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Active Infrared Nanophotonics in van der Waals Materials
Citation
Sherrott, Michelle Caroline
(2018)
Active Infrared Nanophotonics in van der Waals Materials.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/Z9J964M8.
Abstract
Two-dimensional van der Waals materials have recently been introduced into the field of nanophotonics, creating opportunities to explore novel physics and realize first-of-their kind devices. By reducing the thickness of these materials, novel optical properties emerge due to the introduction of vertical quantum confinement. Unlike most materials, which suffer from a reduction in quality as they are thinned, layered van der Waals materials have naturally passivated surfaces that preserve their performance in monolayer form. Moreover, because the thickness of these materials is below typical charge carrier screening lengths, it is possible to actively control their optical properties with an external gate voltage. By combining these unique properties with the subwavelength control of light-matter interactions provided by nanophotonics, new device architectures can be realized.
In this thesis, we explore van der Waals materials for active infrared nanophotonics, focusing on monolayer graphene and few-layer black phosphorus. Chapter 2 introduces gate-tunable graphene plasmons that interact strongly with their environment and can be combined with an external cavity to reach large absorption strengths in a single atomic layer. Chapter 3 builds on this, using graphene plasmons to control the spectral character and polarization state of thermal radiation. In Chapter 4, we complete the story of actively controlling infrared light using graphene-based structures, introducing graphene into a resonant gold structure to enable active control of phase. By combining these resonant structures together into a multi-pixel array, we realize an actively tunable meta-device for active beam steering in the infrared. In Chapters 5 and 6, we present few layer black phosphorus (BP) as a novel material for active infrared nanophotonics. We study the different electro-optic effects of the material from the visible to mid-infrared. We additionally examine the polarization-dependent response of few-layer BP, observing that we can tune its optical response from being highly anisotropic to nearly isotropic in plane. Finally, Chapter 7 comments on the challenges and opportunities for graphene- and BP-integrated nanophotonic structures and devices.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
van der Waals Materials; Infrared; Nanophotonics; Graphene; Black phosphorus; Plasmonics; Metasurfaces
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Materials Science
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Atwater, Harry Albert
Group:
Resnick Sustainability Institute, Kavli Nanoscience Institute
Thesis Committee:
Greer, Julia R. (chair)
Atwater, Harry Albert
Rossman, George Robert
Minnich, Austin J.
Defense Date:
12 January 2018
Non-Caltech Author Email:
michelle.sherrott (AT) gmail.com
Funders:
Funding Agency
Grant Number
DOE ‘Light-Material Interactions in Energy Conversion’ Energy Frontier Research Center
DE- SC0001293
Record Number:
CaltechTHESIS:01262018-171457982
Persistent URL:
DOI:
10.7907/Z9J964M8
Related URLs:
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Description
DOI
Article from which excepts are drawn for Ch. 2
DOI
Article from which excepts are drawn for Ch. 2
DOI
Article from which excepts are drawn for Ch. 2
DOI
Article from which excepts are drawn for Ch. 3
DOI
Article adapted for Ch. 4
DOI
Article adapted for Ch. 5
arXiv
Article adapted for Ch. 6
ORCID:
Author
ORCID
Sherrott, Michelle Caroline
0000-0002-7503-9714
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No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:
10649
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CaltechTHESIS
Deposited By:
Michelle Sherrott
Deposited On:
02 Feb 2018 22:03
Last Modified:
08 Nov 2023 00:12
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Active Infrared Nanophotonics in
van der Waals Materials

Thesis by

Michelle Caroline Sherrott

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

CALIFORNIA INSTITUTE OF TECHNOLOGY
Pasadena, California

2018
Defended January 12, 2018

Michelle Caroline Sherrott
ORCID: 0000-0002-7503-9714

iii

ACKNOWLEDGEMENTS
No thesis is ever completed without the support and input of a great number of people, and
I count myself incredibly lucky to have been surrounded by an amazing group of
individuals these past five years. I am so fortunate to have met the people I have met, and
to be leaving this place makes me profoundly sad, if excited for a new adventure.
First and foremost, none of this would exist without the endless support of my advisor,
Professor Harry Atwater. Harry is a truly unique advisor, and his unwavering enthusiasm
and passion for science has been inspirational. He has challenged me to always do my best,
and has provided me with the freedom to try new things, to fail, and to learn. But more than
this, Harry is a kind and compassionate person. He treats his students and postdocs with
respect and he always has their back. It has been a great honor to work with him.
Alongside Harry, I have a fantastic thesis committee to thank: Professor Julia Greer, who is
a great teacher, whose positive energy is contagious, and who is a fantastic role model for
women in science; Professor George Rossman, who exemplifies what it means to educate,
and who has taught me so much about materials science, infrared spectroscopy, and doing
thoughtful research; and Professor Austin Minnich, who has provided a great number of
ideas and support, particularly for near-field heat transfer collaborations.
Next, I will forever be grateful to my mentor, Victor Brar, the patient postdoc who
somehow turned me into a real grad student when I could barely hold a pair of tweezers.
Victor, shuffling about the lab in his many-pocketed vest, was a source of never-ending
ideas and insights, and pushed me to become a better scientist. I have met few people as
brilliant as Victor, and I have learned so much from him.
There are so many other scientists, postdocs, and grad students that I have been fortunate to
work with, listed here in no particular order. Other co-authors on the works in Chapter 2
and 3: Min Seok Jang, Seyoon Kim, Laura Kim, Josue Lopez, Luke Sweatlock. Chapter 4:
Philip Hon, Juan Garcia, Sam Ponti, Kate Fountaine. Chapter 5 and 6: Will Whitney, Deep
Jariwala, Wei-Hsiang Lin, Joeson Wong, Cora Went. Chapter 7: Nate Thomas. All of these
individuals have taught me so much, and none of this would have happened without them.
It would take pages upon pages of text to describe what they have all brought to this thesis,
and to my life. Many are not just collaborators, but also wonderful friends.

iv
Sharing an office with Will, Deep, and Joeson these past few years has been a true
pleasure, and I have learned so much working and spending time with them. I also thank
Matt Escarra, Naomi Coronel, and Anna Beck, my original officemates, for all they did to
introduce me to Caltech and the Atwater Group.
I also want to thank all the staff members of the KNI for support, training, and friendship:
Guy de Rose, Melissa Melendes, Matt Sullivan-Hunt, Nils Asplund, Steven Martinez, Bert
Mendoza, Nathan Lee, Alex Wertheim, and Barry Baker. They have helped me immensely,
and have made the many hours I spent in the subbasement so much more enjoyable.
So much appreciation additionally needs to be given to the incredible administrators who
hold everything together: Jennifer, Tiffany, Liz, Lyann, Jonathan, and Christy. I have to
especially thank Christy, who was my first point of contact with Caltech, and who made it
so easy to embrace this place as my home.
Outside of scientific works, I have been so lucky in friendship here. Greg: I am so happy
you were a part of this, and you brightened my day each day. My amazing friend of nearly
10 years, Dagny: words cannot express my gratitude for your friendship. Heather, my
wonderful and supportive friend and roommate: I’m so happy to have met you. The entire
Atwater Group: in addition to scientific support and insights, you have all been excellent
friends and made me feel like I was part of a great community.
Finally, I have been endlessly supported by my family: my mom and dad who were always
there with words of love and encouragement, and without whom this never would have
happened; and my sister who has been one of my biggest cheerleaders.

