circuit Parameter

Scaling Factor

Physical dimension 𝐿, 𝑊, 𝑡 𝑜𝑥
Doping concentration 𝑁𝑎
Voltage 𝑉
Current 𝐼
Capacitance 𝐶 = 𝜖 𝐴/𝑡
Delay time per circuit 𝑉𝐶/𝐼
Power dissipation per circuit 𝑉 𝐼
Power density 𝑉 𝐼/𝐴

1/𝜅
1/𝜅
1/𝜅
1/𝜅
1/𝜅
1/𝜅 2

Table 1.1: Basis of Dennard scaling for circuit performance (adapted from [12]).

remaining constant. This geometrical scaling allowed the number of transistors per
chip to double with every new technology generation as well as to operate at higher
maximum frequencies so that the overall performance was improved [12].
Continuous advances in semiconductor process technology were made to shrink the
device dimensions. Most notably, new and improved lithographic techniques were
developed to pattern smaller feature sizes. Lenses of higher numerical apertures
and illumination sources with shorter wavelengths have been introduced. One major
breakthrough has been the launch of extreme ultraviolet (EUV) lithography in chip
manufacturing, which uses a wavelength of 13.5 nm to obtain higher resolution
[13]. Moreover, significant progress has been made in the fabrication techniques
to grow thinner gate oxides and to reduce defect levels at the ambitious dimensions
demanded.
Furthermore, in 1991 the National Technology Roadmap for Semiconductors (NTRS)
was created. The NTRS was a major cooperative effort of the semiconductor industry to coordinate what manufacturers and suppliers were doing so that targets
and expectations for coming technology generations could be set. Every couple
of years, a report predicting the rate of transistor scaling and technical challenges
for the incoming years was released. In 1998, the NTRS was extended to include
countries in Europe and Asia, becoming the International Technology Roadmap for
Semiconductors (ITRS). In this way, the semiconductor industry ensured that new
chips would stay on track with Moore’s law.
However, reducing operating voltages to achieve high performance became steadily
more problematic. As threshold voltages were reduced, subthreshold leakage currents–the current that flows from the source to the drain in a transistor when it is
supposed to be off–exponentially increased. Consequently, static power dissipation
became a dominant component of the total power consumption. In Fig. 1.1, the
effect of reduced gate length in dynamic and subthreshold-leakage-power density is
shown.
Moreover, gate oxide thickness reached its physical limit when Intel released its
65 nm generation transistor in 2005. The thickness of the gate dielectric of the
device was 1.2 nm, which is equivalent to about 5 silicon (Si) atomic layers. At
this thickness, gate leakage currents due to direct tunneling and hot-carrier injection
from the substrate to the gate oxide became significant.

1000
100
10
0.1

100

1000

x10-5
10000
10000
1000

IOFF ∝10(-Vth/S)
S ~ 85 mV/decade

100
10
0.1

10X
0.5

IOFF

1.5

Figure 1.1: Effect of reduced gate length and operating voltages: (a) relationship
between threshold voltage (𝑉𝑡ℎ ) and subthreshold leakage current (𝐼𝑂𝐹𝐹 ) [14], (b)
power density versus gate length [15], and (c) power and delay as a function of
threshold voltage (𝑉𝑡ℎ ) with 𝑉𝐷𝐷 = 0.5V for 0.35 𝜇m process [16].

Dennard scaling also considered that channel doping concentration could be continuously increased. At sufficiently high dopant concentrations, carrier mobility
decreases as a result of increased impurity scattering, which deteriorates device
operation. In addition, direct band-to-band tunneling increases reverse bias-pn
junction leakage from the source/drain into the body [17].
Ultimately, the rapid growth in overall power consumption due to increased leakage
currents became unfeasible. Thus, as fundamental thermal limits were reached
by the early 2000s, Dennard voltage scaling came to an end. Because it became
impossible to simultaneously increase the number of transistors per chip as well as
the maximum operating frequency, clock frequencies plateaued as illustrated in Fig.
1.2 [18]. To keep up with Moore’s law, multi-core architectures were introduced.
In this type of parallel architecture, the operating frequency scaled down inversely
proportionally to the number of cores, so that several processors working at a lower
frequency were equivalent to a single processor working at its aggregate frequency.
In 2001, IBM introduced the first commercially available dual-core microprocessor
chip, the Power4 [19]. Performance was also improved by increasing caches sizes,

107
10

Transistors
(thousands)

Single-Thread
Performance
(SpecINT x 103)

105
104

Frequency (MHz)
103
102

Typical Power
(Watts)

101

Number of
Logical Cores

100
1970

1980

1990

2000

2010

2020

Year
Original data up to the year 2010 collected and plotted by M. Horowitz, F. Labonte, O. Shacham, K.
Olukotun, L. Hammond, and C. Batten. New plot and data collected for 2010-2017 by K. Rupp

Figure 1.2: 42 years of microprocessor trend data [18].

as they are more energy efficient than main memory access [20]. Another ingenious
concept to conserve power was developed, namely dark silicon, wherein a fraction
of the die is underutilized [21]. Furthermore, much research has been conducted in
developing new materials with higher dielectric constants and in stress engineering
for enhanced channel mobility. Lately, new transistor designs have been driving
the latest generation process nodes in which planar devices have given way to 3D
architectures, including fin field-effect transistors (FinFETs), and most recently,
gate-all-around transistors (GAA), as shown in Table 1.2 [22].
Even though dimensions are still shrinking and device performance is still improving, quantum and fundamental 3D topological limits will be reached soon. This can
be seen in Fig. 1.3 [22], which predicts metal and gate pitch scaling ebbing away
in the upcoming years. Thus, it seems that completely new computing paradigms
should be embraced. Two very promising candidates are neuromorphic engineering and quantum computing. Yet, these technologies are still in their early stages
and have a long way to go before they can be released for mass use and become
mainstream. In the meantime, there is room to explore other options, especially for
the applications in which solid-state devices do not excel. One such alternative are
nanoscale field emission devices, which is the focus of this thesis.

YEAR OF
PRODUCTION

2020

2022

2025

2028

2031

2034

Logic device technology
naming

G48M36

G45M24

G45M20

G40M16

G38M16T2

G38M16T4

Logic industry "node
range" labeling (nm)

"5"

"3"

"2.1"

"1.5"

"1.0nm
eq"

"0.7nm
eq"

LOGIC DEVICE GROUND RULES
MPU/SoC M0 1/2 pitch
(nm)

10.5

Physical gate length for
HP logic (nm)

Lateral GAA
(nanosheet) minimum
thickness (nm)

Minimum device width
(FinFET fin, nanosheet,
SRAM) or diameter
(nm)

0.7

0.65

0.6

LOGIC DEVICE ELECTRICAL
Vdd (V)

0.7

LOGIC TECHNOLOGY ANCHORS
Patterning technology
inflection for Mx
interconnect

193i,
EUV DP

193i,
high-NA
EUV

Beyond-CMOS as
complimentary to
platform CMOS

2D
device,
FeFET

2D device,
FeFET

Channel material
technology inflection

SiGe25%

SiGe50%

Ge, 2D
Mat

Process technology
inflection

Conformal
Channel,
doping,
RMG
contact

Lateral/
Atomic
Etch

Non-Cu
Mx

3D VLSI

Stacking generation
inflection

3D
stacking:
W2W,
D2W
Mem-onLogic

3D
stacking,
Finepitch
stacking,
P-overN,
Mem-onLogic

3D
stacking,
3D VLSI:
Mem-onLogic with
Interconnect

3D
stacking,
3D VLSI:
Logic-onLogic

Notes: GxxMxxTx notation refers to Gxx—contacted gate pitch, Mxx—tightest metal pitch in nm, Tx—number
of tiers, MPU—microprocessor unit, SoC—system on chip, HP—high performance,193i—193nm immersion
lithography, DP—double patterning, FeFET—ferroelectric field-effect transistor, Ge—germanium,
SiGe—silicon germanium, RMG—replacement metal gate, VLSI—very large scale integration, W2W—wafer to
wafer, D2W—die to wafer, Mem-on-Logic—memory on logic

Table 1.2: Overall technology progression forecast (adapted from [22]).

Half pitch (nm)

20 M18
15

Scaling is leveling off

M12
M10

10
1/2 metal pitch
2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033

2034

Year

Figure 1.3: Metal and gate half pitch predictions (adapted from [22]).

1.3

The Emergence of Vacuum Micro and Nanoelectronics

After the invention of the transistor and subsequent ICs, it seemed that the days of
vacuum technology were over. Solid-state devices were smaller and easier to fabricate and integrate. However, somewhat ironically, the same fabrication techniques
that advanced SSEs also allowed for the miniaturization of vacuum technology, and
thus, the field of vacuum micro and nanoelectronics was born.
The first person to conceive the idea and lay down the foundations of vacuum
microelectronic devices was K. Shoulders of Stanford Research Institute (SRI)
[23]. In 1961, he suggested reducing the size of electronic components by three
orders of magnitude using microfabrication techniques and envisioned vertical and
lateral field emission micro-triodes. Unlike the mature thermionic cathodes that
needed an external source of heat to emit electrons from their surface, these devices
just required a high enough electrostatic field that would cause the electrons to
quantum mechanically tunnel and escape into vacuum. Even though devices based
on field emission had existed for some time before (for instance, the field emission
microscope had been invented by E. Müller in 1936), they had various weaknesses.
The main issue was that they required high voltages (i.e., thousands of volts) due
to their large cathode-to-anode separation, which often led to vacuum arcing and
destruction.
In Shoulder’s foresight, the smaller device dimensions would substantially reduce
the operating voltage and considerably improve switching times. Another major

10
consequence of lower voltage operation would be a significant increase in lifetime,
as sputtering damage due to ion bombardment would be minimized. Among the
fabrication techniques, he comprehensibly described various material deposition
methods, electron-beam lithography, dry etching, electron-beam microscopy, and
integration with ultra-high vacuum (UHV) systems. These ideas were very innovative at the time as many of these microfabrication techniques had not been thoroughly
developed yet. Overall, his objective was to fundamentally show vacuum ICs.
In spite of Shoulder’s clear vision, it was not until 1968 when C. Spindt, who
also worked at SRI, successfully fabricated and tested the first thin-film field
emission cathodes [24]. The device consisted of a molybdenum/aluminum oxide/molybdenum sandwich with an array of open micro-size cavities fabricated on
top of a sapphire wafer. A single conical molybdenum emitter tip was deposited at
the center of each cavity. In this way, each emitter was surrounded by its own gate to
modulate the emission current, which was in turn collected by an anode positioned
above the array. The first set of devices consisted of an array of approximately 50
cathode tips over an active area of about 10−3 cm2 . Due to the sharp geometry of
the emitter and the small gap between the emitter and the gate electrode, high local
electric fields were produced at gate voltages of around 100 V. Another advantage
of these emitters was that noise from a single emitter was statistically reduced by
virtue of the large number of identical emitter tips. This field emitter array (FEA)
became known as the Spindt emitter.
In the years that followed, the Spindt cathode was further improved, with packing
densities increased to 1.5 × 107 cm2 and current densities over 1000 A/cm2 being
measured. In addition, lifetimes of over 8 years of continuous operation with tip
loading of 20 𝜇A/tip (which was later increased to 50 𝜇A/tip) were reported [25].
In 1972, N. Thomas et al. demonstrated Si-based FEAs. Silicon was a very
convenient material for FEAs as it enabled manufacturers to take advantage of the
highly developed microfabrication technology for mass production of Si ICs, such
as preferential etching and polishing techniques [26]. Furthermore, in 1986 H. Gray
and co-workers fabricated the first planar Si field emitter array vacuum field effect
transistor [27]. In this device, the solid channel of a standard Si FET was replaced
with vacuum, while the source consisted of an array of micron-size Si field emitters.
This transistor not only produced voltage and power gain from gate modulation but
also promised ultra-short transit times due to the faster electron transport inherent in
vacuum at micron-scale cathode-to-anode separations. A breakthrough in electron

11
field emission came in 1982 when G. Binnig and H. Rohrer at IBM Zurich Research
Laboratory invented the scanning tunneling microscope (STM), which allowed to
image surfaces with atomic resolution [28]. A couple of years later, they were
awarded the Nobel prize for their invention. In terms of commercial attention, FEAs
only started to become popular in the late 80s when LETI successfully demonstrated
a flat panel field emission display (FED) using molybdenum FEAs [29, 30]. Thanks
to their high brightness, resolution, and quick response, research in FEDs was very
promising.
As fabrication techniques continued to improve, devices could be manufactured
with nanoscale dimensions, resulting in further reductions of turn-on voltages. For
instance, Han et al. reported a surround gate nanoscale vacuum channel transistor
with a sub-50 nm vacuum gap and a turn-on voltage under 5 V [31]. Additionally,
when the cathode-to-anode separation is smaller than the mean free path of electrons
in air under atmospheric pressure, the vacuum requirement can be effectively relaxed.
The first successful operation of a field emission device at atmospheric pressures
was demonstrated by Driskill et al. [32].
1.4

Could Nothing Be Better Than Something?

Devices based on field emission have several advantages as compared to their solidstate counterpart. First, field emission devices enable ballistic transport of electrons.
In contrast to solid-state devices that employ semiconductor channels, field emission
devices use vacuum as their transport medium. In semiconductors, electrons suffer
from phonon scattering, which limits the maximum velocity a charge carrier can
attain. The saturation velocity for Si is in the order of 1 × 107 cm/s and for
gallium arsenide it is 1.2 × 107 cm/s, while the velocity of an electron in vacuum is
theoretically about 3×1010 cm/s [33]. Consequently, higher cutoff frequencies could
be achieved in vacuum devices. Additionally, due to the lack of energy dissipation
in the channel, vacuum enables higher power operation than equivalent solid-state
devices.
Second, vacuum devices are inherently more resilient to extreme temperatures. In
semiconductors, the concentration of intrinsic carriers 𝑛𝑖 depends exponentially on
temperature 𝑇, as given by
(1.1)
𝑛𝑖 = 𝑛𝑐 𝑛𝑣 𝑒 −𝐸 𝑔 /2𝑘 𝐵𝑇
where 𝑛𝑐 and 𝑛𝑣 are the effective density of states for electrons in the conduction
band and holes in the valence band of the semiconductor, respectively, 𝐸 𝑔 is the

12
bandgap energy, and 𝑘 𝐵 is the Boltzmann constant. Fig. 1.4 illustrates the effect of
temperature on the concentration of intrinsic carriers for various semiconductors.
Thus, at sufficiently high temperatures, dopant atoms become overwhelmed by the
uncontrollable concentration of intrinsic carriers, which ultimately renders the device ineffective at controlling carrier flow. Additionally, the leakage current of a
reverse-biased pn junction is tied to the concentration of intrinsic carriers in semiconductors. Hence, at high temperatures, junction leakage current becomes a major
problem in device operation, as performance is degraded and power consumption
is subsequently increased. In order to circumvent these issues, the semiconductor
industry has moved toward wide bandgap materials such as silicon carbide (SiC)
and gallium nitride (GaN). In this way, while the maximum operating temperature
for Si devices is around 300 ◦ C, this limit is extended to approximately 600 ◦ C in
SiC [34]. Metal field emitters, on the other hand, do not rely on chemical doping
for their device operation. Therefore, they are relatively insensitive to temperature
changes until the onset of thermionic emission. At the other extreme, vacuum devices are also better suited for low-temperature operation. This is because, at low
temperatures, semiconductor devices freeze out due to the lack of thermal energy to
fully ionize impurity atoms.

Intrinsic carrier concentration (cm-3)

Moreover, vacuum devices are more resistant to radiation. Incident energetic heavy
particle radiation can dislodge atoms and create a vacancy-interstitial pair, i.e., a

1015

1010

105
100

10-5

10-10
200

400

600

800

1000

Temperature (K)

Figure 1.4: Intrinsic carrier concentration as a function of temperature for various
semiconductors [34]. The shaded grey area corresponds to typical doping range.

13
Frenkel pair, in a crystalline semiconductor. This displacement damage creates
deep-level traps in the band gap that serve as scattering and trapping centers, which
increases junction leakage currents, reduces carrier mobility, and decreases minority
carrier lifetime. This effect is particularly detrimental for minority carriers and
optoelectronic devices. These collisions are irrelevant in vacuum devices as they
can be manufactured with amorphous materials. Ionizing radiation can generate
electron-hole pairs in gate oxides, which are quickly separated by the electric field.
However, slow holes get easily trapped in oxide and interface traps. As a consequence
of this charge buildup, parasitic fields are slowly created, which may irreversibly alter
device properties such as the threshold voltage. Another type of radiation-induced
damage is single-event effects caused by direct ionization. When a high-energy
charged particle travels through a device, a high-density electron-hole plasma is
created along its path due to the energy it loses by ionizing the device material. This
can cause the device to malfunction, especially if it happens in a depletion region.
The collected anomalous charge can also cause latch-ups, which can permanently
damage ICs if the current is not quickly limited. The incident-charged particle can
also damage thin gate oxides by creating a conduction path through it, which can
lead to dielectric breakdown and subsequent device destruction. Several of these
problems become trivial when vacuum is used instead of a gate dielectric [35, 36].
Field emission devices also enjoy some advantages over thermionic vacuum tubes.
Cold field emission is a quantum mechanical process that does not require heating,
thus reducing power consumption and eliminating the need for thermal management.
As heating is not necessary, the distance between the electrodes can be very small. If
the dimensions of the device are smaller than the elastic mean free path of electrons
in air, which is around 200 nm at low electron energies [37], and the voltages are
kept under the first ionization potential of molecules present in air (12.1 eV, 12.7
eV, 14.4 eV, and 15.6 eV for O2 , H2 O, CO2 , and N2 , respectively) [38], the device
can potentially be operated at atmospheric pressures. Field emission devices can
nowadays be easily miniaturized by employing the same fabrication techniques that
are used to manufacture solid-state devices, offering a cost reduction in comparison
to vacuum tubes. If CMOS-compatible materials are chosen, field emission devices
could be integrated with SSEs for enhanced functionality.
In this way, field emission devices combine the advantages of traditional vacuum
tubes and modern solid-state nanofabrication technology. Potential applications
include sources in electron beam lithography (EBL) [39], microwave power ampli-

14
fiers [40], X-ray sources [41], free electron laser [42], and logic circuits for space
communications. Due to its non-linear current-voltage (IV) characteristic and fast
response time, field emission devices could also be used for high-frequency multipliers and converters. Lastly, the nanoscale vacuum transistor could potentially be
a candidate to keep up with Moore’s law.
1.5

Objective of This Work

The objective of this work is to experimentally study the phenomenon of electron
field emission. Two- and four-terminal devices for use in high-temperature environments are designed, fabricated, and electrically characterized. In addition, two
types of structures are demonstrated for high-frequency operation: a two-terminal
device for frequency mixing, and a plasmonically-enhanced field emission device
at telecommunications wavelength.
There are six chapters in this thesis and they are organized as follows:
Chapter 1 provides a brief introduction to vacuum technology. The history of the
rise and fall of early vacuum devices is presented, followed by a discussion on
the current state of SSEs. A description of the development of micro and nano
field emission electronic devices is given, and the potential advantages over both
solid-state and thermionic devices are discussed.
Chapter 2 details the theoretical background of various electron emission mechanisms. The processes of Fowler-Nordheim field emission, thermionic emission, and
photoemission are analyzed. Bulk-limited conduction mechanism and space charge
effect are also succinctly introduced.
Chapter 3 presents the fabrication, experimental results, and analysis of suspended
lateral two-terminal diode-like and four-terminal triode-like vacuum field emitters
for high-temperature environments. A description of early efforts as well as a
discussion of suggestions for improvement and avenues for future work are included.
Chapter 4 experimentally demonstrates the use of multi-tip field emission devices
for frequency conversion. Device design paradigms based on simulation results are
detailed. In addition, preliminary results illustrating the effect of praseodymium thin
film coating to reduce the work function and enhance emission current are reported.
Chapter 5 describes the efforts in combining Fowler-Nordheim emission with plasmonics to develop high-frequency optoelectronic devices. The design for efficient
photonic mode to hybrid plasmonic mode conversion as well as nanofocusing is

15
presented, along with the fabrication steps and results for the proposed structure.
Various ways to further optimize the architecture are examined.
Chapter 6 concludes the proposed research in nanoscale vacuum field emission
devices.
References
[1] J. W. Han and M. Meyyappan. “The device made of nothing.” IEEE Spectrum
51.7 (2014), pp. 30–35. doi: 10.1109/MSPEC.2014.6840798.
[2] P. A. Redhead. “The ultimate vacuum.” Vacuum 53.1-2 (1999), pp. 137–149.
doi: 10.1016/S0042-207X(98)00349-2.
[3] P. J. Angiolillo. “On thermionic emission and the use of vacuum tubes in the
advanced physics laboratory.” American Journal of Physics 77.12 (2009),
pp. 1102–1106. doi: 10.1119/1.3212463.
[4] P. A. Redhead. “The birth of electronics: Thermionic emission and vacuum.”
Journal of Vacuum Science & Technology A 16.3 (1998), pp. 1394–1401.
doi: 10.1116/1.581157.
[5] H. F. Dylla and S. T. Corneliussen. “John Ambrose Fleming and the beginning
of electronics.” Journal of Vacuum Science & Technology A 23.4 (2005),
pp. 1244–1251. doi: 10.1116/1.1881652.
[6] J. M. Miller. “Dependence of the input impedance of a three-electrode vacuum
tube upon the load in the plate circuit.” Scientific Papers of the Bureau of
Standards 15.351 (1920), pp. 367–385.
[7] G. Gaertner. “Historical development and future trends of vacuum electronics.” Journal of Vacuum Science & Technology B 30.6 (2012), p. 060801.
doi: 10.1116/1.4747705.
[8] P. A. Redhead. “Vacuum and the electron tube industry.” Journal of Vacuum
Science & Technology A 23.4 (2005), pp. 1252–1259. doi: 10 . 1116 / 1 .
1843822.
[9] W. F. Brinkman, D. E. Haggan, and W. W. Troutman. “A history of the
invention of the transistor and where it will lead us.” IEEE Journal of SolidState Circuits 32.12 (1997), pp. 1858–1865. doi: 10.1109/4.643644.
[10] G. Moore. “Cramming more components onto integrated circuits.” Electronics 38.8 (1965), p. 114.
[11] G. Moore. “Progress in digital integrated electronics.” Electron devices meeting 21 (1975), pp. 11–13.
[12] R. H. Dennard et al. “Design of ion-implanted MOSFET’s with very small
physical dimensions.” IEEE Journal of Solid-State Circuits 9.5 (1974), pp. 256–
268. doi: 10.1109/JSSC.1974.1050511.

16
[13] S. E. Thompson and S. Parthasarathy. “Moore’s law: The future of Si microelectronics.” Materials Today 9.6 (2006), pp. 20–25. doi: 10.1016/S13697021(06)71539-5.
[14] J. Kao, S. Narendra, and A. Chandrakasan. “Subthreshold leakage modeling
and reduction techniques.” In: Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design. San Jose, CA, USA, 2002,
pp. 141–148. doi: 10.1109/ICCAD.2002.1167526.
[15] W. Haensch et al. “Silicon CMOS devices beyond scaling.” IBM Journal of
Research and Development 50.4.5 (2006), pp. 339–361. doi: 10.1147/rd.
504.0339.
[16] K. Nose et al. “V𝑇 𝐻 -hopping scheme to reduce subthreshold leakage for
low-power processors.” IEEE Journal of Solid-State Circuits 37.3 (2002),
pp. 413–419. doi: 10.1109/4.987094.
[17] M. Bohr. “A 30 year retrospective on Dennard’s MOSFET scaling paper.”
IEEE Solid-State Circuits Society Newsletter 12.1 (2007), pp. 11–13. doi:
10.1109/N-SSC.2007.4785534.
[18] K. Rupp. 42 Years of microprocessor trend data. 2018. url: https://www.
karlrupp . net / 2018 / 02 / 42 - years - of - microprocessor - trend data/.
[19] J. M. Tendler et al. “POWER4 system microarchitecture.” IBM Journal of
Research and Development 46.1 (2002), pp. 5–25. doi: 10.1147/rd.461.
0005.
[20] S. Kaxiras and M. Martonosi. Computer architecture techniques for powerefficiency. Synthesis Lectures on Computer Architecture. Cham, Switzerland:
Springer, 2008. isbn: 978-1-59829-209-1.
[21] H. Esmaeilzadeh et al. “Dark silicon and the end of multicore scaling.”
In: Proceeding of the 38th annual international symposium on Computer
architecture. San Jose, California, USA, 2011, pp. 365–376. doi: 10.1145/
2000064.2000108.
[22] International roadmap for devices and systems™ 2021 Update. 2021. url:
[23] K. R. Shoulders. “Microelectronics using electron-beam-activated machining
techniques.” In: Advances in Computers. Vol. 2. Elsevier, 1961, pp. 135–293.
isbn: 978-0-12-012102-1.
[24] C. A. Spindt. “A thin-film field-emission cathode.” Journal of Applied Physics
39.7 (1968), pp. 3504–3505. doi: 10.1063/1.1656810.
[25] C. A. Spindt et al. “Field-emitter arrays for vacuum microelectronics.” IEEE
Transactions on Electron Devices 38.10 (1991), pp. 2355–2363. doi: 10.
1109/16.88525.

17
[26] R. N. Thomas and H. C. Nathanson. “Photosensitive field emission from
silicon point arrays.” Applied Physics Letters 21.8 (1972), pp. 384–386. doi:
10.1063/1.1654423.
[27] H. F. Gray, G. J. Campisi, and R. F. Greene. “A vacuum field effect transistor
using silicon field emitter arrays.” In: 1986 International Electron Devices
Meeting. 1986, pp. 776–779. doi: 10.1109/IEDM.1986.191310.
[28] G. Binnig et al. “Surface studies by scanning tunneling microscopy.” Physical
Review Letters 49.1 (1982), pp. 57–61. doi: 10.1103/PhysRevLett.49.57.
[29] J. L. Grand-Climent. “Technology, applications and market analysis for field
emitter displays (FEDs).” In: IEEE 6th International Vacuum Microelectronics Conference (IVMC). Newport, RI, USA, 1993, pp. 3–3. doi: 10.1109/
IVMC.1993.700239.
[30] A. A. Talin, K. A. Dean, and J. E. Jaskie. “Field emission displays: A critical
review.” Solid-State Electronics 45.6 (2001), pp. 963–976. doi: 10.1016/
S0038-1101(00)00279-3.
[31] J. W. Han, D. Moon, and M. Meyyappan. “Nanoscale vacuum channel transistor.” Nano Letters 17.4 (2017), pp. 2146–2151. doi: 10 . 1021 / acs .
nanolett.6b04363.
[32] A. A. G. Driskill-Smith, D. G. Hasko, and H. Ahmed. “Nanoscale field
emission structures for ultra-low voltage operation at atmospheric pressure.”
Applied Physics Letters 71.21 (1997), pp. 3159–3161. doi: 10 . 1063 / 1 .
120276.
[33] J. W. Han, J. S. Oh, and M. Meyyappan. “Cofabrication of vacuum field
emission transistor (VFET) and MOSFET.” IEEE Transactions on Nanotechnology 13.3 (2014), pp. 464–468. doi: 10.1109/TNANO.2014.2310774.
[34] P. G. Neudeck, R. S. Okojie, and L. Y. Chen. “High-temperature electronics
- A role for wide bandgap semiconductors?” Proceedings of the IEEE 90.6
(2002), pp. 1065–1076. doi: 10.1109/JPROC.2002.1021571.
[35] J. R. Schwank, M. R. Shaneyfelt, and P. E. Dodd. “Radiation hardness assurance testing of microelectronic devices and integrated circuits: Radiation environments, physical mechanisms, and foundations for hardness assurance.”
IEEE Transactions on Nuclear Science 60.3 (2013), pp. 2074–2100. doi:
10.1109/TNS.2013.2254722.
[36] R. H. Maurer et al. “Harsh environments: Space radiation environment, effects, and mitigation.” Johns Hopkins APL Technical Digest 28.1 (2008),
p. 13.
[37] T. Wong and S. Ingram. “Observational of Fowler-Nordheim tunnelling at
atmospheric pressure using Au/Ti lateral tunnel diodes.” Journal of Physics
D: Applied Physics 26.6 (1993), pp. 979–985. doi: 10.1088/0022-3727/
26/6/015.

18
[38] R. Arora and W. Mosch. High voltage and electrical insulation engineering.
Hoboken, NJ: John Wiley & Sons, Inc., 2011. isbn: 978-0-470-94790-6.
[39] I. S. Turmyshev, A. M. Murzakaev, and O. R. Timoshenkova. “Field emission
from metal tips covered by ultra-thin films of zirkonia energy spectra features
and current-voltage curves.” In: 25th International Symposium on Discharges
and Electrical Insulation in Vacuum (ISDEIV). Tomsk, Russia, 2012, pp. 595–
598. doi: 10.1109/DEIV.2012.6412590.
[40] D. R. Whaley et al. “Application of field emitter arrays to microwave power
amplifiers.” In: ICOPS 2000. IEEE Conference Record - Abstracts. 27th IEEE
International Conference on Plasma Science. New Orleans, LA, USA, 2000,
p. 122. doi: 10.1109/PLASMA.2000.854745.
[41] P. R. Schwoebel. “Field emission arrays for medical X-ray imaging.” Applied
Physics Letters 88.11 (2006), p. 113902. doi: 10.1063/1.2186388.
[42] P. Hommelhoff et al. “Field emission tip as a nanometer source of free electron
femtosecond pulses.” Physical Review Letters 96.7 (2006), p. 077401. doi:
10.1103/PhysRevLett.96.077401.

19
Chapter 2

THEORETICAL BACKGROUND OF ELECTRON EMISSION
Electron emission is the process by which electrons are extracted from the surface of
a condensed phase, such as a metal, into another (usually a vacuum) through the use
of an external energy source [1]. To free these bound electrons, an energy equal to the
work function has to be provided, which is the minimum energy needed to remove
an electron originally at the Fermi level from a solid to a point at rest in free space
just outside the surface [2]. There are three main methods of electron emission:
thermionic emission, field emission, and photoemission. In thermionic emission,
the material is heated to sufficiently high temperatures, which causes the electron
distribution to broaden so that some higher energy electrons can semi-classically
overcome the work function and emit into vacuum [3, 4]. In field emission, a
high electrostatic field is applied to the surface of the material allowing electrons
to quantum-mechanically tunnel through the surface potential barrier [5, 6]. In
photoemission, one or multiple photons are absorbed by the electron, providing
the required energy to exceed the interfacial potential barrier [7, 8]. Note that
a combination of several of these emission processes can also occur. Fig. 2.1
displays a general potential energy diagram as well as the Fermi-Dirac distribution
function, 𝑓 (𝐸), for the three individual processes of electron emission from a metal
into vacuum. 𝐸 𝐹 is the Fermi level, 𝜙 is the metal work function, 𝑈 is the vacuum
potential level, and 𝐹 is an externally applied electric field. In Fig. 2.1 (a), the FermiDirac distribution function is plotted for a sufficiently high temperature, which, for
illustration purposes, has been greatly exaggerated. In Figs. 2.1 (b) and (c), the
thermal distribution considers the metal to be at room temperature.
In the following sections, the various emission phenomena are analyzed, with a
special emphasis given to field emission, as it constitutes the underlying operating
mechanism of all devices considered in this thesis. Furthermore, bulk-limited
conduction mechanisms and the space charge effect are described.
2.1

Field Electron Emission

The phenomenon of field electron emission is quantitatively described by the FowlerNordheim (FN) theory, which was first introduced in 1928 by R. Fowler and L.
Nordheim [9]. The FN theory is based on the quantum tunneling of electrons

Figure 2.1: The three main electron emission mechanisms from metal to vacuum:
(a) thermionic emission, (b) field emission, and (c) photoemission. 𝐸 𝐹 is the Fermi
level, 𝜙 is the metal work function, 𝑈 is the vacuum potential level, 𝐹 is an externally
applied electric field, and 𝑓 (𝐸) is the Fermi-Dirac distribution function.

21
through the surface potential barrier when a high electric field is applied (107 − 108
V/cm). This high electric field causes the potential barrier at the metal-vacuum
interface to become narrow enough so that electrons have a significant probability of
tunneling into free-space. Thus, the FN theory essentially provides a mathematical
formula that depicts the dependence of the emission current density on the strength
of the applied external field.
To develop the FN theory, the following assumptions are made [10, 11]:
1. The Sommerfeld free-electron model with Fermi-Dirac statistics is used to
model the behavior of the electrons in the metal, which are in thermodynamic
equilibrium at the temperature 𝑇 = 0 K.
2. The metal surface is smooth, flat, and planar. In this way, the effects of
impurities, defects, and geometric shape of the emitter are ignored. This
assumption also reduces the problem to tunneling in one dimension.
3. The metal work function, 𝜙, is uniform. Since the applied electric field does
not penetrate the metal, the electron states within the metal are independent
of the external field. Outside the metal, the vacuum potential barrier can be
regarded as an exact triangular potential.
Consider a metal emitter in the 𝑦𝑧-plane occupying the half-space from 𝑥 = −∞ to
𝑥 = 0, as shown in Fig. 2.2. Since the field emission phenomenon is fundamentally
a quantum-mechanical tunneling process, the number of electrons incident on the
potential barrier and the probability of those electrons tunneling through the surface
barrier have to be determined. Therefore, the emission current density 𝐽𝐹 𝑁 is given
by [6]

𝑁 (𝐸 𝑥 )𝐷 (𝐸 𝑥 )𝑑𝐸 𝑥

𝐽𝐹 𝑁 =

(2.1)

where 𝑁 (𝐸 𝑥 )𝑑𝐸 𝑥 is the number of electrons that cross a unit area from left to right
in a direction parallel to the 𝑦𝑧-plane per unit time with normal energy 𝐸 𝑥 between
𝐸 𝑥 and 𝐸 𝑥 + 𝑑𝐸 𝑥 , and 𝐷 (𝐸 𝑥 ) is the probability of electrons tunneling through the
vacuum potential barrier with normal energy 𝐸 𝑥 . 𝑁 (𝐸 𝑥 ) is more commonly known
as the ‘supply function’ and 𝐷 (𝐸 𝑥 ) as the ‘transmission coefficient.’ Note that the
lower limit of integration is 0 because no electrons are incident from the vacuum
side, i.e., from right to left.

22
Ex
EF+ϕ

USN EF+ϕ-e /16 0x

EF +
EF +
ϕ-e
-eF -e 2/1
Fx

0x

vacuum

x1 x

Figure 2.2: Field emission model: FN (solid) and SN (dashed) barriers.

In the free-electron model, the conduction band electrons are treated as free particles
that do not interact with one another or with the ion cores. Considering the metal
to be a sufficiently large rectangular box of volume 𝐿 3 , where 𝐿 denotes the length
of its sides, and assuming Born-von Karman periodic boundary conditions, the
electronic states are described by plane waves given by [12, 13]
𝜓k (r) = √ 𝑒𝑖k·r
𝐿3

(2.2)

where the wave vector k is

2𝜋
(𝑛𝑥 , 𝑛 𝑦 , 𝑛 𝑧 )
and 𝑛𝑥 , 𝑛 𝑦 , and 𝑛 𝑧 are integers. In addition, the energy eigenvalues are
k=

𝐸k =

ℏ𝑘 2
2𝑚

(2.3)

(2.4)

where 𝑚 is the mass of the electron. This total electron kinetic energy 𝐸 can also
be separated into its normal 𝐸 𝑥 and transverse component 𝐸 𝑝 as [14]
𝐸 = 𝐸𝑥 +

ℏ𝑘 2𝑝
2𝑚

(2.5)

where 𝑘 2𝑝 = 𝑘 2𝑦 + 𝑘 2𝑧 . The wave function 𝜓k (r) is also an eigenstate of the momentum
operator p = ℏ𝑖 ∇ with eigenvalue
p = ℏk.