ABSTRACT
Two-dimensional van der Waals materials have recently been introduced into the field of
nanophotonics, creating opportunities to explore novel physics and realize first-of-their
kind devices. By reducing the thickness of these materials, novel optical properties emerge
due to the introduction of vertical quantum confinement. Unlike most materials, which
suffer from a reduction in quality as they are thinned, layered van der Waals materials have
naturally passivated surfaces that preserve their performance in monolayer form. Moreover,
because the thickness of these materials is below typical charge carrier screening lengths, it
is possible to actively control their optical properties with an external gate voltage. By
combining these unique properties with the subwavelength control of light-matter
interactions provided by nanophotonics, new device architectures can be realized.
In this thesis, we explore van der Waals materials for active infrared nanophotonics,
focusing on monolayer graphene and few-layer black phosphorus. Chapter 2 introduces
gate-tunable graphene plasmons that interact strongly with their environment and can be
combined with an external cavity to reach large absorption strengths in a single atomic
layer. Chapter 3 builds on this, using graphene plasmons to control the spectral character
and polarization state of thermal radiation. In Chapter 4, we complete the story of actively
controlling infrared light using graphene-based structures, introducing graphene into a
resonant gold structure to enable active control of phase. By combining these resonant
structures together into a multi-pixel array, we realize an actively tunable meta-device for
active beam steering in the infrared. In Chapters 5 and 6, we present few layer black
phosphorus (BP) as a novel material for active infrared nanophotonics. We study the
different electro-optic effects of the material from the visible to mid-infrared. We
additionally examine the polarization-dependent response of few-layer BP, observing that
we can tune its optical response from being highly anisotropic to nearly isotropic in plane.
Finally, Chapter 7 comments on the challenges and opportunities for graphene- and BPintegrated nanophotonic structures and devices.

PUBLISHED CONTENT AND CONTRIBUTIONS
Portions of this thesis have been drawn from the following publications with permission
from the publisher:
Michelle C. Sherrott*, William S. Whitney*, Deep Jariwala, George R. Rossman, Harry
A. Atwater, “Electrical Control of Linear Dichroism in Black Phosphorus from the
Visible to Mid-Infrared”, (*Equal author contributors)
arXiv:1710.00131
M.C.S. and W.S.W. conceived the experiment along with co-authors, designed and
fabricated the structure, and performed the measurements. The manuscript was prepared
by M.C.S. and W.S.W. with input from co-authors.
Michelle C. Sherrott*, Philip W. C. Hon*, Katherine T. Fountaine, Juan C. Garcia,
Samuel M. Ponti, Victor W. Brar, Luke A. Sweatlock, Harry A. Atwater, “Experimental
Demonstration of >230° Phase Modulation in Gate-Tunable Graphene-Gold
Reconfigurable Mid-Infrared Metasurfaces”, Nano Lett., 2017, 17 (5), pp 3027–3034
(*Equal author contributors)
DOI: 10.1021/acs.nanolett.7b00359
M.C.S. conceived the experiment along with co-authors, designed and fabricated the
structure, and participated in the measurements. The manuscript was prepared by M.C.S.
with input from co-authors.
William S. Whitney*, Michelle C. Sherrott*, Deep Jariwala, Wei-Hsiang Lin, Hans A.
Bechtel, George R. Rossman, Harry A. Atwater, “Field Effect Optoelectronic Modulation
of Quantum-Confined Carriers in Black Phosphorus”, Nano Lett., 2017, 17 (1), pp 78–84
(*Equal author contributors)
DOI: 10.1021/acs.nanolett.6b03362
M.C.S. and W.S.W. conceived the experiment along with co-authors, designed and
fabricated the structure, and performed the measurements. The manuscript was prepared
by M.C.S. and W.S.W. with input from co-authors.
Excerpts are also included from the below:
Victor W. Brar, Michelle C. Sherrott, Min Seok Jang, Laura Kim, Mansoo Choi, Luke
A. Sweatlock, Harry A. Atwater, “Electronic modulation of infrared radiation in
graphene plasmonic resonators”, Nature Communications, 6, 7032 (2015)
DOI: 10.1038/ncomms8032 (Open Access)
M.C.S. and V.W.B. conceived the experiment along with coauthors. M.C.S. assisted with
experiments, performed calculations to analyze the experimental data, and prepared the
manuscript alongside V.W.B and co-authors.
Min Seok Jang, Victor W. Brar, Michelle C. Sherrott, Josue J Lopez, Laura K Kim,
Seyoon Kim, Mansoo Choi, Harry A. Atwater, “Tunable Large Resonant Absorption in a
Mid-IR Graphene Salisbury Screen”, Phys Rev B 90, 165409 (2014)

vii
DOI: 10.1103/PhysRevB.90.165409
M.C.S. assisted in data analysis and the preparation of the manuscript.
Victor W. Brar, Min Seok Jang, Michelle Sherrott, Seyoon Kim, Josue L. Lopez, Laura
B Kim, Mansoo Choi, Harry A. Atwater, “Hybrid Surface-Phonon-Plasmon Polariton
Modes in Graphene/Monolayer h-BN Heterostructures”, Nano Lett., 2014, 14 (7), pp
3876 – 3880
DOI: 10.1021/nl501096s
M.C.S. performed some of the experimental characterization and assisted in data analysis
and the preparation of the manuscript.
Victor W. Brar, Min Seok Jang, Michelle Sherrott, Josue L. Lopez, Harry A. Atwater,
"Highly Confined Tunable Mid-Infrared Plasmonics in Graphene Nanoresonators", Nano
Lett., 2013,13 (6), pp 2541-2547
DOI: 10.1021/nl400601c
M.C.S. performed some of the experimental characterization and assisted in data analysis
and the preparation of the manuscript.
These manuscript excerpts are included to provide important background to the
remainder of the thesis with support from advisor Professor Harry Atwater.

viii

TABLE OF CONTENTS

Acknowledgements…………………………………………………………...iv
Abstract ………………………………………………………………………vi
Published Content and Contributions…………………………………….......vii
Table of Contents……………………………………………………………. ix
List of Illustrations and/or Tables……………………………………………xii
Chapter I: Introduction ........................................................................................ 1
1.1 Nanophotonics......................................................................................... 1
1.1.1 Plasmonics........................................................................................ 1
1.1.2 Metasurfaces .................................................................................... 4
1.2 van der Waals Materials.......................................................................... 7
1.2.1 Graphene .......................................................................................... 7
1.2.2 Black Phosphorus........................................................................... 11
1.3 The Scope of this Thesis ....................................................................... 13
Chapter II: Graphene Plasmons for Tunable Light Matter Interactions........... 16
2.1 Highly Confined Tunable Mid-Infrared Plasmonics in Graphene
Nanoresonators ............................................................................................ 17
2.1.1 Introduction .................................................................................... 17
2.1.2 Experimental Measurement of Tunable Infrared Graphene
Plasmons......................................................................................... 19
2.1.3 Theoretical Description of Graphene Plasmons ............................ 22
2.2 Hybrid Surface-Plasmon-Phonon Polariton Modes in
Graphene/Monolayer h-BN Heterostructures............................................. 26
2.2.1 Introduction .................................................................................... 26
2.2.2 Experimental Measurement of Coupled 2D Phonon-Plasmon
Polaritons ................................................................................................. 27
2.2.3 Modeling of Coupled Plasmon-Phonon Dispersion ...................... 30
2.3 Tunable Enhanced Absorption in a Graphene Salisbury Screen ......... 33
2.3.1 Introduction .................................................................................... 33
2.3.2 Experimental Demonstration of Enhanced Absorption ................ 34
2.4 Conclusions and Outlook ...................................................................... 37
Chapter III: Graphene-Based Active Control of Thermal Radiation ............... 39
3.1 Electronic Modulation of Thermal Radiation in a Graphene
Salisbury Screen .......................................................................................... 40
3.1.1 Introduction .................................................................................... 40
3.1.2 Experimental Realization of Dynamically Tuned Thermal
Radiation ................................................................................................. 41
3.1.3 Theoretical Interpretation of Results ............................................. 46
3.1.4 Radiated Power and Device Considerations.................................. 51
3.2 Electronic Control of Polarized Emission ............................................ 53
3.2.1 Introduction .................................................................................... 53

ix
3.2.2 Design of Dual-Resonant Structure for Polarization Control ....... 54
3.3 Conclusions and Outlook ...................................................................... 58
Chapter IV: Phase Modulation and Active Beam Steering with
Graphene-Gold Metasurfaces ........................................................................... 60
4.1 Experimental Demonstration of >230° Phase Modulation in
Gate-Tunable Graphene-Gold Reconfigurable Mid-Infrared
Metasurfaces................................................................................................ 61
4.1.1 Introduction .................................................................................... 61
4.1.2 Design of Resonant Phase-Shifting Structure ............................... 63
4.1.3 Experimental Demonstration of Phase Modulation ...................... 65
4.1.4 Beam Steering Calculations ........................................................... 70
4.2 Multi-Element Graphene-Gold Meta-Device for Active Beam
Steering ....................................................................................................... 73
4.3 Conclusions and Outlook ...................................................................... 76
Chapter V: Field Effect Optoelectronic Modulation of Quantum-Confined
Carriers in Black Phosphorus ............................................................................ 77
5.1 Introduction ........................................................................................... 77
5.2 Experimental Design ............................................................................. 79
5.3 Tuning of Infrared Absorption in Few-Layer Black Phosphorus ........ 80
5.3.1 BP Thickness #1............................................................................. 80
5.3.2 BP Thickness #2............................................................................. 83
5.3.3 BP Thickness #3............................................................................. 84
5.4 Conclusions and Outlook ...................................................................... 88
Chapter VI: Electrical Control of Linear Dichroism in Black Phosphorus
from the Visible to Mid-Infrared ...................................................................... 90
6.1 Introduction ........................................................................................... 91
6.2 Experimental Isolation of Electro-Optic Effects .................................. 91
6.3 Thickness-Dependent Electro-Optic Effects ........................................ 96
6.4 Visible-Frequency Gate-Tunability ...................................................... 99
6.5 Conclusions and Outlook .................................................................... 100
Chapter VII: Perspective and Future Works ................................................... 102
7.1 Graphene Research ............................................................................. 102
7.1.1 Control of Far-Field Thermal Radiation...................................... 103
7.1.2 Control of Near-Field Heat Transfer ........................................... 104
7.1.3 Graphene-Based Sensors ............................................................. 106
7.1.4 Graphene Devices in the High-Carrier Concentration Limit ...... 106
7.2 Graphene-Integrated Devices (Commercialization)........................... 109
7.3 Black Phosphorus Research and Development .................................. 110
7.3.1 Black Phosphorus for In-Plane Beam Steering ........................... 111
7.3.2 Black Phosphorus for Far-Field Polarization Control ................. 112
7.4 Nanophotonics and other van der Waals Materials ............................ 113
7.5 Endless Opportunities ......................................................................... 116
Bibliography .................................................................................................... 117
Appendix A: Graphene Fabrication Methods ................................................. 131

Appendix B: Graphene Electromagnetic Simulations .................................... 134
Appendix C: Blackbody Emission Measurements ......................................... 135
Appendix D: Interferometry Measurements ................................................... 136
Appendix E: Black Phosphorus Exfoliation and Fabrication
Methods ........................................................................................................... 137