(2.6)

Thus, the group velocity v = 𝑚p can be expressed as
v=

ℏk

(2.7)

23
In order to calculate the supply function, we first define a supply function density
𝑛(𝐸, 𝐸 𝑥 ) as
𝑑𝑁 (𝐸 𝑥 )
𝑛(𝐸, 𝐸 𝑥 ) ≡
(2.8)
𝑑𝐸
With this definition, the supply function as 𝐿 goes to infinity can be expressed as
∫ ∞
𝑁 (𝐸 𝑥 )𝑑𝐸 𝑥 = 𝑑𝐸 𝑥
𝑛(𝐸, 𝐸 𝑥 )𝑑𝐸.
(2.9)
𝐸𝑥

The probability that an electron state with total energy 𝐸 will be occupied in an
ideal electron gas at equilibrium is given by the Fermi-Dirac distribution function

𝑓 (𝐸) =

1 + 𝑒 [(𝐸−𝐸 𝐹 )/𝑘 𝐵𝑇]

(2.10)

where 𝑘 𝐵 is the Boltzmann’s constant, 𝑇 is the absolute temperature, and 𝐸 𝐹 is the
Fermi level. In reciprocal space, the supply function density can be written as
𝑑3 𝑘
𝑛(𝐸, 𝐸 𝑥 )𝑑𝐸 𝑑𝐸 𝑥 = 2 𝑗𝑥 𝑓 (𝐸)
(2𝜋/𝐿) 3

(2.11)

where 𝑗𝑥 is the current density per unit cross-sectional area given by 𝑗𝑥 = 𝜌 𝑒 𝑣 𝑥 . 𝜌 𝑒
is the volume charge density, namely 𝑒/𝐿 3 , where 𝑒 is the electronic charge, and
𝑣 𝑥 is the component of the group velocity of the electron normal to the unit area
under consideration. Note that the factor of 2 in the equation is to account for spin
degeneracy. Thus, Eq. (2.11) becomes
𝑛(𝐸, 𝐸 𝑥 )𝑑𝐸 𝑑𝐸 𝑥 = 2

𝑒𝑣

𝑓 (𝐸)

𝑑3 𝑘
(2𝜋/𝐿) 3

𝑑3 𝑘
ℏ𝑘 𝑥
𝑓 (𝐸)
= 2𝑒
(2𝜋) 3

(2.12)

The differential 𝑑 3 𝑘 can also be expressed as 𝑑 3 𝑘 = 𝑑 2 𝑘 𝑝 𝑑𝑘 𝑥 . For a given 𝐸 𝑥 ,
𝑑 2 𝑘 𝑝 can be expressed in cylindrical coordinates as 𝑑 2 𝑘 𝑝 = 2𝜋𝑘 𝑝 𝑑𝑘 𝑝 or, in terms
of energy, as 𝑑 2 𝑘 𝑝 = 2𝜋 ℏ𝑚2 𝑑𝐸. Consequently, the supply density function can be
written as
𝑒𝑚
𝑛(𝐸, 𝐸 𝑥 )𝑑𝐸 𝑑𝐸 𝑥 = 2 3 𝑓 (𝐸)𝑑𝐸 𝑑𝐸 𝑥 ,
(2.13)
2𝜋 ℏ
which can be substituted back into Eq. (2.9) to yield
∫ ∞
𝑑𝐸
𝑒𝑚
𝑁 (𝐸 𝑥 ) = 2 3
(𝐸−𝐸
𝐹 )/𝑘 𝐵 𝑇
2𝜋 ℏ 𝐸 𝑥 1 + 𝑒

𝐸 −𝐸
𝑒𝑚𝑘 𝐵𝑇
− 𝑥𝑘 𝑇𝐹
ln 1 + 𝑒
(2.14)
2𝜋 2 ℏ3

24
The next step is to calculate the transmission coefficient. The most widely used
approach is to approximate 𝐷 (𝐸 𝑥 ) utilizing the Wentzel-Kramers-Brillouin (WKB)
method [15].
The general problem is to find solutions to the time-independent Schrödinger equation for the exact triangular potential shown in Fig. 2.2 given by
𝑈 (𝑥) = (𝐸 𝐹 + 𝜙 − 𝑒𝐹𝑥)𝜃 (𝑥)

(2.15)

where 𝜃 (𝑥) is the Heaviside step function. With this potential, the Schrödinger
equation for 𝑥 > 0 becomes
2
𝑝 2 (𝑥)
𝜓(𝑥) = 0
(2.16)
𝑑𝑥 2
ℏ2
where 𝑝(𝑥) = {2𝑚 [𝐸 −𝑈 (𝑥)]}1/2 . If the potential 𝑈 (𝑥) varies slowly in comparison
to de Broglie wavelength 𝜆 given by 𝜆 = 2𝜋ℏ/𝑝(𝑥), it can be expected that over a
region small compared to the distance over which 𝑈 (𝑥) varies considerably, 𝜓 will
closely approximate the free particle state. Yet, since 𝜆 changes slowly with 𝑥, the
change in wavelength over a length 𝜆 is
𝛿𝜆 =

𝑑𝜆
𝜆.
𝑑𝑥

(2.17)

In the classical domain, this only makes sense if 𝛿𝜆 ≪ 𝜆, so that
𝛿𝜆
(𝑑𝜆/𝑑𝑥) · 𝜆

𝑑𝜆
≪ 1.
𝑑𝑥

(2.18)

The expression 𝑑𝜆
𝑑𝑥 can also be written as
𝑑𝜆
2𝜋ℏ 𝑑𝑝
=− 2
𝑑𝑥
𝑝 𝑑𝑥
2𝜋ℏ
(2𝑚) 1/2
𝑑𝑈
1/2
2𝑚 [𝐸 − 𝑈 (𝑥)] 2[𝐸 − 𝑈 (𝑥)]
𝑑𝑥

2𝜋𝑚ℏ 𝑑𝑈
𝑝 3 𝑑𝑥

(2.19)

Therefore, the semi-classical calculation provided by the WKB method is valid as
long as [16]
𝛿𝜆
2𝜋𝑚ℏ 𝑑𝑈
≪ 1.
(2.20)
𝑝 3 𝑑𝑥

25
The ansatz of the solution to Schrödinger equation that is valid in the near-classical
domain is assumed to be of the form [17, 18]
𝑖𝑆 ( 𝑥)

(2.21)

𝜓(𝑥) = 𝑒 ℏ

with 𝑆(𝑥) an unknown complex function. Inserting this function into Eq. (2.16)
yields
2
1 𝜕𝑆
𝑖 𝜕 2 𝑆 𝑝 2 (𝑥)
= 0.
(2.22)
ℏ 𝜕𝑥
ℏ 𝜕𝑥 2
ℏ2
Expanding 𝑆(𝑥) in powers of ℏ gives
𝑆(𝑥) = 𝑆0 (𝑥) + ℏ𝑆1 (𝑥) + ℏ2 𝑆2 (𝑥) + . . .

(2.23)

In the limit ℏ →
− 0, 𝜆 tends to zero, so the spatial variation of the potential can be
regarded to be small. Inserting Eq. (2.23) into Eq. (2.22) and grouping the terms
with the same power of ℏ gives
2#
𝜕𝑆0 𝜕𝑆1
𝜕𝑆
1 𝜕 2 𝑆0
𝑝 −
−2
+ O (ℏ0 ) = 0.
(2.24)
𝜕𝑥
ℏ 𝜕𝑥 2
𝜕𝑥 𝜕𝑥
ℏ2
Note that the coefficients for each power of ℏ must vanish independently. The ℏ−2
term gives
2
𝜕𝑆0
= 𝑝2
(2.25)
𝜕𝑥
or
∫ 𝑥1
| 𝑝(𝑥)| 𝑑𝑥.
𝑆0 (𝑥) = ±
(2.26)
𝑥0

The ℏ−1 terms yields
𝜕 2 𝑆0
𝜕𝑆0 𝜕𝑆1
=2
𝜕𝑥 𝜕𝑥
𝜕𝑥
Substituting Eq. (2.26) into this expression gives

𝑆1 (𝑥) = 𝑖 ln [| 𝑝(𝑥)|] 1/2 .

(2.27)

(2.28)

In this way, 𝜓(𝑥) becomes
𝜓(𝑥) = 𝐶𝑒

− ln [ 𝑝(𝑥)] 1/2

± ℏ𝑖

∫𝑥

1 | 𝑝(𝑥)|𝑑𝑥
𝑥0

± ℏ𝑖 𝑥 1 | 𝑝(𝑥)|𝑑𝑥
[ 𝑝(𝑥)] 1/2

(2.29)

26
where the constant 𝐶 = 𝜓(𝑥 0 ) 𝑝(𝑥 0 ) 1/2 is found by setting 𝑥 = 𝑥 0 . The transmission
coefficient is calculated by
𝑗tra
𝐷 (𝐸 𝑥 ) =
(2.30)
𝑗inc
where 𝑗tra and 𝑗inc are the transmitted and incident probability current densities,
respectively. In general [19, 20],

𝑗 𝛼 = Re(𝜓 † 𝑣ˆ 𝛼 𝜓)

(2.31)

𝑖ℏ
𝜕 †
† 𝜕
𝑗𝛼 =
𝜓𝛼 𝜓𝛼 − 𝜓𝛼 𝜓𝛼
2𝑚
𝜕𝑥
𝜕𝑥

(2.32)

which gives the formula

𝐷 (𝐸) = exp −
so that

𝐷 (𝐸 𝑥 ) = exp −

∫ 𝑥1
| 𝑝(𝑥)| 𝑑𝑥

(2.33)

𝑥0

∫ 𝑥1
{2𝑚 [𝑈 (𝑥) − 𝐸 𝑥 ]}

1/2

𝑑𝑥

(2.34)

𝑥0

𝐹 −𝐸 𝑥
. In order to evaluate
where the limits of integration are 𝑥 0 = 0 and 𝑥 1 = 𝜙+𝐸𝑒𝐹
the definite integral
∫ 𝐸𝐹 +𝜙−𝐸𝑥
𝑒𝐹
𝐷 (𝐸 𝑥 ) = exp −
{2𝑚 [𝐸 𝐹 + 𝜙 − 𝑒𝐹𝑥 − 𝐸 𝑥 ]}1/2 𝑑𝑥
(2.35)
ℏ 0

𝑒𝐹
let 𝑦 ≡ 𝐸 𝐹 +𝜙−𝐸
𝑥. Eq. (2.35) then becomes
#∫
√ !"
2 2𝑚 (𝐸 𝐹 + 𝜙 − 𝐸 𝑥 ) 3/2
𝐷 (𝐸 𝑥 ) = exp −
(1 − 𝑦) 1/2 𝑑𝑦
𝑒𝐹
( √ !"
#
𝑦=1
2 2𝑚 (𝐸 𝐹 + 𝜙 − 𝐸 𝑥 ) 3/2 2
(1 − 𝑦) 3/2
= exp
𝑒𝐹
𝑦=0
4 2𝑚 (𝐸 𝐹 + 𝜙 − 𝐸 𝑥 ) 3/2
= exp −
3ℏ
𝑒𝐹

Note that
(𝐸 𝐹 + 𝜙 − 𝐸 𝑥 )

3/2

=𝜙

3/2

𝐸𝑥 − 𝐸 𝐹
1−

(2.36)

3/2

(2.37)

The approximation (1 − 𝑥) 3/2 ≈ 1 − 23 𝑥 can be used to expand 𝐸 𝑥 at 𝐸 𝐹 so that
3/2

𝐸𝑥 − 𝐸 𝐹
3 𝐸𝑥 − 𝐸 𝐹
3/2
3/2
1−
≈𝜙
1−
= 𝜙3/2 − (𝐸 𝑥 − 𝐸 𝐹 )𝜙1/2 .

(2.38)

27
Let 𝑏 𝐹 𝑁 ≡ 3𝑒

√︃

2𝑚
and 𝑑1𝐹 ≡ 2
ℏ2

√︃

2𝑚 𝜙1/2
. The transmission coefficient then becomes
ℏ2 𝑒𝐹

𝑏 𝐹 𝑁 𝜙3/2
𝐸𝑥 − 𝐸 𝐹
𝐷 (𝐸 𝑥 ) ≈ exp −
exp
𝑑𝐹

(2.39)

The final step is to combine the results of Eq. (2.14) and Eq. (2.39) with Eq. (2.1)
to obtain the field emission current density
∫ ∞

𝑒𝑚𝑘 𝐵𝑇
𝑏 𝐹 𝑁 𝜙3/2
𝐸𝑥 − 𝐸 𝐹
𝐸𝑥 − 𝐸 𝐹
𝐽𝐹 𝑁 ≈
exp −
exp
ln 1 + exp −
𝑑𝐸 𝑥 .
𝑑𝐹
𝑘 𝐵𝑇
2𝜋 2 ℏ3
(2.40)
i
Notice that near 𝑇 = 0K, the expression 𝑘 𝐵𝑇 ln 1 + exp − 𝐸 𝑘𝑥 −𝐸
can be approx𝐵𝑇
imated as

𝐸𝑥 − 𝐸 𝐹
𝐸𝑥 − 𝐸 𝐹
𝑘 𝐵𝑇 ln 1 + exp −
≈ 𝑘 𝐵𝑇 −
𝑘 𝐵𝑇
𝑘 𝐵𝑇
= 𝐸 𝐹 − 𝐸𝑥 .

(2.41)

As the emission process is dominated by electrons near the Fermi energy, the
emission current density becomes
∫ 𝐸𝐹
𝑒𝑚
𝑏 𝐹 𝑁 𝜙3/2
𝐸𝑥 − 𝐸 𝐹
𝐽𝐹 𝑁 ≈ 2 3 exp −
(𝐸 𝐹 − 𝐸 𝑥 )𝑑𝐸 𝑥
exp
𝑑𝐹
2𝜋 ℏ

𝑒𝑚
𝑏 𝐹 𝑁 𝜙3/2
− 𝑑𝐹
− 𝑑𝐹
= 2 3 exp −
𝑑𝐹 − 𝑑𝐹 𝐸𝐹 𝑒 𝐹 − 𝑑𝐹 𝑒 𝐹 .
(2.42)
2𝜋 ℏ

− 𝐹

𝑒 𝑚
For field emission, 𝐸 𝐹 ≫ 𝑑 𝐹 , thus 𝑒 𝑑𝐹 ≈ 0. Also, let us define 𝑎 𝐹 𝑁 ≡ 16𝜋
2ℏ .
Therefore, the current density ultimately becomes
𝐹2
𝑏 𝐹 𝑁 𝜙3/2
𝐽𝐹 𝑁 ≈ 𝑎 𝐹 𝑁
exp −
(2.43)

This is the basic field emission equation, also known as the FN equation. The
constants 𝑎 𝐹 𝐵 and 𝑏 𝐹 𝐵 given by
𝑒3 𝑚
≈ 1.54[𝜇A] [eV] [V] −2
16𝜋 2 ℏ
√︂
4 2𝑚
𝑏𝐹𝑁 =
≈ 6.83[V] [nm] −1 [eV] −3/2
3𝑒 ℏ
𝑎𝐹𝑁 =

are the so-called first and second FN field emission constants, respectively. It is
important to notice that the two most important variables in field emission are the

(a)

(b)

Figure 2.3: Emission current density as (a) a function of electric field for various
work function values and (b) as a function of work function for various electric field
values.
magnitude of the electric field and the work function. Fig. 2.3 shows the effect of
these two parameters on the emission characteristic.
As we can see in Eq. (2.43), the FN equation relates current density and electric
field intensity. Unfortunately, these quantities are hard to measure experimentally,
especially at the nanoscale. Therefore, Eq. (2.43) is usually expressed in terms of
the applied voltage 𝑉 and the measured current 𝐼 [21]. The applied voltage is related
to the electric field by
𝐹 = 𝛽𝑉
(2.44)
where 𝛽 is the so-called field factor. As the emission does not take place from a
single point on the emitter but rather an area, the current is obtained by integrating
the current density 𝐽𝐹 𝑁 over the whole emitting surface
𝐼=
𝐽𝐹 𝑁 𝑑𝑆
(2.45)
(𝑆)

where 𝑆 is the total surface of the emitting area. Often, it is assumed that the
observable current is simply proportional to its density, i.e.,
𝐼 = 𝑆𝐽𝐹 𝑁 .

(2.46)

It is important to mention that the emission current density depends on the position
at the emitter, so the relation shown above is just an estimate based on the fact that
the derivation of the FN equation ignored the emitter dimension and shape. A more
detailed study on the effective emission area is given in [22–25].

29
With these two relations, Eq. (2.43) is written as
(𝛽𝑉) 2
𝑏 𝐹 𝑁 𝜙3/2
𝐼 = 𝑎𝐹𝑁 𝑆
exp −
𝛽𝑉

(2.47)

In practice, measured field electron emission IV data is often analysed by means of
the so-called FN plot, which allows us to quickly distinguish the field emission characteristic from other emission mechanisms. The FN plot is obtained by linearizing
Eq. (2.47) to [26, 27]

𝑎 𝐹 𝑁 𝑆𝛽2
𝑏 𝐹 𝑁 𝜙3/2 1
(2.48)
ln 2 = ln
In the FN plot, the 𝑦-axis is given by ln 𝐼/𝑉 2 and the 𝑥-axis by (1/𝑉), so that the
emission data in this semi-logarithmic plot forms a straight line. The slope is given
by
𝑏 𝐹 𝑁 𝜙3/2
slope = −
(2.49)
and the 𝑦-intercept by
𝑎 𝐹 𝑁 𝑆𝛽2
𝑦−intercept = ln
(2.50)
Notice that there are three variables present in these two parameters: the work
function 𝜙, the emission area 𝑆, and the field factor 𝛽. If one of them is known a
priori, the other two can be estimated from the values of the slope and intercept.
According to classical electrodynamics, the macroscopic electric field 𝐹𝑀 between
two planar structures, e.g., a parallel-plate capacitor, is given by 𝐹𝑀 = 𝑉/𝑑, where
𝑑 is the separation between the two electrodes. However, it has been experimentally
found that certain geometries support electron emission at fields smaller than the
expected 𝐹𝑀 . Sharp structures, such as lightning rods, can distort and bend the
equipotential lines that exist from 𝐹𝑀 in the proximity of the sharpened point,
leading to an augmented electric field. The ratio between the local electric field 𝐹
and the macroscopic field 𝐹𝑀 is known as the field enhancement factor 𝛾
𝛾=

𝐹𝑀

(2.51)

The local field 𝐹 can also be expressed as a function of the distance between the
emitter and collector electrodes, 𝑑, by the relation 𝐹 = 𝛾 𝑉𝑑 [28].
So far, the derivation of the FN equation has assumed a simple triangular barrier.
However, a more realistic model should include the exchange-and-correlation interaction between the electron just outside the emitter and the emitter surface [29].

30
In electrostatics, this image potential arises because an escaped electron located at
a distance 𝑥 away from the surface of the metal induces a charge distribution on
the surface to screen the electric field of the electron inside the bulk. Effectively,
this surface charge behaves as if there were a positive electron equidistant from the
emitter surface. As a consequence, this interaction modifies the barrier potential
function so that outside the surface of the metal it becomes
𝑈 (𝑥) = 𝐸 𝐹 + 𝜙 − 𝑒𝐹𝑥 −

𝑒2
16𝜋𝜖 0 𝑥

(2.52)

where 𝜖0 is the vacuum permittivity [30]. This barrier potential is often referred to
as the Schottky-Nordheim (SN) barrier. As seen in Fig. 2.2, the addition of this
image potential has the effect of rounding the triangular potential, so that the peak
3 1/2
𝑒 𝐹
. The emission current density can
of the barrier is reduced by Δ𝑈𝑆𝑁 ≡ 4𝜋𝜖
also be derived using the WKB approximation to obtain
𝑏 𝐹 𝑁 𝜙3/2
𝐹2
exp −𝜈(𝑦 𝐹 )
𝐽𝐹 𝑁 = 𝑎 𝐹 𝑁
(2.53)
[𝜏(𝑦 𝐹 )] 2 𝜙
where 𝜏(𝑦) and 𝜈(𝑦) are barrier shape correction factors that have been approximated
to [31]

𝜈(𝑦) ≈ 1 − 𝑦 2 + 𝑦 2 ln 𝑦
𝜏(𝑦) ≈ 1 + 𝑦 2 − 𝑦 2 ln 𝑦
with
𝑦=
(𝐸 𝐹 + 𝜙 − 𝐸 𝑥 )

(2.54)
(2.55)
√︄

𝑒3 𝐹
4𝜋𝜖 0

(2.56)

and noting that 𝑦 𝐹 indicates that 𝑦 is evaluated at 𝐸 𝑥 = 𝐸 𝐹 . The SN barrier is
considered to be a better model, as it has been shown that the basic FN equation
under-predicts current densities by a factor of order 100, and also leads to incorrect
estimates of the emitting area [32].
Furthermore, recall that the temperature was assumed to be 0 K so mere field emission was studied. This assumption has been shown to be accurate up to well above
room temperature [33, 34]. Because of this approximation, the emission process is
commonly known as ‘cold field emission.’ If the effects of temperature on the FN
model were to be considered, Eq. (2.43) can be modified to include a correction

Current Density J FN,T [nA/nm2]

60
50

Electric eld F

8 V/nm
9 V/nm
10 V/nm

30
20
10

300

600

900

1200

1500

Temperature [K]

Figure 2.4: Emission current density as a function of temperature for various field
values and a representative work function of 4.5 eV.
factor Θ𝐹 𝑁 (𝑇) so that the field emission current density at finite temperature 𝐽𝐹 𝑁,𝑇
becomes
𝑘 𝐵𝑇 𝜋/𝑑 𝐹
𝐽𝐹 𝑁
𝐽𝐹 𝑁,𝑇 =
sin (𝑘 𝐵𝑇 𝜋/𝑑 𝐹 )

(2.57)

with Θ𝐹 𝑁 (𝑇) ≡ sin𝑘(𝑘𝐵𝑇𝐵𝜋/𝑑
𝑇 𝜋/𝑑 𝐹 ) . Fig. 2.4 illustrates the effects of finite temperature on
the characteristics of field emission for various electric fields. We can see that even
at relatively high temperatures, the variation in 𝐽𝐹 𝑁,𝑇 is small so temperature effects
can usually be neglected.

2.2

Thermionic Emission

The first equation for the emission current density from metal surfaces was proposed by O. Richardson using the Clausius-Clapeyron equation [35]. It was later
modified by S. Dushman using quantum mechanics theory, leading to the renowned
Richardson-Dushman (RD) equation for thermionic emission [36, 37], given by
(2.58)
𝐽 𝑅𝐷 = 𝐴𝑇 exp −
𝑘 𝐵𝑇
where 𝐴 is a constant equal to
𝐴=

𝑒𝑚𝑘 2𝐵
2𝜋 2 ℏ3

≈ 120[A] [cm] −2 [K] −2 .

(2.59)

32
Eq. (2.58) is derived assuming that the electrons inside the metal behave as free particles and that the Fermi-Dirac distribution can be replaced by Maxwell-Boltzmann’s
distribution because at high temperatures only the electrons in the thermal tail of
the supply function can escape from the metal, i.e., electrons with 𝐸 ≫ 𝐸 𝐹 [38].
As we can see in Eq. (2.58), thermionic emission is strongly dependent on temperature. Therefore, to obtain significant electron emission, the metal emitter must
be held at sufficiently high temperatures (over 1000 K). Also, similarly to FN,
thermionic emission depends on work function, so materials with low work functions are desired to enhance emission.
2.3

Photoemission

The first experiments on the photoelectric effect were done by H. Hertz in 1887, years
before the discovery of the electron by J. Thompson. In his experiment, he generated
electromagnetic waves by spark discharge using an induction coil connected to a pair
of capacitor plates attached to two metal spheres. The primary spark generated by
this apparatus would then induce a secondary spark in a receiving circuit consisting
of a micrometer spark gap attached to an open ring of wire. To see the spark better,
he placed the secondary spark gap in a dark box and noticed that the voltage at which
the sparking took place changed. He concluded that light produced by the primary
spark was affecting the receiving spark. By using a quartz prism, he dispersed the
radiation from various light sources and discovered that ultraviolet radiation was the
cause for the increase in sparking. At the time, he could not explain his observations
[39, 40]. Further experiments were later carried out by W. Hallwachs and P. Lenard.
Yet, they were only explained in 1905 with A. Einstein’s quantum theory of the
photoelectric effect, for which he received the Nobel Prize in 1921 [41, 42].
In his article, Einstein suggested that the energy of light is not distributed continuously in space as J. Maxwell’s theory dictated, but rather quantized [43]. The
derivation of the concept of a quantum of light—the photon—was not based on
experimental results but rather on statistical mechanics. Specifically, he considered
that an isothermal change in volume from an initial volume 𝑉1 to a final volume 𝑉2
would cause a change in entropy due to radiation equal to (𝑘 𝐵 𝑑𝐸/ℎ𝜈) ln (𝑉1 /𝑉2 ),
where 𝑑𝐸 is the total energy of the radiation in a frequency interval 𝜈 to 𝜈 + 𝑑𝜈, in
which Wien’s radiation law is satisfied. This expression showed the same logarithmic dependence on volume as the equation for the entropy of a monoatomic ideal gas
as long as the number of particles in the gas is 𝑑𝐸/ℎ𝜈, leading Einstein to conclude

33
that light must consist of particles with energy ℎ𝜈. This concept allowed him to
explain several experiments, such as photoluminescence, the ionization of gases by
ultraviolet radiation, and black-body radiation, which could not be explained using
continuous spatial functions to describe light. He also ventured to explain the energy
transfer from photons to electrons, leading him to the fundamental equation that is
now known as the “photoelectric effect,” given by

𝐸 𝑘𝑖𝑛 = ℎ𝜈 − 𝑃

(2.60)

where 𝐸 𝑘𝑖𝑛 is the maximum kinetic energy of the emitted electrons and 𝑃 is the
amount of work an electron must do to leave a solid and is characteristic of that solid,
which is currently known as the work function 𝜙. Even though this linear frequency
relation was consistent with Lenard’s experiments, which Einstein referred to in his
publication, it was not until several years later that experiments conducted by A.
Hughes, O. Richardson, K. Compton, and R. Millikan finally led to Einstein’s model
being generally accepted by the scientific community.
In the photoelectric effect, the absorption of photons by bound electrons in solids
causes these electrons to transition to higher energy levels. If the energy of the
photon is sufficiently large to overcome the material work function, the excited
electrons can travel above the potential barrier and become free electrons. This is
commonly referred to as photoemission [44, 45]. In the simplest case, one photon
provides the required energy to overcome the work function, as shown in Fig. 2.5
(a). If multiple photons are absorbed to lift the electron over the potential barrier, the
process is known as multi-photon emission. Moreover, in the special case where a
greater number of photons than required for emission are absorbed, i.e., 𝑁 > 𝜙/ℎ𝜈,
the process is termed above-threshold photoemission. Both cases of multi-photon
emission are depicted in Fig. 2.5 (b). It has been shown that in multi-photon
emission, the photoelectron current density 𝐽𝑚𝑢𝑙𝑡𝑖 is proportional to the nth power
of laser intensity 𝐼, i.e., 𝐽𝑚𝑢𝑙𝑡𝑖 ∝ 𝐼 𝑁 , where 𝑁 denotes the total number of photons
absorbed [46–48].
In addition, an electron can be emitted into free space even if 𝑁 ℎ𝜈 < 𝜙. In this
case, the electron is promoted to a non-equilibrium electron distribution by the
absorption of one or more photons and tunnels through the potential barrier, which
has been narrowed by an applied DC bias [49, 50]. The emitted current density can

Multiphoton Emission

Photoemission

Above-Threshold Photoemission

vacuum

(a)

(b)

Photo-Assisted
Field Emission

EF
vacuum

(c)

Optical Field
Emission

vacuum

(d)

Figure 2.5: Electron emission processes from metal to vacuum under optical illumination: (a) single photon photoemission (photoelectric effect), (b) multi-photon
emission and above-threshold photoemission, (c) photo-assisted field emission, and
(d) optical field emission.

be described using Eq. (2.43) with an effective work function 𝜙 𝑒 𝑓 𝑓 = 𝜙 − 𝑁 ℎ𝜈.
This process is called photo-assisted field emission and is illustrated in Fig. 2.5 (c).
Furthermore, there is another way in which an electron can interact with an optical
field. If the laser intensity is sufficiently high, the local electric field associated with
the optical field modulates the potential barrier such that during part of the optical
cycle, the barrier becomes narrow enough to allow an electron from the Fermi level
to tunnel through it [51–53]. This process is known as optical field emission and is
displayed in Fig. 2.5 (d). The emitted current density can also be expressed using
Eq. (2.43), where the total field is now given by the sum of the DC and AC electric
fields: 𝐹 → 𝐹 + 𝐹𝑙𝑎𝑠𝑒𝑟 .

35
To distinguish between emission regimes, L. Keldysh proposed a dimensionless
adiabaticity parameter 𝛾 𝑘 given by the ratio of the optical driving frequency 𝜔 to
the tunneling frequency 𝜔𝑡 [54]

𝛾𝑘 =

𝜔𝑡

(2.61)

The tunneling frequency can be determined by the mean free time of the electron traversing a barrier of width 𝑙 = 𝜙/𝑒𝐹𝑙𝑎𝑠𝑒𝑟 with an average electron velocity
proportional to (𝜙/𝑚) 1/2 , thus allowing 𝛾 𝑘 to be expressed as
√︁
𝜔 2𝑚𝜙
𝛾𝑘 =
𝑒𝐹𝑙𝑎𝑠𝑒𝑟

(2.62)

In addition, 𝛾 𝑘 can be written in terms of the ponderomotive energy of electrons 𝑈 𝑝 ,
i.e., the cycle-averaged kinetic energy of a free electron in an alternating electric
field
√︄
𝛾𝑘 =

2𝑈 𝑝

(2.63)

𝑒2 𝐹 2

𝑙𝑎𝑠𝑒𝑟
with 𝑈 𝑝 = 4𝑚𝜔
2 . Therefore, for relatively weak fields, the field decay length is
larger than the quiver amplitude, yielding 𝛾 𝑘 ≫ 1 [55]. In this regime, electron
emission is governed by photoemission processes. In the strong field regime, the
ponderomotive energy becomes comparable to the electron binding energy, and
𝛾 𝑘 < 1. In this limit, the electron tunneling adiabatically follows the instantaneous
optical field, and the dominant process is optical field emission [56].

2.4

Bulk Conduction in Dielectrics

The conduction mechanisms studied so far have focused on the metal-vacuum interface. However, practical electronic devices are fabricated on top of a substrate,
which is generally chosen to be an insulator. When high temperatures or high
electric fields are applied, electron transport through the supporting insulator can
occur. One of the most common bulk-limited conduction mechanisms in dielectric
films is Frenkel-Poole (FP) emission [57]. In this emission mechanism, electron
transport is assisted by traps from stored charges or structural defects. In terms
of trap topology, the trap sites are positively charged when empty and uncharged

36
when filled so that the electron interaction with the positively charged trap leads to
a Coulombic potential barrier as shown in Fig. 2.6 [58].
If the trap sites are sufficiently close together, the wave function of the electrons
can overlap so that the charge carriers can “jump” between trapping centers. In
a system of trapping centers at equilibrium, the emission and capture processes
are balanced so that there is a constant density of localized electrons. Assuming
thermally activated emission and using the principle of detailed equilibrium, the
emission rate from the localized levels within the band gap 𝑒𝑇 is related to the
ionization energy 𝐸𝑖 by an Arrhenius-type relationship [59]
𝐸𝑖
(2.64)
𝑒𝑇 = 𝐴𝑇 exp −
𝑘 𝐵𝑇
where 𝐴 is a constant.
When an external potential +𝐹𝑥 across the insulator is applied, the Coulombic
potential energy of an electron in a trapping center is reduced. Thus, the potential
energy of the electron is given by
𝑈 (𝑟) = −

𝑒2
− 𝑒𝐹𝑥
4𝜋𝜖𝑟 𝜖0𝑟

(2.65)

where 𝜖𝑟 is the effective dielectric constant of the insulator [60]. Notice that the
external electric field distorts the electrostatic interaction potential between the

elec ric field F

rmax
conduction band edge

b tr
lom 0
F=

FP emission
eU0

Co
ap
tr
om 0
ul F

er=0

Figure 2.6: Schematic of FP emission: Coulombic trap potential at equilibrium
(grey) and under an external field (green).

37
electron and trap center, such that the barrier is lowered in the direction of the
applied field, as illustrated in Fig. 2.6. Consequently, the amount of energy required
by an electron to escape the trap is reduced. This field-assisted thermal ionization
of trapped electrons into the conduction band is known as FP emission [61, 62].
In the absence of the externally applied electric field, the potential barrier has a
maximum value of 𝑈max,F=0 = 0 at an infinite distance from the trap. In the presence
of the applied field, the maximum value of the potential barrier 𝑈max,F≠0 occurs at
a distance
√︂
𝑟 max =

4𝜋𝜖𝑟 𝜖0 𝐹

(2.66)

and the potential barrier is reduced by an amount Δ𝑈 given by
Δ𝑈 = 𝑈max,F≠0 − 𝑈max,F=0
= −𝑒𝐹𝑟 max
𝑒3
=−
𝜋𝜖𝑟 𝜖0

1/2

(2.67)

𝐹.

The ionization energy becomes field-dependent so that
𝑒3 𝐹
𝐸𝑖 (𝐹) = 𝐸𝑖 (0) −
𝜋𝜖𝑟 𝜖0

1/2
(2.68)

where 𝐸𝑖 (0) = 𝐸𝑇 is the binding energy of the electron on the trap when 𝐹 = 0. As
a consequence, the emission rate given in (2.64) becomes
Δ𝑈
𝑒𝑇 (𝐹) = 𝑒𝑇 (0) exp
(2.69)
𝑘 𝐵𝑇
As the emission rate is proportional to the electrical conductivity, by making use of
a modified form of Ohm’s law, the FP current density is proportional to

√︁

 −𝑒 𝑈0 − 𝑒𝐹/𝜋𝜖𝑟 𝜖0 
𝐽𝐹𝑃 ∝ 𝐹 exp 
(2.70)
𝑘 𝐵𝑇
where 𝑒𝑈0 (= 𝐸𝑖 (0)) is the ionization potential at zero field. Because FP emission
is caused by thermal activation when an external field is applied, this conduction
mechanism is often found at both high fields and high temperatures. In a similar

38
fashion to FN emission, the FP effect can be identified by the so-called FP plot
where ln (𝐽𝐹𝑃 /𝐸) versus 𝐸 1/2 is plotted and a straight line indicates FP emission.
In addition, two other bulk-limited conduction mechanisms in dielectrics include
hopping conduction and Ohmic conduction. In hopping conduction, trapped electrons “hop” between trap sites by tunneling through them. In this way, unlike in FP
emission where electrons in trap sites acquire sufficient thermal energy to overcome
the potential barrier, in hopping conduction the electrons tunnel through trap sites
since they lack the necessary energy to surpass the trap barrier. Mathematically, the
expression for hopping conduction is

𝑒𝑎𝐹
𝐸𝑎
𝐽ℎ𝑜 𝑝 = 𝑒𝑛𝑎𝜈𝑇 exp
𝑘 𝐵𝑇 𝑘 𝐵𝑇

(2.71)

where 𝑛 is the electron concentration in the conduction band of the dielectric, 𝑎 is
the mean spacing between trap sites, 𝜈𝑇 is the frequency of thermal vibration of
electrons at trap sites, and 𝐸 𝑎 is the activation energy of traps.
Lastly, in Ohmic conduction, a small number of electrons from the valence band
of the dielectric or some impurity level become thermally activated and are excited
to the conduction band. The current density is linearly proportional to the applied
electric field and the relationship is defined as

𝐽𝑜ℎ𝑚𝑖𝑐 = 𝑒𝑛𝜇𝐹

(2.72)

where 𝜇 is the electron mobility. Since the band gap is large for a considerable
intrinsic conductivity, the contribution from this conduction mechanism is very
small and mainly detected at small fields [63].
2.5

Space Charge Effects

As described above, there are multiple ways in which the emission current from
a cathode can increase, such as higher emitter temperature, larger applied electric
fields, and radiation. However, as this current increases, the emitted electrons form
a cloud of negative charge in the vicinity of the cathode, which in turn limits the
electric field at the emitting surface. This is known as the space charge effect [30,
64]. Note that space charge is not an emission mechanism but rather a current
limitation mechanism.

39
The effects of space charge on thermionic emission were first recognized by C. Child
and I. Langmuir [65, 66]. They solved the one-dimensional Poisson’s equation for
a planar diode geometry subject to a zero electric field on the cathode surface
boundary condition, and (neglecting the effect of initial velocities of the electrons)
obtained the following relation for the maximum steady-state current density:
√ √︂
𝑒 𝑉 3/2
4 2
𝐽𝐶 𝐿 =
𝜖0
𝑚 𝑑2

(2.73)

where 𝑑 is the diode gap separation. This equation is known as the Child-Langmuir
law.
For field emission, the boundary condition of zero cathode field is not valid. A
detailed mathematical treatment on space charge effects in field emission can be
found in [67, 68]. It has been shown that, when the applied field is large compared
with the value required for significant field emission, the emission current density
approaches the Child-Langmuir law. In terms of the FN plot, the effects of space
charge can be seen as the characteristic straight line turning over at high fields.
However, in real-life emitters, the space charge limited regime is hard to attain
because Joule heating and electromigration in the emitter would ultimately lead to
device self-destruction.
References
[1] K. L. Jensen. “General formulation of thermal, field, and photoinduced electron emission.” Journal of Applied Physics 102.2 (2007), p. 024911. doi:
10.1063/1.2752122.
[2] A. Kahn. “Fermi level, work function and vacuum level.” Materials Horizons
3.1 (2016), pp. 7–10. doi: 10.1039/C5MH00160A.
[3] S. Dushman. “Thermionic emission.” Reviews of Modern Physics 2.4 (1930),
pp. 381–476. doi: 10.1103/RevModPhys.2.381.
[4] W. B. Nottingham. “Thermionic emission.” In: Electron-Emission Gas Discharges I. Encyclopedia of Physics. Springer, 1956, pp. 1–175. isbn: 978-3642-45844-6.
[5] R. Gomer. Field emission and field ionization. AVS Classics in Vacuum
Science and Technology. New York: American Institute of Physics, 1993.
isbn: 978-1-56396-124-3.
[6] A. Modinos. “Secondary electron emission spectroscopy.” In: Field, thermionic,
and secondary electron emission spectroscopy. Boston, MA: Springer, 1984.
isbn: 978-1-4757-1450-0.

40
[7] L. A. DuBridge. “Theory of the energy distribution of photoelectrons.” Physical Review 43.9 (1933), pp. 727–741. doi: 10.1103/PhysRev.43.727.
[8] W. E. Spicer. “Photoemissive, photoconductive, and optical absorption studies of alkali-antimony compounds.” Physical Review 112.1 (1958), pp. 114–
122. doi: 10.1103/PhysRev.112.114.
[9] R. Fowler and L. Nordheim. “Electron emission in intense electric fields.”
Proceedings of the Royal Society of London. Series A, Containing Papers of
a Mathematical and Physical Character 119.781 (1928), pp. 173–181. doi:
10.1098/rspa.1928.0091.
[10] G. N. Fursey. Field emission in vacuum microelectronics. Microdevices. New
York: Springer, 2005. isbn: 978-0-387-27419-5.
[11] S. D. Liang. Quantum tunneling and field electron emission theories. World
Scientific, 2014. isbn: 978-981-4440-21-9.
[12] N. W. Ashcroft and N. D. Mermin. Solid state physics. Cengage Learning,
1976. isbn: 978-0-03-083993-1.
[13] C. Kittel. Introduction to solid state physics. Hoboken, NJ: Wiley, 2005. isbn:
978-0-471-41526-8.
[14] R. Forbes. “Simple derivation of the formula for Sommerfeld supply density
used in electron-emission physics and limitations on its use.” Journal of
Vacuum Science & Technology B 28.6 (2010), pp. 1326–1329. doi: 10 .
1116/1.3501118.
[15] J. W. Gadzuk and E.W. Plummer. “Field emission energy distribution (FEED).”
Reviews of Modern Physics 45.3 (1973), pp. 487–548. doi: 10 . 1103 /
RevModPhys.45.487.
[16] R. L. Liboff. Introductory quantum mechanics. San Francisco: AddisonWesley, 2003. isbn: 978-0-8053-8714-8.
[17] R. Shankar. Principles of quantum mechanics. New York: Springer Science
& Business Media, 2013. isbn: 978-1-4615-7675-4.
[18] S. C. Miller and R. H. Good. “A WKB-type approximation to the Schrödinger
equation.” Physical Review 91.1 (1953), pp. 174–179. doi: 10 . 1103 /
PhysRev.91.174.
[19] L. Landau and E. Lifshitz. Quantum mechanics: non-relativistic theory.
Vol. 3. Course of Theoretical Physics. Pergamon, 1987. isbn: 978-0-08019012-9.
[20] D. K. Roy. Quantum mechanical tunnelling and its applications. World Scientific, 1986. isbn: 978-9971-5-0024-5.
[21] N. Egorov and E. Sheshin. Field emission electronics. Springer Series in Advanced Microelectronics 60. Springer International Publishing, 2017. isbn:
978-3-319-56561-3.