LIST OF ILLUSTRATIONS

Number
Page
1.1 Dispersion relation of the coupled odd and even modes for an
air/silver/air multilayer with a metal core of thickness 50 nm
(dashed black curves). Silver is modeled as a Drude metal with
negligible damping. ......................................................................................... 4
1.2 Schematic illustration of Snell’s law for refracted light passing
from medium 1 to medium 2. .......................................................................... 5
1.3 Metasurface element: By controlling the geometric parameters and
dielectric environment of a resonant antenna, the reflected or
transmitted phase of light can be controlled. The interference
between each scattering element then results in a propagating
wavefront that has been redirected ................................................................... 6
1.4 Honeycomb lattice of graphene with two atoms per unit, A and B,
defined by lattice vectors a1 and a2 and with nearest neighbor
vectors δI, i = 1,2,3. Corresponding Brillouin Zone. Dirac points are
located at the K and K’ points. Adapted from [27]. ......................................... 8
1.5 Calculated band structure of graphene, from [27], with linear
dispersion near the K point highlighted. .......................................................... 9
1.6 Lattice structure of black phosphorus (left). Calculated electronic
band gap of black phosphorus as a function of number of layers
(right, from [34].) ............................................................................................ 12
1.7 A pictorial representation of this thesis. Chapter 2 presents tightly
confined graphene plasmons. Chapter 3 discusses control of the
amplitude and polarization of thermal emission. Chapter 4
introduces a gate-tunable graphene-gold metasurface for active
beam steering. Chapter 5 examines the electro-optic effects in fewlayer black phosphorus, and Chapter 6 extends this to the

xii
polarization-dependent tunable optical response from the visible to
mid-infrared. Chapter 7 proposes future experiments based on
graphene and black phosphorus, including the steering of thermal
radiation. ........................................................................................................15
2.1 Schematic of experimental device. (a) SEM image of a 80 × 80 um2
graphene nanoresonator array etched in a continuous sheet of CVD
graphene. The graphene sheet was grounded through Au(100
nm)/Cr(3 nm) electrodes that also served as source−drain contacts,
allowing for in situ measurements of the graphene sheet
conductivity. A gate bias was applied through the 285 nm SiO2
layer between the graphene sheet and the doped Si wafer (500 um
thick). FTIR transmission measurements were taken over a 50 µm
diameter spot. (b) SEM and AFM images of 40 and 15 nm
graphene nanoresonator arrays. A nanoresonator width uncertainty
of ±2 nm was inferred from the AFM measurements. (c) A
resistance vs gate voltage curve of the graphene sheet showing a
peak in the resistance at the charge neutral point (CNP), when the
Fermi level (EF) is aligned with the Dirac point. ........................................... 20
2.2 Gate-induced modulation of transmission through graphene
nanoresonator arrays normalized to transmission spectra obtained at
the CNP. (a) Width dependence of optical transmission through
graphene nanoresonator arrays with EF = −0.37 eV. The width of
the nanoresonators is varied from 15 to 80 nm. (b) Fermi level
dependence of optical transmission through 50 nm wide graphene
nanoresonators, with EF varying from −0.22 to −0.52 eV. The
dotted vertical line in both (a) and (b) indicates the zone-center
energy of the in-plane optical phonons of graphene ........................................ 22
2.3 Dispersion of GP and SPPP plasmonic resonances in graphene
nanoresonator arrays. (a) Fermi level dependence of the measured
energy of “GP” (open colored symbols) and “SPPP” (filled colored

xiii
symbols) features observed in nanoresonators with varying widths.
Solid and dashed colored lines indicate the two solutions to eq. 2.1
using the same experimental widths and continuously varying EF.
(b) Theoretical dispersion of bare graphene/SiO2 plasmons (solid)
and SPPPs (dashed), for diﬀerent EF values. Open and filled
symbols plot the measured energy of “GP” and “SPPP” features
(respectively) from graphene nanoresonators at equivalent EF
values. Wavevector values for experimental points are obtained
from AFM measurements of the nanoresonator widths followed by
a finite elements simulation to calculated the wavelength of the first
order supported plasmon modes. The dotted blue lines indicate the
theoretical plasmon dispersion of graphene on a generic,
nondispersive dielectric with ε∞ = 2.1, which is the high frequency
permittivity of SiO2. Dashed and dotted black lines in (a) and (b)
indicate the energy of the TO optical phonon of SiO2 and the zonecenter energy of the in-plane optical phonons of graphene,
respectively. (c) Mode profile of the GP mode of a 50 nm graphene
nanoresonator with EF = −0.37 eV, obtained from a finite element
electromagnetic simulation. ............................................................................ 24
2.4 (a) Schematic of device measured and modeled in this paper.
Graphene nanoresonators are fabricated on a monolayer h-BN sheet
on a SiO2 (285 nm)/Si wafer. Gold contact pads are used to contact
the graphene sheet and the Si wafer is used to apply an in situ
backgate voltage (VG). Zoom-in shows a cartoon of graphene
plasmon coupling to h-BN optical phonon. (b) Optical image of
unpatterned area of device where both the graphene and h-BN
monolayers have been mechanically removed. (c) Scanning
electron microscope image of the 80 nm graphene nanoresonators
(light regions). ................................................................................................ 27

xiv
2.5 (Left

axis)

Normalized transmission

spectra

graphene

nanoresonators with width varying from 30 to 300 nm, as well as
transmission through the unpatterned graphene/h-BN sheet. Spectra
are measured at carrier densities of 1.0 X 1013 cm−2 and normalized
relative to zero carrier density. For 80 nm ribbons, the four different
observable optical modes are labeled with the symbols used to
indicate experimental data points in Figure 3. (Right axis, bottom
spectrum) Infrared transmission of the bare monolayer h-BN on
SiO2 normalized relative to transmission through the SiO2 (285
nm)/Si wafer. The narrow (∼19 cm−1) peak that occurs at 1370
cm−1 has previously been assigned to an optical phonon in h-BN.
The dotted vertical line indicates this peak position as a reference
for the other spectra. ....................................................................................... 29
2.6 Calculated change in transmission for graphene/monolayer hBN/SiO2 nanoresonators of varying width at a carrier density of 1.0
x 1013 cm−2, normalized relative to zero carrier density. The
wavevector is determined by considering the ribbon width, W, as
well as the phase of the plasmon scattering off the graphene ribbon
edge, as described in the text. Experimental data is plotted as
symbols indicating optical modes assigned in Figure 2.5. The error
bars represent uncertainty in the resonator width that is obtained
from AFM measurements. For small k-vectors (large resonators),
this uncertainty is smaller than the symbol size. The dashed line
indicates the theoretical dispersion for bare graphene plasmons,
while the dash-dot line indicates the dispersion for graphene/SiO2
The three horizontal dotted lines indicate the optical phonon
energies of h-BN and SiO2. ............................................................................ 31
2.7 (a) Schematic of experimental device. 70 × 70 µm2 graphene
nanoresonator array is patterned on 1 µm thick silicon nitride (SiNx)

xv
membrane via electron beam lithography. On the opposite side, 200
nm of gold layer is deposited that serves as both a mirror and a
backgate electrode. A gate bias was applied across the SiNx layer
in order to modulate the carrier concentration in graphene. The
reflection spectrum was taken using a Fourier Spectrum Infrared
(FTIR) Spectrometer attached to an infrared microscope with a 15X
objective. The incident light was polarized perpendicular to the
resonators. The inset schematically illustrates the device with the
optical waves at the resonance condition. (b) DC resistance of
graphene sheet as a function of the gate voltage. The inset is an
atomic force microscope image of 40 nm nanoresonators ............................ 35
2.8 (a) The total absorption in the device for undoped (red dashed) and
highly hole doped (blue solid) 40 nm nanoresonators. Absorption
peaks at 1400 cm-1 and a peak at 3500 cm-1 are strongly modulated
by varying the doping level, indicating these features are originated
from graphene. On the other hand, absorption below 1200 cm-1 is
solely due to optical phonon loss in SiNx layer. (b) The change in
absorption with respect to the absorption at the charge neutral point
(CNP) in 40 nm wide graphene nanoresonators at various doping
levels. The solid black curve represents the absorption difference
spectrum of bare (unpatterned) graphene. (c) Width dependence of
the absorption difference with the carrier concentration of 1.42 ×
1013 cm-2. The width of the resonators varies from 20 to 60 nm. The
dashed curve shows the theoretical intensity of the surface parallel
electric field at SiNx surface when graphene is absent. Numerical
aperture of the 15X objective (0.58) is considered ........................................ 36
3.1 Device and experimental set-up (a) Schematic of experimental
apparatus. 70 × 70 µm2 graphene nanoresonator arrays are placed
on a 1 µm thick SiNx membrane with 200 nm Au backreflector. The
graphene was grounded through Au(100 nm)/Cr(3 nm) electrodes

xvi
that also served as source-drain contacts. A gate bias was applied
through the SiNx membrane between the underlying Si frame and
graphene sheet. The temperature controlled stage contains a
feedback controlled, heated silver block that held a 2mm thick
copper sample carrier, with a 100 µm thick sapphire layer used for
electrical isolation.

The temperature was monitored with a

thermocouple in the block, and the stage was held at a vacuum of 1
mtorr. A 1mm thick potassium bromide (KBr) window was used to
pass thermal radiation out of the stage, which was collected with a
Cassegrain objective and passed into an FTIR with an MCT
detector.

(b) A representative SEM image of 30 nm graphene

nanoresonators on a 1µm thick SiNx membrane. (c) Source-drain
resistance vs gate voltage curve of the device. The peak in the
resistance occurs at the charge neutral point (CNP), when the Fermi
level (EF) is aligned with the Dirac point ....................................................... 42
3.2 Experimental emission results (left axis) Emitted thermal radiation
at 250°C from soot (black dotted line) and 40 nm graphene
nanoresonators at zero (red) and 1.2 × 1013 cm-2 (green) carrier
density. (right axis, blue line) Change in emissivity of 40 nm
nanoresonators due to increase in carrier density. Soot reference is
assumed to have emissivity equal to unity. .................................................... 44
3.3 Emissivity tunability (a) Carrier density dependence of change in
emissivity with respect to the CNP for 40 nm graphene
nanoresonators at 250°C. (b) Width dependence of change in
emissivity for 20, 30, 40, 50, and 60 nm wide nanoresonators at
250°C and for a carrier density of 1.2 × 1013 cm-2. (black line)
Emissivity change for a nearby region of bare, unpatterned
graphene at the same carrier density and temperature. (c)
Polarization dependence of the emissivity change for 40 nm

xvii
graphene nanoresonators at 250°C, for a carrier density of 1.2 ×
1013 cm-2 .......................................................................................................... 45
3.4 Finite element power density simulations (a) Finite element
electromagnetic simulation of

∇ ⋅ S (electromagnetic power

density) in graphene/SiNx structure for 40 nm graphene
nanoresonators on 1 µm SiNx with a gold backreflector. The
simulation is performed at 1357 cm-1 (on plasmon resonance) at a
carrier density of 1.2 × 1013 cm-2. The dotted white line indicates
the mode volume of the plasmon. (b) Integrated power density
absorbed in the 40 nm graphene nanoresonator, the SiNx within the
plasmon mode volume (Top SiNx), and the remaining bulk of the
SiNx (Bulk SiNx) for carrier densities of 1.2 × 1013 cm-2 and ~ 0 cm2

(the charge neutral point). ........................................................................... 48

3.5 kHz modulated emission signal. Temporal waveform of applied
voltage signal (black line) and detector signal of emission from 50
nm ribbons at 250°C (green line). A voltage of 60V corresponds to
a doping level of 1.2 × 1013 cm-2, resulting in a positive detector
signal. A voltage of 0V corresponds to the charge neutral point of
the graphene and therefore the measurement of an ‘off’ signal .................... 53
3.6 Schematic illustration of graphene-dielectric dual resonant structure
for controlling the polarization state of reflected or emitted infrared
light. A 7.5 µm thick Si cavity with Au back-reflector results in
enhanced absorption in the graphene nanoresonators at the surface. ........... 55
3.7 Graphene absorption at EF = 0.4 eV normalized to EF = 0 eV for
different nanoresonator widths. High order dielectric resonances of
the silicon cavity are matched to the plasmon resonances. ........................... 56
3.8 (a) Tunable absorption in graphene resonators of selected widths
(40 and 60 nm) and Fermi energies (0.3 and 0.45 eV) for
selectively enhanced absorption. (b – e) Field profiles for each
width/EF combination at a wavelength of 9.34 µm. ........................................ 57

xviii
3.9 (a) Geometry of graphene crosses for polarization switching and
corresponding absorption, (b), normalized to EF = 0 eV for X and Y
polarizations as defined in the reference frame of the schematic .................... 58
4.1 Tunable resonant gap-mode geometry. (a) Schematic of graphenetuned antenna arrays with field concentration at gap highlighted.
Resonator dimensions: 1.2 µm length by 400 nm width by 60 nm
height, spaced laterally by 50 nm. SiNx thickness 500 nm, Au
reflector thickness 200 nm. (b, c) Field profile in the antenna gap
shows detuned resonance at different EF at a wavelength of 8.70
µm. Scale bar is 50 nm. (d) Simulated tunable absorption for
different graphene Fermi energies. (e) Simulated tunable phase for
different graphene Fermi energies. (f) Phase modulation as a
function of Fermi energy for three different wavelengths – 8.2 µm,
8.5 µm, 8.7 µm. ................................................................................................. 63
4.2 (a) Schematic of a gate-tunable device for control of reflected
phase. (b) SEM image of gold resonators on graphene. Scale bar
indicates 1 µm. (c) Tunable absorption measured in FTIR at
different gate voltages corresponding to indicated Fermi energies.
A peak shift of 490 nm is measured. ............................................................... 66
4.3 (a) Schematic of a Michelson interferometer used to measure
reflection phase modulation. (b) Representative interferometer
measurements for different Fermi energies with linear regression
fits at a wavelength of 8.70 µm. (c) Interferometry data fitted for all
EF at 8.70 µm. (d) Extracted phase modulation as a function of EF at
8.70 µm demonstrating 206° tuning and corresponding reflectance
between 1.5 and 12%. ....................................................................................... 67
4.4 Demonstration of phase modulation over multiple wavelengths. (a)
Phase modulation at wavelengths of 8.2 µm, 8.50 µm, and 8.7 µm
(circles – experiment, line – simulation). (b) Maximum phase