41
[22] R. Forbes and K. Jensen. “New results in the theory of Fowler–Nordheim
plots and the modelling of hemi-ellipsoidal emitters.” Ultramicroscopy 89.1
(2001), pp. 17–22. doi: 10.1016/S0304-3991(01)00101-2.
[23] R. Forbes. “Field electron emission theory (October 2016).” 2016 Young
Researchers in Vacuum Micro/Nano Electronics (VMNE-YR) (2016), pp. 1–
8. doi: 10.1109/VMNEYR.2016.7880403.
[24] R. Forbes et al. “Fowler-Nordheim plot analysis: a progress report.” arXiv
(2016). doi: arXiv:1504.06134.
[25] R. Forbes. “Field emission: new theory for the derivation of emission area
from a Fowler–Nordheim plot.” Journal of Vacuum Science & Technology B
17.2 (1999), p. 526. doi: 10.1116/1.590588.
[26] V. T. Binh and V. Semet. “Planar cold cathodes.” In: Advances in Imaging
and Electron Physics. Vol. 148. Elsevier, 2007, pp. 1–73. isbn: 978-0-12373910-0.
[27] E. W. Müller. “Work function of tungsten single crystal planes measured
by the field emission microscope.” Journal of Applied Physics 26.6 (1955),
pp. 732–737. doi: 10.1063/1.1722081.
[28] R. Forbes, C. J. Edgcombe, and U. Valdrè. “Some comments on models for
field enhancement.” Ultramicroscopy 95 (2003), pp. 57–65. doi: 10.1016/
S0304-3991(02)00297-8.
[29] L. W. Nordheim. “The effect of the image force on the emission and reflexion
of electrons by metals.” Proceedings of the Royal Society of London. Series
A, Containing Papers of a Mathematical and Physical Character 121.788
(1928), pp. 626–639. doi: 10.1098/rspa.1928.0222.
[30] W. Zhu, ed. Vacuum microelectronics. New York: Wiley, 2001. isbn: 978-0471-32244-3.
[31] R. Forbes. “Simple good approximations for the special elliptic functions in
standard Fowler-Nordheim tunneling theory for a Schottky-Nordheim barrier.” Applied Physics Letters 89.11 (2006), p. 113122. doi: 10.1063/1.
2354582.
[32] R. Forbes and J. Deane. “Reformulation of the standard theory of Fowler
Nordheim tunnelling and cold field electron emission.” Proceedings of the
Royal Society A: Mathematical, Physical and Engineering Sciences 463.2087
(2007), pp. 2907–2927. doi: 10.1098/rspa.2007.0030.
[33] E. L. Murphy and R. H. Good. “Thermionic emission, field emission, and
the transition region.” Physical Review 102.6 (1956), pp. 1464–1473. doi:
10.1103/PhysRev.102.1464.

42
[34] P. H. Cutler et al. “Theory of electron emission in high fields from atomically sharp emitters: Validity of the Fowler-Nordheim equation.” Progress
in Surface Science 42.1-4 (1993), pp. 169–185. doi: 10 . 1016 / 0079 6816(93)90068-7.
[35] O. W. Richardson. “The electrical conductivity imparted to a vacuum by hot
conductors.” Proceedings of the Royal Society of London 71 (1902), pp. 415–
418.
[36] S. Dushman. “Electron emission from metals as a function of temperature.”
Physical Review 21.6 (1923), pp. 623–636. doi: 10.1103/PhysRev.21.
623.
[37] S. Dushman. “Electron emission.” Electrical Engineering 53.7 (1934), pp. 1054–
1062. doi: 10.1109/EE.1934.6541794.
[38] K. L. Jensen. Introduction to the physics of electron emission. Hoboken, New
Jersey: John Wiley & Sons, Inc., 2017. isbn: 978-1-119-05189-3.
[39] H. Hertz. “Ueber einen Einfluss des ultravioletten Lichtes auf die electrische
Entladung.” Annalen der Physik und Chemie 267.8 (1887), pp. 983–1000.
doi: 10.1002/andp.18872670827.
[40] J. Mulligan. “Heinrich Hertz and the development of physics.” Physics Today
42.3 (1989), pp. 50–57. doi: 10.1063/1.881211.
[41] H. Bonzel and C. Kleint. “On the history of photoemission.” Progress in
Surface Science 49.2 (1995), pp. 107–153. doi: 10.1016/0079-6816(95)
00035-W.
[42] G. Margaritondo. “100 years of photoemission.” Physics Today 41.4 (1988),
pp. 66–72. doi: 10.1063/1.881150.
[43] A. Einstein. “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt.” Annalen der Physik 322.6 (1905),
pp. 132–148. doi: 10.1002/andp.19053220607.
[44] B. Saleh and M. Teich. Fundamentals of photonics. Hoboken, N.J: John Wiley
& Sons, 2007. isbn: 978-0-471-35832-9.
[45] E. Forati et al. “Photoemission-based microelectronic devices.” Nature Communications 7.1 (2016), p. 13399. doi: 10.1038/ncomms13399.
[46] V. Nathan, S. S. Mitra, and A. H. Guenther. “Review of multiphoton absorption in crystalline solids.” Journal of the Optical Society of America B 2.2
(1985), p. 294. doi: 10.1364/JOSAB.2.000294.
[47] S. Anisimov, V. Benderskiı̆, and G. Farkas. “Nonlinear photoelectric emission
from metals induced by a laser radiation.” Soviet Physics Uspekhi 20.6 (1977),
pp. 467–488. doi: 10.1070/PU1977v020n06ABEH005404.

43
[48] J. P. Girardeau-Montaut and C. Girardeau-Montaut. “Theory of ultrashort
nonlinear multiphoton photoelectric emission from metals.” Physical Review
B 51.19 (1995), pp. 13560–13567. doi: 10.1103/PhysRevB.51.13560.
[49] M. Lee. “Field emission of hot electrons from tungsten.” Physical Review
Letters 30.24 (1973), pp. 1193–1196. doi: 10.1103/PhysRevLett.30.
1193.
[50] P. Hommelhoff et al. “Field emission tip as a nanometer source of free electron
femtosecond pulses.” Physical Review Letters 96.7 (2006), p. 077401. doi:
10.1103/PhysRevLett.96.077401.
[51] C. Kealhofer et al. “Ultrafast laser-triggered emission from hafnium carbide
tips.” Physical Review B 86.3 (2012), p. 035405. doi: 10.1103/PhysRevB.
86.035405.
[52] S. Piltan and D. Sievenpiper. “Field enhancement in plasmonic nanostructures.” Journal of Optics 20.5 (2018), p. 055401. doi: 10 . 1088 / 2040 8986/aab87e.
[53] P. Hommelhoff, C. Kealhofer, and M. A. Kasevich. “Ultrafast electron pulses
from a tungsten tip triggered by low-power femtosecond laser pulses.” Physical Review Letters 97.24 (2006), p. 247402. doi: 10.1103/PhysRevLett.
97.247402.
[54] L. Keldysh. “Ionization in the field of a strong electromagnetic wave.” Journal
of Experimental and Theoretical Physics 20.5 (1965), pp. 1307–1314.
[55] S. M. Teichmann et al. “Strong-field plasmonic photoemission in the midIR at <1 GW/cm2 intensity.” Scientific Reports 5.1 (2015), pp. 1–5. doi:
10.1038/srep07584.
[56] G. Herink et al. “Field-driven photoemission from nanostructures quenches
the quiver motion.” Nature 483.7388 (2012), pp. 190–193. doi: 10.1038/
nature10878.
[57] F. C. Chiu. “A review on conduction mechanisms in dielectric films.” Advances in Materials Science and Engineering 2014 (2014), pp. 1–18. doi:
10.1155/2014/578168.
[58] J. G. Simmons. “Poole-Frenkel effect and Schottky effect in metal-insulatormetal systems.” Physical Review 155.3 (1967), pp. 657–660. doi: 10.1103/
PhysRev.155.657.
[59] O. Mitrofanov and M. Manfra. “Poole-Frenkel electron emission from the
traps in AlGaN/GaN transistors.” Journal of Applied Physics 95.11 (2004),
pp. 6414–6419. doi: 10.1063/1.1719264.
[60] R. B. Hall. “The Poole-Frenkel effect.” Thin Solid Films 8.4 (1971), pp. 263–
271. doi: 10.1016/0040-6090(71)90018-6.

44
[61] J. Frenkel. “On pre-breakdown phenomena in insulators and electronic semiconductors.” Physical Review 54.8 (1938), pp. 647–648. doi: 10 . 1103 /
PhysRev.54.647.
[62] S. M. Sze and K. K. Ng. Physics of semiconductor devices. Hoboken, N.J:
John Wiley & Sons, 2007. isbn: 978-0-471-14323-9.
[63] C. Neusel, H. Jelitto, and G. A. Schneider. “Electrical conduction mechanism
in bulk ceramic insulators at high voltages until dielectric breakdown.” Journal of Applied Physics 117.15 (2015), p. 154902. doi: 10.1063/1.4917208.
[64] A. Kyritsakis, M. Veske, and F. Djurabekova. “General scaling laws of
space charge effects in field emission.” New Journal of Physics 23.6 (2021),
p. 063003. doi: 10.1088/1367-2630/abffa8.
[65] C. D. Child. “Discharge from hot CaO.” Physical Review (Series I) 32.5
(1911), pp. 492–511. doi: 10.1103/PhysRevSeriesI.32.492.
[66] I. Langmuir. “The effect of space charge and residual gases on thermionic
currents in high vacuum.” Physical Review 2.6 (1913), pp. 450–486. doi:
10.1103/PhysRev.2.450.
[67] R. Forbes. “Exact analysis of surface field reduction due to field-emitted
vacuum space charge, in parallel-plane geometry, using simple dimensionless
equations.” Journal of Applied Physics 104.8 (2008), p. 084303. doi: 10.
1063/1.2996005.
[68] J. P. Barbour et al. “Space-charge effects in field emission.” Physical Review
92.1 (1953), pp. 45–51. doi: 10.1103/PhysRev.92.45.

45
Chapter 3

FIELD EMISSION DEVICES FOR HIGH-TEMPERATURE
OPERATION
Semiconductor devices face several challenges in harsh conditions including extreme
temperatures and radiation environments. To circumvent these adversities, currently
a considerable amount of electronic components are located remotely or cooled to
below 125 ◦ C. However, if high-temperature or radiation-proof electronics would be
employed, costs and weight would substantially decrease, and apparatus reliability
and performance would improve.
Continuous proper operation in hostile surroundings is crucial for various applications in the automotive, nuclear, down-hole, and aerospace industries. Historically,
the main driving force in the development of high-temperature electronics has been
the down-hole oil and gas industry, which can encounter temperatures of around 300
◦ C. Geothermal drilling operations can experience temperatures of 500 ◦ C and even
higher for deeper wells. Well-logging requires refined data acquisition instruments
to obtain information about the surrounding geologic formations as well as sophisticated sensors to monitor various parameters such as temperature, pressure, and
vibrations, all of which must be able to withstand the high surrounding temperatures.
In the automotive industry, in particular with drive-by-wire technology, sensors and
actuators are required close to the engine, exhaust, and brakes, where temperatures
can range between 200 ◦ C to 850 ◦ C. Similarly, sensors and instrumentation are used
in jet engines for monitoring and control, which can face temperatures over 300 ◦ C.
Other aircraft parts that could benefit from robust electronics placed in their vicinity
include braking systems and landing gear, as well as densely packed high-power
electronics that release a lot of waste heat. Nowadays, the avionics and aerospace
industry has become a fairly substantial market for high-temperature electronics
[1–3].
Space exploration is another field that would benefit from more resilient electronics.
In particular, extended missions to Venus are incredibly challenging, which explains
why it remains almost completely unexplored. The record for the longest-lasting
lander on its surface has been set at 127 minutes by the Soviet Venera 13 in 1982.
Even though pressure vessels and cooling systems were used, Venus’ ambient condi-

46
tions were too harsh for the electronics to properly function. The daily temperature
approaches 500 ◦ C and it has a corrosive 92 atm caustic atmosphere. Its very thick
atmosphere is mainly composed of supercritical CO2 and N2 , and it also supports
greenhouse warming as it contains sufficient SO2 to form sulfuric acid clouds. Despite its very different climate, Venus is commonly referred to as the Earth’s twin
due to its similar density, distance to the Sun, and size. Therefore, a long-term
mission to Venus to deeper study its geology and greenhouse effect atmosphere
would provide a better understanding of the Earth [4, 5].
Furthermore, electronics that can operate in very cold temperatures would also be
valuable. Examples of extremely cold environments in space include the moon’s
permanently shadowed regions with a temperature of -230 ◦ C, Neptune’s moon
Triton at -250 ◦ C due to its extreme distance from the Sun, and comet nuclei that
can reach temperatures of -270 ◦ C.
Unlike carrier transport in semiconductors, field emission is essentially independent
of temperature and resistant to radiation. Therefore, devices based on this emission
process could prove to be a good candidate to develop robust electronics for harsh
environments. In terms of high-temperature environments, since elevated temperatures promote the desorption of surface contaminants, field emission devices should
even have more stable electrical performance in these environments than at room
temperature.
In this chapter, suspended in-plane two- and four-terminal field emission devices for
high-temperature operation are demonstrated. Tungsten, a refractory metal, is the
chosen electrode material due to its theoretical low work function (∼ 4.5 eV) and
high-temperature tolerance. A brief description of early proposals is also included.
Finally, a discussion, as well as directions for future research, is provided.
Parts of this chapter were adapted from [6].
3.1

General Design Paradigm

While the conventional design of field emission devices relies on vertical Spindt
emitters, wherein electron emission is out-of-plane, a lateral geometry was chosen
instead for the devices discussed in this chapter. This design allows for taking advantage of high-resolution lithography, which simplifies the fabrication process and
provides greater control over the main physical dimensions, namely the separation
between the electrodes and the cathode geometry. Consequently, lower turn-on voltages can be achieved, thus decreasing power consumption and potentially increasing

47
device lifetime by reducing the harmful impact of ion sputtering. Furthermore, lateral devices are more practical and easier to integrate with widespread CMOS
technology.
Tungsten was selected as the electrode material because it has a relatively low work
function (∼ 4.5 eV [7]) and the highest melting point of all metals (3,422 ◦ C). These
two properties are critical for developing devices with high current density emission
for high-temperature operation. It also has high electrical and thermal conductivity. Other common alternatives for field emission devices include Si and carbon
nanotubes (CNTs). Si is an attractive material due to its ease of fabrication and
advanced micro processing technology. However, emission from Si is inferior due
to its higher work function (∼ 4.85 eV), and poor mechanical and thermal properties. Additionally, impurity adsorption from residual gaseous molecules can affect
emission stability, so UHV environments are generally required [8–11]. CNTs are
becoming increasingly popular due to their high mechanical, thermal, and chemical
stability. Their high aspect ratio yields large local electric field enhancement, which,
combined with their intrinsically low work function of ∼ 4.5 eV, provides high field
emission currents at moderately low applied biases. Nonetheless, CNTs have several drawbacks. The presence of metallic and carbonaceous impurities, which occur
regardless of the synthesis method employed, can have unfavourable effects on their
thermal, electric, and mechanical properties. Specific and reproducible geometries
are required to fabricate field emission devices; yet, achieving uniform chirality and
precise sizes within a batch of CNTs as well as their controlled placement can prove
to be challenging. Poor interfacial interaction with metals can result in high contact resistance and lower electron emission currents than predicted. Furthermore,
temperatures over 500 ◦ C are necessary to grow CNTs, which hinders the use of
polymer substrates [12, 13].
Two types of devices were made: two (diode-like) and four (triode-like) terminal
devices. A schematic of both devices is shown in Fig. 3.1. In both cases, one of the
terminals, the so-called ‘emitter,’ is sharpened so that it has a larger field enhancement factor 𝛾 compared to the other terminals and thus, emits at a smaller applied
bias [14]. The effect of various radii of curvature on the emitter tip can be seen in Fig.
3.2, which was simulated using COMSOL Multiphysics 5.4. The blunt electrode
located in line with the emitter is referred to as the ‘collector.’ In the two-terminal
device, we intended that this asymmetric geometry created by the sharp emitter and
the blunt collector would mimic the IV curves characteristic of diodes. The other

Gate

Emitter

Collector

Emitter

Collector

Gate

(a)

(b)

Figure 3.1: Top-view of schematic for two types of proposed devices: (a) twoterminal diode-like device and (b) four-terminal triode-like device.

two blunt electrodes of the four terminal device were oriented perpendicularly to
the emitter and collector. These are referred to as ‘gate’ electrodes. The gates act
by modulating the electric field at the tip of the emitter, which affects the tunneling
probability [15]. Fig. 3.3 shows a two-dimensional finite element method (FEM)
simulation (COMSOL Multiphysics 5.4) of the electric field norm and streamlines
of a schematic for a gated device at two different gate biases. The collector was
grounded while the emitter was biased negatively to induce electron emission. In
(a), the gates were biased negatively, which ultimately steered the electrons toward
the collector terminal, while in (b) they were grounded, which caused no emission
toward the collector. Furthermore, ideally the non-axial component of the electric
field between the emitter and collector cancels out, which minimizes the leakage
of field-emitted current into the gates. Yet, asymmetries inevitably arise during the
fabrication process. To account for this unevenness, the gates were electrically separated and their biases were independently controlled. In the four-terminal device,
we concentrated on maximizing the field enhancement factor to reduce the leakage
of field-emitted current from either the on-axis collector or the off-axis gates.
Yet, even though field enhancement was maximized for the emitter tip, the main
focus was to fabricate the smallest gap between the emitter and collector. This
would yield less resistive heating, which increases the lifetime of the device. A low
operating voltage can also be achieved with small gaps.

(a)

(b)

(c)

(d)

Radius (m)
(e)

Figure 3.2: Electric field norm and calculated field enhancement factor for various
emitter radius of curvature: (a) 1 nm, (b) 5 nm, (c) 10 nm, and (d) 20 nm. Field
enhancement factor as a function of emitter radius of curvature.

50
V/m

Collector

Gate
Emitter
Gate

(a)
V/m

Collector

Gate
Emitter
Gate

(b)

Figure 3.3: Simulated electric field norm with streamlines (white lines) for a general
four-terminal device. The collector was grounded while the emitter was biased
negatively to induce electron emission. In (a) the gates were biased negatively, and
in (b) they were grounded.

3.2

Early Work on PECVD SiNx Substrate

The first device fabricated was a lateral metallic four-terminal triode-like field emission device. Plasma-enhanced chemical vapour deposition (PECVD) silicon nitride
(SiNx ) was selected as the supporting dielectric material due to its high dielectric
breakdown and fast deposition rate. However, the combination of the large electric
field required for field emission with a high-temperature environment in an insulator
can be detrimental to device operation, as it leads to undesirable FP current leakage
[16, 17]. This is the field-assisted thermal ionization effect by which an insulator
becomes electrically conductive before reaching dielectric breakdown [18, 19]. One
approach to reducing the effect of this parasitic leakage pathway that competes with
FN field emission is to distance the insulator from the emission area [20]. Thus,
to avoid the increased surface leakage currents across dielectric layers that come

51
Field Emission
Current
Emitter

Collector

Field Emission
Current
Emitter

Collector

Leakage Current

SiNx
Undoped Si

(a)

(b)

Figure 3.4: Emission and leakage current pathways for: (a) unetched substrate, (b)
deeply etched substrate.

along higher temperatures, deep nanoscale anisotropic dry etching was employed.
Long etched paths decrease the parasitic leakage pathways that compete with FN
emission, as shown in Fig. 3.4.
The fabrication steps are summarized in Fig. 3.5. The devices were fabricated
on an undoped Si wafer (resistivity of 10 Ω·m) to minimize leakages across the
substrate. A layer of 500 nm amorphous SiNx was deposited by PECVD (Oxford
Instruments Plasmalab System 100) using silane and ammonia gas chemistry at 350
◦ C and 1 Torr. The resistivity of this SiN layer was measured to be 229 Ω·m.
Following the dielectric deposition, a layer of 200 nm of tungsten (W) was sputtered
in a custom-made deposition chamber at 7 mTorr in an argon atmosphere with
the RF power set to 200 Watts. The resistivity of the sputtered W was measured
to be 6.83×10−7 Ω·m. The sample was cleaned using a hydrogen plasma at 50
Watts and 30 mTorr (Plasma-Therm SLR 720) to remove oxides that may have
formed on the surface of tungsten during processing [21, 22]. Standard EBL using
poly(methyl methacrylate) (PMMA)–a positive-tone e-beam resist–was employed to
pattern the devices. 950 PMMA A2 (MicroChem) was spin-coated on the substrate
immediately after the H2 plasma at 1500 rpm for 40 s and subsequently baked at
180 ◦ C for 4 minutes, which yielded a thickness of approximately 100 nm. The
devices were written using direct-write EBL (Raith EBPG 5200) at an acceleration
voltage of 100 keV, followed by development in a freshly made 1:3 solution of
methyl isobutyl ketone (MIBK) and isopropyl alcohol (IPA) at room temperature.
A layer of 35 nm chrome (Cr) was e-beam evaporated (CHA Industries Mark 40)
at a rate of 0.5 Å/s and lifted-off in hot PG-remover to be used as an etching hard
mask. The devices were dry etched using a mixture of SF6 and C4 F8 at a ratio of
26 sccm/35 sccm with a chamber pressure of 10 mTorr and a capacitively coupled

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 3.5: Fabrication steps: (a) initial undoped Si substrate, (b) deposition of 500
nm PECVD SiNx layer, (c) sputtering of 200 nm W, (d) spin-coating of 100 nm 950
PMMA A2 e-beam resist, (e) EBL and development, (f) evaporation of 35 nm Cr
hard-mask, (g) lift-off, and (h) dry etching in pseudo Bosch process. Note that the
sketch is not to scale.
plasma (CCP) power of 50 Watts and an inductively coupled plasma (ICP) power
of 1500 Watts (Oxford Instruments Plasmalab System 100 ICP-RIE 380). The 200

53
nm thick W electrodes, the 500 nm SiNx layer, as well as 500 nm of the Si substrate
were etched to increase the length of the leakage pathway. To wire-bond, contact

500 nm
(a)

500 nm
(b)

500 nm
(c)

Figure 3.6: SEM of fabricated W triode-like device on SiNx : (a) top-view (b) 52◦
tilt, (c) 52◦ tilt and rotation.

54
pads were photolithographically defined. AZ9245 (MicroChem) was spin-coated
on the sample at 2000 rpm for 30 seconds, followed by a 2-minute 110 ◦ C soft bake.
Exposure for 30 seconds at a wavelength of 405 nm and a dose of 25 mW/cm2
was done using a contact mask aligner (Suss MicroTec MA6), and the sample was
developed in a 1:3 mixture of AZ400K and water for 2 minutes. Any leftover Cr was
removed using Cr-7S (Cyantek) to improve the adhesion and contact conductivity.
An adhesion layer of 7 nm titanium (Ti) (rate of 0.5 Å/s) and 200 nm gold (Au) (rate
of 1 Å/s) were evaporated (CHA Industries Mark 40), followed by lift-off in hot PGremover. Fig. 3.6 shows a scanning electron micrograph (SEM) of a representative
fabricated device.
The device was ultrasonically wedge wire-bonded with aluminum wires to a ceramic
pin grid array package (Spectrum Semiconductor Materials CPG15504). The chip
carrier was then placed over a ceramic heater (ThorLabs HT24S2), and a thermocouple was attached to the back of the chip carrier. To reduce sample contamination that
could alter the work function and affect electron emission and stability, the setup was
loaded into a custom stainless-steel vacuum chamber, which was pumped to ∼ 10−6
Torr. The four terminals on the device were connected to separate sourcemeters
(Keithley 2450) to independently control the bias and measure the current at each
terminal. The measurement acquisition was automated using serial communication
and MATLAB scripts.
Several IV scans per device were done to remove further adsorbates from the
emitting surfaces. This ‘conditioning’ [23] process was repeated until the emission
characteristics appeared to be stable. For all measurement runs, the collector bias
was kept at 0 V while the emitter voltage was negatively swept to promote electron
emission. An initial current limit of 100 nA was imposed to prevent excessive
resistive heating and potential tip destruction. Fig. 3.7 shows the IV curve of
the triode-like device for several gate biases tested at room temperature. Three
independent measurements for each voltage setting were taken, and the average
values along with error bars are depicted in the plots. The emitter-to-collector
distance for the specific device tested measured 212 nm. The measured currents
for all four terminals of the device are displayed to accurately monitor any leakage.
Owing to the field enhancement factor of the sharp emitter tip, the operating voltage
was under 10 V, which is comparable to CMOS technology. In 3.7 (a), both
gates were kept at 0 V. With this bias configuration, most of the emitted current
was directed to both gates and only a small fraction went to the collector. This was

55
100

100
Emitter
Gate 1 at 0V
Gate 2 at 0V
Collector

Current (nA)

Emitter
Gate 1 at 0V
Gate 2 at -0.5V
Collector

75
50

Current (nA)

25
-25
-50

-75

-100

-7

-6

-5

-4

-3

-2

-1

-7

-6

Emitter Voltage (V)
(a)

-3

-2

-1

100
Emitter
Gate 1 at -0.45V
Gate 2 at -0.5V
Collector

25
-25

-50

-75

-75
-7

-6

-5

-4

-3

Emitter Voltage (V)
(c)

-2

-1

Emitter
Gate 1 at 0.15V
Gate 2 at 0.15V
Collector

Current (nA)

-4

Emitter Voltage (V)
(b)

100

-100

-5

-100

-7

-6

-5

-4

-3

-2

-1

Emitter Voltage (V)
(d)

Figure 3.7: IV characteristic for triode-like device on SiNx for various gate bias:
(a) both gates were grounded, (b) one gate we negatively biased to repel electrons,
(c) both gates were biased to steer electrons exclusively towards the collector, (d)
both gates were biased to prevent electron emission to the collector. In all cases, the
collector was kept grounded and the measurements were taken at room temperature.

expected, as the gates were located closer to the emitter compared to the collector, and
all three terminals were grounded. In (b), the bias on one of the gate terminals was
changed to -0.5 V to reflect electrons that would otherwise be emitted to it. This was
successful, as more electrons were directed toward the collector terminal. Several
combinations for gate bias were tested to steer all electron emission exclusively
toward the collector terminal to attain an ‘on’ state. This was achieved at -0.45 V
for one gate and -0.5 V for the other, as depicted in (c). Lastly, in (d), the gate bias
was chosen to achieve an ‘off’ state, wherein no current would be directed towards
the collector. These measurements successfully showed that the gates did modulate
the electric field at the emitter tip, confirming that the emission mechanism was FN
emission.

56
Next, emission at various temperatures was studied. Fig. 3.8 (a) shows the IV
characteristic for the same device at temperatures ranging from 33 ◦ C to 125 ◦ C. As
adsorbates can alter the work function of the emitter tip and, consequently, affect
electron emission, the temperature was initially raised to the maximum testing

33°C
36°C
38°C
40°C
56°C
65°C
71°C
78°C
90°C
125°C

250

Current (nA)

200

150

100

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

Emitter Voltage (V)

(a)
-15
-15.5
-16
-16.5

log(I/V )

-17
-17.5
-18
-18.5
-19
-19.5
-20
0.2

0.4

0.6

0.8

1.2

1.4

1/|V|

(b)

Figure 3.8: Effect of temperature on electron emission: (a) IV characteristic, and
(b) FN plot.

57
Temperature (◦ C)

Parallel Leakage
Resistance (MΩ)

Slope

𝑦-intercept

R2 value

33
36
38
40
56
65
71
78
90
125

394
333
271
217
116
63
45
34
19

-18.53
-17.33
-15.33
-12.72
-8.75
-4.50
-3.54
-3.41
-2.00
-0.86

-14.15
-14.20
-14.31
-14.71
-15.20
-16.22
-16.29
-16.06
-16.32
-15.54

0.994
0.993
0.994
0.984
0.971
0.963
0.959
0.974
0.973
0.744

Table 3.1: Device data as a function of temperature.
value of 125 ◦ C. At this temperature, the first IV characteristics was measured.
Subsequently, the temperature was slowly lowered, and the rest of the measurements
followed in order of decreasing temperature. A low-field linear leakage current was
observed that increased with increasing temperature. The values from this parasitic
series resistance as a function of temperature were extracted by performing a linear
fit from the small field data and are presented in Table 3.1. A decrease of almost two
orders of magnitude for the resistance was seen between the data measured at both
extremes of the measured temperature range, which indicated that the substrate was
not suitable for high temperatures. Fig. 3.8 (b) depicts the data in FN coordinates
for currents above 30 nA. This value was chosen to remove the effects of the small
field leakage current. Additionally, least squares regression lines were fitted to
the resulting data. The corresponding coefficients of determination are included
in Table 3.1, as well as the extracted values for the slope and 𝑦-intercept. The
experimental data exhibited linear behaviour in accordance with the FN emission
mechanism up to 90 ◦ C. This provided further proof that the substrate was not
adequate for high-temperature applications. Moreover, as illustrated in Table 3.1,
the magnitude for the extracted slope decreased as a function of temperature while
the magnitude for the extracted 𝑦-intercept increased. These two parameters are
related to physical parameters, namely 𝛾 and 𝜑. Their relations are given by Eq.
(2.49) and Eq. (2.50). Therefore, it seemed that either 𝛾 was increasing, 𝜑 was
decreasing, or a combination of both. This is further addressed in Section 3.4.

58
3.3

Suspended Devices: Design and Fabrication

After the work on deep anisotropic etch on SiNx , the next attempt to increase the
resistance of the leakage current pathways that became notably troublesome at high
temperatures was to fabricate suspended devices. This design would eliminate the
current leakage pathway in the vertical direction.
The devices were fabricated on a suspended, stoichiometric silicon nitride (Si3 N4 )
membrane with planar dimensions of 5 mm × 5 mm, and a thickness of 200
nm (Norcada QX10500DS). The membrane was laterally supported by a 200 µm
thick Si frame. The main fabrication steps are sketched in Fig. 3.9. Standard
EBL was used to pattern connected terminals, interconnect lines, alignment marks,
and contact pads. The membrane was stuck face-up on a piece of blue low tack
tape (commonly used with the scriber-breaker) so that it could be spin-coated.
950 PMMA A8 (MicroChem) was spun at 4000 rpm for 1 minute. This yielded
a thickness of approximately 1 𝜇m. A layer of a conductive polymer, namely
AquaSAVE (Mitsubishi Chemical Corporation), was spun at 1500 rpm for another
minute to avoid charging effects during EBL. The blue tape was removed before
baking the membrane at 180 ◦ C for 5 minutes. The devices were written using
direct-write EBL (Raith EBPG 5200) at an acceleration voltage of 100 keV, a beam
current of 100 nA, and a dose of 1500 𝜇C/cm2 . The contact pads were written
on the supporting Si frame. An SEM showing the resulting connected terminals
for a two-electrode device is shown in Fig. 3.10. After lithography, the layer of
AquaSAVE was removed in water, and the resist was developed in 1:3 solution of
MIBK and IPA at room temperature. Oxygen treatment was used for descum in a
plasma cleaner in remote mode (PIE Scientific Tergeo Plus).
Next, a conducting layer consisting of 150 nm of W with a 7 nm Ti adhesion
layer was sputtered. Due to the high tensile stress of the membranes (1.0 GPa as
stated by the manufacturer), various attempts to sputter W at low pressure failed
as the deposited layer would quickly peel off. The sputter conditions had to be
optimized to reduce the stress of the deposited layer [24, 25]. A quick method
to determine if the deposited layer has too much residual stress is to first sputter
on a test sample that has been spin-coated with a layer of photoresist. Due to the
softness of the resist layer, cracks appear if the deposited W layer has residual tensile
stress while buckling delamination would occur if the sputtered layer has residual
compressive stress. Fig. 3.11 shows photos of the test samples at various sputtering
conditions. Silicon chips coated with a uniform layer of photoresist were used as

Figure 3.9: Fabrication steps for diode-like device: (a) initial Si3 N4 membrane, (b)
spin-coating of 1 µm 950 PMMA A8 electron beam resist, (c) EBL and development,
(d) sputtering of 150 nm of W, (e) lift-off, (f) Ne focused ion beam milling. Note
that the sketch is not to scale.
test substrates. The deposition was carried out in a UHV magnetron sputtering
system (AJA) with argon as the sputtering gas. The optimal sputtering condition
was found at an RF power of 300 Watts and a sputtering pressure of 40 mTorr. A
high power was desired to increase the deposition rate. While higher sputtering
pressures were also tested, the minimum pressure at which we observed no stress
was chosen as the resistivity of the deposited W increased with higher sputtering
pressures. The resistivity of the deposited W layer at the optimal conditions was

500 nm

Figure 3.10: SEM of the two-terminal device after first lithography step. At this
point, the two terminals were connected.
1.1×10−5 Ω·m. Unfortunately, this was two orders of magnitude more resistive than
the W deposited in the custom vacuum chamber at lower power and pressure for the
device on PEVCD SiNx substrate.
Once the electrode material layer had been deposited, lift-off was performed in
acetone. Aligned EBL was employed to redefine the electrical contact pads with
the same recipe as previously. A layer of 150 nm gold with a 10 nm Ti adhesion
layer was deposited using electron beam evaporation at a pressure of ∼ 10−7 Torr
(Kurt J. Lesker Labline). This thicker contact layer enabled ultrasonic wire-bonding
to connect the devices without punching through the silicon nitride layer to the
partially-conductive silicon frame.
The connected terminals were separated manually using neon focused ion beam
(FIB) patterning (Zeiss Orion NanoFab). This enabled the creation of two-terminal
diode-like (Fig. 3.12 (a)) and four-terminal triode-like lateral devices (Fig. 3.12
(b)). The circles in Fig. 3.10 were used as focusing marks to align the column.
Neon was chosen instead of gallium FIB due to better milling precision and to avoid
undesired Ga implantation and contamination. As previously described in Section
3.1, the emitter terminal was sharpened to obtain a higher field enhancement factor
compared to the other terminals. This resulted in a macroscopic tip diameter
of approximately 10 nm in (a) and around 40 nm in (b). Before ion milling, the
membrane was coated with a ∼ 10 nm conductive carbon layer for charge dissipation
using a carbon evaporator (Leica EM ACE600). To prevent crack propagation and
relieve stress, two stop holes on the off-axis plane of the terminals were milled before

(a)

(b)

(c)

Figure 3.11: Various sputtering conditions on test samples: (a) RF power: 100
Watts; pressure: 2 mTorr, (b) RF power: 250 Watts; pressure: 3 mTorr, (c) RF
power: 300 Watts; pressure: 40 mTorr.

500 nm
(a)

1 µm
(b)

Figure 3.12: Ion micrograph of suspended (a) two-terminal diode-like device and
(b) four-terminal triode-like device. In (a), the emitter-collector gap measured 95
nm, and in (b) the emitter-collector gap measured 367 nm.

the terminals were separated. This eliminated the possibility of sharp corners that
could serve as nucleation sites for cracks in the Si3 N4 [26]. The FIB patterning
was also used to remove the silicon nitride membrane near the terminals, thus
minimizing potential leakage pathways across the insulating substrate. The milling
current was 14 pA, the acceleration voltage was 20 keV, the pressure was 4×10−6
Torr, and the working distance was 8 mm. For the annuli used to mill the stop holes
and the polylines used to remove the rest of the big features, a dose ranging between
4-25 nC/𝜇m2 was used, while for the thin lines used to define the gap separating the
emitter from the collector a dose of 1 nC/𝜇m2 was employed.

63
Temperature (◦ C)

Parallel Leakage
Resistance (MΩ)

80
158
204

16200
357
44

Table 3.2: Measured resistance values of membrane and ceramic pin grid array
package at low fields as a function of temperature.

Finally, the membrane was subjected to an oxygen plasma at 80 Watts and 20 mTorr
using reactive-ion etching (RIE) (Plasma-Therm SLR 720) to remove the conductive
carbon layer. To prevent heating of the membrane, the cleaning was divided into
four intervals of 5 minutes each with a 1-minute pause in between.
3.4

Suspended Devices: Results and Discussion

The membrane was ultrasonically wedge wire-bonded with aluminium wires to the
ceramic pin grid array package previously used (Spectrum Semiconductor Materials
CPG15504). The parallel resistance at low voltages as a function of temperature was
measured to determine whether the membrane and chip carrier would be suitable.
A hot plate with a T-type thermocouple were used to set the desired temperature.
The results are given in Table 3.2. Additionally, the pin connected to the membrane
that sourced the current was disconnected and connected to a randomly chosen pin
on the chip carrier at 204 ◦ C, and the resistance was measured to be 120 MΩ. This
indicated that the chip carrier was leaking at modest temperatures, so a substitute
was needed.
Next, a custom-made, high-temperature chip was fabricated. Macor, a glass-mica
ceramic sheet, was chosen as the material since it can sustain temperatures up to
1,470 ◦ C, is easy to machine, and is electrically insulating. The membrane was
ultrasonically wedge wire-bonded with aluminium wires to conductive strips on a
one-inch square Macor plate. The conductive strips were attached to the ceramic
board using UHV and high-temperature conductive silver paste (Ted Pella Pelco
16047). The membrane and the substrate were placed on top of a vacuum-safe
heater (HeatWave Labs) with a thermocouple attached to the surface of the ceramic
substrate. The experimental setup was loaded in a stainless-steel vacuum system
at the Jet Propulsion Laboratory (JPL). The membrane, ceramic substrate, and
thermocouple were held via compression by temperature-resistant molybdenum

(a)

(b)

(c)

(d)

Figure 3.13: Photograph of (a) wire-bonded membrane, (b) membrane on ceramic
substrate sitting on top of heater with the heater off, (c) membrane on ceramic
substrate sitting on top of heater with the heater on, and (d) testing setup at JPL.

springs, as shown in Fig. 3.13. The strips on the ceramic substrate were connected
to an electrical feedthrough of the vacuum chamber, and each terminal was linked
to individual picoammeters/voltage sources (Keithley 6487). Additionally, 10 MΩ
current-limiting resistors were placed in series with each terminal as ballast resistors
to avoid thermal runaway and surge currents. The vacuum chamber was pumped
to ∼ 10−7 Torr and baked at 150 ◦ C for several hours before testing, which helped
with the desorption of water vapour and other contaminants from the surface of the
terminals.
Multiple IV scans per device with a forward and reverse sweep were initially conducted at 150 ◦ C to remove adsorbates from the emitting surfaces until the turn-on
voltage stabilized. The turn-on voltage was defined as the voltage that yields a current above the noise floor (approximately 5 nA). This threshold current was chosen

65
100
80

40
20
-20
-40
-60
-80

Collector Current (nA)

-100
-25

-2
-2

-1
Emitter Voltage (V)

-15

-5

0.12

0.14

Emitter Voltage (V)

(a)
-21

ln(I/V2)

-21.5

-22

-22.5

-23

-23.5
0.04

0.06

0.08

0.1

1/V

(b)

Figure 3.14: Electrical measurements for the tow-terminal device as a function of
temperature: (a) IV characteristic removing the series resistance and (b) its FN
plot for currents over 15 nA for temperatures between 150 ◦ C to 450 ◦ C. The lines
correspond to the least-squares regression.

66
as 15 nA. Fig. 3.14 (a) shows the IV plot for the diode-like device shown in Fig. 3.12
(a) tested from 150 ◦ C up to 450 ◦ C in increments of 50 ◦ C. The emitter-to-collector
gap measured 95 nm. The emitter voltage 𝑉 is calculated as 𝑉 = 𝑉𝐴 − 𝐼 𝑅, where 𝑉𝐴
is the applied voltage on the emitter, 𝐼 is the emission current, and 𝑅 is the series
resistance of the ballast resistors. A current limit of 100 nA was imposed to prevent
excessive resistive heating and potential tip destruction.
The device displayed turn-on voltages of less than 13 V, which is desirable for
atmospheric pressure operation [27]. As the energy of the electrons is not high
enough to ionize the atoms present in the atmosphere, ion bombardment of the
terminals can be diminished. Additionally, the turn-on voltage can be reduced
further by decreasing the size of the emitter-to-collector gap [28].
Unfortunately, the emission from either terminal was symmetric. This could be
explained by the fact that the collector terminal was not completely blunt but rather
had an undesired sharp protrusion, which effectively yielded a 𝛾 comparable to the
one at the emitter tip.
The inset of Fig. 3.14 (a) shows a magnified view of the zero-corrected IV curve for
voltages near 0 V. It can be observed that before the onset of field emission, current
increased linearly with increasing voltage. In a similar fashion to the devices
described in Section 3.2, parasitic leakage dominated at these small fields. A linear
fit of the small field data was performed and the values for the parasitic series
resistance at the various temperatures were extracted and presented in Table ??.
This parasitic resistance decreased with increasing temperature. Since the substrate
in the vicinity of the high fields was removed, the likely leakage pathway was via the
supporting silicon ring, which had a resistivity of 1-30 Ω·cm at room temperature,
as stated by the manufacturer.
Fig. 3.14 (b) shows the IV characteristic in FN coordinates for currents above 15
nA to focus exclusively on field emission current. The experimental data displayed
linear behaviour up to 300 ◦ C, in agreement with FN emission mechanism. At
temperatures above 350 ◦ C, the fit deteriorated and the measured current did not
seem to follow a purely FN behavior. To confirm that the emission current was not
thermionic, the current was plotted in RD coordinates (ln 𝐼/𝑇 2 versus 1/𝑇) [29]
for various applied voltages on the emitter, as shown in Fig. 3.15. Since the resulting
plot was clearly non-linear for all potentials shown, thermionic emission was ruled
out. This could suggest thermally-promoted field emission. At higher temperatures,
thermally excited electrons transmit through a thinner potential barrier as these

67
Temperature (◦ C)

Parallel Leakage
Resistance (MΩ)

Slope

𝑦-intercept

R2 value

150
200
250
300
350
400
450

94.0
45.2
17.6
7.6
8.9
5.4
0.8

-45.95
-20.73
-15.12
-12.22
-16.64
-17.52
-9.05

-20.36
-21.05
-20.72
-20.72
-20.18
-20.29
-20.77

0.970
0.916
0.948
0.946
0.909
0.886
0.753

Table 3.3: Suspended two-terminal device data as a function of temperature.

electrons have the tail of the energy distribution above the Fermi energy. This
contribution of thermal electrons and resultant deviation from merely FN emission
is particularly noticeable for low currents [30], as for higher fields FN emission
dominates [31]. Additionally, this enhanced tunneling probability may explain the
lower turn-on voltages observed at higher temperatures, as for the same potential
the emission current was larger [32, 33].
Table 3.3 shows the values for the slope and 𝑦-intercept of the least squares regression
line, along with the value for the coefficient of determination for all measured
temperatures. Based on the reported literature work function of tungsten (𝜑 = 4.5
-30
-31
-32

ln(I/T 2)

-33
-34
-35
-36
-1 V
-5 V
-10 V

-37
-38

1.4

1.6

1.8

1/T (K-1 )

2.2

2.4
10-3

Figure 3.15: Emission current in RD coordinates for various applied voltages.

Collector

Emitter

Figure 3.16: COMSOL simulation of the component of the electric field normal to
the emitting surface in V/m for the diode-like device. The emitter was set to -10 V.

eV) and the slope of the FN plot, a value of 133 for the field enhancement factor 𝛾 was
calculated at 150 ◦ C. A two-dimensional FEM simulation (COMSOL Multiphysics
5.4) was performed based on the device dimension values extracted from the ion
micrograph to numerically compute the normal component of the electric field at
the emission tip, as illustrated in Fig. 3.16. The simulation suggested a more modest
𝛾 of 3.5, a value two orders of magnitude smaller than that obtained experimentally.
This discrepancy could be due to uncertainty in the efficient emitter tip radius, as
emission may be taking place locally at nanoprotusions, grain boundaries, or groups
of atoms [34], which may not be accurately resolved via an ion micrograph.
Overall, the magnitude of the slope decreased as a function of temperature. As the
slope depends on both 𝛾 and 𝜑, it is possible that with increasing temperature either
𝛾 increased, 𝜑 decreased, or a combination of both. An increasing 𝛾 could be a consequence of temperature-dependent desorption of residual molecules that alter the
surface roughness of the emitter tip [35]. Temperature-induced release of gaseous
adsorbates may also explain the potential decrease in 𝜑 [36, 37]. Electronegative adsorbates in the emitter surface, such as oxygen, have been shown to increase the work
function. In this way, traditional techniques to analyze FN plots are challenging to
apply [38], as it is hard to remove all contaminants and produce an atomically clean
surface. We should also consider the possibility that electromechanical motion due
to the suspended nature of the devices as well as thermal expansion of the electrode
materials could shrink the gap, which would impact the extracted parameters.

69
100

-200
-300

-330

-110V
-90V
-70V
-50V
-30V

-25

-100

ln(I/V 2)

Current (nA)

-26
-27
-28
0.007

-340

-400

-350

0.008

0.009

1/V
-140

-360

-120

-100

-80

-60

-40

Emitter Voltage (V)

-370

(a)

-380
-153

-152

-151

-25

-50

ln(I/V 2)

Current (nA)

-100
-150

-90V
-70V
-50V
-30V

-26

-27
0.01

0.012

0.014

1/V

-200
-100

-80

-60

-40

-20

Emitter Voltage (V)
(b)
50

Emitter + Collector
Current (nA)

-110V
-90V
-70V
-50V
-30V

-10

-20

30
10
-10

-90V
-70V
-50V
-30V

-30
-50

-140

-120

-100

-80

Emitter Voltage (V)
(c)

-60

-40

-100

-80

-60

-40

-20

Emitter Voltage (V)
(d)

Figure 3.17: Electrical measurements for triode-like device: (a) IV characteristic at
various gate bias at 150 ◦ C and (b) for 300 ◦ C, respectively. The insets present the
data in FN coordinates for currents over 15 nA. (c) Summed emitter and collector
currents to illustrate leakage to the gate terminal for 150 ◦ C and (d) for 300 ◦ C. All
legends indicate the gate voltages.

Next, building upon our two-terminal device, we also fabricate in-plane four-terminal
triode-like structures, as shown in Fig. 3.12 (b). The emitter-to-collector distance
is 367 nm. In addition, the top gate is 442 nm away from the emitter tip, while
the bottom gate is separated by 462 nm. Even though we attempted to achieve

70
symmetry in fabrication, we can overcome any disparity by independently biasing
the terminals.
Fig. 3.17 shows the IV curve of the triode-like device for various gate biases tested
at (a) 150 ◦ C and (b) 300 ◦ C. The current shown is the emitter current. In this
way, we concentrated on FN currents between the emitter and collector and ignored
leakage of field-emitted currents to the gates, which is addressed later. For both
(a) and (b), the collector was kept at ground. Various combinations for gate bias
were tested to minimize the preferential current leakage to an individual gate and
achieve as close to a symmetric behavior as possible. Ultimately, this condition
was achieved when the bias offset between them was set to +10 V for (a) and
+50 V for (b), such that the top gate was at a more negative potential compared
to the bottom gate. The gate voltage reported in the plot corresponds to the top
gate bias. The runs were not performed in a monotonically decreasing gate bias
sequence as the legend suggests but in a randomized sequence to rule out heating
effects of the emitter tip as the justification for any observed gating. The device
displayed turn-on voltages at around -120 V for (a) and -80 V for (b). Once again, we
observed thermally-promoted field emission, as the turn-on voltage became smaller
at higher temperatures. However, these devices displayed larger turn-on voltages
compared to the two-terminal devices previously discussed due to the larger emitterto-collector distance. The insets correspond to the data plotted in FN coordinates.
The linearity of the plots for higher emitter voltages confirmed FN current as the
emission mechanism. As the gate bias became more negative, the measured current
was reduced for a given emitter potential. This illustrates the effect of gating at the
emitter tip–as the potential difference between the emitter and gates decreases, the
magnitude of the electric field at the emission tip is reduced, thus diminishing the
emitted current.
Fig. 3.17 (c) and (d) show the addition of the emitter and collector currents (with
signs) as a function of emitter bias for the various gate biases at 150 ◦ C and 300
◦ C, respectively. The purpose of these graphs is to show the field-emitted current
leakage from either the emitter to the top gate or from the top gate to the collector.
We can ignore the leakage to the bottom gate, as it was measured for all emitter
voltages to consistently be under 1 nA at 150 ◦ C and under 7 nA at 300 ◦ C (this value
was measured when the leakage to the top gate was the largest). This may be due to
the greater distance between the emitter tip and the bottom gate. A positive value
in the plots corresponds to collector leakage, while a negative value corresponds to

Field Factor (m -1 )

3.2

108

2.8
2.4
1.6
1.2
0.8
-110

-90

-70

-50

-30

Top Gate Voltage (V)

Figure 3.18: Calculated field factor for the four-terminal device as a function of top
gate voltage at 150 ◦ C and 300 ◦ C.

emitter leakage. When the potential difference between the emitter and the gates was
increased, current leaked from emitter to the gate. The leakage path then shifted,
with most leakage occurring from gate to collector, when the potential difference
between the emitter and gates was decreased. We tracked all currents to make sure
that none were unaccounted for. To reduce the emitter-to-gate leakage, we should
improve the symmetry of the gates so that no gate is favoured electrically. To prevent
gate-to-collector leakage, we may consider fabricating the gates with a metal of a
higher work function, which would hinder the onset of exponential emission.
We fitted a linear regression model to the data and extracted the vertical axis intercept
and slope. We assumed 𝜑 = 4.5 eV and calculated 𝛽, as seen in Fig. 3.18. For
both temperatures, an increase in the potential difference between the emitter and
the gates led to a greater 𝛽. This agreed with the increase in current for a given
emitter voltage when the gate voltage became more positive, which confirmed that
the gate electric field modulated the emission current.
Next, we compared the measured data to a simulation of our device operation. We
selected the lower temperature data with the smallest average leakage current to the
gates (top gate at -70 V) and calculated an emission area 𝐴 of 6.5 nm2 . Using COMSOL, we determined that an emitter tip radius of 0.25 nm was necessary to achieve
the 𝛽 previously calculated (Fig. 3.18) for the specific potential configuration. We
then simulated the expected gating as shown in Fig. 3.19 (a) and (b). We calculated
the expected DC transconductance 𝑔𝑚 using
𝑔𝑚 =

Δ𝐼
Δ𝑉𝑔

(3.1)

72
where 𝑉𝑔 is the gate voltage. From the simulation at -153 V, the computed transconductance was 24.5 nS. From the data in Fig. 3.17 (a), we calculated an experimental
transconductance of 0.3 nS at the same emitter potential. This value was 0.1 nS if
we used the collector current. Similarly, the simulated 𝑔𝑚 was 4.9 nS at -110 V,
while the experimental at 300 ◦ C for the same potential was 0.7 nS (and 0.6 nS if we
had considered collector current). A potential reason for the discrepancy between
the simulated and the experimental values is that the simulated transconductance
did not take into account leakage to or from the gate, which was present in the
experimental data. The simulated Maxwell’s capacitance 𝐶 was 7.059 ×10−17 F,
and we calculated the experimental cut-off frequency 𝑓𝑐 given by [39]
𝑓𝑐 =

(3.2)

Top Gate: -110 V; Bottom Gate: -100 V
Top Gate: -90 V; Bottom Gate: -80 V
Top Gate: -70 V; Bottom Gate: -60 V
Top Gate: -50 V; Botom Gate: -40 V
Top Gate: -30 V; Bottom Gate: -20 V

1000
800

Current (nA)

𝑔𝑚
2𝜋𝐶

600
400
200

-140

-120

-100

-80

-60

-40

Emitter Voltage (V)

(a)
100

Top Gate: -90 V; Bottom Gate: -40 V
Top Gate: -70 V; Bottom Gate: -20 V
Top Gate: -50 V; Bottom Gate: 0 V
Top Gate: -30 V; Botom Gate: 20 V

Current (nA)

80
60
40
20
-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

Emitter Voltage (V)

(b)

Figure 3.19: Simulated IV characteristics for the current device geometry for the
various gate potential configurations experimentally tested at (a) 150 ◦ C and at (b)
300 ◦ C.

73
to be 0.676 MHz at 150 ◦ C and 1.578 MHz at 300 ◦ C. Using the simulated 𝑔𝑚 ,
𝑓𝑐 for this geometry, values of 55.23 MHz and 11.05 MHz, respectively, could be
achieved. This 𝑔𝑚 is much lower than previously reported values for single-tip field
emission transistors. For example, Han et al. [40] demonstrated a gate-insulated
vacuum channel transistor with 𝑔𝑚 = 0.2 𝜇S. To increase 𝑓𝑐 , we need to increase
the transconductance. As the distance between the gates and the emitter affects the
field between them, reducing this distance can enhance the control of the emitted
current. For instance, if we move the gates away from the collector and closer to
the emitter, such that the distance between the gates and the emitter is 100 nm, the
simulated transconductance becomes 130 nS. However, this would unfortunately
also increase the capacitance to 8.456 ×10−17 F. Additionally, since FN current
increases exponentially, a larger emitter bias can also increase 𝑔𝑚 . Lastly, 𝑔𝑚 has
been found to exponentially increase with the gate potential [41], although this may
come at the cost of a higher leakage current.
Note that after all tests were completed on the membrane, there were no visible
changes in morphology when inspected via scanning electron microscopy. Fig. 3.20
shows an SEM of the same devices portrayed in Fig. 3.12 after all measurements
presented in this section were conducted.
3.5

Challenges and Suggestions for Improvement

In this chapter, we have presented various two- and four-terminal devices based on
field emission for high-temperature applications. All devices were made of tungsten
due to its low work function and high-temperature tolerance. Initially, devices on
PECVD SiN𝑥 on undoped Si substrate were fabricated. Unfortunately, they were
unsuccessful for operation at elevated temperatures due to the increase in substrate
conductivity and current leakages, which altered the emission characteristic so it
no longer resembled pure FN emission. The next set of devices was fabricated
on stoichiometric Si3 N4 membranes. To increase the resistance of the leakage
pathway, the dielectric substrate in the vicinity of the emission site was removed.
The emission characteristic at higher temperatures was improved compared to the
first device up to temperatures around 300 ◦ C. However, above that, the detrimental
effects of high temperatures began to occur again.
Field emission devices should, in theory, be able to withstand high temperatures.
However, several practical factors can make this difficult. One of these is the dependence of field emission on the work function. At higher temperatures, residual

300 nm
(a)

500 nm
(b)

Figure 3.20: SEM after testing for (a) diode-like and (b) triode-like devices.

gases that have chemisorbed or physisorbed onto the surface of the emitter can
desorb, which changes the work function and affects the emission characteristics.
Additionally, the adsorption and desorption of gases can randomly modulate field
emission and cause burst noise in the emission current. Consequently, circuit design
can become problematic as a fluctuating or noisy IV characteristic is not desirable.
One possible solution is to heat the device under test to a high enough temperature
to boil off contaminants, but this may lead to the redeposition of adsorbates if they
are not pumped out quickly enough before the temperature is lowered. Encapsulating the devices during the fabrication process may be helpful [42]. Ideally, this
should be done in the same deposition run as the electrode material deposition, so
that the devices do not become contaminated after leaving the deposition vacuum
chamber. However, this may be difficult to achieve because the pattern must first
be transferred to the substrate, which requires the chip to be briefly at atmospheric

75
pressure. An alternative solution might be to perform the encapsulation at a later
step in a deposition chamber that has substrate heating capability, which can remove
contaminants before encapsulation.
Tungsten and other refractory metals are prone to surface oxidation [43, 44], which
can be problematic. Tungsten trioxide (WO3 ) is the most thermodynamically stable
tungsten oxide, and its reported work function ranges between 4.7 and 6.4 eV
[45]. The rate of oxidation increases with temperature, particularly above 300 ◦ C.
As a result, tungsten devices are typically used in vacuum environments or inert
atmospheres. One potential solution is to use anti-oxidation coatings. Surface
coatings made from silicon and boron have been suggested for this purpose [46–48].
Additionally, as temperature increases, diffusion effects arise, which is particularly
problematic for vacuum field emission devices. Atoms on the surface of the emitter
tip can move more easily due to thermal fluctuations because there are fewer bonds at
the solid/vacuum interface compared to the bulk. This surface diffusion can change
the morphology of the sharp emitter tip and affect the field enhancement factor,
which in turn alters the emission characteristics. Electromigration, in which atom
diffusion is caused by a high current density, is also a concern for field emission
devices because of the high fields involved. The strong fields at the emitter tip
can cause deformational sharpening, as well as nanoscale protuberances due to
spontaneous surface migration. These changes in electrode surface geometry can
increase Joule heating on the cathode due to heat localization. Field emission
current density is also increased as a result of the increase in the local strength
of the electric field. Ultimately, heating of the emitter tip by high field emission

5 µm

Figure 3.21: SEM that shows device destruction due to electromigration that occurred during emission testing.

76
current densities can lead to electrical breakdown in the form of low-impedance
vacuum arcing, resulting in device destruction [49, 50]. Fig. 3.21 shows an SEM
of a four-terminal early-work device fabricated according to the steps outlined in
Fig. 3.5. The micrograph was taken after the emission characteristic no longer
resembled FN emission during high-temperature measurements, and it unveiled the
catastrophic demise.
In addition to the emission electrodes, vacuum field emission devices also have other
materials and components. At high temperatures, leakages from these parts may
cause parasitic-dominated measurements, which can mask electron field emission,
as the devices discussed in this chapter have experienced. Some of these other
components are discussed below.
The device is usually fabricated on an insulator substrate, which may allow leakages
through it, such as FP emission, at high temperatures and fields that could interfere
with FN emission. Even if the substrate conduction at high fields and elevated
temperatures is not a problem, packaging can be challenging. Metal interconnects,
bond pads, and bond wires must be carefully chosen. In this chapter, Ti/Au pads
and Al wires, which are readily available in the cleanroom and are a popular choice,
were used. However, these materials become incompatible at temperatures above
300 ◦ C due to intermetallic formation and Kirkendall voiding, which can weaken
the bonds’ strength and increase their electrical resistance [51]. Aluminum is also
not a good choice because it readily electromigrates at moderate temperatures. Gold
is a better choice for wire bonds, but it can alloy with the adhesion layer at high
temperatures. Therefore, metal layers with low mutual diffusivities are needed.
A promising metallization scheme that has been successful as a diffusion barrier
against oxidation, has good adhesion, and prevents gold from wire bonds from
intermixing with other metal layers is Ti/TaSi2 /Pt. Ti forms a good Ohmic contact
and has great adhesion, and Pt can be easily wire bonded using Au wires. The TaSi2
layer also reacts with Pt to form Pt2 Si, which serves as a diffusion barrier [52, 53].
A package that can withstand the stresses of elevated temperatures and does not
contribute to parasitic conduction is also needed. Traditional plastic PCB materials,
such as FR4, can only tolerate temperatures below the glass transition, which are
usually moderately low. A prototype ceramic package made with 96% polycrystalline aluminum oxide and thick gold metallization has successfully operated over
10,000 hours at 500 ◦ C [53]. However, a more commercially available package
would be preferred. High-temperature co-fired ceramic (HTCC) alumina packages

77
are a good option, but they can be hard to come by, especially for custom-sized
dies [54]. The choice of die-attach material is also important, as the coefficient of
thermal expansion between the substrate die material, die-attach, and package must
be matched to avoid stresses or fractures.
Moreover, uniformity in the fabrication of the suspended devices discussed in this
chapter is challenging due to the custom nature of the milling process. Consequently,
the emission characteristic between fabricated devices varies a lot, which can be
burdensome for circuit design. Membranes are also fragile, so the fabrication
yield is lower compared to devices made on bulk substrate. Fig. 3.22 shows
an example of a membrane that broke during the milling step. Therefore, the
fabrication process must be modified if mass production is desired. Nonetheless,
nanoprotrusions are inevitable, which can cause noise in the emission characteristic
in the form of discrete jumps in the measured current. In many cases, these emission
instabilities go away over time as ion bombardment can blunt these nanoprotrusions
[55]. However, there are some instances wherein the large field enhancements caused
by these nanoprotrusions can lead to device destruction. In any case, as the field
enhancement factor is tightly connected to the presence of nanoprotrusions, which
are impossible to predict, it is very hard to model field emission currents a priori.
Also, the effects of surface roughness and nanoprotrusions become more significant
as the emitter-to-collector gap is reduced to the smallest attainable dimensions.
As mentioned in Section 3.1, we aimed to fabricate the smallest emitter-to-collector
gap as this would yield low turn-on voltages. This was easier to achieve with the
devices fabricated on a thick substrate, as we used high-resolution standard EBL.

1 mm

Figure 3.22: Suspended device that broke during milling.

78
However, it was hard to accomplish with the devices on membranes due to the
residual stress that would oppose this effort. As a result, the operating voltages were
higher than our desired < 10 V. One way to achieve a shorter electrode separation
is to use the stress to our advantage by patterning stress-release cuts in the vicinity
that shrink the gap rather than expand it [56].
One approach that has been shown to reduce the operating voltage is to coat the
emitter terminal with a thin layer of an electropositive element relative to the cathode
material. This layer reduces the barrier for electron emission by lowering the work
function. The deposited layer must be thin enough so that the electropositive material
is ionically bonded to the substrate and forms a surface dipole layer through the
redistribution of electron density, which helps the electrons escape into vacuum.
If the coating is too thick, the work function becomes closer to the coating work
function as the coating becomes metallic [57]. Common electropositive materials
used to enhance cathode performance include alkali metals, alkaline earth metals,
and their oxides, such as cesium [58, 59], barium [60], and cesium oxide [61].
Other pure elements and oxides can also be used; for example, the deposition of
monolayers of zirconium (work function ∼4.1 eV) on W has been shown to reduce
the work function to 2.62 eV [62]. In addition, surface coating has the potential to
reduce outgassing as the coating layer can act as a barrier at the surface. However,
this may not be a permanent solution to enhance emission current as high operating
voltages can eventually erode the coating layer through ion sputtering.
The field emission devices reported in this chapter were prone to flicker noise that
cause current instabilities. Unlike thermionic emitters that operate in a space charge
limited regime, the nanoscale single-tip emitters described in this chapter are exposed to the statistical fluctuation and randomness of electron field emission. While
the specific reason for the observed current instabilities is not known with certainty,
several plausible causes include the sharpening and blunting of nanoprotrusions on
the emitter tip, changes on an atomic scale in the work function due to the adsorption and desorption of gas molecules, and electromigration of impurities. Emission
stability has been shown to improve with lower ambient pressures [63] so a better
vacuum is desired. Another potential improvement is to increase the number of
emitter tips. The benefit of having multiple identical tips is that current fluctuation
from a single emitter can be statistically reduced by ensemble averaging the emission current from a group of emitters operating simultaneously [64]. Additionally,

79
having many emitter tips allows for higher currents to be sourced, improving device
parameters. This concept is further discussed in the following chapter.
Generally, the emission characteristic can be modified by either engineering the material properties, specifically the work function of the electrodes, or by manipulating
the physical geometry. In this way, either of these approaches could be used to
improve the efficiency of the four-terminal devices and reduce power consumption.
Materials with higher work function, such as Pt, could be deposited onto the collector and gate terminals to minimize leakage currents from the gate into the collector
and achieve rectifying behaviour. A wrap-around gate could be fabricated to reduce
operating voltages and maximize the gate control in electron emission [65]. Overall,
these refinements should improve the transconductance of the devices.
In our analysis, it is important to note that while we tried to extract physical meaningful parameters from the linear fit of the FN plot in line with the field emission
community, it is difficult to make definite claims on the specifics of the emission
process. This is because the linearized FN equation is degenerate, as both the slope
and the 𝑦-intercept are needed to describe it. However, these two parameters are
related to three physical variables: the field enhancement factor, the emission area,
and the work function. Therefore, even though we kept the value of one physical
parameter constant (i.e., the work function) to extract the other two, it is possible
that all three of them changed as experimental conditions were modified.
Further work should extend to studying the radiation hardness performance of the
proposed lateral nanoscale field emission devices for space and nuclear applications,
as well as studying the emission characteristic at low temperatures for the design of
cryogenic electronic circuits. Operating at cold temperatures may reduced leakage
currents associated with high temperatures, leading to more stable emission.
3.6

An Attractive Material: Diamond

Diamond is a promising material for robust field emission devices that has attracted
significant attention due to its interesting properties, including:
• high thermal conductivity, which prevents overheating (particularly useful for
high-power and high-temperature operation),
• chemical inertness (advantageous for stable emission current),
• high physical hardness to withstand ion bombardment (and thus, avoid tip
erosion and improve device lifetime),

80
• large intrinsic breakdown field (good for high-power applications),
• large band gap (suitable for high-temperature operation).
However, its most fascinating property for field emitter fabrication is its negative
electron affinity (NEA) or low positive electron affinity. The electron affinity is
the energy needed to remove an electron from the conduction band minimum of a
semiconductor and escape into vacuum. A NEA is attractive due to the small barrier
for field emission, which results in low voltage operation. This efficient electron
emission, in theory, removes the need to fabricate sharp tips to achieve large field
enhancement factors, increasing the durability of field emitters and facilitating
fabrication.
It has been reported that partially hydrogenated (100) and (111) diamond surfaces
have effective NEA [66, 67]. Thin metallic films, such as titanium, cobalt, copper,
nickel, and zirconium, can also induce effective NEA in diamond [68–71]. Even
though the work function of cobalt is higher than that of zirconium or titanium, it is
less reactive. While surface coatings, such as cesium and barium, have been used
on silicon and metal field emitters to lower their effective work functions [57, 72],
they tend to be chemically reactive, limiting their lifetime. In contrast, diamond
surfaces offer the benefits of chemical stability and mechanical strength.
However, undoped diamond cannot support sustained electron emission due to its
wide band gap (∼ 5.5 eV). Thus, a continuous source of electrons is needed to
supply charge carriers into the conduction band of diamond. To take advantage of
diamond’s NEA and induce emission with a low applied electric field, the Fermi
level must be close to the conduction band, requiring n-type donor impurities,
which is an experimentally challenging task. Introducing such impurities into
diamond is limited by the solubility and ionizability of donors used, as well as
by the host crystal’s difficulty in spontaneously creating defects to compensate the
dopant species due to the tight lattice structure [73]. Lithium, phosphorous, and
sodium have been predicted to be shallow donors that occupy interstitial sites,
but their low solubility makes in-diffusion processes unsuccessful, requiring ionimplantation [74]. However, ion-implantation can cause substantial damage, leading
to poor film quality and irreversible graphitization in diamond crystallites, which
can adversely affect field emission [75, 76].
Substitutional nitrogen in nanocrystalline diamond is a promising donor candidate
due to its small covalent radii and high solubility. Even though it forms a deep

81
donor level around 1.7 eV below the conduction band of diamond, as the donor
energy level still lies above the Fermi energy of several metals, a depletion layer
of ionized donors forms in equilibrium. If the donor concentration is sufficiently
high, band bending causes the tunneling barrier to narrow so that electrons emit
into diamond [77–79]. Fig. 3.23 illustrates the energy levels for n-type diamond
when it is positively biased to induce electron emission. For electrons to emit from
the metal into vacuum through diamond, they must first tunnel through the metaldiamond interface, which depends on the donor concentration and choice of metal,
then conduct through the diamond layer, which is affected by the content of 𝑠𝑝 3 and
𝑠𝑝 2 phase (this is discussed below) and impurity doping concentration, and finally
tunnel from diamond into vacuum, which is controlled by the geometry [80, 81].

n-type
diamond

metal
(cathode)

vacuum

metal
(anode)

EVAC

EV
EF

Figure 3.23: Simplified band diagram illustrating the field electron emission mechanism from a metal cathode coated with n-type diamond with an effective NEA
under forward bias. A depletion layer of width 𝑤 with ionized donors forms at the
metal-diamond interface.

82
Traditional diamond thin films are usually synthesized by hot filament chemical
vapour deposition (HFCVD), which requires substrate temperatures above 500 ◦ C.
In addition, mechanical substrate polishing is often required to enhance diamond’s
nucleation density [82, 83]. The high deposition temperatures and added fabrication
steps needed for a high-quality film have deterred the fabrication of diamond field
emitters. Instead, a simpler manufacturing process that can easily combine diamond
with other materials is preferred. Ultrananocrystalline diamond (UNCD) synthesized using microwave plasma-assisted chemical vapour deposition (MPCVD) has
emerged as a very promising material. UNCD diamond can be deposited at temperatures as low as 350 ◦ C on a wide range of substrates including Si, SiO2 , Ta, Ti, W,
and SiN. While it preserves the robustness of the mechanical, thermal, and chemical
properties of conventional CVD microcrystalline diamond films, UNCD has ultrasmall (3–5 nm) grain size and a higher volume density of grain boundaries [83–85].
This facilitates the incorporation of nitrogen dopants for n-type conductivity. It
has also been reported that diamond films with high defect contents and smaller
grain sizes have higher electron emission than films with fewer defect structures
and larger grain sizes [86, 87]. Additionally, smaller grains improve the mechanical
resistance to breakdown. UNCD is smoother, eliminating the need for mechanical
polishing. By controlling the deposition parameters such as the gas flow rate and
gas concentration, the size and 𝑠𝑝 2 phase content can be easily controlled [88]. This
is particularly beneficial as it has been shown that an optimal content of 𝑠𝑝 3 and
𝑠𝑝 2 exists for improved field electron emission. If the 𝑠𝑝 3 content is too high, then
the effective supply of electrons is too low for sustained field emission. If the 𝑠𝑝 2
content is too high, the electron affinity increases and the tunneling barrier becomes
higher [89]. UNCD is synthesized using a CH4 /N2 /Ar/H2 gas mixture plasma. CH4
is the carbon source gas due to its high purity and shared tetrahedral structure with
diamond, Ar modifies the grain size, H2 introduces the surface hydrogen termination for NEA, and N2 adds the n-type dopant [90]. Moreover, UNCD can be easily
etched using ICP-RIE techniques in an oxygen plasma with good selectivity [83].
Electron emission experiments using MPCVD n-type diamond have shown lower
threshold fields, and improved emission stability compared to conventional Si or
metal emitters. For example, Subramanian et al. [91] have demonstrated a lateral
field emission diamond diode fabricated on silicon-on-insulator (SOI) wafer with
an anode-to-cathode separation of 3 µm. The device exhibited a low turn-on voltage
of 5.9 V and a high emission current of 1.1 mA at an anode voltage of 100 V from
a six-finger configuration. The electron emission was stable with a ∼ 4% current

83
fluctuation over 10 hrs at a vacuum pressure of 10−6 Torr. They also showed high
radiation tolerance of diamond field emitters [92, 93]. In a separate experiment, they
demonstrated a lateral vacuum field emission microtriode utilizing nanocrystalline
diamond with a measured anode current of 4 µA and a transconductance of 0.3 µS
from a single emitter-finger at a gate voltage of 40 V and anode voltage of 65 V.
The gate-cathode spacing was 3 µm and the anode-cathode spacing was 12 µm [41].
These are very promising results that illustrate the suitability of MPCVD n-type
diamond as a field emitter material for harsh environment operation. Moreover, if
higher-resolution lithography is used to achieve even smaller device dimensions [94,
95], improved device operation is expected.
References
[1] P. L. Dreike et al. “An overview of high-temperature electronic device technologies and potential applications.” IEEE Transactions on Components,
Packaging, and Manufacturing Technology: Part A 17.4 (1994), pp. 594–
609. doi: 10.1109/95.335047.
[2] J. Watson and G. Castro. “A review of high-temperature electronics technology and applications.” Journal of Materials Science: Materials in Electronics
26.12 (2015), pp. 9226–9235. doi: 10.1007/s10854-015-3459-4.
[3] R. K. Kirschman. High-temperature electronics. New York, NY, USA: WileyIEEE Press, 1999. isbn: 978-0-470-54488-4.
[4] P. Neudeck et al. “Prolonged silicon carbide integrated circuit operation in
Venus surface atmospheric conditions.” AIP Advances 6.12 (2016), p. 125119.
doi: 10.1063/1.4973429.
[5] R. M. Wilson. “Circuitry made robust enough for Venus.” Physics Today 70.3
(2017), pp. 19–21. doi: 10.1063/PT.3.3484.
[6] L. B. De Rose, A. Scherer, and W. M. Jones. “Suspended nanoscale field emitter devices for high-temperature operation.” IEEE Transactions on Electron
Devices 67.11 (2020), pp. 5125–5131. doi: 10.1109/TED.2020.3019765.
[7] C. Davisson and L. H. Germer. “The thermionic work function of tungsten.”
Physical Review 20.4 (1922), pp. 300–330. doi: 10.1103/PhysRev.20.
300.
[8] Y. H. Song. “Analysis of electron emission degradation in silicon field emitter
arrays.” Journal of Vacuum Science & Technology B 16.2 (1998), p. 815. doi:
10.1116/1.589912.
[9] M. S. Choi, J. H. Kim, and Y. S. Kim. “Field-emission characteristics of
nitrogen-doped diamond-like carbon film deposited by filtered cathodic vac-

84
uum arc technique.” Journal of Non-Crystalline Solids 324.1 (2003), pp. 187–
191. doi: 10.1016/S0022-3093(03)00331-4.
[10] Y. Li, Y. Sun, and J. T. W. Yeow. “Nanotube field electron emission: Principles, development, and applications.” Nanotechnology 26.24 (2015), p. 242001.
doi: 10.1088/0957-4484/26/24/242001.
[11] H. D. Nguyen et al. “High-performance field emission based on nanostructured tin selenide for nanoscale vacuum transistors.” Nanoscale 11.7 (2019),
pp. 3129–3137. doi: 10.1039/C8NR07912A.
[12] F. Daneshvar et al. “Critical challenges and advances in the carbon nanotube–metal interface for next-generation electronics.” Nanoscale Advances
3.4 (2021), pp. 942–962. doi: 10.1039/D0NA00822B.
[13] M. Ahmad and S. R. Silva. “Low temperature growth of carbon nanotubes –
A review.” Carbon 158 (2020), pp. 24–44. doi: 10.1016/j.carbon.2019.
11.061.
[14] V. T. Binh and V. Semet. “Planar cold cathodes.” In: Advances in Imaging
and Electron Physics. Vol. 148. Elsevier, 2007, pp. 1–73. isbn: 978-0-12373910-0.
[15] A. Di Bartolomeo et al. “A WSe2 vertical field emission transistor.” Nanoscale
11.4 (2019), pp. 1538–1548. doi: 10.1039/C8NR09068H.
[16] M. Le-Huu et al. “Investigation of the reliability of 4H–SiC MOS devices
for high temperature applications.” Microelectronics Reliability 51.8 (2011),
pp. 1346–1350. doi: 10.1016/j.microrel.2011.03.015.
[17] M. Sometani et al. “Temperature-dependent analysis of conduction mechanism of leakage current in thermally grown oxide on 4H-SiC.” Journal of
Applied Physics 117.2 (2015), p. 024505. doi: 10.1063/1.4905916.
[18] J. Frenkel. “On pre-breakdown phenomena in insulators and electronic semiconductors.” Physical Review 54.8 (1938), pp. 647–648. doi: 10 . 1103 /
PhysRev.54.647.
[19] J. G. Simmons. “Poole-Frenkel effect and Schottky effect in metal-insulatormetal systems.” Physical Review 155.3 (1967), pp. 657–660. doi: 10.1103/
PhysRev.155.657.
[20] W. M. Jones. “Nanoscale field emission devices.” Ph.D. Dissertation. Pasadena,
CA: California Institute of Technology, 2018.
[21] P. R. Schwoebel and C. A. Spindt. “Field-emitter array performance enhancement using hydrogen glow discharges.” Applied Physics Letters 63.1 (1993),
pp. 33–35. doi: 10.1063/1.109741.
[22] A. Vesel, M. Mozetič, and M. Balat-Pichelin. “Sequential oxidation and
reduction of tungsten/tungsten oxide.” Thin Solid Films 591 (2015), pp. 174–
181. doi: 10.1016/j.tsf.2015.02.019.

85
[23] V. V. Zhirnov et al. ““Standardization” of field emission measurements.”
Journal of Vacuum Science & Technology B 19.1 (2001), pp. 87–93. doi:
10.1116/1.1342006.
[24] T. J. Vink et al. “Stress, strain, and microstructure in thin tungsten films
deposited by dc magnetron sputtering.” Journal of Applied Physics 74.2
(1993), pp. 988–995. doi: 10.1063/1.354842.
[25] Y. G. Shen et al. “Residual stress, microstructure, and structure of tungsten
thin films deposited by magnetron sputtering.” Journal of Applied Physics
87.1 (2000), pp. 177–187. doi: 10.1063/1.371841.
[26] M. Ghaderi et al. “Minimizing stress in large-area surface micromachined perforated membranes with slits.” Journal of Micromechanics and Microengineering 25.7 (2015), p. 074010. doi: 10.1088/0960-1317/25/7/074010.
[27] A. A. G. Driskill-Smith, D. G. Hasko, and H. Ahmed. “Nanoscale field
emission structures for ultra-low voltage operation at atmospheric pressure.”
Applied Physics Letters 71.21 (1997), pp. 3159–3161. doi: 10 . 1063 / 1 .
120276.
[28] W. M. Jones, D. Lukin, and A. Scherer. “Practical nanoscale field emission devices for integrated circuits.” Applied Physics Letters 110.26 (2017),
p. 263101. doi: 10.1063/1.4989677.
[29] S. Dushman. “Electron emission from metals as a function of temperature.”
Physical Review 21.6 (1923), pp. 623–636. doi: 10.1103/PhysRev.21.
623.
[30] P. H. Cutler et al. “Theory of electron emission in high fields from atomically sharp emitters: Validity of the Fowler-Nordheim equation.” Progress
in Surface Science 42.1-4 (1993), pp. 169–185. doi: 10 . 1016 / 0079 6816(93)90068-7.
[31] W. P. Dyke and W. W. Dolan. “Field Emission.” In: Advances in Electronics
and Electron Physics. Vol. 8. Academic Press, 1956, pp. 89–185.
[32] C. M. Tan, J. Jia, and W. Yu. “Temperature dependence of the field emission
of multiwalled carbon nanotubes.” Applied Physics Letters 86.26 (2005),
p. 263104. doi: 10.1063/1.1957117.
[33] J. Li et al. “Temperature dependence of the field emission from the fewlayer graphene film.” Applied Physics Letters 99.16 (2011), p. 163103. doi:
10.1063/1.3651323.
[34] K. L. Jensen. “An analytical model of an emission-gated Twystrode using a
field emitter array.” Journal of Applied Physics 83.12 (1998), pp. 7982–7992.
doi: 10.1063/1.367980.