xix
tuning achievable at wavelengths from 8.15 um to 8.75 um,
simulation and experiment indicating up to 237° modulation. ....................... 69
4.5 Calculation of proposed reconfigurable metasurface based on
experimentally realized design. (a) Schematic of beam steering
device, where each of the 69 unit cells is assigned a different EF. (b)
Steering efficiency, η, for a 69 element metasurface with a lattice
spacing of 5.55 µm illuminated with a plane wave at 8.60 µm. (c)
Steering efficiency calculated for 360° and 237° phase modulation
with unity reflectance. (d) Steering efficiency for 215° phase
modulation incorporating simulated absorption losses. .................................. 71
4.6 Fabricated tunable metadevice. (a) Optical microscope image of
completed device with 28 independently gate-tunable elements.
Other dark regions correspond to additional metasurface devices
fabricated for performing a dose array to optimize the design. Gold
reference pads are included for measurement ease. (b) Zoomed in
SEM image of fabricated device showing gold resonators spaced by
50 nm and the electrical isolation between pixels. .......................................... 74
4.7 Beam steering designs for reconfigurable meta-device. (a) A threeelement blazed grating style reflectarray with three phases of 0°,
105°, and 204° repeated across all 28 pixels. Steers to
approximately 25°. (b) A four-element blazed grating style
reflectarray with four phases of 0°, 64°, 132°, and 204° repeated
across 28 pixels. Steers to approximately 18°. (c) Calculated
steering angles for each configuration (a) and (b). ......................................... 75
5.1 (a) Schematic illustration of transmission modulation experiment.
Broadband mid-IR beam is transmitted through black phosphorus
sample. Variable gate voltage applied across SiO2 modulates
transmission extinction. (b) Schematic band diagram of few-layer
black phosphorus with subbands arising from vertical confinement ................. 80

xx
5.2 Gate modulation of lightly doped 7 nm flake. (a) FTIR transmission
extinction vs photon energy normalized to zero bias. (b) Sourcedrain current vs gate voltage. Ambipolar conduction is seen. (c)
Calculated optical conductivity of a 4.5 nm thick BP flake at
different carrier concentrations, normalized to the universal
conductivity of graphene. No field effects included. (d) Schematic
of electronic band structure and allowed interband transitions at
different voltages. (e) Optical microscope image of flake. Scale bar
is 10 µm. .............................................................................................................. 81
5.3 Gate modulation of lightly doped 14 nm flake. (a) FTIR
transmission extinction vs photon energy normalized to zero bias
(b) Source-drain current vs gate voltage. Ambipolar conduction is
seen. (c) Calculated optical conductivity of a 10 nm thick BP flake
at different carrier concentrations, normalized to the universal
conductivity of graphene. No field effects included. (d) Schematic
of electronic band structure and allowed interband transitions at
different voltages. (e) Optical microscope image of flake. Scale bar
is 10 µm. ............................................................................................................. 83
5.4 Gate modulation of a heavily doped 6.5 nm flake. (a) FTIR
transmission extinction vs photon energy normalized to zero bias
(b) Source-drain current vs gate voltage. Only hole-type conduction
is seen. (c) Schematic of electronic band structure and allowed
interband

transitions

different

voltages.

(d)

Schematic

representation of quantum confined Franz-Keldysh Effect (e)
Calculated optical conductivity of a 6.5 nm thick BP flake at
different carrier concentrations, normalized to the universal
conductivity of graphene. No field effects included (f) Optical
microscope image of flake. Scale bar is 10 µp. ................................................ 85
6.1 Anisotropic electro-optical effects in few-layer BP. (a) Schematic
figure of infrared modulation devices. Few-layer BP is

xxi
mechanically exfoliated on 285 nm SiO2/Si and then capped with
45 nm Al2O3 by ALD. A semitransparent top contact of 5 nm Pd is
used to apply field (VG1) while the device floats and 20 nm Ni/200
nm Au contacts are used to gate (VG2) the contacted device. (b)
Crystal structure of BP with armchair and zigzag axes indicated. (c)
Illustration of quantum-confined Stark effect and symmetrybreaking effect of external field. Under zero external field, only
optical transitions of equal quantum number are allowed. An
external field tilts the quantum well-like energy levels, causing a
red-shifting of the optical band gap and allowing previously
forbidden transitions. (d) Illustration of anisotropic Burstein-Moss
shift in BP. Intersubband transitions are blocked due to the filling of
the conduction band. Along the ZZ axis, all optical transitions are
disallowed regardless of carrier concentration. (e) Raman spectra
with excitation laser polarized along AC and ZZ axes. The strength
of the Ag2 peak is used to identify crystal axes. ............................................... 93
6.2 Electrically tunable linear dichroism: quantum-confined Stark and
Burstein-Moss effects and forbidden transitions. (a) Optical image
of fabricated sample. (b) Zero-bias infrared extinction of 3.5 nm
flake, polarized along armchair (AC) axis. (c) Calculated index of
refraction for 3.5 nm thick BP with a Fermi energy at mid-gap. (d)
Modulation of BP oscillator strength with field applied to floating
device, for light polarized along the AC axis. (e) Corresponding
modulation for light polarized along the zigzag (ZZ) axis. (f)
Modulation of BP oscillator strength with gating of contacted
device, for light polarized along the AC axis. (g) Corresponding
modulation for light polarized along the ZZ axis.............................................. 94
6.3 Variation of modulation with BP thickness. (a) Optical image of
fabricated 8.5 nm sample. (b) Zero-bias extinction of 8.5 nm flake,
polarized along AC axis. (c) Calculated index of refraction for 8.5