86
[35] F. Charbonnier. “Arcing and voltage breakdown in vacuum microelectronics
microwave devices using field emitter arrays: causes, possible solutions, and
recent progress.” Journal of Vacuum Science & Technology B 16.2 (1998),
p. 880. doi: 10.1116/1.589924.
[36] J. Chen et al. “The hysteresis phenomenon of the field emission from the
graphene film.” Applied Physics Letters 99.17 (2011), p. 173104. doi: 10.
1063/1.3655912.
[37] H. Yin et al. “Fabrication and temperature-dependent field-emission properties of bundlelike VO2 nanostructures.” ACS Applied Materials & Interfaces
3.6 (2011), pp. 2057–2062. doi: 10.1021/am200291a.
[38] E. O. Popov, A. G. Kolosko, and S. V. Filippov. “Electrical field admissible
values for the classical field emitter regime in the study of large area emitters.”
AIP Advances 9.1 (2019), p. 015129. doi: 10.1063/1.5080439.
[39] J. W. Han et al. “Nanoscale vacuum channel transistors fabricated on silicon
carbide wafers.” Nature Electronics 2.9 (2019), pp. 405–411. doi: 10.1038/
s41928-019-0289-z.
[40] J. W. Han, J. Sub Oh, and M. Meyyappan. “Vacuum nanoelectronics: Back to
the future?—Gate insulated nanoscale vacuum channel transistor.” Applied
Physics Letters 100.21 (2012), p. 213505. doi: 10.1063/1.4717751.
[41] K. Subramanian, W. P. Kang, and J. L. Davidson. “Nanocrystalline diamond
lateral vacuum microtriode.” Applied Physics Letters 93.20 (2008), p. 203511.
doi: 10.1063/1.3036008.
[42] A. Hilton and D. Temple. “Wafer-level vacuum packaging of smart sensors.”
Sensors 16.11 (2016), p. 1819. doi: 10.3390/s16111819.
[43] E. Lassner and W. D. Schubert. “Important aspects of tungsten chemistry.”
In: Tungsten. Boston, MA: Springer US, 1999, pp. 85–132. isbn: 978-1-46137225-7.
[44] A. Warren, A. Nylund, and I. Olefjord. “Oxidation of tungsten and tungsten
carbide in dry and humid atmospheres.” International Journal of Refractory
Metals and Hard Materials 14.5-6 (1996), pp. 345–353. doi: 10 . 1016 /
S0263-4368(96)00027-3.
[45] S. Han et al. “Improving performance of organic solar cells using amorphous
tungsten oxides as an interfacial buffer layer on transparent anodes.” Organic
Electronics 10.5 (2009), pp. 791–797. doi: 10.1016/j.orgel.2009.03.
016.
[46] T. Fu et al. “Oxidation protection of tungsten alloys for nuclear fusion applications: A comprehensive review.” Journal of Alloys and Compounds 884
(2021), p. 161057. doi: 10.1016/j.jallcom.2021.161057.

87
[47] D. Rowe. “Refractory metals.” Heat Treating Progress (ASM International)
3 (2003). url: https://www.asminternational.org/c/portal/pdf/
download?articleId=HTP00307P056&groupId=10192.
[48] H. J. Nolting and R. A. Jefferys. Oxidation resistant high temperature protective coatings for tungsten. Tech. rep. Cleveland, Ohio: Thompson Ramo
Wooldridge Inc. TRW Electromechanical Div., 1963.
[49] G. N. Fursey. “Field Emission and Vacuum Breakdown.” IEEE Transactions
on Electrical Insulation EI-20.4 (1985), pp. 659–670. doi: 10.1109/TEI.
1985.348883.
[50] W. P. Dyke et al. “The field emission initiated vacuum arc. I. experiments on
arc initiation.” Physical Review 91.5 (1953), pp. 1043–1054. doi: 10.1103/
PhysRev.91.1043.
[51] P. Hagler, P. Henson, and R. W. Johnson. “Packaging technology for electronic
applications in harsh high-temperature environments.” IEEE Transactions on
Industrial Electronics 58.7 (2011), pp. 2673–2682. doi: 10 . 1109 / TIE .
2010.2047832.
[52] R. S. Okojie et al. “Reliability assessment of Ti/TaSi2 /Pt ohmic contacts
on SiC after 1000 h at 600◦ C.” Journal of Applied Physics 91.10 (2002),
pp. 6553–6559. doi: 10.1063/1.1470255.
[53] P. G. Neudeck et al. “Extreme temperature 6H-SiC JFET integrated circuit
technology: Extreme temperature 6H-SiC JFET integrated circuit technology.” Physica Status Solidi (a) 206.10 (2009), pp. 2329–2345. doi: 10 .
1002/pssa.200925188.
[54] L. Y. Chen et al. “Electrical performance of a high temperature 32-I/O HTCC
alumina package.” Additional Conferences (Device Packaging, HiTEC, HiTEN,
and CICMT) 2016.HiTEC (2016), pp. 000066–000072. doi: 10 . 4071 /
2016-HITEC-66.
[55] N. S. Xu and W. E. Huq. “Novel cold cathode materials and applications.”
Materials Science and Engineering R: Reports 48.2-5 (2005), pp. 47–189.
doi: 10.1016/j.mser.2004.12.001.
[56] J. M. Fink et al. “Quantum electromechanics on silicon nitride nanomembranes.” Nature Communications 7.1 (2016), p. 12396. doi: 10 . 1038 /
ncomms12396.
[57] J. M. Macaulay et al. “Cesiated thin-film field-emission microcathode arrays.”
Applied Physics Letters 61.8 (1992), pp. 997–999. doi: 10.1063/1.107699.
[58] G. G. P. van Gorkom. “Performance of silicon cold cathodes.” Journal of
Vacuum Science & Technology B 4.1 (1986), p. 108. doi: 10 . 1116 / 1 .
583357.

88
[59] W. K. Wong et al. “Field-emission properties of multihead silicon cone arrays
coated with cesium.” Applied Physics Letters 80.5 (2002), pp. 877–879. doi:
10.1063/1.1446990.
[60] R. Forman. “Surface studies of barium and barium oxide on tungsten and its
application to understanding the mechanism of operation of an impregnated
tungsten cathode.” Journal of Applied Physics 47.12 (1976), pp. 5272–5279.
doi: 10.1063/1.322602.
[61] K. C. Mishra, R. Garner, and P. C. Schmidt. “Model of work function of
tungsten cathodes with barium oxide coating.” Journal of Applied Physics
95.6 (2004), pp. 3069–3074. doi: 10.1063/1.1646451.
[62] V. N. Shrednik. “Investigation of zirconium atomic layers on tungsten crystal
faces by means of electron and ion projectors.” Fizika Tverdogo Tela (USSR)
3.6 (1961), pp. 1750–1761.
[63] J. T. Trujillo. “Effects of vacuum conditions on low frequency noise in silicon
field emission devices.” Journal of Vacuum Science & Technology B 15.2
(1997), p. 401. doi: 10.1116/1.589326.
[64] S. Yamamoto. “Fundamental physics of vacuum electron sources.” Reports
on Progress in Physics 69.1 (2006), pp. 181–232. doi: 10 . 1088 / 0034 4885/69/1/R04.
[65] J. W. Han, D. Moon, and M. Meyyappan. “Nanoscale vacuum channel transistor.” Nano Letters 17.4 (2017), pp. 2146–2151. doi: 10 . 1021 / acs .
nanolett.6b04363.
[66] J. van der Weide and R. J. Nemanich. “Influence of interfacial hydrogen
and oxygen on the Schottky barrier height of nickel on (111) and (100)
diamond surfaces.” Physical Review B 49.19 (1994), pp. 13629–13637. doi:
10.1103/PhysRevB.49.13629.
[67] F. J. Himpsel et al. “Quantum photoyield of diamond(111)—A stable negativeaffinity emitter.” Physical Review B 20.2 (1979), pp. 624–627. doi: 10.1103/
PhysRevB.20.624.
[68] P. K. Baumann and R. J. Nemanich. “Electron affinity and Schottky barrier
height of metal–diamond (100), (111), and (110) interfaces.” Journal of
Applied Physics 83.4 (1998), pp. 2072–2082. doi: 10.1063/1.366940.
[69] J. van der Weide et al. “Negative-electron-affinity effects on the diamond
(100) surface.” Physical Review B 50.8 (1994), pp. 5803–5806. doi: 10 .
1103/PhysRevB.50.5803.
[70] J. van der Weide. “Schottky barrier height and negative electron affinity of
titanium on (111) diamond.” Journal of Vacuum Science & Technology B
10.4 (1992), p. 1940. doi: 10.1116/1.586162.

89
[71] P. K. Baumann. “Comparison of electron affinity and Schottky barrier height
of zirconium and copper–diamond interfaces.” Journal of Vacuum Science &
Technology B 15.4 (1997), p. 1236. doi: 10.1116/1.589444.
[72] L. A. Bol’shov et al. “Submonolayer films on the surface of metals.” Soviet
Physics Uspekhi 20.5 (1977), pp. 432–451. doi: 10.1070/PU1977v020n05ABEH005398.
[73] E. Abubakr et al. “Laser-induced phosphorus-doped conductive layer formation on single-crystal diamond surfaces.” ACS Applied Materials & Interfaces
12.51 (2020), pp. 57619–57626. doi: 10.1021/acsami.0c18435.
[74] J. Bernholc et al. “Theory of native defects, doping and diffusion in diamond
and silicon carbide.” Materials Science and Engineering: B 11.1-4 (1992),
pp. 265–272. doi: 10.1016/0921-5107(92)90222-U.
[75] J. F. Prins. “Onset of hopping conduction in carbon-ion-implanted diamond.”
Physical Review B 31.4 (1985), pp. 2472–2478. doi: 10.1103/PhysRevB.
31.2472.
[76] S. Koizumi et al. “Growth and characterization of phosphorous doped {111}
homoepitaxial diamond thin films.” Applied Physics Letters 71.8 (1997),
pp. 1065–1067. doi: 10.1063/1.119729.
[77] M. W. Geis. “Diamond emitters fabrication and theory.” Journal of Vacuum
Science & Technology B 14.3 (1996), p. 2060. doi: 10.1116/1.588986.
[78] J. Robertson and W. Milne. “Band model for electron emission from diamondlike carbon and diamond.” Journal of Non-Crystalline Solids 227-230 (1998),
pp. 558–564. doi: 10.1016/S0022-3093(98)00189-6.
[79] J. Robertson. “Mechanisms of electron field emission from diamond, diamondlike carbon, and nanostructured carbon.” Journal of Vacuum Science & Technology B 17.2 (1999), p. 659. doi: 10.1116/1.590613.
[80] P. W. May et al. “Field emission from chemical vapor deposited diamond and
diamond-like carbon films: Investigations of surface damage and conduction
mechanisms.” Journal of Applied Physics 84.3 (1998), pp. 1618–1625. doi:
10.1063/1.368231.
[81] K. Subramanian. “Development of nanocrystalline diamond lateral vacuum
field emission devices.” PhD thesis. Nashville, TN: Vanderbilt University,
2008.
[82] E. Staryga et al. “Field emission from diamond and diamond-like carbon
films.” Journal of Superhard Materials 29.3 (2007), p. 189. doi: 10.3103/
S1063457607030161.
[83] A. Zhou et al. “Ultrananocrystalline diamond nanowires: Fabrication, characterization, and sensor applications.” Materials 14.3 (2021), p. 661. doi:
10.3390/ma14030661.

90
[84] A. R. Krauss et al. “Ultrananocrystalline diamond thin films for MEMS
and moving mechanical assembly devices.” Diamond and Related Materials
10.11 (2001), pp. 1952–1961. doi: 10.1016/S0925-9635(01)00385-5.
[85] J. E. Gerbi et al. “Electrical contacts to ultrananocrystalline diamond.” Applied Physics Letters 83.10 (2003), pp. 2001–2003. doi: 10 . 1063 / 1 .
1609043.
[86] V. V. Zhirnov and J. J. Hren. “Electron emission from diamond films.” MRS
Bulletin 23.9 (1998), pp. 42–48. doi: 10.1557/S0883769400029365.
[87] W. P. Kang et al. “Effect of sp2 content and tip treatment on the field emission
of micropatterned pyramidal diamond tips.” Journal of Vacuum Science &
Technology B 16.2 (1998), pp. 684–688. doi: 10.1116/1.589881.
[88] K. Subramanian et al. “The effect of growth rate control on the morphology
of nanocrystalline diamond.” Diamond and Related Materials 14.3-7 (2005),
pp. 404–410. doi: 10.1016/j.diamond.2005.01.027.
[89] A. Wisitsorat-at. “Micropatterned diamond vacuum field emission devices.”
PhD thesis. Nashville, TN: Vanderbilt University, 2002.
[90] O. Chubenko. “Detailed modeling of physical processes in electron sources
for accelerator applications.” PhD thesis. Washington, DC: George Washington University, 2019.
[91] K. Subramanian et al. “Nanodiamond planar lateral field emission diode.”
Diamond and Related Materials 14.11-12 (2005), pp. 2099–2104. doi: 10.
1016/j.diamond.2005.08.068.
[92] W. P. Kang et al. “Nanodiamond lateral VFEM technology for harsh environments.” IEEE Transactions on Nuclear Science 54.4 (2007), pp. 1061–1065.
doi: 10.1109/TNS.2007.892117.
[93] J. Davidson et al. “Diamond vacuum electronic device behavior after high neutron fluence exposure.” IEEE Transactions on Nuclear Science 56.4 (2009),
pp. 2225–2229. doi: 10.1109/TNS.2009.2020603.
[94] S. M. Lewis et al. “Plasma-etched pattern transfer of sub-10 nm structures
using a metal–organic resist and helium ion beam lithography.” Nano Letters
19.9 (2019), pp. 6043–6048. doi: 10.1021/acs.nanolett.9b01911.
[95] S. M. Lewis et al. “Tuning the performance of negative tone electron beam
resists for the next generation lithography.” Advanced Functional Materials
32.32 (2022), p. 2202710. doi: 10.1002/adfm.202202710.

91
Chapter 4

FIELD EMISSION DEVICES FOR HIGH-FREQUENCY
OPERATION
Field emission devices are promising candidates for high-frequency electronics due
to the intrinsic superiority of vacuum as a transport medium. While carriers in
semiconductor channels suffer from acoustic and optical phonon scattering, electrons in vacuum can, in theory, travel ballistically. This means that the saturation
velocity for electrons is restricted to about 1 × 107 cm/s in Si, the most widely-used
semiconductor material, whereas it can reach 3 × 1010 cm/s in vacuum. In addition,
advanced nanofabrication techniques used in the solid-state industry can be employed to manufacture the smallest nanoscale vacuum channels, potentially leading
to the production of field emission devices that can operate at GHz frequencies or
higher.
The FN theory, which is based on the time-independent Schrödinger equation, forms
the foundation of field electron emission theory. When an AC field is applied, the
FN theory is still valid as long as the tunneling time, 𝜏𝑡𝑢𝑛 , is small relative to the
rate of change of the applied field so that the tunneling electron does not feel the
changing vacuum potential barrier. Thus, the value of the instantaneous electric field
is used in the conventional FN equation. This adiabatic condition can be expressed
as 𝜔|𝜏𝑡𝑢𝑛 | ≪ 1, where 𝜔 is the frequency of the dynamic field [1]. For practical
devices based on the direct interaction of field emission and electromagnetic waves,
it has been shown that for frequencies up to about 1014 Hz, the FN equation still
holds [2], and the time-dependent transmission coefficient preserves phase with
the electric field. Therefore, field emission devices are an attractive option for
microwave cathode applications because their response to applied electric fields is
virtually instantaneous, as the emission is a quantum mechanical process that does
not require heating.
Additionally, high-frequency operation of field emission devices reduces ion bombardment. This is due to an effective repulsive potential that forms near the surface
of the cathode when a microwave field is applied, making emission under a fast
AC field more stable [3]. This can ultimately increase the lifetime of the device.
Another interesting characteristic of field electron emission is its non-linear rela-

92
tionship between the applied electric field and the emitted current, which enables
the development of cold cathodes as practical microwave devices that can perform
non-linear operations such as frequency mixing and harmonic generation.
In this chapter, we demonstrate a multi-tip field emission two-terminal device for
frequency mixing. We describe the fabrication steps, testing setup, and results.
We also introduce some preliminary results in work function reduction by thin-film
praseodymium (Pr) evaporation.
Parts of this chapter were adapted from [4, 5].
4.1

Fundamentals of Frequency Multipliers and Mixers

Frequency multipliers and mixers are essential components of modern electromagnetic technology. They are used in radar and high-bandwidth communication
industries for military, radio astronomy, and civil use, as well as in high-speed
transmitters and receivers in sensing systems.
To achieve frequency conversion, an element with a non-linear IV characteristic is
required. Fig. 4.1 illustrates a generalized field emission IV plot. Due to its nonlinear nature, FN electron emission is a good candidate for achieving harmonics-rich
current. When an applied small AC voltage, 𝑉1 (𝑡) = 𝑣 cos (𝜔𝑡), is superimposed on
a large DC bias, 𝑉0 , defining the Q point shown (an operating point located on the
non-linear part of the IV characteristic), the resulting field emission current, 𝐼1 (𝑡),

I(t)
I0

V(t)=V0+vcos(ωt)

Figure 4.1: Generalized FN emission IV characteristic and harmonic-rich resulting
current due to the inherent non-linearity of the transfer function.

93
is not symmetric about 𝐼0 but rather has different amplitudes on the positive and
negative half-cycles. This distortion is mainly due to a second harmonic component
at frequency 2𝜔 [6].
For a quantitative analysis of frequency conversion, consider the simplified FN
equation given by
𝐼 = 𝐴𝑉 2 exp (−𝐵/𝑉)
(4.1)
where A and B are constants that incorporate the work function, field enhancement
factor, emitting area, and the FN constants. Let the input voltage, 𝑉 (𝑡), be represented by the sum of a DC bias component, 𝑉0 , and a small AC signal, 𝑣 cos (𝜔𝑡),
so that
𝑉 (𝑡) = 𝑉0 + 𝑣 cos (𝜔𝑡)
(4.2)
where |𝑣| ≪ |𝑉0 |. A Taylor series expansion of Eq. (4.1) about 𝑉0 yields
𝐼 (𝑡) = 𝐼0 +

1 𝑑2 𝐼
𝑑𝐼
[𝑣 cos (𝜔𝑡)] +
[𝑣 cos (𝜔𝑡)] 2 + · · ·
𝑑𝑉 𝑉=𝑉0
2 𝑑𝑉 2 𝑉=𝑉0

(4.3)

where 𝐼0 = 𝐴𝑉02 exp (−𝐵/𝑉0 ). If we compute the derivatives, we obtain
𝑑𝐼
= 2𝐴𝑉0 exp (−𝐵/𝑉0 ) + 𝐴𝐵 exp (−𝐵/𝑉0 )
𝑑𝑉 𝑉=𝑉0

(4.4)

and
𝑑2 𝐼
𝐴𝐵2
2𝐴𝐵
exp (−𝐵/𝑉0 ) + 2𝐴 exp (−𝐵/𝑉0 )
exp (−𝐵/𝑉0 ) +
𝑉0
𝑑𝑉 𝑉=𝑉0
𝑉0

(4.5)

so that
𝐼 (𝑡) = 𝐴𝑉02 exp (−𝐵/𝑉0 ) + (2𝐴𝑉0 exp (−𝐵/𝑉0 ) + 𝐴𝐵 exp (−𝐵/𝑉0 )) [𝑣 cos (𝜔𝑡)]+
𝐴𝐵2
2𝐴𝐵
exp (−𝐵/𝑉0 ) +
exp (−𝐵/𝑉0 ) + 2𝐴 exp (−𝐵/𝑉0 ) [𝑣 cos (𝜔𝑡)] 2 + · · ·
𝑉0
(4.6)
If we use the trigonometric identity: cos2 (𝜃) = 12 + 21 cos (2𝜃), we can rewrite Eq.
(4.6) as
𝑣 2 𝐵𝑣 2 𝐵2 𝑣 2
2𝑣 𝐵𝑣
𝐼 (𝑡) = 𝐼0 1 + 2 + 3 +
+ · · · + 𝐼0
+ · · · cos (𝜔𝑡)+
𝑉0 𝑉02
𝑉0
2𝑉04
𝑉0
(4.7)
𝑣 2 𝐵𝑣 2 𝐵2 𝑣 2
𝐼0 2 + 3 +
+ · · · cos (2𝜔𝑡) + · · ·
𝑉0
2𝑉04
𝑉0
The first term corresponds to the DC bias current that leads to rectification, the
second term is the attenuator or amplifier of the fundamental frequency, and the

94
third term is the second harmonic that arises due to the non-linearity in the transfer
function. Higher-order terms can also be present, but they were omitted for simplicity as their power decreases with increasing multiplication factors in resistive
multipliers. This is the basic principle of operation of a frequency multiplier, in
which a non-linear device is used to generate harmonic frequencies that were not
present in the original AC or fundamental signal.
Next, we consider a two-tone input signal given by
𝑉 (𝑡) = 𝑉0 + 𝑣 1 cos (𝜔1 𝑡) + 𝑣 2 cos (𝜔2 𝑡).

(4.8)

Similarly to the previous analysis, if we apply this voltage to a non-linear device
whose output current is obtained by performing a Taylor expansion around the Q
point at (𝑉0 , 𝐼0 ), we get
𝑑𝐼
[𝑣 1 cos (𝜔1 𝑡) + 𝑣 2 cos (𝜔2 𝑡)]+
𝑑𝑉 𝑉=𝑉0
1 𝑑2 𝐼
[𝑣 1 cos (𝜔1 𝑡) + 𝑣 2 cos (𝜔2 𝑡)] 2 + · · ·
2 𝑑𝑉 2 𝑉=𝑉0

𝐼 (𝑡) =𝐼0 +

(4.9)

If we plug in the results from Eq. (4.4) and Eq. (4.5), and recall the trigonometric
identity: 2 cos 𝜃 cos 𝜙 = cos (𝜃 − 𝜙) + cos (𝜃 + 𝜙), we obtain
𝑣 21 𝐵𝑣 21 𝐵2 𝑣 21 𝑣 22 𝐵𝑣 22 𝐵2 𝑣 22
𝐼 (𝑡) =𝐼0 1 + 2 + 3 +
··· +
𝑉0
2𝑉04 𝑉02 𝑉03
2𝑉04
𝑉0
2𝑣 2 𝐵𝑣 2
2𝑣 1 𝐵𝑣 1
+ 2 + · · · cos (𝜔1 𝑡) + 𝐼0
+ 2 + · · · cos (𝜔2 𝑡)+
𝐼0
𝑉0
𝑉0
𝑉0
𝑉0
𝑣 21 𝐵𝑣 21 𝐵2 𝑣 21
𝐼0 2 + 3 +
+ · · · cos (2𝜔1 𝑡)+
𝑉0
2𝑉04
𝑉0
(4.10)
𝑣 22 𝐵𝑣 22 𝐵2 𝑣 22
𝐼0 2 + 3 +
+ · · · cos (2𝜔2 𝑡)+
𝑉0
2𝑉04
𝑉0
2𝑣 1 𝑣 2 2𝐵𝑣 1 𝑣 2 𝐵 𝑣 1 𝑣 2
𝐼0
+ · · · cos ((𝜔1 − 𝜔2 )𝑡)+
𝑉02
𝑉04
𝑉03
2𝑣 1 𝑣 2 2𝐵𝑣 1 𝑣 2 𝐵 𝑣 1 𝑣 2
𝐼0
+ · · · cos ((𝜔1 + 𝜔2 )𝑡) + · · ·
𝑉02
𝑉04
𝑉03
Therefore, a signal that has a frequency equal to the sum of both input frequencies,
𝜔1 + 𝜔2 , and a signal that has a frequency equal to the difference of both input
frequencies, 𝜔1 − 𝜔2 , have been generated. For simplicity, only the square term
in the Taylor expansion has been considered to solely focus on the second-order

95
intermodulation products (i.e., mixing terms). If the cube term is used, third
harmonics as well as higher-order intermodulation products are created.
Thus, the main function of a frequency mixer is to convert information from one
frequency to another frequency. If the second frequency is higher, making the
information easier to transmit or radiate, the process is known as up-conversion,
while if the second frequency is smaller, making the information easier to receive or
capture, the process is called down-conversion. In down-conversion, the two input
signals are more commonly referred to as the local oscillator (LO) signal and the
radio frequency (RF) signal, while the output signal is known as the intermediate
frequency (IF). In up-conversion, the LO and the IF signals are mixed to generate
the RF signal. The first case illustrates a device that is used as a receiver, while the
second scenario depicts a device that is used as a transmitter. In both cases, the LO
port is usually driven with a sinusoidal continuous wave or square wave signal. The
process of heterodyning is depicted in Fig. 4.2 [7].
One of the most important figures of merit that define the performance of a mixer
is the conversion loss, which is defined as the ratio of the available input power,
𝑃𝑖𝑛 (𝑅𝐹), over the obtained IF power, 𝑃𝑜𝑢𝑡 (𝐼 𝐹):
𝑃𝑖𝑛 (𝑅𝐹)
Conversion loss in dB = 10 log10
(4.11)
𝑃𝑜𝑢𝑡 (𝐼 𝐹)

RF1

Power

LO
IF

Frequency

=| - |
IF

(a)

RF2

RF=

LO±

(b)

Figure 4.2: Generalized frequency mixer: (a) down-conversion, and (b) upconversion. Note that in (a) the product 𝜔 𝐿𝑂 + 𝜔 𝑅𝐹 also forms but is not shown.

96
The most simple frequency mixer can be made by using a single diode in its design.
While single-diode mixers tend to have poor isolation and low conversion efficiency,
they are particularly useful at very high frequencies and wide bandwidths.
4.2

General Design Paradigm

One of the most important considerations when designing high-frequency devices
is minimizing the capacitance, as this parameter is inversely proportional to the
maximum speed of operation. There have been multiple attempts to fabricate field
emission devices for high-frequency operation, but most of them have employed
traditional Spindt-type vertical field emitter arrays, which have a large overlapping
area between the electrodes. As a result of the large capacitance between the gate
and the base electrode, their operation has been limited to a few gigahertz [8, 9].
To minimize the overlapping area between the electrodes and reduce the capacitance,
lateral devices were fabricated, which provide more design freedom compared to
vertical devices. Using advanced nanofabrication techniques and high-resolution
electron lithography [10, 11], nanoscale gap spacings between the emitter and collector terminals were achieved. This allows for operation at low voltages, which is
desirable to reduce power consumption and Joule heating, increase device lifetime
by minimizing ion sputtering, and produce high transconductance devices that are
essential for practical electronic devices [12, 13]. Additionally, low voltage operation can reduce leakage currents that arise at high fields and compete with field
emission, such as Frenkel-Poole emission or Ohmic conduction [14]. Small gaps
also shorten the electron transit time for high-speed operation.
Furthermore, devices with many emitter tips per device were fabricated to source
higher currents. This enables operation at a higher Q point along the non-linear IV
characteristic for better mixing and lower conversion loss. Emission from multiple
tips should also decrease flicker noise by number averaging, which is desirable for a
more stable emission. Additionally, devices with 10, 20, 30, 40, 50, 60, and 70 tips
were fabricated to study the effect of the number of tips on field emission current.
It is expected that higher currents are achieved for a given voltage and a more stable
emission with devices that have higher number of emitter tips.
Gold was selected as the electrode material. Even though it has a relatively high work
function (∼5.3 eV [15]), Au was chosen due to its chemical unreactivity, ensuring
that the value of the work function would not vary and affect emission stability.
In addition, lift-off is relatively easy and results in clean edges and reproducible

97
fabrication. Pt was also considered, but lift-off unfortunately resulted in a large
number of flags that caused device shorting and inconsistent fabrication results.
Fused silica was chosen as the substrate due to its low loss tangent, which makes it a
suitable low-loss material at microwave frequencies. It is also easy to undercut with
wet HF etching, allowing for the creation of a trench-like structure in the vicinity
of the emitting region to increase the length of the leakage pathway. Removing
any insulating material near high electric fields prevents charging effects that cause
hysteretic behavior, as well as avoids dielectric breakdown and device failure. Undercutting the substrate near the emitter also minimizes electron collisions onto the
substrate and back-scattering. Fused silica is also an appealing material due to its
low cost.
Two kinds of geometries were considered: a symmetric structure, in which the
emitter and collector were indistinguishable, and an asymmetric structure, in which
one terminal consisted of a multi-tip array (i.e., the emitter) while the other terminal
was blunt (i.e., the collector). The sharp terminal was expected to start emitting
electrons at a smaller voltage compared to the blunt terminal due to the field enhancement it experiences. The goal of such a device was to mimic the asymmetric
IV characteristic of traditional solid-state diodes. However, due to the increased
size of the collector terminal, the capacitance of such a structure was expected to be
higher than that of the symmetric structure.
For high-frequency measurements, the input signal was coupled to the device via a
coplanar waveguide. The widths of the trace and ground plane spacing were chosen
to match the characteristic impedance of 50 Ω.
4.3

Selection of Physical Design Parameters

COMSOL Multiphysics 6.0, a three-dimensional FEM simulator, was used to determine the optimum dimensions for the lateral field emitter multi-tip array. The goal
was to maximize the field enhancement factor and minimize the capacitance of the
device. Fig. 4.3 sketches the design parameters that were optimized:
• tip length
• tip base
• metal thickness
• undercut radius

98
air

thickness
Au
undercut
tip base

spacing
SiO2
tip length

(a)

(b)

Figure 4.3: Simulation geometry: (a) top-view, and (b) cross-sectional view.
• spacing (period)
The undercut was modeled as a semi-sphere to roughly mimic an isotropic wet etch.
Only the symmetric geometry was considered due to its lower expected capacitance.
For all simulations, the gap dimension was set to 30 nm.
First, an individual tip with no undercut was modeled, as shown in Fig. 4.4 (a).
Before proceeding with any design parameter sweep, a mesh study was conducted to
optimize for accuracy and speed of the simulation. A box enclosing the gap between
the terminals was defined to create a finer mesh at the region of interest, as shown
in Fig. 4.4 (b). A mesh with a maximum element size of 2 nm was chosen for this
box. Note that to achieve realistic modeling results and avoid electromagnetic field
singularities, a fillet with a radius of 15 nm was used to round the edges of the tip.
This provided a lower bound for the field enhancement factor, as nanoprotrusions
created during fabrication give rise to higher field enhancement factors that are
impossible to determine a priori. In addition, a cut line within the gap bounded
by the two electrodes and located halfway up the metal layer, as illustrated in Fig.

(a)

(b)

(c)

Figure 4.4: Single-tip simulation: (a) overall geometry, (b) fine mesh box, and (c)
cut line (red line).

Field enhancement factor

Tip length (m)

Maxwell capacitance (F)

(a)

Tip length (m)

(b)

Figure 4.5: Single-tip simulation results: (a) field enhancement factor and (b)
Maxwell capacitance as a function of tip length.

4.4 (c), was used to determine the field enhancement factor to avoid anomalous
enhancement from the bottom and top layers.
For the studies, only one variable was swept at a time and the rest were kept constant.
The results for the field enhancement factor and Maxwell capacitance for tip length,
tip base, and metal thickness are shown in Figs. 4.5, 4.6, and 4.7, respectively. It was
observed that for a shorter tip length, the field enhancement factor decreased while
the capacitance increased. However, it was interesting to see that when the tip length
became too short, the capacitance increased again, as it became dominated by the
parallel plate capacitance of the connecting terminal rather than the tip. Ultimately,

Field enhancement factor

100

Tip base (m)

Maxwell capacitance (F)

(a)

Tip base (m)

(b)

Figure 4.6: Single-tip simulation results: (a) field enhancement factor and (b)
Maxwell capacitance as a function of tip base.

a tip length of 1000 nm was selected to compromise between the field enhancement
factor and capacitance.
In terms of tip base dimension, a narrower base led to both decreased capacitance
and increased field enhancement factor. While at first it would seem best to fabricate
emitter tips with the smallest base as it would also provide the advantage of more tips
per device, a very narrow tip also suffers from high resistance. This can adversely
affect the speed of operation of the devices as well as the lifetime, as Joule heating
can become problematic. In this way, a tip base of 200 nm was chosen.
The effect of varying metal thickness on the field enhancement factor became
considerable when the thickness was < 30 nm. In addition, the capacitance increased

Field enhancement factor

101

Tip base (m)
Thickness
(m)

Maxwell capacitance (F)

(a)

Thickness (m)

(b)

Figure 4.7: Single-tip simulation results: (a) field enhancement factor and (b)
Maxwell capacitance as a function of metal thickness.

with increasing thickness. This was expected as a thicker device meant more
overlapping electrode area. A further advantage of thin devices is that lift-off
is easier. However, due to the considerable increase in resistance that very thin
structures may bring about, a metal thickness of 60 nm was selected for the gold
arrays.
Next, the effect of isotropic undercut was studied. The results are presented in Fig.
4.8. Varying the undercut had a considerably less significant effect on the overall
change of the field enhancement factor. This is valuable because it is hard to control
the exact amount of undercut when a wet etch at such small dimensions is used.
However, it is worth noting that the capacitance decreased roughly by half when

Field enhancement factor

102

Undercut (m)

Maxwell capacitance (F)

(a)

Undercut (m)

(b)

Figure 4.8: Single-tip simulation results: (a) field enhancement factor and (b)
Maxwell capacitance as a function of substrate undercut.

the sample was undercut, as expected due to the decrease in the dielectric constant
when air replaces fused silica. While it is desirable to undercut the structures
as much as possible in terms of capacitance, a tip that is too suspended can lose
structural stability during the wet etch and bend. The devices may also experience
electromechanical motion when high fields are applied and could ultimately become
electromechanical switches. Therefore, an undercut of around 100 − 200 nm was
attempted for the structures.
For the single-tip structure with a tip length of 1 µm, a tip base of 200 nm, a metal
thickness of 60 nm, and an undercut of 100 nm, the simulated field enhancement
factor was 1.189 and the capacitance was 15 aF.

Field enhancement factor

103

Spacing (m)

Maxwell capacitance (F)

(a)

Spacing (m)

(b)

Figure 4.9: Multi-tip simulation results: (a) field enhancement factor and (b)
Maxwell capacitance as a function of tip spacing.

To study the effect of shielding due to closely spaced emitters, an array of 10 tips
with varying separation between them, i.e., period, was modeled. The connecting
terminal for the sweep had a constant size so a larger period did not mean that the
connecting terminal became wider. The results are given in Fig. 4.9. The field
enhancement factor was plotted for the top half of the tips as it was expected that the
same results would be obtained for the bottom half due to symmetry. The numbering
in the legend is in order. In this way, “gap 1” corresponds to the tip at the edge of
the array (only has one neighbour), and “gap 5” corresponds to the tip at the center
of the array. It was observed that there was no effect of changing the spacing on the
field enhancement factor, so shielding at these dimensions does not seem to be an

104
issue. The capacitance increased when the spacing was increased. Therefore, no
spacing between the tips returned a capacitance of 24 aF/tip for a multi-tip device.
4.4

Device Fabrication

The fabrication steps for the field emission multi-tip arrays are illustrated in Fig.
4.10. The devices were fabricated on 1.3 mm square chips that were diced from a 500
µm-thick JGS2 fused silica wafer. The chips were first cleaned using acetone and
IPA, as they had been previously coated with resist for protection during dicing. To
remove any leftover organics, a 20-minute-long oxygen plasma clean was performed
at 80 Watts and 20 mTorr using RIE (Plasma-Therm SLR 720).
Next, the devices were coated with a 25 nm layer of Cr, which was deposited using
electron beam evaporation at a rate of 0.5 Å/s and a base pressure of ∼ 10−7 Torr
(CHA Industries Mark 40). The purpose of this thin metal layer was twofold. Due
to the highly insulating nature of glass, a charge dissipation layer was needed for
subsequent EBL. In addition, glass is transparent to the laser wavelength used during
EBL height measurement. An inaccurate substrate height measurement can lead
to a defocused beam at the top of the chip surface, which is detrimental to highresolution patterning. Therefore, the metal layer also provided sufficient reflectivity
for the height check.
The devices were patterned using standard EBL. A pre spin-coating clean using
acetone and IPA was performed immediately before spin-coating the substrate. 950
PMMA A4 (MicroChem) at 4000 rpm for 45 s was used, and the sample was baked
at 180 ◦ C for 4 minutes. Direct-write EBL (Raith EBPG 5200) was carried out at
an acceleration voltage of 100 keV. To achieve high-resolution and optimal pattern
transfer, proximity effect correction (PEC) with Genisys Beamer software and the
“bulk & sleeve” technique were used. This technique consists of using a lower
current beam to write the boundary of the features (i.e., the sleeve) and a larger
current beam to write the center of the pattern (i.e., the bulk). A current of 20 nA
(300 µm aperture) was used for the sleeve and a current of 200 nA (400 µm aperture)
was used for the bulk, with a dose of 900 µC/cm2 for both. In addition, the emitter
tips were patterned with a dose of 675 µC/cm2 and a current of 500 pA (300 µm
aperture). The sample was developed for 60 s in a 1:3 solution of MIBK and IPA
at room temperature, followed by a 20 s IPA bath as a stopper. The sample was
constantly agitated in the developing solution to aid with the process.

105

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

Figure 4.10: General fabrication steps for field emitter multi-tip array: (a) initial
fused silica substrate, (b) evaporation of 25 nm Cr, (c) spin-coating of 200 nm
950 PMMA A4 electron beam resist, (d) EBL and development, (e) Cr etch, (f)
evaporation of 6 nm Ti, 60 nm Au, and 20 nm Ti, (g) lift-off, (h) residual Cr
removal, (i) dry etching, and (j) wet etching in BHF. Note that the sketch is not to
scale.

106

2 µm
(a)

2 µm
(b)

1 µm
(c)

200 nm
(d)

Figure 4.11: Images of representative devices after lift-off. (a) HIM of a device
with 40 tips. (b) SEM of a device with 10 tips and ground planes in the vicinity. (c)
and (d) are HIM of a device with 20 tips (same device). Voltage contrast arises due
to the difference in surface potential between both tips once they were separated.

Next, the Cr over the exposed pattern was removed using Cr-7s (Cyantek). A 6 nm
adhesion layer of Ti (rate of 1 Å/s), a 60 nm electrode layer of Au (rate of 1 Å/s), and
a 20 nm etch mask layer of Ti (rate of 1 Å/s) were deposited using electron beam
evaporation at a pressure of ∼ 10−8 Torr (Kurt J. Lesker Labline). Ti was chosen
as an etch mask due to the limited evaporation sources available in the chamber.
The sample was left in acetone overnight for the lift-off process, which was aided
by sonication. A lift-off process was chosen for ease of fabrication and to help form
sharp tips. Fig. 4.11 shows images of the devices after lift-off.
All the leftover Cr that remained under the now-removed resist was etched away in
Cr-7s. The next step of the fabrication process was to remove the substrate material
in the area surrounding the emission sites. To help the hydrofluoric acid (HF) in
undercutting the structures, a dry etch was first used to increase the exposed surface
area. A C4 F8 /O2 etch chemistry at a ratio of 40 sccm/3 sccm, a substrate temperature

107

200 nm

(a)

200 nm

(b)

(c)

Figure 4.12: HIMs of representative devices after dry etch: (a) 45 s etch (DC bias:
186 V) for a depth of ∼200 nm (image at 50◦ tilt), and (b) and (c) 40 s etch (DC
bias: 206 V) for a depth of ∼120 nm (images at 52◦ tilt).

1 µm

(a)

200 nm

(b)

200 nm

(c)

200 nm

(d)

Figure 4.13: HIMs of a finished field emission multi-tip arrays. (a) device with
ground planes at 45◦ tilt and rotation; (b) device as seen at 0◦ tilt and (c) at 45◦
tilt. The undercut measured in average 130 nm in depth. (d) Image at 52◦ tilt and
rotation. On average, the gaps between the two terminals measured 30 nm.

108
of 20 ◦ C, and a chamber pressure of 7 mTorr were used to perform the etch (Oxford
Instruments Plasmalab System 100 ICP-RIE 380). The CCP power was set to 200
Watts and the ICP power to 2100 Watts. Fig. 4.12 shows helium ion micrographs
(HIMs) of various devices after the dry etch step.
After the dry etch step, the sample was undercut using buffered hydrofluoric acid
(BHF) (Transene Company, Inc.) for 20 s. To prevent bubble formation during
the wet etch that leads to a non-uniform undercut, the sample was first dipped into
a mixture of Triton 100X (Sigma-Aldrich) and water. The surfactant also helped
BHF reach the very small gaps between the emitter and collector tips for a more
reproducible etch. To avoid damage from surface tension, the devices were gently
dried using a critical point dryer (Tousimis 915B). Fig. 4.13 shows HIMs of the final
undercut devices. The distance between the emitter and collector varied between
tips, ranging from 20 nm to 40 nm, with an average vacuum gap of 30 nm. Fig. 4.14
also shows devices with asymmetric geometry. Note that the fabrication throughput
was lower for these devices compared to the symmetric devices, as lift-off became

500 nm

(a)

200 nm

(b)

200 nm

(d)

200 nm

(c)

200 nm

(e)

1 µm

(f)

Figure 4.14: Images of asymmetric devices. HIM of finished device with a blunt
multi-finger collector structure at (a) 0◦ tilt, and at (b) and (c) 45◦ tilt. HIM of a
finished device with a block collector design at (d) 0◦ tilt and at (e) 52◦ tilt. (e) is a
less-magnified SEM of the device after lift-off.

109

Figure 4.15: Chip wire-bonded to signal lines and ground plane of custom PCB.

more challenging with the denser structure. The average distance between the two
terminals for both structures was around 40 nm.
Lastly, the devices were ultrasonically wedge wire-bonded with aluminum wires to
the gold pads of a custom-designed printed circuit board (PCB), as shown in Fig.
4.15. The PCB design is discussed in the following section.
4.5

PCB Design

The through-hole PCB was designed using EAGLE software (Autodesk). It consisted of three coplanar waveguides with a ground reference plane that route from

Figure 4.16: Relevant PCB design dimensions.

110

Figure 4.17: Photo of PCB with soldered SMA edge connectors and wire-bonded
chip.

SMA edge connectors to a ground pad where the device was attached using doublesided copper tape. The dimensions for the signal trace width, spacing between the
return ground, and via diameter are shown in Fig. 4.16. These were optimized for
50 Ω impedance matching. Only three signal traces were included on the PCB due
to size limitations inside the testing chamber. The stitching vias were designed to
be spaced no more than 1/8th of the maximum testing wavelength from each other.
For a maximum frequency of 3 GHz, or a maximum wavelength of 100 mm, the
vias were separated by a maximum of 12.5 mm. In addition, a through transmission
line for PCB calibration was included.
Tg 170 FR-4 was selected as the dielectric material, with a dielectric constant of
∼4.3 and a thickness of 1.6 mm. While FR-4 is not usually the material of choice for
high-frequency measurements due to its high losses, it should still perform well up
to frequencies below 5 GHz [16]. The copper thickness was 1 oz. and the surface
finish was electroless nickel immersion gold (ENIG) with a thickness of 2U". Fig.
4.17 shows a photo of the final PCB with the soldered SMA edge connectors and
wire-bonded chip.
The S-parameters were measured using a vector network analyzer (Keysight P9372A)
and the real impedance was calculated. The results are shown in Fig. 4.18.
4.6

DC and AC Measurements

The PCB with the wire-bonded chip was loaded into a custom stainless-steel vacuum
chamber to prevent contamination that could affect emission stability. The chamber
was pumped to a pressure of ∼ 10−6 Torr. The PCB was connected to a custom-made

111

(a)
70
65
60
55
50
45
40
35

0.5

1.5

2.5

(b)

Figure 4.18: PCB experimental data: (a) S-parameters and (b) calculated real
impedance using S11.

electrical feed-through using Kapton-insulated UHV coaxial cables (Accu-Glass
Products Inc. 110755). The electrical feed-through was built using a blank KF flange
with holes drilled into it to fit hermetically-sealed RF adapters (Pasternack PE9184).
Fig. 4.19 shows the custom-built feed-through for frequency measurements up to
18 GHz.
The DC voltage needed to bias the field emission tips was provided by two picoammeter/voltage sources (Keithley 6487), which also monitored the emission current
independently at each terminal to check that all currents were accounted for and
that there were no significant leakages. Two independent AC voltages for the highfrequency measurements were supplied by function generators (Keysight N5171B

112

Figure 4.19: Custom-built electrical feed-through for frequency measurements up
to 18 GHz.
and Rohde & Schwarz SMC100A), which have a maximum frequency of operation
of 3 GHz. These two sources were coupled using a power combiner (Mini-Circuits
ZAPD-30-S+), which also provided isolation between them. A bias tee (MiniCircuits ZFBT- 4R2GW-FT+) was used to insert both DC and AC power into the
device, while another identical bias tee was employed to deconvolute the two signals
at the output. Lastly, the output AC signal was measured using a digital phosphor
oscilloscope (Tektronix DPO7254). All AC components were connected using 50 Ω
coaxial cables. The DC sourcemeters were controlled via GPIB interface and data
acquisition was automated using MATLAB scripts. Control of the AC equipment
vRF1

power
combiner

oscilloscope

vacuum chamber
bias T

vRF2
bias T

VDC

Figure 4.20: Schematic diagram of the test circuitry.

113

Figure 4.21: Photos of the experimental setup: (a) vacuum chamber (front view)
and (b) electrical connections (back view).

including signal generators and oscilloscope was done manually. A schematic of the
equivalent circuit of the measurement system is provided in Fig. 4.20, and photos
of the experimental setup are shown in Fig. 4.21.
Examination of electron emission to confirm that the conduction mechanism was
FN emission and not an alternative process was initially carried out. The DC power
supplies were connected and the AC lines were shorted, followed by a conditioning
process identical to that of the previous chapter, for which multiple IV sweeps were
taken until there was no discernible change between consecutive runs. No resistor
in series with the emitter for protection was added to this experimental setup, as it
would significantly limit high-frequency modulation.
The effect of geometry on the emission process was first studied to determine whether
an asymmetric structure could recreate the IV characteristic profile of existing solidstate diodes for rectification. Two designs for the collector terminal, a blunt multifinger structure and a block structure, were considered. Despite the slightly smaller
capacitance of the first design, the second structure was also taken into account due
to its higher fabrication throughput. For these measurements, the bias on the emitter
terminal was kept at 0 V, while the voltage on the collector terminal was swept.
Positive voltages induced emission from the emitter and negative voltages promoted
emission from the collector.
Fig. 4.22 shows the output IV characteristics of both asymmetric devices, with a
representative SEM of the design considered included on the top left corner of each

114
500
400
300

Current (nA)

200
100

emit from

-100
-200

collector emitter

-300
-400
-500
-15

-10

-5

Voltage (V)

(a)
100
80
60

Current (nA)

40
20

emit from

-20
-40

collector emitter
-60
-80
-100
-10

-5

Voltage (V)

(b)

Figure 4.22: IV curves for both asymmetric designs considered: (a) blunt multifinger collector structure and (b) block collector structure.

sub-figure. Unfortunately, the curves for the forward and backward sweeps had the
same turn-on voltage, which was likely due to nanoprotrusions that formed on the
surface of the collector terminal, dominating emission at the nanoscale and rendering
any macroscopic geometry ineffective. In light of these results, we decided to focus
on symmetric structures from here on out.

115
700

1 0 tip s
2 0 tip s

C u rre n t (n A )

600

3 0 tip s
4 0 tip s

500

7 0 tip s
400
300
200
100

V o lta g e (V )

(a)
1 0 tip s

-1 0

2 0 tip s
3 0 tip s

-1 1

log(I/V2)

4 0 tip s
7 0 tip s

-1 2

-1 3

-1 4

-1 5
0 .1 4

0 .1 6

0 .1 8

0.20

0.22

1 /V

(b)

Figure 4.23: Electrical characterization as a function of the number of tips per
device: (a) IV characteristics and (b) FN plot.

The effect of the number of field emission tips on the measured current was examined.
Fig. 4.23 displays the experimental result for electron emission as a function of the
number of tips per device. Unfortunately, the devices with 50 and 60 tips blew up
early on during testing so no useful data could be acquired. Also, a maximum current
of 100 nA per tip was deliberately imposed to prevent overheating and potential
damage. It was shown that, at a given applied bias, the measured current increased
as a function of the number of emitter tips. Therefore, by increasing the number of

116
Number of tips

Slope

𝑦-intercept

Number of tips
(effective)

R2 value

10
20
30
40
70

-41.82
-42.24
-35.97
-43.30
-37.27

-7.235
-6.023
-6.166
-5.383
-5.370

10
33
29
63
64

0.989
0.990
0.985
0.981
0.988

Table 4.1: Linear regression analysis data as a function of number of tips.
tips per emitter, the turn-on voltage for electron emission was successfully lowered,
which is beneficial in terms of power consumption and lifetime considerations.
In addition, data was plotted using FN coordinates, as illustrated in Fig. 4.23
(b). Currents lower than 10% of the maximum measured current were ignored, as
these are usually associated with other types of emission such as FP leakage [17],
unaccounted resistance paths [18], or Schottky emission [19]. A linear model was
well fit to the measured data, affirming FN emission process. As the multi-tip array
is equivalent to having many individual emitters in parallel, the overall FN current
for the multi-tip array, 𝐼 𝑀𝑇 , can be expressed in terms of a single-tip emitter current,
𝐼𝑆𝑇 , as
𝐼 𝑀𝑇 = 𝑛𝐴𝑉 2 exp (−𝐵/𝑉)
≡ 𝑛𝐼𝑆𝑇

(4.12)

where 𝑛 is the number of emitter tips, and 𝐴 and 𝐵 are constants that depend on,
among others, the emission area, field enhancement factor, and work function. In
FN coordinates this becomes

𝐼 𝑀𝑇
ln
(𝑛𝐴)
(4.13)
ln
𝑉2
Roughly the same slope was obtained from the linearization of the measured data
for all devices. This agrees with Eqn. (4.13), as the slope is independent of the
number of emitter tips. Furthermore, the magnitude of the 𝑦-intercept decreased
as the number of emitter tips per device increased, also in agreement with Eqn.
4.13, as the vertical intercept of a multi-tip device changes by a fixed amount
given by ln (𝑛) compared to single-tip emission. Using the 𝑦-intercept value of
the 10-tip device, the efficient number of emitter tips was calculated and presented

117

Figure 4.24: SPICE schematic for a 10 tip device.
in Table 4.1, alongside the values for the slope, 𝑦-intercept, and 𝑅 2 of the least
squares regression line. A smaller value of effective emitter tips was expected
due to fabrication discrepancies between gaps of individual tips, which ultimately
cause only a fraction of the fabricated tips per device to turn on at a given bias.
However, a higher effective number of tips than the actual number of tips was
observed for some devices. Note that the analysis in Eq. (4.12) assumed an equal
field enhancement factor for all tips. While this may seem an oversimplification,
due to the highly sensitive dependence of field emission on the atomic structure of

118

Current (nA)

f: 0.6
f: 0.8
f: 1.0
f: 1.2
f: 1.4
f: 1.6

Voltage (V)

Figure 4.25: Result of SPICE simulation illustrating effect of fractional change in
field enhancement factor for a single tip within an array in measured total current.

the emitter tip, it is hard-if not impossible-to achieve controllable field enhancement
[20]. In this way, the devices with a larger effective number of tips probably had
a higher field enhancement factor as a result of any local nanoprotrusions created
during fabrication. Figs. 4.24 and 4.25 show a SPICE schematic and simulation
result (LTspice XVII, Analog Devices Inc.) portraying the effect of fractional change
in field enhancement factor for a tip within a 10-tip device with the representative
field emission tip modeled as a voltage-controlled current source. The parameters
in the emission current equation were obtained by curve fitting to data from an
early device using MATLAB. A 1 Ω resistor was placed in series before each tip to
account for their inherently small resistance. The simulation results concluded that
the total emission current of a multi-tip device can be dominated by a single emitter
tip with a higher field enhancement factor, which is problematic as tips with higher
field enhancements can easily blow up. It also increases noise in the measurements,
which is troublesome for some applications such as amplification.
Lastly, for the frequency mixing experiments, the AC lines were connected as
illustrated in Figs. 4.20 and 4.21. Before any AC power was coupled in, a static
analysis was performed on the device under test to confirm the FN emission process

119
and determine the dynamic resistance of the device at the current level that would
be sourced. Fig. 4.26 shows the IV curve, corresponding FN plot, and dynamic
conductance right before the AC tests were carried out for a 10-tip device. The
dynamic conductance as a function of voltage was calculated by differentiating
the IV curve. From (c), a dynamic impedance of 𝑅 = 0.67 MΩ was calculated.
Recalling the simulated capacitance of 𝐶 =24 aF/tip, an RC cutoff frequency, 𝑓𝑐 ,
given by [21]
𝑓𝑐 =
(4.14)
2𝜋𝑅𝐶
of ∼1 GHz was estimated.
Once an estimate for the cutoff frequency of the specific device under test was
calculated, we proceeded with the mixing experiments as follows. The DC bias was
-18.5

400

300

log(I/V2 )

Current (nA)

-19

y = 13.4740x - 16.9857
R2: 0.9682

200

-19.5

-20
100
-20.5

-0.25

-0.2

Voltage (Volts)

1/V

(a)

(b)

-0.15

10-6

1.5
0.5
-0.5
-1

Voltage (Volts)

(c)

Figure 4.26: Electrical measurements before frequency mixing experiment: (a)
static characteristic, (b) corresponding FN plot, and (c) differential conductance.

120
Current (nA)

400
300
200
100

100

200

300

400

500

600

700

500

600

700

Time (s)
(a)

Voltage (V)

100

200

300

400

Time (s)
(b)

Figure 4.27: DC bias feedback loop to stabilize emission current for frequency mixing measurements: (a) shows the DC current as a function of experiment duration,
and (b) illustrates how the voltage was adjusted to maintain the current constant at
some chosen level.
Fig. 4.28 (a)
Frequency
(MHz)
𝑓1
35
𝑓2
50
𝑓1 + 𝑓2
85
| 𝑓1 − 𝑓2 |
15
2 𝑓1
70
2 𝑓2
2 𝑓1 − 𝑓2
20
2 𝑓2 − 𝑓1
65
Label

Power
(dBm)
-79.6
-75.1
-95.1
-97.9
-103.0
-113.9
-98.5

Fig. 4.28 (b)
Frequency
(MHz)
35
45
80
10
70
90
25
55

Power
(dBm)
-79.5
-76.5
-99.1
-98.0
-102.4
-103.5
-101.6
-102.5

Fig. 4.28 (c)
Frequency
(MHz)
30
35
65
60
70
25
40

Power
(dBm)
-80.9
-79.6
-115.3
-110.7
-108.0
-111.4
-109.6
-124.2

Table 4.2: Measured power for all frequencies of interest shown in Fig. 4.28.

121
-50

Power (dBm)

350 nA
f1+f2

|f1-f2|
-100

2f2-f1
2f1-f2

2f1

-150

Frequency (Hz)
(a)

10
10

-50

Power (dBm)

350 nA

|f1-f2|

f1+f2

-100

2f1-f2

2f1

2f2-f1

2f2

-150

Frequency (Hz)
(b)

Power (dBm)

-60

10
10

0 nA

-80

f1+f2

|f1-f2|

-100

2f2-f1

2f1-f2

-120

2f1

2f2

-140
-160

Frequency (Hz)
(c)

10
10

Figure 4.28: Power spectra of the output signal. Each AC signal has an amplitude
of 1 V 𝑅𝑀𝑆 . (a) 𝑓1 = 35 MHz and 𝑓2 = 50 MHz with 350 nA DC current, (b) 𝑓1 = 35
MHz and 𝑓2 = 45 MHz with 350 nA DC current, and (c) 𝑓1 = 30 MHz and 𝑓2 = 35
MHz when the device is ‘off’ (0 nA).

gradually increased up to a set current level of 350 nA, at which the current was kept
constant for a specified time interval. A feedback loop was created, in which the
voltage was automatically modified if the measured current dropped or increased
from the specified value, due to possible emission instabilities. Fig. 4.27 portrays
both the measured current and automatically set voltage as a function of time. With
the current stable at the set value, two AC signals with an amplitude of 1 V 𝑅𝑀𝑆 at
frequencies 𝑓1 = 35 MHz and 𝑓2 = 50 MHz were applied. Fig. 4.28 (a) shows the
power spectrum obtained by computing the Fast Fourier Transform (FFT) with the

122

1 µm

500 nm

(a)

(b)

Figure 4.29: HIM (a) before and (b) after testing.

oscilloscope. Power values at all frequencies of interest are included in Table 4.2.
We observed peaks at the sum ( 𝑓1 + 𝑓2 = 85 MHz) and difference (| 𝑓1 − 𝑓2 | = 15
MHz) frequencies, confirming that the field emitter array successfully achieved
frequency mixing. The conversion loss, due to the high impedance of the device,
was about 108 dBm. However, this value only serves as a worst-case scenario as the
input signal frequencies were not matched to the device. Therefore, significantly
better results are expected if impedance matching is attempted. Moreover, due to the
considerable loss, neither harmonics nor third-order terms could not be measured.
We also changed the input frequencies to 𝑓1 = 35 MHz and 𝑓2 = 45 MHz and
measured similar results as illustrated in Fig. 4.28 (b). In addition, we confirmed
that no peaks at the sum or difference were present when the device was ‘off’ (i.e.,
no DC bias was applied and no field emission current was measured), as exhibited
in Fig. 4.28 (c). Lastly, we verified that no peaks at the input frequencies 𝑓1 and
𝑓2 were measured when the device was ‘on’ (i.e., DC bias was applied and field
emission current was measured) but the AC sources were switched off.
After various experiments, the device ultimately blew up. Fig. 4.29 shows an HIM
of the tested device before and after measurements were taken.
4.7

Work Function Reduction

There are various mechanisms by which the emission current can be increased, such
as:
1. Increasing the bias voltage

123
2. Increasing the field enhancement factor
3. Increasing the emission area
4. Reducing the separation between the emitter and collector terminals
5. Reducing the emitter work function.
Increasing the potential can be problematic if the device is not under UHV, as
electrons can ionize ambient gases and cause sputtering that can lead to device
destruction. Additionally, this option is not ideal due to power consumption and
device lifetime. Moreover, an increase in the field enhancement factor can cause
overheating and device failure. In terms of emission area, in the previous section we
described how fabricating multi-tip devices successfully led to an augmentation of
the total emission current. Furthermore, despite our attempts to create the smallest
vacuum gaps, fabrication constraints limited the separation between the emitter and
collector terminals.
In this section, we explore the effect of lowering the emitter work function to increase
field emission current. In particular, we present preliminary results of coating the
emitter with Pr, which has a work function of 2.7 eV [22]. To our knowledge,
improvements in field emission current using Pr have not been previously reported.
Let us examine the effect in the emission characteristics of reducing the emitter
work function by a factor 𝑐 (𝑐 < 1), so that the new work function 𝜙𝑛𝑒𝑤 can be
expressed as 𝜙𝑛𝑒𝑤 = 𝑐𝜙𝑜𝑙𝑑 , where 𝜙 𝑜𝑙𝑑 is the original high work function. From the
FN emission equation given in Eq. (2.47), the measured current is increased by

𝑏 𝐹 𝑁 𝜙3/2 3/2
𝐼𝑛𝑒𝑤 1
= exp −
𝑐 −1
(4.15)
𝐼𝑜𝑙𝑑
where 𝐼𝑛𝑒𝑤 is the current with the reduced work function 𝜙𝑛𝑒𝑤 , and 𝐼𝑜𝑙𝑑 is the
current with the original work function 𝜙 𝑜𝑙𝑑 . Fig. 4.30 shows a SPICE simulation
that illustrates the effect in emission current when the emitter work function is
decreased by a factor 𝑐.
Furthermore, consider the following simplified version of Eq. 2.48 given by

ln 2 = 𝐴
+𝐵
(4.16)

124
where 𝐴 and 𝐵 are the slope and 𝑦-intercept, respectively. In terms of physical
parameters, these are given by
𝐴=−

𝑏 𝐹 𝑁 𝜙3/2

(4.17a)

𝑎 𝐹 𝑁 𝑆𝛽2
𝐵 = ln
(4.17b)
By reducing the emitter work function by a factor of 𝑐 while keeping the field factor
𝛽 fixed, the slope 𝐴 is reduced by a factor 𝑐3/2 while the 𝑦-intercept 𝐵 is modified
by ln(𝑐). Thus, the new slope 𝐴𝑛𝑒𝑤 and 𝑦-intercept 𝐵𝑛𝑒𝑤 can be expressed by the
original slope 𝐴𝑜𝑙𝑑 and 𝑦-intercept 𝐵𝑜𝑙𝑑 as

𝐴𝑛𝑒𝑤 = 𝑐3/2 𝐴𝑜𝑙𝑑

(4.18a)

𝐵𝑛𝑒𝑤 = 𝐵𝑜𝑙𝑑 − ln(𝑐).

(4.18b)

(a)
c: 0.5
c: 0.6
c: 0.7

Current (nA)

c: 0.8
c: 0.9
c: 1.0

Voltage (V)

(b)

Figure 4.30: SPICE (a) circuit schematic and (b) IV characteristic simulation showing the effect of reducing the work function by a factor 𝑐.

125
For the experimental verification, the same device design employed in the frequency
mixing experiments was used, so all fabrication steps are found in Section 4.4. The
chip was ultrasonically wedge wire-bonded with aluminum wires to a ceramic pin
grid array package (Spectrum Semiconductor Materials CPG15504).
A 10 nm-thick layer of Pr was deposited on the samples via thermal angle evaporation
in a custom-built deposition chamber at a base pressure of 6 × 10−6 Torr. The angle
of evaporation was about 45◦ with respect to the sample plane to achieve conformal
coating of the emitter tip. To prevent oxidation or contamination that could modify
Pr work function due to air exposure, a feedthrough with electrical connections
for in situ measurements was added to the chamber. Two sourcemeters (Keithley
2450) measured the IV characteristic of the devices before and after Pr evaporation.
Measurement acquisition was automated using serial communication and MATLAB
scripts.
Fig. 4.31 (a) shows the IV characteristic of the non-coated and Pr-coated field
emitter device. The Pr coating reduced the turn-on voltage, defined as the voltage
required to measure a current of 10 nA, from 8.2 V to 4.3 V. This indicates that, for
a given bias, the emission current is drastically increased by the Pr layer compared
to the bare device. Fig. 4.31 (b) plots the measured data using FN coordinates along
with the fitted least squares regression lines. After the Pr coating, the slope in the FN
plot becomes significantly less steep. As the slope is related to the work function and
the field factor, a decrease in the observed slope corresponds to either a reduction in
100
non-coated
Pr-coated

-20

non-coated
Pr-coated

80
60

ln(I/V2)

Current (nA)

-20.5

-21
-21.5
-22

10 nA
-22.5

Voltage (V)
(a)

0.1

0.15

0.2

0.25

1/V
(b)

Figure 4.31: Effect of Pr coating in field emission: (a) IV characteristics of Pr coated
and non-coated device and (b) FN plots. A dashed line at 10 nA is included in (a)
to determine the turn-on voltage.

126
the effective work function, an increase in the field factor, or a combination of both.
The values for the expected and measured slope, 𝑦-intercept, and R2 value obtained
from the regression lines fitted to the FN plot before and after the deposition of Pr
on the sample are included in Table 4.3. From the ratio of the slopes, we infer the
following experimentally measured 𝑐 𝑚,𝐴 :

𝐴𝑛𝑒𝑤
𝑐 𝑚,𝐴 =
𝐴𝑜𝑙𝑑

(4.19)

Based on our experimental results, we obtain a value of 𝑐 𝑚,𝐴 = 0.605, which is
slightly larger than the expected 𝑐 𝑥 = 0.509 that was calculated using the work
functions of pristine Au (𝜙 𝐴𝑢 = 5.3 eV) and Pr (𝜙 𝑃𝑟 = 2.7 eV). However, if we
consider the difference between the 𝑦-intercepts before and after Pr coating so that
𝑐 𝑚,𝐵 = 𝑒 𝐵𝑜𝑙𝑑 −𝐵𝑛𝑒𝑤 ,

(4.20)

we obtain 𝑐 𝑚,𝐵 = 0.497. The difference between 𝑐 𝑚,𝐴 and 𝑐 𝑚,𝐵 likely arises from
the assumption of a constant field factor and emission area, which may be an
oversimplification since the surface roughness of the Pr film can easily modify
them.
Let us assume that the field factor is modified after the Pr evaporation by a factor 𝑓
so that
𝛽𝑛𝑒𝑤 = 𝑓 𝛽𝑜𝑙𝑑 .
(4.21)
Thus, we have the following relations between the non-coated and Pr-coated regression coefficients
𝐴𝑛𝑒𝑤 𝑐3/2
= 𝑚
(4.22a)
𝐴𝑜𝑙𝑑
𝑓𝑚
2
𝐵𝑛𝑒𝑤 − 𝐵𝑜𝑙𝑑 = ln 𝑚 ,
(4.22b)
𝑐𝑚
where 𝑓𝑚 corresponds to the experimentally measured field factor modification.
Solving the system of equations leads to the values 𝑐 𝑚 = 0.667 and 𝑓𝑚 = 1.159,
indicating that the Pr coating not only reduced the effective work function but also
increased the field factor.
An attempt to add another 10 nm of Pr unfortunately shorted the device. Fig. 4.32
shows an HIM of the device, which displays the formation of a thin bridges between
the terminals. It also showcases the roughness of the evaporated film, which may
explain the deviation between expected and measured FN fit parameters.

127
Parameter
Slope (𝐴)
𝑦-intercept (𝐵)
R2 value

Before Pr
-39.26
-17.79
0.966

Expected
-15.11
-17.15
NA

After Pr
-18.45
-17.09
0.968

Table 4.3: Expected and extracted FN parameters.

4.8

Discussion

In this chapter, we discussed the design, fabrication, and experimental testing of
multi-tip emitters for frequency conversion, to determine if vacuum field emitters
can effectively operate at RF frequencies. Multi-tip devices were studied due to
their increased emission area, which should enhance emission current. Gold was
chosen as the electrode material owing to its unreactivity, providing good emission
stability. The empirical results showed that, due to the strong non-linearity in the
FN emission equation, the devices are capable of frequency mixing in the MHz
range. Furthermore, the effect of Pr evaporation to reduce the emitter work function
for higher emission current was investigated. The preliminary measurements were
promising, as a considerable enhancement in emission current and reduction in
turn-on voltage were observed. Nevertheless, further experiments for repeatability
should be conducted. Moreover, a study on deposition conditions and resulting film
roughness (e.g., via atomic force microscopy) should be undertaken to determine

200 nm

Figure 4.32: HIM of the device after a second layer of Pr was evaporated.

128
whether the improvement in emission was solely due to the reduced work function
of Pr or if it was also a result of the atomic-level roughness of the film.
Although frequency mixing was observed, the conversion loss was excessively high
for any practical application. This loss can be attributed to the lack of impedancematching circuitry in the measurement setup. As a result of the high impedance
in the system, it is especially difficult to impedance match to the traditional 50
Ω impedance of the external circuitry because conventional techniques, such as
impedance matching transformers, LC networks, or matched attenuators, cannot be
used. One possible solution for distributed impedance matching is to use a short stub
tuner, which involves adding a specific length of transmission line in either opencircuit or short-circuit configuration at a particular distance from the load [23–26].
An advantage of such a method is that parasitic effects, such as stray capacitances,
are minimized. Even though a single stub can be used for simplicity, its matched
bandwidth is very narrow, as the reflection coefficient is minimized for the specific
load only at the chosen centre frequency. Therefore, stubs should be added to all
three ports for maximum power transfer. Additionally, several stubs could be used
for wider bandwidth impedance matching at the expense of increased complexity.
Another way to improve the impedance of the device is to fabricate more tips
per device. In this chapter, we have shown that an increase in measured current
for a given voltage can be achieved when larger arrays of field emitters are used.
Consequently, if even more tips are designed per device such that the total current
sourced is increased beyond our reported values, the dynamic resistance could be
further reduced, thereby improving the RF performance of the device. Although the
overall device capacitance would increase, this cost could be tolerated due to the
considerably small device capacitance. Furthermore, more tips enable operation at
a higher bias, which is advantageous in terms of cutoff frequency.
Further improvements to the measurement setup include adding circulators to prevent noise from reflecting back to the source and/or sample as well as to improve
isolation. Additionally, filters in the output port should be employed for additional verification of the integrity of the measurement setup. This will be done in
subsequent experiments.
In addition, the emission stability could be improved with a better vacuum. Flicker
noise manifested as pulses of random duration at arbitrary intervals is presumed to be
related to the adsorption and desorption of gases that modify the local work function
at the emitter tip. This is in agreement with the observed data, as fluctuations in the

129
current were considerably more noticeable during the conditioning process before
Pr was deposited compared to the mixing experiments, which had an order of
magnitude better vacuum. This illustrates how tiny amounts of contamination can
have strong effects on emission. Similarly, the chamber and PCB could be baked
to evaporate contaminants before measurements are taken. Note that the PCB can
only be baked at a maximum temperature of 170◦ C, as stated by the manufacturer,
to avoid exceeding the glass transition temperature.
One distinct problem of nanoscale vacuum field emission arrays is their poor emission uniformity. It is very difficult, if not impossible, to fabricate all tips within an
array with identical field factors. Small variations in gap sizes and nanoprotrusions
greatly modify the electric field between tips, which can lead to a single tip dominating emission within the device. This is highly undesirable, as this "hot" tip becomes
particularly vulnerable to destruction due to ion bombardment or overheating. Conditioning processes, used to clean the emitter tips, can also erode nanoprotrusions
and in some cases, the sharpest emitter tips. Even though this may diminish the
measured current, emission can become more stable. However, repeatable performance between different devices remains a major challenge, making it difficult to
develop practical devices.
Furthermore, recall that the applied voltage limits the energy to accelerate the
electrons. Owing to the nanoscale dimensions, we have successfully decreased
the applied voltage to sub-10 V operation, which is favourable in terms of power
consumption. However, decreasing voltages also reduces the maximum velocity the
electron can be accelerated, regardless of the transport medium. Therefore, even
though transport in vacuum is faster than in any other material due to the lack of
scattering, the maximum attainable velocity is limited by the applied voltage. Hence,
the increase in device performance may not be as large-scale as hoped, which may
hinder the path for field emission devices to prosper in high-density applications,
such as storage and processors [27].
Lastly, it is worth noting that, even though gold was used for the electrical terminals, the fabrication process can also be extended to other metals that can be
evaporated. Gold is not a hard metal and thus, can experience self-diffusion at high
temperatures. This can, in turn, sharpen the emitter tip, which ultimately reduces
the threshold voltage for emission and affect stability and reliability. Even though
the measurements were carried out at room temperature, Joule and/or Nottingham
heating can significantly elevate the device temperature and damage the device.

130
Therefore, harder materials or protective coatings could be used [28, 29]. Additionally, post-processing schemes, such as high-temperature annealing in hydrogen and
argon atmosphere, may be useful in further strengthening the gold structures [30].
References
[1] G. N. Fursey. Field emission in vacuum microelectronics. Microdevices. New
York: Springer, 2005. isbn: 978-0-387-27419-5.
[2] F. V. Bunkin and M. V. Fedorov. “Cold emission of electrons from surfaces
of metals in strong electric field of radiation.” Journal of Experimental and
Theoretical Physics 48 (1965), pp. 1341–1345.
[3] L. M. Baskin et al. “Ion Bombardment Suppression Effect of a Field-Emission
Cathode.” Radiotechnics and Electronics (USSR) 28.12 (1983), pp. 2462–
2464.
[4] L. B. De Rose, W. M. Jones, and A. Scherer. “Lateral nanoscale field emission
comb for frequency mixing.” [Manuscript submitted] (2023).
[5] L. B. De Rose et al. “Effect of praseodymium coating on electron emission
from a nanoscale gold field emitter array.” [Manuscript submitted] (2023).
[6] M. B. Steer. Microwave and RF design: A systems approach. Edison, NJ:
Scitech Publishing, 2013. isbn: 978-1-61353-021-4.
[7] D. M. Pozar. Microwave engineering. Hoboken, NJ: Wiley, 2012. isbn: 9780-470-63155-3.
[8] C. A. Spindt. “Field-emitter-array development for high-frequency operation.” Journal of Vacuum Science & Technology B 11.2 (1993), p. 468. doi:
10.1116/1.586842.
[9] J. H. Nam. “Characteristics and circuit model of a field emission triode.”
Journal of Vacuum Science & Technology B 16.2 (1998), p. 916. doi: 10.
1116/1.589930.
[10] S. M. Lewis et al. “Tuning the performance of negative tone electron beam
resists for the next generation lithography.” Advanced Functional Materials
32.32 (2022), p. 2202710. doi: 10.1002/adfm.202202710.
[11] S. M. Lewis et al. “Plasma-etched pattern transfer of sub-10 nm structures
using a metal–organic resist and helium ion beam lithography.” Nano Letters
19.9 (2019), pp. 6043–6048. doi: 10.1021/acs.nanolett.9b01911.
[12] W. M. Jones, D. Lukin, and A. Scherer. “Practical nanoscale field emission devices for integrated circuits.” Applied Physics Letters 110.26 (2017),
p. 263101. doi: 10.1063/1.4989677.

131
[13] J. Kim et al. “Work function consideration in vacuum field emission transistor
design.” Journal of Vacuum Science & Technology B 35.6 (2017), p. 062203.
doi: 10.1116/1.5000549.
[14] F. C. Chiu. “A review on conduction mechanisms in dielectric films.” Advances in Materials Science and Engineering 2014 (2014), pp. 1–18. doi:
10.1155/2014/578168.
[15] W. M. H. Sachtler, G. J. H. Dorgelo, and A. A. Holscher. “The work function
of gold.” Surface Science 5.2 (1966), pp. 221–229. doi: 10.1016/00396028(66)90083-5.
[16] S. Hageman. What PCB material do I need to use for RF? 2012. url: https:
//www.edn.com/what-pcb-material-do-i-need-to-use-for-rf/.
[17] A. Di Bartolomeo et al. “Leakage and field emission in side-gate graphene
field effect transistors.” Applied Physics Letters 109.2 (2016), p. 023510. doi:
10.1063/1.4958618.
[18] R. Forbes. “Development of a simple quantitative test for lack of field emission
orthodoxy.” Proceedings of the Royal Society A: Mathematical, Physical and
Engineering Sciences 469.2158 (2013). doi: 10.1098/rspa.2013.0271.
[19] M. Turchetti et al. “Electron emission regimes of planar nano vacuum emitters.” IEEE Transactions on Electron Devices 69.7 (2022), pp. 3953–3959.
doi: 10.1109/TED.2022.3175706.
[20] G. Wu et al. “Tunable graphene micro-emitters with fast temporal response
and controllable electron emission.” Nature communications 7.1 (2016),
p. 11513. doi: 10.1038/ncomms11513.
[21] R. E. Neidert et al. “Field emission triodes.” IEEE Transactions on Electron
Devices 38.3 (1991), pp. 661–665. doi: 10.1109/16.75178.
[22] V. S. Fomenko and G. V. Samsonov, eds. Handbook of thermionic properties.
Boston, MA: Springer US, 1966. isbn: 978-1-4684-7295-0.
[23] G. Puebla-Hellmann and A. Wallraff. “Realization of gigahertz-frequency
impedance matching circuits for nano-scale devices.” Applied Physics Letters
101.5 (2012), p. 053108. doi: 10.1063/1.4739451.
[24] S. Hellmüller et al. “Optimization of sample-chip design for stub-matched
radio-frequency reflectometry measurements.” Applied Physics Letters 101.4
(2012), p. 042112. doi: 10.1063/1.4739248.
[25] T. Hasler. “Microwave noise detection of a quantum dot with stub impedance
matching.” PhD thesis. Basel, Switzerland: Universität Basel, 2016.
[26] V. Ranjan et al. “Clean carbon nanotubes coupled to superconducting impedancematching circuits.” Nature Communications 6.1 (2015), p. 7165. doi: 10.
1038/ncomms8165.

132
[27] W. Zhu, ed. Vacuum microelectronics. New York: Wiley, 2001. isbn: 978-0471-32244-3.
[28] K. L. Jensen. “Field emitter arrays for plasma and microwave source applications.” Physics of Plasmas 6.5 (1999), pp. 2241–2253. doi: 10.1063/1.
873502.
[29] F. M. Charbonnier et al. “Enhanced field emission from carbide-coated field
emitters, and device applications.” Ultramicroscopy 79.1-4 (1999), pp. 73–
82. doi: 10.1016/S0304-3991(99)00078-9.
[30] J. Xu et al. “Nanoscale vacuum channel transistor with in-plane collection
structure.” Nanotechnology 31.6 (2019), p. 065202. doi: 10.1088/13616528/ab51cb.

133
Chapter 5

PLASMONICALLY-ENHANCED FIELD EMISSION
So far we have only discussed devices that operate solely through FN electron emission. Thanks to advancements in fabrication capabilities, nanoscale gaps between
the electrical terminals can be manufactured, allowing for ballistic transport and
very short transit times. However, even though field emission is inherently a fast
process, data modulation and transmission is still limited by electronic interconnects. To increase bandwidth and speed, as well as reduce power consumption,
the ideal approach would be to use light to modulate and carry electrical signals,
effectively creating optoelectronic circuits.
Nonetheless, the integration of photonics and field emission circuits is limited by
their spatial dimensions, as the Abbe’s diffraction limit places a fundamental constraint on the attainable spatial confinement of light to dimensions below half the
wavelength [1]. To overcome this limit and combine electronics and photonics at the
nanoscale, surface plasmon polaritons (SPPs) can be used. SPPs are propagating
surface waves confined within a dielectric-metal interface. They arise due to the
coupling between an incident electromagnetic wave propagating parallel to a metallic surface with appropriate momentum and the coherent collective oscillation of the
free electrons at this surface. SPPs have a shorter wavelength (and higher momentum) compared to the incident light, resulting in deep sub-wavelength confinement
and strong local electromagnetic field intensities.
In this chapter, we merge field emission and plasmonics on-chip and introduce
devices that can be modulated by both electrical and optical fields. Fabricated on
SOI substrates for compatibility with current silicon photonics, these devices take
advantage of a hybrid geometry for adiabatic nanofocusing of the photonic mode into
the plasmonic mode to guide light into the nanoscale field emitting region and obtain
sub-wavelength confinement. Due to the strong plasmonic field enhancement as well
as the nanoscale separation between emitter and collector terminals, a suggested
application for the proposed device is as an ultra-fast, low-power photodetector for
the C-band.

134
5.1

Plasmonics Review

Before diving into the specifics of the device, we first provide a theoretical introduction to the field of plasmonics. We summarize the most important aspects of the
response of noble metals to incident electromagnetic fields, as well as the generation
and propagation of SPPs based on Maxwell’s equations. Additionally, a brief review
of the metal-insulator-metal (MIM) waveguide upon which the hybrid plasmonic
waveguide is built, is included.
The Drude Model
In the simplest case, the optical properties of noble metals can be described by the
Drude or plasma model. In this model, the electrons within the metal are treated as
a gas of free electrons that move in opposition to a background of fixed positive ion
cores [2, 3]. The equation of motion for an electron when an electromagnetic field
is applied is given by
𝑑r
𝑑2r
= −𝑒E
(5.1)
𝑚 2 + 𝑚𝛾
𝑑𝑡
𝑑𝑡
where 𝛾 is a frictional damping constant to include the effect of collisions with
other electrons. If we consider a time-dependent driving electric field of the form
E(𝑡) = E0 exp (−𝑖𝜔𝑡) with frequency 𝜔, a solution to Eq. (5.1) is given by
r = r0 exp (−𝑖𝜔𝑡) =
E.
(5.2)
𝑚(𝜔 + 𝑖𝛾𝜔)
Therefore, the incident field causes the electrons to oscillate with respect to the
immobile ion cores. The resulting polarization can be expressed as
P = −𝑛𝑒E = −

𝑛𝑒 2
𝑚(𝜔2 + 𝑖𝛾𝜔)

(5.3)

where 𝑛 is the concentration of electrons. Recall that the dielectric displacement D
in linear, isotropic, and non-magnetic media is given by D = 𝜖0 𝜖 (𝜔)E, where 𝜖 (𝜔)
is the dielectric function, and it is related to P by D = 𝜖0 E + P. In this way, if we
substitute our result for P given in Eq. (5.3), the dielectric function for the Drude
model is given by
𝜔2𝑝
𝜖 (𝜔) = 1 − 2
(5.4)
𝜔 + 𝑖𝛾𝜔
√︃
where 𝜔 𝑝 is the plasma frequency given by 𝜔 𝑝 = 𝜖𝑛𝑒0 𝑚 . For noble metals, to
improve the fit with empirical data in the region 𝜔 > 𝜔 𝑝 , we include a background
dielectric constant 𝜖∞ . In this way, Eq. (5.4) is slightly modified to
𝜖 (𝜔) = 𝜖∞ −

𝜔2𝑝
𝜔2 + 𝑖𝛾𝜔

(5.5)

-50

[ ( )]

135

-100
-150

J&C data
Drude model

15
10

J&C data
Drude model

-200

-250

(a)

(b)

Figure 5.1: Complex dielectric function of gold: (a) real and (b) imaginary components. A comparison between the Drude model (solid line) and empirical data
adapted from Johnson & Christy [4] is shown.

This modification is included to account for the residual polarization resulting from
the positive ion core background. We can also separate the dielectric function into
its real and imaginary components as
𝜖 1 (𝜔) = 𝜖∞ −

𝜖2 (𝜔) =

𝜔2𝑝
𝜔2 + 𝛾 2

(5.6)

𝜔2𝑝 𝛾

(5.7)
𝜔(𝜔2 + 𝛾 2 )
The real part of the dielectric constant is associated with the degree of polarization,
while the imaginary part is related to dissipative energy losses into the medium.
Fig. 5.1 illustrates the real and imaginary components of the dielectric function
for gold based on Drude model and empirical data from Christy & Johnson [4]. It
is noteworthy that for optical frequencies, 𝜖1 (𝜔) is negative and large. Above the
plasma frequency, the Drude model is no longer valid due to interband transitions
that cause an increase in 𝜖2 (𝜔).
Table 5.1 shows 𝜔 𝑝 , 𝛾, and the complex dielectric constant at 1550 nm for the four
most commonly used metals in plasmonics. The onset of interband transitions has
also been included. The data has been adapted from [5–7]. Silver has the lowest
dissipative losses at telecom wavelengths and is capable of supporting plasmons
throughout the entire visible spectrum; however, it is known for its quick degradation
and fabrication challenges [8]. Copper is an especially attractive material because
of its compatibility with CMOS fabrication processes but it oxidizes quickly, a
disadvantage that is shared with aluminium. Additionally, the interband transition

136
Material

𝜔p (eV)

𝛾 (eV)

𝜖1

𝜖2

Onset of interband
transition (eV)

Ag
Al
Au
Cu

9.04
12.04
8.89
8.76

0.02125
0.1287
0.07088
0.0955

-131.31
-238.80
-116.17
-114.90

8.6156
34.966
12.943
16.069

3.9
1.4
2.3
2.1

Table 5.1: Drude model parameters, complex dielectric constant at 1550 nm, and
onset of interband transition for common noble metals. Adapted from [5–7].

energy for aluminium is the lowest of all, so its use for plasmonic applications is
restricted to the blue and UV range. Gold is the most popular material choice for
plasmonic devices due to its chemical stability and relatively low losses.
Surface Plasmon Polaritons
As briefly described in the introduction of this chapter, SPPs are formed at the
interface between a conductor and a dielectric. When an incident electromagnetic
wave propagating in free space with appropriate momentum strikes the interface, it
penetrates slightly into the conductor. The resulting lateral displacement of the free
electrons causes a net separation of charge. The electromagnetic wave that arises due
to the coupling between the incident electromagnetic field and the coherent electron
plasma oscillation modes is referred to as an SPP. These waves propagate in the
direction tangential to the interface and are evanescently bound in the perpendicular
direction, as shown in Fig. 5.2.

Figure 5.2: Illustration of the SPP propagation along the 𝑥-axis. The evanescent
confinement on both sides of the interface is shown by the purple exponential decay
curves.

137
To describe their propagation, we must resort to Maxwell’s equations at the metaldielectric interface. In the absence of any external current densities or charges,
𝜕B
𝜕𝑡
𝜕D
∇×H=
𝜕𝑡
∇·D=0

∇×E=−

∇·B=0

(5.8a)
(5.8b)
(5.8c)
(5.8d)

where B is the magnetic induction, H is the magnetic field, and D is the electric
displacement field. If we assume a linear, non-magnetic, and isotropic medium, we
further have
D = 𝜖0 𝜖E
(5.9a)
(5.9b)

B = 𝜇0 H.
If we combine Eqs. (5.8a) and (5.8b), we obtain
∇ × ∇ × E = −𝜇0

𝜕2D
𝜕𝑡 2

(5.10)

Recall the identities ∇ × ∇ × E ≡ ∇(∇ · E) − ∇2 E and ∇ · (𝜖E) ≡ E · ∇𝜖 + 𝜖 ∇ · E.
If we assume that the dielectric profile is homogeneous so that ∇𝜖 = 0, Eq. (5.10)
reduces to the wave equation
𝜖 𝜕2E
∇ E= 2 2.
𝑐 𝜕𝑡

(5.11)

A solution to the wave equation is a time-harmonic plane wave 𝐸 (r, 𝑡) = E(r)𝑒 −𝑖𝜔𝑡 ,
where k is the wave vector of the propagating wave. If we insert this into Eq. (5.11),
we obtain the famous Helmholtz equation
∇2 E + 𝑘 02 𝜖E = 0

(5.12)

where 𝑘 0 = 𝜔𝑐 is the free space wave vector. Without loss of generality, let us
assume for simplicity a one-dimensional problem in which the geometry consists
of a metal-dielectric interface at 𝑧 = 0 and parallel to the 𝑥𝑦 plane. The waves
propagate along the 𝑥 direction in the 𝑥𝑧 plane so that E(𝑥, 𝑦, 𝑧) = E(𝑧)𝑒𝑖𝛽𝑥 , where
𝛽 = 𝑘 𝑥 is the propagation constant and is the same in both regions. The geometry is
illustrated in Fig. 5.2. Therefore, Eq. (5.12) simplifies to
𝜕 2 E(𝑧)
+ (𝑘 02 𝜖 − 𝛽2 )E = 0.
𝜕𝑧

(5.13)

138
Due to the harmonic time dependence, 𝜕𝑡𝜕 = −𝑖𝜔. Additionally, we have 𝜕𝑥
= 𝑖𝛽 as
= 0 due to the homogeneity of the
the propagation is along the 𝑥 direction, and 𝜕𝑦
𝑦 direction. We can then use Eqs. (5.8a) and (5.8b) to obtain

𝜕𝐸 𝑦
= −𝑖𝜔𝜇0 𝐻𝑥
𝜕𝑧
𝜕𝐸 𝑥
− 𝑖𝛽𝐸 𝑧 = 𝑖𝜔𝜇0 𝐻 𝑦
𝜕𝑧
𝑖𝛽𝐸 𝑦 = 𝑖𝜔𝜇0 𝐻𝑧
𝜕𝐻 𝑦
= 𝑖𝜔𝜖0 𝜖 𝐸 𝑥
𝜕𝑧
𝜕𝐻𝑥
− 𝑖𝛽𝐻𝑧 = −𝑖𝜔𝜖0 𝜖 𝐸 𝑦
𝜕𝑧
𝑖𝛽𝐻 𝑦 = −𝑖𝜔𝜖0 𝜖 𝐸 𝑧 .

(5.14a)
(5.14b)
(5.14c)
(5.14d)
(5.14e)
(5.14f)

This system has two sets of self-consistent solutions: transverse magnetic (TM)
modes, in which the only non-zero components are 𝐸 𝑥 , 𝐸 𝑧 , and 𝐻 𝑦 , and transverse
electric (TE) modes, in which the only non-zero components are 𝐻𝑥 , 𝐻𝑧 , and 𝐸 𝑦 .
For the TM mode, Eq. set (5.14) yields
𝐸 𝑥 = −𝑖

1 𝜕𝐻 𝑦
𝜔𝜖0 𝜖 𝜕𝑧

(5.15a)

𝐻𝑦
𝜔𝜖0 𝜖

(5.15b)

𝐸𝑧 = −
and Eq. (5.13) reduces to

𝜕2 𝐻𝑦
+ (𝑘 02 𝜖 − 𝛽2 )𝐻 𝑦 = 0
𝜕𝑧

(5.16)

while for the TE mode we have
𝐻𝑥 = 𝑖

1 𝜕𝐸 𝑦
𝜔𝜇0 𝜕𝑧

(5.17a)

𝐸𝑦
𝜔𝜇0

(5.17b)

𝐻𝑧 = −
and

𝜕2 𝐸𝑦
+ (𝑘 02 𝜖 − 𝛽2 )𝐸 𝑦 = 0.
(5.18)
𝜕𝑧
If we return to the geometry shown in Fig. 5.2, where the top half-space (𝑧 > 0)
consists of dielectric material with ℜ(𝜖 𝑑 ) > 0 and the bottom half-space is metal
with ℜ(𝜖 𝑚 ) < 0, then the solutions for the TM mode become
𝐻 𝑦 (𝑧) = 𝐴𝑑 𝑒𝑖𝛽𝑥 𝑒 −𝑘 𝑑 𝑧

(5.19a)

139
𝑘 𝑑 𝑒𝑖𝛽𝑥 𝑒 −𝑘 𝑑 𝑧
𝜔𝜖0 𝜖 𝑑
𝐸 𝑧 (𝑧) = −𝐴𝑑
𝑒𝑖𝛽𝑥 𝑒 −𝑘 𝑑 𝑧
𝜔𝜖0 𝜖 𝑑

𝐸 𝑥 (𝑧) = 𝑖 𝐴𝑑

(5.19b)
(5.19c)

for 𝑧 > 0 and
𝐻 𝑦 (𝑧) = 𝐴𝑚 𝑒𝑖𝛽𝑥 𝑒 𝑘 𝑚 𝑧

(5.20a)

𝑘 𝑚 𝑒𝑖𝛽𝑥 𝑒 𝑘 𝑚 𝑧
(5.20b)
𝜔𝜖0 𝜖 𝑚
𝐸 𝑧 (𝑧) = −𝐴𝑚
𝑒𝑖𝛽𝑥 𝑒 𝑘 𝑚 𝑧
(5.20c)
𝜔𝜖0 𝜖 𝑚
for 𝑧 < 0. Note that 𝑘 𝑑,𝑚 refers to the 𝑘 𝑧 component of the wave vector in the
dielectric and metal, respectively. If we insert Eqs. (5.19a) and (5.20a) into Eq.
(5.16), then
𝑘 2𝑑 = 𝛽2 − 𝑘 02 𝜖 𝑑
(5.21a)
𝐸 𝑥 (𝑧) = −𝑖 𝐴𝑚

𝑘𝑚
= 𝛽2 − 𝑘 02 𝜖 𝑚 .

(5.21b)

Moreover, as a result of the continuity of 𝐻 𝑦 and 𝜖 𝐸 𝑧 at the interface, it follows that
for TM modes
𝐴 𝑑 = 𝐴𝑚
(5.22a)
𝜖𝑑
𝑘𝑑
=− .
(5.22b)
𝑘𝑚
𝜖𝑚
Therefore, SPPs can only exist if the real component of the dielectric permittivity
changes sign at the interface. The dispersion relation of SPPs is
√︂
𝜖𝑚 𝜖 𝑑
(5.23)
𝛽 = 𝑘0
𝜖𝑚 + 𝜖 𝑑
If we follow the same analysis for TE modes and apply the continuity of 𝐸 𝑦 and 𝐻𝑥
at the interface, we obtain
𝐴𝑚 (𝑘 𝑚 + 𝑘 𝑑 ) = 0.
(5.24)
Bound modes require that the real component of the wave vectors be positive,
implying that 𝐴𝑚 = 𝐴𝑑 = 0. Hence, there are no TE SPPs for 𝜇 = 1.
The dispersion relation given in Eq. (5.23) is plotted in Fig. 5.3 for air and SiO2
interfaces. The Drude model with negligible loss was used to describe the dielectric
function of the metal, as given by Eq. (5.4). We observe an energy splitting
between two branches that lie on either side of the light line. The upper branch
has frequencies above the plasma frequency 𝜔 > 𝜔 𝑝 , corresponding to unbound
modes where radiation can propagate into the metal; these are known as bulk or

140
1.4

1.4
Air
SiO2

Air
SiO2

1.2

0.8

1.2

0.6

0.4

0.2

0.5

1.5

k xc/

2.5

0.5

1.5

k xc/

(a)

2.5

(b)

Figure 5.3: Normalized SPP dispersion relation assuming Drude model with negligible damping for propagation in air (blue) and SiO2 (red): (a) real and (b) imaginary
components. Note that the light lines (dashed lines) with 𝜔 = 𝑐𝑘 are also included.

volume plasmon polaritons. The lower branch has frequencies below the plasma
frequency 𝜔 < 𝜔 𝑝 , representing the bound solutions corresponding to SPPs. Due to
the mismatch between the wave vector of the incident light and of the SPP, special
wave vector matching techniques, such as prism coupling or gratings, must be used
to excite SPPs at higher frequencies. A frequency gap with purely imaginary wave
vectors that forbids propagation separates both branches.
For small wave vectors at low frequency, the SPP branch lies close to the light line.
Here, the nature of the SPP resembles an electromagnetic plane wave propagating
parallel to the interface. This wave propagates for many wavelengths into the dielectric, barely penetrating the metal. These are the Sommerfeld-Zenneck waves [9].
For large wave vectors, the dispersion curve for the SPP asymptotically approaches
the characteristic surface plasmon frequency
𝜔𝑝
𝜔 𝑆𝑃 = √
1 + 𝜖𝑑

(5.25)

If we consider no losses in the metal such that ℑ[𝜖 𝑚 (𝜔)] = 0, then the wave vector
𝛽 approaches infinity and the group velocity goes to zero. This also corresponds
to ℜ(𝜖 𝑚 ) = −ℜ(𝜖 𝑑 ). At 𝜔 𝑆𝑃 , the mode becomes a stationary electron oscillation
known as the surface plasmon [10]. For wave vectors between these two limiting
cases, the resulting polariton behaves like a hybrid of both extremes.
To make the model more realistic, we should consider metal losses due to free
electrons and interband damping effects so that ℑ(𝜖 𝑚 ) ≠ 0. Consequently, the

141
propagation constant becomes complex, so that 𝛽 = 𝛽1 + 𝑖𝛽2 , with 𝛽1 related to the
confinement of the mode and 𝛽2 associated with the losses. We can rewrite our
expression for the propagating wave as
E(𝑥, 𝑦, 𝑧) = E(𝑧)𝑒𝑖𝛽1 𝑥 𝑒 −𝛽2 𝑥 .

(5.26)

Therefore, the wave becomes exponentially attenuated in the direction of propagation. The resulting propagation length, i.e., the distance at which the intensity of the
SPP decreases to 1/𝑒 of its initial value, is given by
𝐿=

2𝛽2

(5.27)

When losses are included, 𝛽1 does not approach infinity, but rather a finite maximum
value at 𝜔 𝑆𝑃 . As a result, the wavelength of the surface plasmon becomes finite
with a minimum value of 𝜆 𝑆𝑃 = 2𝜋/𝛽1 . Additionally, the 𝑧-component of the wave
vector at either side of the interface, given by Eqs. (5.21), decays exponentially.
The penetration depth into either half-space, which corresponds to the distance
perpendicularly from the interface where the amplitude of the field has decreased to
1/𝑒 of its value at 𝑧 = 0, is given by
√︄
𝜖𝑚 + 𝜖 𝑑
(5.28)
𝛿 𝑑,𝑚 =
|𝑘 𝑑,𝑚 | 𝑘 0
𝜖 𝑑,𝑚 2
with 𝜖 𝑑 𝛿 𝑑 = |𝜖 𝑚 |𝛿𝑚 [11, 12]. The penetration depth is related to the energy confinement of the mode on either side. Generally, |𝜖 𝑑 | < |𝜖 𝑚 |, so that the mode is mainly
confined in the dielectric.
In conclusion, at frequencies close to 𝜔 𝑆𝑃 , the energy confinement at the interface,
as gauged by the penetration depth, is strong; however, this comes at the cost of
small propagation distances due to the increased interaction with the metal and its
associated damping losses. This inseparable connection between confinement and
loss is the main limitation of plasmonics so a trade-off is always required.
The Metal-Insulator-Metal Waveguide
So far, we have studied the case of a single dielectric-metal interface, which only
supports bound TM modes. Now, let us consider what would happen if we add
another metallic layer, such that the resulting system consists of a dielectric slot
between two metal planes, as shown in Fig. 5.4. When the slot width 𝑤 is
comparable to or smaller than the penetration depth of the single interface mode

142
εd2

εm
εd

εd1
εd2

εm

(a)

(b)

Figure 5.4: Field distribution of the fundamental mode for (a) MIM structure and
(b) all dielectric multilayer with 𝜖 𝑑1 > 𝜖 𝑑2 for comparison.

𝛿 𝑑 , the field overlap causes the modes to interact, resulting in hybridized modes.
Following the same analysis described in the previous section based on solving the
Helmholtz equation under the appropriate boundary conditions for the tangential
and normal electric field components at the interface, we arrive at the following
dispersion relation [13]
𝜖𝑑 𝑘 𝑚
(5.29)
tanh (𝑘 𝑑 𝑤) = −
𝜖𝑚 𝑘 𝑑
√︃
with 𝑘 𝑑,𝑚 = 𝛽2 − 𝑘 02 𝜖 𝑑,𝑚 . Note that the system supports both symmetric and
antisymmetric modes; however, we focus on the symmetric mode, which exhibits
odd symmetry of the longitudinal electric field component 𝐸 𝑥 and even symmetry
of the transverse field component 𝐸 𝑧 , as this mode extends for all slot values. This
mode is sketched in Fig. 5.4. For sufficiently small slot widths (i.e., 𝑤 → 0), we
can approximate tanh 𝑥 ≈ 𝑥, allowing us to express the wave vector as
√︄
2
𝜖𝑑
(5.30)
𝛽 ≈ 𝑘 0 𝜖𝑑 +
𝑤𝑘 0 𝜖 𝑚
An interesting characteristic of these structures is that as the slot width goes to zero,
the propagation wave vector increases indefinitely as 𝛽 ≈ −𝜖 𝑑 /(𝑤𝜖 𝑚 ) → ∞. This
implies that the hybrid mode allows for tighter confinement that can be modified
by merely adjusting the geometry. Fig. 5.5 depicts the normalized electric field
intensity of the fundamental mode for various slot widths. The mode is strongly
confined within the dielectric slot and rapidly decreases at the metallic interfaces.
The mode confinement for an all-dielectric waveguide (Fig. 5.4 (b)) is also included
for comparison. While the all-dielectric waveguide is limited by diffraction, the
MIM geometry is capable of achieving extreme confinement below this limit. This

0.8
0.6
0.4
0.2
-500

Normalized electric field

143

Position (nm)
(a)

500

0.8
0.6
0.4
0.2
-500

Position (nm)
(b)

500

MIM
Dielectric

0.8
0.6
0.4
0.2
-500

Position (nm)
(c)

500

Figure 5.5: Normalized electric field of the fundamental mode for the MIM structure
(blue) and all-dielectric geometry (red) for various slot widths: (a) 𝜆/100, (b) 𝜆/10,
and (c) 𝜆/2, where 𝜆 = 1550 nm.

characteristic is especially useful for designing metal waveguides for sub-wavelength
guided mode propagation.
5.2

The Hybrid Plasmonic Waveguide

In this section, we describe the hybrid plasmonic waveguide, which forms the basis
of the device explored in this chapter. For a more detailed review of the structure,
refer to [14–16]. Note that their hybrid plasmonic waveguides were capped with
SiO2 . Since our devices experience very large fields at the metallic terminals due to
the merging of plasmonics with field emission, we replaced the oxide that surrounds
the structure with air to avoid dielectric breakdown of the insulator.
Building upon the MIM geometry, we aimed to create a waveguide with a twodimensional lateral sub-wavelength confinement of the mode in the plane normal
to the propagation direction. An approach that is compatible with traditional silicon photonics platform and can achieve strong field enhancements is the hybrid

144

Air

Au
SiO2
Si

Figure 5.6: Illustration of the cross-section of the hybrid plasmonic waveguide.

plasmonic waveguide. This system consists of a MIM plasmonic slot coupled to
an underlying photonic waveguide, as shown in Fig. 5.6. A low refractive index
dielectric spacer between the top MIM structure and the bottom photonic waveguide was included to modify the effective refractive index and provide strong mode
confinement. It was also useful in mitigating plasmonic propagation losses, which
scale with the real part of the dielectric permittivity as ∝ 𝜖 𝑑3/2 [14, 17].
To confine the in-plane mode, metal loading was employed to spatially modify the
effective refractive index 𝑛𝑒 𝑓 𝑓 . The effect of metal loading a silicon slab for both TE
and TM polarizations is shown in Fig. 5.7. In the case of TE polarization, the metal
layer pushed the mode down into the underlying SiO2 substrate layer, resulting in
a decrease of 𝑛𝑒 𝑓 𝑓 since a larger fraction of the energy now resides in the lower
layer. For TM polarization, metal loading the Si waveguide caused the mode to
be confined in the metal-dielectric interface. Boundary conditions require that the
perpendicular component of the displacement field be continuous across interfaces.
TE

Air

Au
SiO2
Si

(a)

(b)

Figure 5.7: Effect of metal loading a Si slab for both TE and TM polarizations.
(a) Shows a metal-loaded Si slab waveguide and (b) illustrates an unloaded Si slab
waveguide.

145

20 nm oxide

30 nm oxide

2.5

(n eff)

2.5

1.5

Bare Slab TE mode
Metal-loaded TE mode
Metal-loaded TM mode

100

1.5

Bare Slab TE mode
Metal-loaded TE mode
Metal-loaded TM mode

150
200
Si thickness (nm)

100

150
200
Si thickness (nm)

(a)

(b)

40 nm oxide

50 nm oxide

2.5

(n eff)

2.5

1.5

Bare Slab TE mode
Metal-loaded TE mode
Metal-loaded TM mode

100

150
200
Si thickness (nm)
(c)

1.5

Bare Slab TE mode
Metal-loaded TE mode
Metal-loaded TM mode

100

150
200
Si thickness (nm)
(d)

Figure 5.8: Real component of 𝑛𝑒 𝑓 𝑓 for the bound TE mode of region II and both
TE and TM modes of region I as a function Si thickness and the following spacer
oxide thicknesses: (a) 20 nm, (b) 30 nm, (c) 40 nm, and (d) 50 nm.

As the magnitude of the real component of the dielectric permittivity of the metal
and the Si is larger than that of the SiO2 layer, the electric field in the SiO2 region
was enhanced to satisfy the interface condition. This strong confinement increased
𝑛𝑒 𝑓 𝑓 compared to the TM mode in the bare Si slab.
For simplicity, we considered the overall structure to be composed of three regions:
two identical metal-loaded Si slab waveguides on either side and a bare Si slab
waveguide in the center. These corresponded to region I and region II, respectively,
as shown in Fig. 5.6. Confinement in the center slot was achieved when 𝑛𝑒 𝑓 𝑓 of
the fundamental mode in region II was larger than in region I. This is analogous to
how confinement is accomplished in a Si photonics ridge waveguide, wherein 𝑛𝑒 𝑓 𝑓

146

Figure 5.9: Difference in the 𝑛𝑒 𝑓 𝑓 between the bound TE mode of the bare Si slab
waveguide of region II and the largest of either TE or TM modes of the metal-loaded
waveguide of regions I as a function of Si and oxide thickness.

is modified by selectively etching away parts of the Si. 𝑛𝑒 𝑓 𝑓 was further modified
by tuning the spacer oxide and the underlying Si thicknesses. Fig. 5.8 illustrates the
effect of varying Si and spacer oxide thicknesses on 𝑛𝑒 𝑓 𝑓 for the bound TE mode
of the bare Si slab, which had the highest 𝑛𝑒 𝑓 𝑓 in region II, and for both TE and
TM modes of the metal-loaded waveguide of region I. A two-dimensional FEM
simulation (COMSOL Multiphysics 5.4) was used to extract these values. Note that
𝜆 = 1550 nm and the thickness of gold was set to 50 nm. The material properties
used were obtained from empirical data by Johnson et al. for gold [4], Gao et al.
for SiO2 [18], and Li for Si [19]. Next, the difference in the real component of 𝑛𝑒 𝑓 𝑓
between the bound TE mode of the bare Si slab and the largest of the metal-loaded
TE or TM mode was plotted as shown in Fig. 5.9 as a function of oxide and Si
thickness. The graph shows that the difference was small for either thin spacer oxide
due to the large metal-loaded TM mode and for large Si thickness as a result of
the large metal-loaded TE mode. The maximum confinement occurred for oxide
thicknesses larger than 40 nm with a Si thickness of approximately 110 nm. For

147

air

gap
Au
SiO2
oxide
thickness
Si

Si
thickness

SiO2

Finer mesh box

Cut line

Figure 5.10: Simulation parameters: (a) two-dimensional geometry and (b) mesh
employed.

practical photonics applications, a slab thickness of 110 nm may be too slim, so we
chose a Si thickness of 160 nm and an oxide thickness of 30 nm.
We studied mode confinement for the full device using the previously selected Si and
oxide thickness with a two-dimensional COMSOL simulation to model the crosssection of our structure. The geometry and the mesh employed are presented in
Fig. 5.10. Sharp corners were rounded to avoid calculation singularities that could
produce anomalous results, and a box surrounding the gap between both metal layers
that penetrated 10 nm in the metal layers was defined to create a finer optimized
mesh. Fig. 5.11 shows the real and imaginary components of 𝑛𝑒 𝑓 𝑓 as a function
of gap width. Both the highest confinement and the largest loss were computed for
the smallest gap (10 nm). At this gap width, the mode was mainly plasmonic in

2.6

0.04

2.55

0.03

2.5

0.02

2.45

0.01

2.4
10

50
60
Gap (nm)

ℑ(n eff)

ℜ(n eff)

148

100

Figure 5.11: Complex 𝑛𝑒 𝑓 𝑓 for the proposed structure as a function of gap size: (a)
real and (b) imaginary components.

10 nm gap

50 nm gap

Figure 5.12: Electric field distribution as a function of gap width: (a) 10 nm gap,
(b) 30 nm gap, (c) 50 nm gap, and (d) 70 nm gap. Note that all figures have the
same intensity scale.

149

Figure 5.13: Normalized field energy distribution along cut line as defined in Fig.
5.10 for various gap widths.

nature, resembling that of the MIM waveguide described in the previous section.
The lowest loss was calculated for the largest gap size (100 nm), as illustrated by
the electric field distribution in Fig. 5.12. The structure with the smallest gap had
the largest proportion of the mode energy residing within the slot, which explained
the large 𝑛𝑒 𝑓 𝑓 . Conversely, the design with the widest gap had the highest fraction
of the mode energy existing in the underlying Si. Furthermore, the normalized field
intensity distribution for various gap widths is presented in Fig. 5.13. A cut line
in the middle of the gap, as shown in Fig. 5.10 (b), was used to avoid anomalous
high field regions in the corners. As expected, the largest field was located at the
interface between the metal and vacuum gap, decaying exponentially away from it.
As the gap width decreased, the coupling between both sets of interfaces increased.
Therefore, the energy storage was highest for the smallest gap and decayed as the
gap widens, as the coupling between both sets of interfaces weakened.
For a more quantitative analysis, the percentage of the mode in the gap region and
in the metal tips was computed. This corresponds to the fraction of the mode that
influences field emission. Recall that the time-average stored energy density ⟨𝑊⟩
for a non-magnetic, dispersive medium is given by [20]

⟨𝑊⟩ =
(𝜔𝜖 (𝜔)) |E| + 𝜇0 |H| .
(5.31)
𝑑𝜔
The total time-average field energy within a cross-sectional plane with respect to
the direction of propagation is calculated by integrating across the desired area

150

Percentage of Time Average
Energy Density (%)

50
60
Gap (nm)

100

Figure 5.14: Percentage of time average energy density in metal tips and all gap
area as a function of gap width.
𝐴, i.e., ⟨𝑊⟩𝑡𝑜𝑡𝑎𝑙 = 𝐴 ⟨𝑊⟩𝑑𝐴. Fig 5.14 shows the computed percentage of the total
electromagnetic energy in the mode for the gap region and the metal tips as a function
of varying gap width. Both areas of integration are shown in the top right corner.
As the previous qualitative analysis concluded, when the gap decreased in size, the
mode became more plasmonic in nature, characterized by a significant fraction of
the total mode energy residing in the slot area. Additionally, the fraction of the mode
energy that was found within the metal tips also increased, which explains the high
losses. Consequently, the propagation length of the mode was adversely impacted,
as exhibited in Fig. 5.15.
To couple free-space light into (as well as out of) the TE mode of a photonic Si
slab waveguide, a gold grating was used, which enabled matching the wavenumber
of the incident light beam to the propagation constant of the waveguide. This
technique has several advantages compared to other 𝑘-vector matching methods,
such as prism coupling, end-fire coupling, and nanoparticle coupling [21, 22], one
of which is the grating coupler’s fairly relaxed positioning tolerance of the input
beam. Additionally, it allows for both the device as well as the grating to be patterned
in a single lithographic step. For normal incidence, the grating period, Λ, is given
by [23]
Λ=
(5.32)
𝑛𝑒 𝑓 𝑓

151
22

Propagation length (µm)

20
18
16
14
12
10

100

Gap (nm)

Figure 5.15: Propagation length as a function of gap size.

where 𝜆 is the wavelength of the incident light.
Next, nanofocusing of the photonic mode into the plasmonic mode was employed to
mitigate the large size mismatch between both modes. Nanofocusing was achieved
through an adiabatic taper that gradually increased the energy confinement of the
mode by slowing down its group velocity. As shown in Fig. 5.16, by reducing
the width of the central region bounded by metal layers on either side, the Si slab
photonic mode hybridized with the plasmonic mode. This technique also allowed
the generation of very high optical field intensities at the apex due to the energy
accumulation from the considerable reduction of the mode area and the slow-down of
the local group velocity of the hybrid mode. For example, Güsken et al. calculated
an optical enhancement of over 400 in a simulated structure with a 20 nm gap
[15], while Nielsen et al. experimentally measured via photoluminescence of threephoton excited CdSe/ZnS quantum dots an enhancement of about 170 in a 24 nm
gap [16]. This strong optical field confinement can be particularly attractive for
various non-linear effects in the nanoscale, as usually large-scale interaction lengths
are needed to obtain detectable signals.
Two types of losses need to be considered when designing the taper: propagation
losses and back-reflections. Propagation losses arise due to the strong interaction
of the mode with the nearby lossy metal, so the taper must be as short as possible

152

Figure 5.16: Top-view of the hybrid plasmonic structure. A grating coupler was
used to couple free space light into the photonic mode of the waveguide, which was
subsequently adiabatically converted into a plasmonic mode by means of an metallic
taper. Simulations of the electric field at various locations along the taper to depict
mode hybridization were also included.

to minimize these losses. However, as the gap width is reduced, the effective index
is increased. If this rate is too high, back-reflections occur, which adversely affect
mode confinement. Thus, effective nanofocusing requires that the taper angle be
large enough to minimize dissipative losses, but also small enough to reduce backscattering losses. Following the analysis presented in [24], a mathematical criterion
for adiabaticity, given by the Eikonal parameter, can be calculated as follows:
𝛿(𝑧) =

1 𝑑 (ℜ(𝛽(𝑧)) −1 )
𝑘0
𝑑𝑧

(5.33)

where 𝑧 is the distance along the taper direction. Adiabatic nanofocusing is achieved
when 𝛿(𝑧) < 1. The derivation of the Eikonal parameter assumed that the length
scale over which the mode varies is much larger than the SPP wavelength so the
WKB approximation can be used to study the propagation of the mode along the
taper. Hence, as long as 𝛿 remains below the limit for the entire length of the taper,
energy loss due to back-reflections or scattering is negligible. Fig. 5.17 shows the
computed Eikonal parameter as a function of gap width for a taper angle of 45◦ . As
the adiabatic condition was satisfied for all gap widths, the chosen taper angle was
adequate for nanofocusing.

153
0.02

Eikonal parameter δ

0.015

0.01

0.005

10 1

10 2

10 3

10 4

Gap (nm)

Figure 5.17: Computed Eikonal parameter as a function of gap width for a taper
angle of 45◦ .

5.3

Field Emission Simulations

Previously, the optical properties of the proposed device were analyzed. In this
section, the electrostatic properties related to field emission are discussed. The
thicknesses for the various layers chosen are as follows: 160 nm for Si, 30 nm SiO2 ,
and 50 nm Au.
Fig. 5.18 displays the three electrical terminals. The gold metal layer used to confine
the mode in the center region served as the emitter and collector terminals, which
were indistinguishable from one another due to the symmetry of the device. The
underlying Si, which carried the photonic mode, was doped to make it conductive
and act as an electrical gate, allowing for field emission to be modulated. The

Emitter

Collector

Gate

Figure 5.18: Cross-sectional view of the schematic for the proposed device with
electrical terminals.

154

(a)

(b)

Figure 5.19: Electric field distribution (a) without and (b) with undercut. The
chosen gap was 30 nm.

metal terminals were separated from the gate by the spacer oxide, as required by
the hybrid plasmonic waveguide. To prevent dielectric breakdown due to the large
static electric fields experienced at the emitter tip, the oxide was undercut in the
vicinity of the metal. Fig. 5.19 shows the electric field distribution for a device with
a 30 nm gap, where the emitter voltage was set to 1 V while the other terminals
were grounded. The largest electrostatic field was located at the bottom corner of
the emitter terminal. Notice that when no undercut was present, this hot spot was
larger and it extended into the oxide region.
Thus far, devices whose geometry had been carefully chosen to induce static field
enhancement at the emitter apex have been described. Unfortunately, the structures
proposed in this chapter were blunt to accommodate the hybrid plasmonic waveguide. Fig. 5.20 plots the static field enhancement factor as a function of gap width.
Note that the same cut line as in fig. 5.10 was used to determine the field at the
emitter tip. As expected, no static field enhancement due to geometry was present.
The apparent enhancement was the result of the superposition of fields experienced

155

Field enhancement factor

1.8
With gate
No gate

1.6

1.4

1.2

40
60
Gap (nm)

100

Figure 5.20: Static field enhancement factor as a function of gap width.

by the emitter tip 𝐸 𝑡𝑜𝑡𝑎𝑙
𝐸 𝑡𝑜𝑡𝑎𝑙 = 𝐸 𝐸𝐶 + 𝐸 𝐸𝐺

(5.34)

where 𝐸 𝐸𝐶 is the field due to the potential difference between the emitter and
collector, and 𝐸 𝐸𝐺 is the field due to the potential difference between the emitter
and gate. The structure composed of the emitter and gate created a parallel plate
capacitor. In this way, the magnitude of 𝐸 𝐸𝐺 resembled that of its fringing field, in
agreement with Fig. 5.20.

Electric field norm (V/nm)

×10 7

gap=10 nm
gap=30 nm
gap=50 nm

0.5

Voltage gate (V)

1.5

Figure 5.21: Maximum electric field norm on the emitter tip as a function of gate
voltage for various emitter-to-collector gaps.

156
The effect of gating on the maximum electric field norm on the emitter tip for various
gaps is demonstrated in Fig. 5.21. The maximum field was obtained when the gate
was set to the same bias as the collector, resulting in the highest potential difference
between the emitter and the other terminals. As the gate voltage was increased, the
potential difference between the emitter and gate decreased, leading to a reduced
maximum field on the emitter tip. Once the emitter and gate were at the same
voltage, emission was controlled by the potential difference between the emitter and
collector. If the gate voltage surpassed the emitter voltage, 𝐸 𝐸𝐺 reversed direction

VE=1V

VC=0V

VE=1V

VC=0V

VG=0V

VG=0.5V

(a)

(b)

VE=1V

VC=0V

VE=1V

VC=0V

VG=1V

VG=1.5V

(c)

(d)

VE=1V

VC=0V

VG=2V
(e)

Figure 5.22: Potential distribution for various gate bias: (a) 𝑉𝐺 = 𝑉𝐶 = 0 V, (b)
𝑉𝐺 = 𝑉𝐸 /2, (c) 𝑉𝐺 = 𝑉𝐸 , (d) 𝑉𝐺 = 1.5𝑉𝐸 , and (e) 𝑉𝐺 = 2𝑉𝐸 . The red lines are
streamlines illustrating the electron trajectory under the specified bias.

157
and impeded field emission, further reducing the maximum field at the emitter tip. It
is also noteworthy that the gate was more effective at modulating emission in devices
with wider gaps, as 𝐸 𝐸𝐶 increased for smaller emitter-to-collector separations. For
example, the gate modified the field at the emitter tip by more than an order of
magnitude in a device with a gap of 50 nm only being able to modify the field by a
factor of 1.2 when the gap was 10 nm. Lastly, Fig. 5.22 depicts streamlines based on
the Cartesian components of the electric field for various potential configurations.
These serve as an approximation for the electron trajectories leaving the emitter tip
in a device in a device with a 30 nm gap. As expected, electrons were emitted to
the collector and gate when both terminals were set to ground. With increasing
potential of the gate terminal, electrons were discouraged from going to the gate.
However, due to symmetry, it is important to note that at high enough gate biases,
the gate may start emitting electrons to the collector if the separation between the
emitter and collector is similar to that between the gate and collector (not pictured).
5.4

Device Fabrication

The devices were fabricated on SOI wafers, consisting of a 220 nm top silicon
layer and a 2 𝜇m buried oxide layer (SOITEC). Native oxide was removed using
6:1 buffered hydrofluoric acid (BHF) (Transene Company, Inc.), and the top silicon
layer was doped with phosphorous using spin-on-glass (SOG) P-250 (Desert Silicon,
Inc.). The SOG was applied by spin-coating at 500 rpm for 5 seconds and 3000 rpm
for 35 seconds to achieve a thickness of approximately 210 nm. The sample was
then baked on a hotplate for 15 min at 200◦ C and pre-deposition was carried out
in a tube furnace at 700◦ C in a nitrogen atmosphere for 40 min. Subsequently, the
SOG was removed by immersing the sample in BHF 6:1 for 5 minutes. Four-point
probe measurements yielded a surface resistance of 6.12 ±0.98 kΩ, corresponding
to a resistivity of 0.13 Ω·cm and a dopant concentration of 5.7×1016 cm−3 .
Photolithography was performed to electrically isolate individual devices, for which
AZ 5214E (EMD Electronics) was spin-coated on the sample at 3000 rpm for
30 seconds and then baked for 1 minute at 110 ◦ C on a hot plate. The pattern
was exposed for 4 seconds at 15 mW/cm2 using a contact mask aligner (Suss
MicroTec MA6) in soft-contact mode at a wavelength of 365 nm, and subsequently
developed in Microposit MF 319 developer (Rohm and Haas Electronic Materials)
for 2 minutes. The pattern was transferred to the underlying Si via ICP-RIE (Oxford
Instruments PlasmaLab 100 ICP-RIE 380) using SF6 and C4 F8 at a ratio of 35
sccm/57 sccm. The chamber pressure and temperature were set to 10 mTorr and

158
15 ◦ C, respectively, while the CCP and ICP powers were set to 20 Watts and 1200
Watts, respectively. Afterward, the sample was immersed in acetone to remove
residual resist.
The silicon was thinned down to a thickness of approximately 172 nm by means of a
dry oxidation at 1000°C (Tystar Tytan Horizontal Diffusion Furnace) and subsequent
oxide etch in BHF. This was followed by another dry oxidation to grow a thermal
oxide layer approximately 30 nm thick, leaving an underlying Si layer of 160 nm.
Additionally, the SiO2 was annealed for 12 hours in a nitrogen atmosphere to improve
its electrical properties and minimize gate leakage. Then, a 400 nm SiO2 layer was
deposited on a pair of opposite sides of the substrate where the emitter and collector
terminals would later be located via PECVD (Oxford Instruments Plasmalab System
100). The deposition was carried out at a temperature of 350 ◦ C and a pressure of
1000 mTorr with a flow rate of 170 sccm and 270 sccm of 5% SiH4 in Ar and N2 O,
respectively. The RF power generator was set to 20 Watts. The purpose of this
thick oxide layer was to prevent shorting of the gate to the other electrical terminals
during ultrasonic wire-bonding. Shadow-masking with a smaller piece of Si over
the substrate was used to selectively deposit the oxide layer on the sides.
Standard EBL at 100 keV (EBPG 5200, Raith GmbH) with 950 PMMA A8 (MicroChem) was employed to pattern the junction region (which at this point was
joined as shown in Fig. 5.24), electrical connections to the emitter and collector
pads, optical gratings with a 626 nm period and 67% duty cycle, as well as small
arrays of circles for later FIB alignment in the junction vicinity. A pre spin-coating
clean with acetone and IPA was followed by a 5 minutes bake at 180 ◦ C and PMMA
spin-coating at 4000 rpm for 60 seconds and baking at 180 ◦ C for 4 minutes. The
same “bulk & sleeve” lithography technique used to fabricate the devices described
in the previous chapter was used, with a 1700 𝜇C/cm2 dose and 150 nA beam
current for the bulk, and 1000 𝜇C/cm2 dose and 10 nA beam current for the sleeve.
Development was done in a 1:3 MIBK/IPA at room temperature for 30 seconds.
Then, a 5 nm Ti adhesion layer and a 50 nm Au device layer were deposited via
electron beam evaporation in a UHV evaporation chamber at a pressure of ∼ 10−7
Torr (Kurt J. Lesker Labline). The deposition rate for both materials was 0.5 Å.
Lift-off was done in hot PG-remover, and sonication for a few seconds was also
utilized to facilitate the process.
Photolithography was performed on thick oxide rails to define the gate contact
pads, and then a BHF bath was used to remove the oxide for Ohmic contact with

159

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 5.23: Main fabrication steps for plasmonically-enhanced field emission device: (a) initial SOI substrate, (b) doping of top Si layer, (c) Si thinning via thermal
oxidation and subsequent HF etch, (d) thermal oxidation to grow spacer oxide layer,
(e) EBL and development using 950 PMMA A8, (f) gold electron beam evaporation
and lift-off, (g) Ne focused ion beam milling, and (h) undercut in HF of cut area.
Note that the sketch is not to scale.

160

10 µm

Figure 5.24: SEM of device before milling the gap between the emitter and collector.
Grating and focusing marks are also visible.

the doped silicon layer. The photoresist was removed with solvent, and a second
photolithography step was done to define the electrical contact pads. A 10 nm Ti
adhesion layer and a 400 nm Au layer were electron beam evaporated to prevent
punching through the 30 nm oxide layer during ultrasonic wire-bonding, followed
by overnight lift-off in acetone.
The plasmonic waveguides were defined using neon FIB lithography (Carl Zeiss
Orion NanoFab) at 20 keV and a pressure of 4 ×10−6 Torr with a 6 mm working
distance, 10 𝜇m aperture, 2.5 pA current, 0.011 nC/𝜇m dose, step spacing of 1 nm,
and a dwell time of 10 𝜇s. Fig. 5.25 shows top-view (a)-(b) and (c) 52◦ tilt view
of SEMs of a representative device after being milled. To reduce the likelihood of
dielectric breakdown due to the high fields, we removed the oxide in the gap area.
10 𝜇m square boxes were defined with photolithography to enclose the gap region
and thus protect the device. The devices were then immersed in 50:1 BHF for 80
seconds to undercut the gaps, followed by a solvent and oxygen plasma clean to
remove the leftover photoresist. Fig. 5.25 (d) shows a cross-sectional view of a
finished device with a 12 nm gap. Note that Pt was used to protect the gold surface
during the fibbing process.
Finally, each individual device was wedge wire-bonded (WestBond 7476D-79) to a
side-brazed dual in-line (DIP) ceramic package (Spectrum Semiconductor Materials
CSB02842) using Al wires at a low power of 230 for the chip bonds to be as gentle
as possible and avoid damaging the thin oxide layer. The power for chip carrier
bonds was set to 350.

161
5.5

Results

The devices were loaded into a 4.5-inch-cube vacuum chamber and pumped to a
pressure of about 3 × 10−6 Torr. To aid with the desorption of water molecules and
other contaminants, the chamber walls were heated to a temperature of around 120
◦ C. The pins of the chip carrier were connected to a multi-pin electrical feedthrough
on the vacuum chamber, which routed to a BNC patch panel. This setup allowed us
to easily change the device under test.
We proceeded with the electrical characterization of our devices by first measuring
the gate resistance via two separate contact pads on the doped Si layer located at
either side of the junction region to guarantee its ohmicity (yielding a typical value
of 4.2 kΩ). We used three sourcemeters (Keithley 2400 and 2410) with a common
ground to simultaneously measure all currents flowing into and out of all terminals,
monitoring surface leakage currents. Fig. 5.26 shows the schematic of this setup.
The IV characteristic of the device was recorded by negatively sweeping the voltage
of the emitter terminal while fixing the voltage of the other two terminals at ground
(the emitter terminal was arbitrarily chosen due to symmetry). To clean the devices

5 µm

(a)

1 µm

(b)

162

300 nm

(c)

Au
SiO2
Si

SiO2
100 nm

(d)

Figure 5.25: SEM of fabricated device: (a) top view of a device after milling the
plasmonic waveguide, (b) zoomed-in view of the gap region illustrating the extent
of the mill cut line, (c) side view at 52◦ of the edge of the plasmonic waveguide
before HF undercut, and (d) cross-sectional view of the hybrid plasmonic waveguide
of the finished device. The separation between the emitter and collector measured
12.1 nm in its narrowest region. Pt was used to protect the top surface of the device
during ion cross-section milling.

from surface contaminants and obtain stable field emission, multiple forward and
reverse sweeps were performed until no significant hysteresis between both sweeps
was measured, as shown in Fig. 5.27.
The device exhibited a low turn-on voltage of ∼1.5 V, likely caused by its larger
emission surface compared to previously discussed devices. With a larger surface
area, contaminants that could reduce the work function were more likely to be
adsorbed, thus decreasing the onset of field emission. Nanoscale protrusions that
experience higher field enhancements may have also contributed to the lower turn-

163
on voltage. The results were plotted in FN coordinates, yielding a straight line that
indicated field emission as the electron transport mechanism.
We then tested the doped Si layer as an electrical gate, as shown in Fig. 5.28. The
current on all three terminals is plotted as a function of emitter voltage for two
different gate biases. No significant leakage into the gate terminal was observed. As
expected, decreasing the potential difference between the emitter and gate increased
the turn-on voltage due to the reduced electric field at the emitter.
We studied the effect of gate modulation on the emission current by applying a timevarying voltage signal on the gate terminal. It should be noted that the previous
device blew up during testing; hence, these measurements were taken using another
device with a slightly different IV characteristic. Fig. 5.29 shows the input voltage
signal on the gate terminal and the measured currents as a function of time on all
terminals. The FFTs of all measured data were computed to discern any modulation
in the current that may hide under the flicker noise in the emission characteristic.
The presence of a peak at the same frequency as the applied voltage signal on all
measured currents confirmed successful electrical gate modulation. Unfortunately,
the device blew up before tests at higher frequencies could be conducted.
We then analyzed the optical properties of the device. A schematic of the measurement setup is depicted in Fig. 5.30. Light from a C-band tunable laser (Keysight
81689A) was amplified by an erbium-doped fiber amplifier (EDFA) (Calmar Optcom) and launched into free-space via a fiber-optic collimator (ThorLabs F230FCvacuum chamber
VE

Figure 5.26: Schematic of the measurement setup to electrically characterize the
devices. The collector was fixed at 0 V for all tests.

164
1550). A linear polarizer was included to eliminate any residual unwanted polarization. A periscope assembly was used to redirect and change the height of the
beam, shown by a dotted line in Fig. 5.30, to guide it into the vacuum chamber
where the devices were loaded. A half wave-plate was employed to shift the input
beam polarization and maximize the power coupled into the grating. The beam was
then focused onto the device input grating via a 100X near-infrared (NIR) objective
(Mitutoyo M Plan Apo) mounted on a micrometer adjustable stage for fine focus
adjustment. The free-space polarized light entered the vacuum chamber through a
7056 Borosilicate glass viewport (∼ 90% transmission at 1550 nm). Reflected and
out-coupled light was collected by the same objective and directed with a 50:50

(V)

(b)

165

(c)

Figure 5.27: IV characteristic of a representative plasmonically-enhanced field
emission device during (a) forward and (b) reverse voltage sweeps. The gate and
collector were grounded. No leakage from the emitter into the gates was measured.
In (c), the data for both sweeps is plotted in FN coordinates, indicating that field
emission is the electron transport mechanism, as evidenced by the straight line.

IC (VG=0V)
IE (VG=0V)
IG (VG=0V)
IC (VG=-0.5 V)
IE (VG=-0.5 V)
IG (VG=-0.5 V)

(V)

Figure 5.28: IV characteristic for two different gate biases: 0 V and -0.5 V. No
significant leakage into the gate terminal was measured.

166
beamsplitter (BS) into a NIR camera (Merlin Indigo) for focusing the NIR beam.
Natural density filters were added to the beam path as needed to avoid saturation
on the camera. This free-space beam path is shown in red. Moreover, a white light
source (ThorLabs SLS201L/M) was added to the beam path by means of a second
50:50 BS on a flip mount to navigate through the samples, as shown by the green
line. To minimize signal loss during data acquisition, this second BS was removed
from the beam path before the measurements. Furthermore, the vacuum chamber
was mounted on a two-axis linear stage for navigation (Newport Model 401). Photos
of the measurement assembly are shown in Fig. 5.31.

(A)

(V)

A mechanical chopper (ThorLabs MC1000) was added to the setup to modulate
the input optical signal, which was also used as the reference frequency for a
lock-in amplifier (Stanford Research Systems SR810 DSP) to accurately measure
the optically-induced current from the collector terminal. The emitter and gate
terminals’ electrical connections were not modified. Similarly to the first electrical
measurements, the emitter voltage was swept negatively while the gate and collector
terminals were held at 0 V. The chopper speed was set to 3169 Hz. Fig. 5.32 shows

(a)

167

Frequency (Hz)

(b)

Figure 5.29: Effect of applying a time-varying voltage signal on the electrical gate.
In (a), the signal applied to the gate and the measured currents in all three terminals
as a function of time are shown. In (b), the Fourier transforms for all time-varying
measured data were computed.

the effect of various EDFA output powers on emission. As the optical power was
increased, emission was enhanced, demonstrating the sensitivity of the device to
optical input.
The response of the grating coupler to the input polarization was also analyzed. Fig.
5.33 shows two NIR camera images when the 1550 nm laser was on and focused on
the input grating. Coupling was minimized in (a), while it was maximized in (b).
During coupling maximization, light entering the plasmonic waveguide was visible
on the right side of the input beam. The isolated optically-induced current for the
two perpendicular polarizations as a function of emitter voltage is shown in Fig.
5.34. The EDFA output power was set to 1000 mW. The results demonstrated the
effectiveness of the grating, as little optically-induced current was measured when
the coupling was minimized compared to when it was maximized.

168
IR camera

periscope
linear
polarizer
1550 nm laser

EDFA

chopper

white light
source

vacuum
chamber

Figure 5.30: Schematic of the setup for optical measurements. The path of the
1550 nm free-space beam that is coupled to the device is shown in red. For sample
navigation, a white light source is also focused onto the sample during measurement
setup, as shown by the green line. The dotted lines represent an elevation change in
the beam.
Unfortunately, after multiple consecutive runs, the device was destroyed, as shown
in Fig. 5.35.
5.6

Discussion

In this chapter, we demonstrated a waveguide-integrated plasmon-assisted field
emission device, developed on the SOI platform to achieve compatibility with existing Si photonics and reduce costs. The waveguide couples the TE photonic mode of
an underlying Si slab waveguide to the plasmonic mode of a slot in a thin gold layer
via an adiabatic taper that minimizes losses in the metal and avoids back-reflection
and scattering. Geometry-induced nanofocusing results in efficient sub-wavelength
spatial confinement of light and strong optical field enhancement. These high electromagnetic fields can modulate FN emission, which is exponentially dependent on
the electric field perpendicular to the electron-emitting surface. Field emission can
be readily integrated into the optical structure since thin metal layers serving as the
hybrid plasmonic waveguide can also be used as emitter and collector terminals,
while doping the Si photonic waveguide forms an electrical gate. This enables our
proposed device to emit electrons both electrically and optically.
First, we measured the IV characteristics of the device under no illumination and
successfully demonstrated low voltage operation due to the nanoscale gap between
the emitter and collector. We verified that emission occurred via FN tunneling

169

Device

Vacuum chamber
(a)

WG
EDFA

Sourcemeters

Camera

Laser

Lock-in

Vacuum chamber
(b)

Figure 5.31: Photos of the (a) free-space optical setup and (b) electronic rack.
by plotting the IV characteristic in 1/𝑉 versus log (𝐼/𝑉 2 ) and excluded thermallyenhanced emission as a significant contribution due to the large electrode surface
area and gold’s high thermal conductivity. We would also like to note that the

170
0.2
EDFA at 0 mW
EDFA at 200 mW
EDFA at 300 mW
EDFA at 400 mW

Lock-in Collector Current (nA)

0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
-8

-7

-6

-5

-4

-3

-2

-1

Emitter voltage (V)

Figure 5.32: Optical response of the field emission device to various EDFA output
powers as a function of emitter voltage.

underlying doped Si layer would have collected any thermally-generated leakage
current.
We confirmed that the underlying doped Si layer acts as an electrical gate that
modifies the maximum electric field at the emitter tip without significant leakage
into the collector. We also applied a time-varying voltage signal on the gate and
observed current modulation. Unfortunately, we measured a device capacitance of
1.49 nF, which severely limits our maximum operating frequency to less than 1
kHz. A way to significantly reduced the capacitance is to minimize the overlapping
area between the vertical terminals, which forms a large parallel plate capacitor. By

Minimize

Maximize

Figure 5.33: NIR camera images of the input beam when coupling into the grating
is (a) minimized and (b) maximized via a 90◦ rotation of the half wave-plate.

171
Maximized
Minimized

Figure 5.34: Optically-induced current measured by the lock-in amplifier as a function of emitter voltage when coupling into the grating is minimized and maximized.

5 µm

Figure 5.35: SEM of the blown device after multiple continuous measurements.

replacing the planar Si waveguide that constitutes the gate with a ridge waveguide,
we could drop the capacitance to less than 1 fF.
Furthermore, we demonstrated optically-induced field emission by modulating the
input optical signal with a chopper and using a lock-in amplifier to isolate the
optically-induced contribution to the measured current. However, our opticallyinduced currents did not exceed 0.2 nA even at laser output powers of 400 mW. We
characterized the loss in our free-space setup (up to the chamber) to be -7.57 dBm
with an optical power meter mounted on a flip mirror. In addition, we employed a
confocal setup to separately estimate the efficiency of our grating using our 100X

172
microscope, which yielded an 8% coupling efficiency. This resulted in an overall
system loss of over -18.54 dBm, which did not include the losses from the coupling
between the photonic mode and the hybrid plasmonic mode.
There are several ways to improve the system’s efficiency. Firstly, we can remove
the Ti adhesion layer for Au, as adhesion layers have been shown to significantly
increase losses [8]. Additionally, we can replace our lossy gold flat gratings with
curved Si gratings, which can increase the grating efficiency to 80% [15], as they
significantly minimize the amount of incident energy scattered into higher order
modes [15]. Curved Si gratings could be easily integrated into our system in an
additional lithographic and etching step. Furthermore, we could replace the gratings
altogether with edge coupling. A single-mode ridge waveguide would replace the
slab waveguide, and an inverted taper clad in polymer would be used to couple light
from a lensed fiber. This coupling mechanism comes with additional fabrication
steps, as the waveguide and taper need to be patterned and etched on the Si layer
and the polymer overlay for spot size conversion has to be selectively deposited.
However, edge coupling eliminates free-space setup losses and improves the overall
system coupling efficiency into the photonic mode to over 80% [25, 26], with losses
mainly due to reflections at the chip facet and spot-size converter losses.
In Chapter 2, we discussed electron emission resulting from optical illumination.
This process can be either field-driven, wherein the potential barrier is modulated
and emission occurs by electron tunneling, or photon-driven, wherein the electrons
acquire the necessary energy by photon absorption. Unfortunately, in practical
devices, photoemission is still challenging, requiring lasers with very high powers
or short wavelengths. For instance, in the mid-IR range, photoemission has been
demonstrated in metallic nanostructures using femtosecond pulse irradiation at laser
intensities on the order of 1 TW/cm2 [27]. However, if SPPs are excited, laser
intensities of about 1 GV/cm2 [28] are sufficient due to the high plasmonic field
confinement and enhancement, which facilitate electron emission and augment the
ponderomotive forces caused by the large electric field gradients.
The application of a static bias to optical emission can further reduce the necessary
fields to instigate vacuum electron transport by field-assisted photoemission. For
instance, it has been demonstrated that static and optical fields under 1 GV/m are
sufficient to cause emission from a tungsten tip with no plasmonic enhancement
[29]. This is due to the strong non-linearity of field emission wherein a weak optical
field can substantially enhance emission.

173
These experiments paved the way to combine field emission with plasmonicallyenhanced photoemission in order to reduce the required applied voltages and laser
power. For instance, Piltan et al. observed multiphoton emission by using a DC
bias of 10 V and optical powers on the order of W/cm2 at 785 nm in resonant
plasmonic structures with optical field enhancements of 3 orders of magnitude [30].
Similarly, Turchetti et al. demonstrated that with the usage of the large static fields
that arise in nanoscale vacuum gaps, ultra-fast optical field emission can occur in
weak-field (under 10 V/nm) with a Keldysh parameter of 𝛾 𝑘 = 898 in a plasmonic
bow-tie nanoantenna with mid-IR excitation [31]. Additionally, the larger DC field
compared to the optical field sets the emission direction from cathode to anode,
preventing electrons from being back-accelerated at each half-cycle of the optical
field. Although our proposed structure requires considerable optimization (our
current optical field of ≈ 1 MV/m and the barrier-reduced work function of 4.3 eV
result in a Keldysh parameter of about 8500), the concept of merging field emission
and plasmonics at the nanoscale constitutes a major step towards the development
of ultra-high-speed, low-power, nanoscale optoelectronic systems.
An interesting application for the proposed device is as an ultra-fast photodetector
for THz electronics [32, 33], integrated microwave photonics [34], and carrierenvelope phase (CEP) detection [35, 36]. Thermoelectric detectors have a wide
spectral bandwidth and are relatively inexpensive. However, they suffer from slow
response times due to a phonon-dominated transport [37, 38]. Superconducting
detectors have ps response times and single-photon sensitivity [39–41], but require
cryogenic cooling, limiting system integration and increasing costs. Furthermore,
conventional semiconductor photodetectors are laterally constrained by the diffraction limit and vertically confined by the required absorption depth, limiting their
maximum speed and efficiency. Additionally, complex band structure engineering
is required to effectively detect IR signals [42]. In this way, as field emission depends on the material work function and the maximum field at the surface, and the
device capacitance can be adjusted by tuning its geometry, plasmonically enhanced
field-assisted photoemission detectors can be sensitive, fast, and easy to integrate
with practical systems.
Finally, we could pair our proposed optoelectronic devices with non-linear electrooptic polymers to convert electric signals into optical pulses at high frequencies.
By using optical interconnects, Tbit/s signal transmission speed could be achieved.
Therefore, thanks to the miniaturization provided by plasmonics, we could con-

174
ceivable develop full optical circuits on SOI platform with chip-level, high-density
integration.
References
[1] L. Novotny and B. Hecht. Principles of nano-optics. New York: Cambridge
University Press, 2006. isbn: 978-0-511-16704-1.
[2] N. W. Ashcroft and N. D. Mermin. Solid state physics. Cengage Learning,
1976. isbn: 978-0-03-083993-1.
[3] C. Kittel. Introduction to solid state physics. Hoboken, NJ: Wiley, 2005. isbn:
978-0-471-41526-8.
[4] P. B. Johnson and R. W. Christy. “Optical constants of the noble metals.”
Physical Review B 6.12 (1972), pp. 4370–4379. doi: 10.1103/PhysRevB.
6.4370.
[5] E. Zeman and G. Schatz. “An accurate electromagnetic theory study of surface
enhancement factors for silver, gold, copper, lithium, sodium, aluminum,
gallium, indium, zinc, and cadmium.” The Journal of Physical Chemistry
91.3 (1987), pp. 634–643. doi: 10.1021/j100287a028.
[6] H. J. Hagemann, W. Gudat, and C. Kunz. “Optical constants from the far
infrared to the X-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2 O3 .” Journal
of the Optical Society of America 65.6 (1975), pp. 742–744. doi: 10.1364/
JOSA.65.000742.
[7] P. West et al. “Searching for better plasmonic materials.” Laser & Photonics
Reviews 4.6 (2010), pp. 795–808. doi: 10.1002/lpor.200900055.
[8] M. P. Nielsen et al. “Plasmonic materials for metal insulator semiconductor
insulator metal nanoplasmonic waveguides on silicon on insulator platform.”
en. Optical Materials 36.2 (2013), pp. 294–298. doi: 10.1016/j.optmat.
2013.09.011.
[9] G. Goubau. “Surface waves and their application to transmission lines.”
Journal of Applied Physics 21.11 (1950), pp. 1119–1128. doi: 10.1063/1.
1699553.
[10] S. Maier. Plasmonics: Fundamentals and applications. New York: Springer,
2007. isbn: 978-0-387-33150-8.
[11] C. L. C. Smith et al. “Gap and channeled plasmons in tapered grooves: a review.” Nanoscale 7.21 (2015), pp. 9355–9386. doi: 10.1039/C5NR01282A.
[12] J. Homola, ed. Surface plasmon resonance based sensors. Vol. 4. Springer
Series on Chemical Sensors and Biosensors. Springer, 2006. isbn: 978-3540-33918-2.
[13] A. Maradudin, J. Sambles, and W. Barnes. Modern plasmonics. Handbook
of surface science 4. Elsevier, 2014. isbn: 978-0-444-59526-3.

175
[14] L. Lafone, T. Sidiropoulos, and R. Oulton. “Silicon-based metal-loaded plasmonic waveguides for low-loss nanofocusing.” Optics Letters 39.15 (2014),
p. 4356. doi: 10.1364/OL.39.004356.
[15] N. Güsken et al. “Nanofocusing in SOI-based hybrid plasmonic metal slot
waveguides.” Optics Express 26.23 (2018), p. 30634. doi: 10.1364/OE.26.
030634.
[16] M. Nielsen et al. “Adiabatic nanofocusing in hybrid gap plasmon waveguides
on the silicon-on-insulator platform.” Nano Letters 16.2 (2016), pp. 1410–
1414. doi: 10.1021/acs.nanolett.5b04931.
[17] L. Lafone. “Metal loading of semiconductor on insulator architectures for
nanoscale optoelectronic devices.” PhD thesis. London, UK: Imperial College
London, 2015.
[18] L. Gao, F. Lemarchand, and M. Lequime. “Exploitation of multiple incidences
spectrometric measurements for thin film reverse engineering.” Optics Express 20.14 (2012), p. 15734. doi: 10.1364/OE.20.015734.
[19] H. Li. “Refractive index of silicon and germanium and its wavelength and
temperature derivatives.” Journal of Physical and Chemical Reference Data
9.3 (1980), pp. 561–658. doi: 10.1063/1.555624.
[20] L. D. Landau, E. M. Liftshitz, and L. P. Pitaevskij. Electrodynamics of continuous media. Vol. 8. Elsevier, 2009. isbn: 978-0-7506-2634-7.
[21] E. Voges. “Coupling techniques: Prism-, grating- and endfire-coupling.” In:
Integrated Optics. Boston, MA: Springer, 1983, pp. 323–333. isbn: 978-14613-3663-1.
[22] T. P. H. Sidiropoulos, S. A. Maier, and R. F. Oulton. “Efficient low dispersion compact plasmonic-photonic coupler.” Optics Express 20.11 (2012),
p. 12359. doi: 10.1364/OE.20.012359.
[23] D. Taillaert et al. “Grating couplers for coupling between optical fibers
and nanophotonic waveguides.” Japanese Journal of Applied Physics 45.8A
(2006), pp. 6071–6077. doi: 10.1143/JJAP.45.6071.
[24] M. Stockman. “Nanofocusing of optical energy in tapered plasmonic waveguides.” Physical Review Letters 93.13 (2004), p. 137404. doi: 10.1103/
PhysRevLett.93.137404.
[25] T. Shoji et al. “Low loss mode size converter from 0.3 µm square Si wire
waveguides to singlemode fibres.” Electronics Letters 38.25 (2002), p. 1669.
doi: 10.1049/el:20021185.
[26] R. Marchetti et al. “Coupling strategies for silicon photonics integrated chips.”
Photonics Research 7.2 (2019), p. 201. doi: 10.1364/PRJ.7.000201.

176
[27] B. Piglosiewicz et al. “Carrier-envelope phase effects on the strong-field
photoemission of electrons from metallic nanostructures.” Nature Photonics
8.1 (2014), pp. 37–42. doi: 10.1038/nphoton.2013.288.
[28] S. M. Teichmann et al. “Strong-field plasmonic photoemission in the midIR at <1 GW/cm2 intensity.” Scientific Reports 5.1 (2015), pp. 1–5. doi:
10.1038/srep07584.
[29] P. Hommelhoff, C. Kealhofer, and M. A. Kasevich. “Ultrafast electron pulses
from a tungsten tip triggered by low-power femtosecond laser pulses.” Physical Review Letters 97.24 (2006), p. 247402. doi: 10.1103/PhysRevLett.
97.247402.
[30] S. Piltan and D. Sievenpiper. “Field enhancement in plasmonic nanostructures.” Journal of Optics 20.5 (2018), p. 055401. doi: 10 . 1088 / 2040 8986/aab87e.
[31] M. Turchetti et al. “Impact of DC bias on weak optical-field-driven electron
emission in nano-vacuum-gap detectors.” Journal of the Optical Society of
America B 38.3 (2021), p. 1009. doi: 10.1364/JOSAB.413680.
[32] K. Sengupta, T. Nagatsuma, and D. Mittleman. “Terahertz integrated electronic and hybrid electronic–photonic systems.” Nature Electronics 1.12
(2018), pp. 622–635. doi: 10.1038/s41928-018-0173-2.
[33] A. Schiffrin et al. “Optical-field-induced current in dielectrics.” Nature 493.7430
(2013), pp. 70–74. doi: 10.1038/nature11567.
[34] D. Marpaung, J. Yao, and J. Capmany. “Integrated microwave photonics.”
Nature Photonics 13.2 (2019), pp. 80–90. doi: 10 . 1038 / s41566 - 018 0310-5.
[35] D. Mor et al. “PHz electronic device design and simulation for waveguideintegrated carrier-envelope phase detection.” Journal of Lightwave Technology 40.12 (2022), pp. 3823–3831. doi: 10.1109/JLT.2022.3150246.
[36] Y. Yang et al. “Light phase detection with on-chip petahertz electronic
networks.” Nature Communications 11.1 (2020), p. 3407. doi: 10.1038/
s41467-020-17250-0.
[37] X. Lu, P. Jiang, and X. Bao. “Phonon-enhanced photothermoelectric effect in SrTiO3 ultra-broadband photodetector.” Nature Communications 10.1
(2019), p. 138. doi: 10.1038/s41467-018-07860-0.
[38] X. Lu et al. “Progress of photodetectors sased on the photothermoelectric
effect.” Advanced Materials 31.50 (2019), p. 1902044. doi: 10.1002/adma.
201902044.
[39] C. Natarajan, M. Tanner, and R. Hadfield. “Superconducting nanowire singlephoton detectors: Physics and applications.” Superconductor Science and
Technology 25.6 (2012), p. 063001. doi: 10 . 1088 / 0953 - 2048 / 25 / 6 /
063001.

177
[40] G. N. Gol’tsman et al. “Picosecond superconducting single-photon optical
detector.” Applied Physics Letters 79.6 (2001), pp. 705–707. doi: 10.1063/
1.1388868.
[41] B. Korzh et al. “Demonstration of sub-3 ps temporal resolution with a superconducting nanowire single-photon detector.” Nature Photonics 14.4 (2020),
pp. 250–255. doi: 10.1038/s41566-020-0589-x.
[42] V. Adinolfi and E. Sargent. “Photovoltage field-effect transistors.” Nature
542.7641 (2017), pp. 324–327. doi: 10.1038/nature21050.

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Chapter 6

CONCLUDING REMARKS
Despite the revolution vacuum technology brought to the field of electronics in the
early 20th century, leading to industrial growth and improvements in quality of life,
it has since been almost entirely replaced by SSEs. This transition was spurred by
the ease of fabrication, integration (e.g., ICs), long lifetime, and decreased power
consumption of semiconductors, rather than any intrinsic advantage as a charge
carrier transport medium. Moreover, novel applications and the demand for new
capabilities led to an astonishing improvement in the fabrication techniques that
progressively shrank the size of SSDs to achieve higher operating speeds following
Moore’s Law scaling.
However, the steady miniaturization and proposed complex architectures are hindering further optimization of semiconductor devices. Effective thermal management
challenges are limiting their speed, power, and minimum dimensions, as inherent
constraints imposed by electron mobility and bandgap are reached. In this context,
the work presented in this thesis seeks to employ the same fabrication techniques
that allowed SSDs to scale down to unprecedented dimensions to design nanoscale
field emission devices that could address some of these issues.
Vacuum nanoelectronics offers several intrinsic advantages compared to SSEs. For
instance, electron mobility in vacuum is higher than in any other material as it theoretically supports ballistic transport and suppresses phonon scattering. Moreover,
device capacitance and impedance can be tailored through geometry design, which
makes them highly appealing for high-frequency operations. Vacuum devices are
also more robust to high-temperature environments and radiation exposure. In addition, while substantial electric fields are required to induce emission, low-voltage
operation can be enabled by exploiting the nanoscale gaps that can be easily fabricated using state-of-the-art lithographic equipment, thereby resulting in increased
efficiency and reduced power consumption. Furthermore, it is often claimed that
the vacuum channel dimensions under the mean free path of the electron in air
combined with sub-10 V bias to avoid ionization of gas molecules removes the need
for packaging and allows atmospheric operation. Consequently, these devices have
the potential to surpass the limitations of current technologies.

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In this work, we experimentally demonstrated design paradigms for nanoscale field
emission devices. We studied how various physical parameters affect the performance of vacuum devices and provided comprehensive guidelines for reproducible
fabrication. Ultimately, these devices were designed for two distinct applications:
high-temperature environments and high-frequency operation.
The development of robust technology capable of withstanding high temperatures is
especially attractive to the aerospace, military, nuclear, and automotive industries,
among others. To tackle the usual SSEs’ shortcomings in such extreme conditions,
we developed suspended lateral two- and four-terminal vacuum field emission devices. Constructed with tungsten due to its heat-resistant capability, we strove to
increase the resistance of the leakage current pathways that arise at high temperatures
by removing the underlying solid substrate. Moreover, we opted for planar architectures for their convenience in manufacturing with current lithographic capabilities
and conventional semiconductor fabrication techniques.
Furthermore, two distinct architectures were considered for high-frequency operation. The first proposal relied solely on the fast response of field emission and
consisted of a two-terminal multi-tip array for frequency conversion. To improve
its efficiency, we analyzed the effect of thin-film coating with Pr to reduce the work
function and boost the emission current. For the second proposal, we augmented
FN emission with plasmonics, developing plasmonically-enhanced field emission
optoelectronic devices at telecommunication wavelengths on SOI platform. By
utilizing the strong confinement and significant optical field enhancement of plasmons, we sought to create devices that can be modulated electrically and optically
at dimensions smaller than those of purely photonic architectures.
Nonetheless, we have also demonstrated that several challenges must be addressed to
realize the potential of the proposed field emission devices for practical applications
and be competitive with modern semiconductor technology. However, we are
optimistic that further refinements will let us overcome these limitations and enable
us to combine the inherent advantages of vacuum as a transport medium with the
integrability and fabrication ease favoured by SSEs to revolutionize high-speed
telecommunication and provide resilient, long-lasting operation in harsh conditions.
While in the short-term vacuum field emission devices could work alongside SSEs
and complement it, in the long-term we aspire to create full vacuum electronic
circuits and systems. Overall, the research and development of nanoscale field

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emission devices is an exciting field and holds significant potential for advancing
the field of electronics.