xxii
nm thick BP. (d) Modulation of BP oscillator strength with field
applied to floating device, for light polarized along the AC axis. (e)
Modulation of BP oscillator strength with gating of contacted
device, for light polarized along the AC axis. ................................................. 98
6.4 Lower photon energy spectra for the 8.5 nm flake. Modulation of
BP oscillator strength with field applied to floating device, for light
polarized along the AC axis, normalized to the maximum oscillator
strength as previously. ....................................................................................... 99
6.5 Modulation in the visible. (a) Schematic figure of visible
modulation device. Few-layer BP is mechanically exfoliated on 45
nm Al2O3/5 nm Ni on SrTiO3 and then coated with 45 nm Al2O3. A
5 nm thick semitransparent Ni top contact is used. (b) Optical
image of fabricated sample with 20 nm thick BP. Dashed white line
indicates the boundary of the top Ni contact. (c) Modulation of
extinction with field applied to floating device, for light polarized
along the AC axis. (d) Corresponding modulation for light
polarized along the ZZ axis. (e) Calculated index of refraction for
20 nm thick BP for the measured energies. (f) Calculated imaginary
index of refraction of several thicknesses of BP from the infrared to
visible. .............................................................................................................. 100
7.1 A conceptual representation of the steering of thermal radiation
using a metasurface with a linear phase gradient on a heated polar
substrate for steering of radiation. Active control could be
incorporated by using graphene as a tunable dielectric environment.
.......................................................................................................................... 104
7.2 (a) Schematic of experimentally realistic structure for tunable nearfield heat transfer. (b) Spectral absorption coefficients for unequal
Fermi energies on the top and bottom sheets, minimizing heat
transfer. (c) Spectral absorption coefficients for equal Fermi

xxiii
energies, maximizing NFHT. Electrostatic gating can be used to
tune the Fermi energies to be matched/unmatched ......................................... 105
7.3 A map of the thickness and carrier concentration dependence of the
plasmon resonance of graphene, illustrating the importance of small
resonators and high carrier concentrations to reach high energies ................. 107
7.4 Suspended graphene nanoresonators of 5 nm width and an aspect
ratio of 60:1 fabricated by He ion FIB. From Zeiss white paper. .................. 108
7.5 Gartner Hype Cycle. A visualization of the phases of maturity of
new technologies, useful (if not scientifically validated) for
understanding the life cycle of graphene to date. Adapted from
[287] ................................................................................................................ 110
7.6 A schematic proposal of using black phosphorus as an active
dielectric material for steering of surface plasmons. (a) When BP is
optically isotropic, the surface plasmon propagates in a straight line
from input to output gratings. (b) When the optical anisotropy of
the BP is increased, the surface plasmon is redirected. In this case,
we simply use this as a switch; multiple gratings or multiple
branches of a slot waveguide mode could be used to route light. ................. 111
7.7 A schematic representation (top-down) of a nanophotonic structure
that could be used for actively controlling the polarization of
absorbed (or thermally emitted) light using the tunable linear
dichroism of BP. ............................................................................................. 113
7.8 Schematic of resonant geometry designed for enhancing absorption
in monolayer TMDCs. Insert in upper right is a SEM image of
fabricated TiO2 resonators. ............................................................................. 114
7.9 Simulated absorption of TiO2/WS2 resonant structure. 85% of
absorption is into the monolayer WS2 at its exciton peak of 625 nm. ............ 114
7.10 Simulated absorption in WSe2 using TiO2 resonators on an Ag back
reflector, with varying width of the TiO2 and a fixed separation
between resonators of 100 nm. ....................................................................... 115

xxiv
E.1 Intensity of the green channel of light reflected from BP flakes as
the linear polarization of the incident light is rotated for the 6.5 nm
flake from Chapter 5. In both cases, the polarization angle is
defined as the angle between the x (armchair) crystal axis and the
linear polarizer. The green component of the pixel RGB of the
flakes is normalized to that of the adjacent substrate. .................................... 139

Chapter 1

INTRODUCTION
1.1 Nanophotonics
The field of nanophotonics is concerned with the nature of interactions between light and
materials at a scale comparable to, or smaller than, the wavelength of light, i.e., at the
nanoscale. In particular, there is a focus on controlling these interactions by nanostructuring
metals, dielectrics, or semiconductors in order to realize novel functions (for example the
focusing of light to very small volumes1, 2, spectrally selective transmission or reflection3,
or the deterministic accumulation of phase4, 5). Modern nanophotonics seeks to control
fully the complex electromagnetic field: amplitude, phase, and polarization in the near- and
far-field. In this way, light can be manipulated in ways not allowed by conventional optical
components, and we can replace traditional bulky optics with wavelength-scale structures.
This is of great technological interest in a number of different fields: chemical sensing6, 7,
holographic displays8, hyper-spectral imaging9, and others, which take advantage of the
ways we can control light-matter interactions at the nanoscale.
1.1.1 Plasmonics
The study of plasmons is concerned with the excitation of resonant oscillations of charge in
a heavily doped material (traditionally associated with metals, but more recently expanded
into heavily doped semiconductors and semimetals). A surface plasmon polariton is an
electromagnetic excitation that propagates at the interface between a dielectric and a
conductor, confined in the direction perpendicular to the propagation vector.10 In the most
general case, we consider propagating modes at the interface between conductors and
dielectrics, which can be solved for exactly starting from Maxwell’s equations, below.

∇ ⋅ D = ρext
∇⋅B = 0

(1.1a-d)

∂B
∇×E =∂t
∇ × H = J ext +

∂D
∂t

These equations link the four macroscopic fields – D (the dielectric displacement), E (the
electric field), H (the magnetic field), and B (the magnetic induction) – with charge carrier
density ρext and current density Jext. We can then write down additional relationships to
polarization, P, and magnetization, M, defined in regards to the permittivity and
permeability of free space, ε0 and µ0, respectively.

D = ε 0 E+ P = εε 0 E

(1.2a,b)

H=
B-M =
µ0
µ0µ
where we assume non-magnetic, linear, isotropic media with relative permittivity ε and
permeability µ (and from here onwards ignore the magnetic response). The full derivation
is omitted here for conciseness, but instead we write down the main governing equation
that is drawn from Maxwell’s equations in the absence of external charge and current, the
wave equation:

∇ × ∇ × E = -µ 0

∂2 D
∂t 2

ω2
K(K ⋅ E) - K E = −ε (K, ω ) 2 E

(1.3a,b)

in the time and momentum domains, respectively. This can be simplified to the key
governing equation of propagating waves by using a few mathematical identities and
setting a permittivity ε that is invariable with position:
∇2E −

ε ∂2 E
=0
c 2 ∂t 2

From here, if we assume a harmonic time dependence of the electric field

(1.4)

-iωt

E(r,t) = E(r)e , we arrive at the Helmholtz equation:

∇ 2 E + k02ε E = 0

(1.5)

where k0 is the wave vector of a propagating wave in vacuum, k0 = ω/c. From this equation,
applying appropriate boundary conditions at material interfaces (and using Maxwell’s
equations where needed), the fundamental properties of propagating plasmons for
numerous geometries can be defined. Most importantly, this allows us to define the
dispersion relation for surface plasmon polaritons (SPPs); the relationship between
frequency ω and wavevector k based on the geometry and permittivity of the conductive
medium and surrounding dielectric. And indeed, a very interesting and powerful aspect of
the study of nanophotonics is that all of the complex structures we explore can be fully
described by Maxwell’s equations: commercial software packages self-consistently solve
these equations at different points in space (and sometimes time), and analytic solutions for
the optical response of a wide variety of geometries can be derived. This allows us to
design nanophotonic structures with incredible precision.
An example of relevance is plotted below, adapted from an exercise presented in S. Maier,
Plasmonics: Fundamentals and Applications10, considering the case of an insulator-metalinsulator stack. This geometry is of particular relevance in the ultrathin limit for the
discussion of plasmons in two-dimensional materials, as will be elaborated on later. We
note the presence of odd and even modes as different solutions to the above equations,
wherein the confinement of modes behaves differently as a function of thickness. For even
modes, the confinement factor increases dramatically as the metal layer thickness
decreases, and the mode remains allowed, a feature that becomes particularly interesting in
the zero-thickness limit of 2D materials.

Frequency ω (1015 Hz)

Light line

Odd mode

Even mode

Wavevector k (107 m-1)
Figure 1.1: Dispersion relation of the coupled odd and even modes for an air/silver/air
multilayer with a metal core of thickness 50 nm. Silver is modeled as a Drude metal with
negligible damping. Modeled after [6].
While the formal derivation of plasmons in 2D materials will follow a slightly modified
approach, this shows us the nature of the plasmons that we observe in the ultrathin limit, in
particular the large momentum mismatch with respect to the light line and resulting large
confinement factor. This confinement factor is one of the unique features of plasmons:
whereas bulk optical components are restricted in how much they can focus light by the
diffraction limit, plasmonic materials can squeeze light down into extremely small
volumes, with interesting implications for enhancing the strength of light-matter
interactions under high field strengths.
1.1.2 Metasurfaces
Since the year 2011, subwavelength nanophotonic structures have been employed to
expand how we write Snell’s Law, classically written as below:
sin θ1 v1 λ1 n2
= =
sin θ 2 v2 λ2 n1

(1.6)

where θ1,2 are the incident and refracted angle of propagation of light, v1,2 are the speed of
light in each medium 1, 2, λ1,2 are the wavelengths of light in each medium, and n1,2 are the
refractive indices of the media, illustrated in Figure 1.2:

Surface normal

θ1
n1
n2
θ2

Figure 1.2: Schematic illustration of Snell’s law for refracted light passing from medium 1
to medium 2.
By incorporating a phase gradient at an interface, we rewrite this equation to account for
the accumulated phase as a function of position. This yields the generalized law of
refraction (1.7) and reflection (1.8).
nt sin (θ t ) − ni sin (θ i ) =

1 dΦ
k0 dx

1 dΦ
cos (θ t ) sin (ϕ t ) =
nt k0 dy

sin (θ r ) − sin (θ i ) =

1 dΦ
ni k0 dx

1 dΦ
cos (θ r ) sin (ϕ r ) =
nt k0 dy

(1.7)

(1.8)

where dΦ/dx and dΦ/dy are phase gradients in the x and y dimensions, θi,t,r are the incident,
transmitted, and reflected angles in the x dimension, and φt,r are the transmitted and
reflected angles along the y dimension, where the light has been reflected/refracted away
from the incident plane (defined as the x-z plane here).11 In this way, light can be redirected
in the far-field in almost arbitrary ways, as long as we have access to a full 2π (360°) phase
range in continuous increments. By carefully selecting the accumulated phase as well as
polarization at each position on the metasurface, far-field beam profiles can be generated at
will (we are not bounded to simply reflecting/refracting light to different angles as written
in equations 1.7 and 1.8). This has been taken advantage of for applications including
anomalous reflection and refraction, focusing/lensing4, 5, and more complex functionalities
such as polarization conversion, cloaking, and three-dimensional image reconstruction12-16,
among others11, 17-21.
In order to realize this ‘designer’ phase gradient, resonant nanophotonic elements are
required. By controlling the geometry of the element, different scattered phases are
realized. In the seminal work from Yu et al11, v-shaped metallic structures are used, which
result in different phases of light based on the angle between arms of the resonator. This
can be generalized as shown in Figure 1.3, below: by changing the geometry of the
resonant element (which can be plasmonic or dielectric) as well as its surroundings (which
will be the focus of our work), different phases can be achieved20, 22-24.

ksca
ϕ = ϕ0+Δϕ

kinc
ϕ = ϕ0

εENV

Figure 1.3: Metasurface element: By controlling the geometric parameters and dielectric
environment of a resonant antenna, the reflected or transmitted phase of light can be
controlled. The interference between each scattering element then results in a propagating
wavefront that has been redirected.
These elements can then be arrayed together as desired to control propagating phase fronts.
This can therefore be used to create wavelength-scale thickness versions of bulk optical
components, and additionally enables the possibility of realizing novel functions that are
otherwise challenging or impossible. In this thesis, we take advantage of actively tunable
materials to control the reflected phase from a resonant element and array these together to
design a reconfigurable metasurface.
1.2 van der Waals Materials
Van der Waals materials are a class of materials defined by a strong in-plane bonding
character, and weak (van der Waals) out of plane interactions between layers. These have
attracted a substantial amount of attention in recent years because their weak van der Waals
interactions allow for the isolation of individual atomic layers, which are naturally
passivated and therefore stable in the ultrathin limit. Early studies of these materials have
been done by mechanically exfoliating bulk crystals down to ultrathin and even monolayer
thicknesses. Using Scotch tape, layers of the material are sequentially removed, leaving
behind ultrathin samples that are then ‘stamped’ onto a substrate of choice. In this way,
research has been performed on a wide range of ultrathin van der Waals materials, enabled
by this straightforward experimental methodology. In this thesis, we focus on the optical
response of monolayer graphene and few-layer black phosphorus.
1.2.1 Graphene
Discovered experimentally in 2004 by Nobel laureates Andre Geim and Konstantin
Novoselov, graphene is a monolayer of sp2-bonded carbon atoms arranged in a honeycomb
lattice (a three-fold symmetric lattice composed of a two-atom basis, shown below)25, 26.

Figure 1.4: Honeycomb lattice of graphene with two atoms per unit, A and B, defined by
lattice vectors a1 and a2 and with nearest neighbor vectors δI, i = 1,2,3. Corresponding
Brillouin Zone. Dirac points are located at the K and K’ points. Adapted from [27].
Due to its unique atomic structure, it possesses exotic optical, electronic, thermal, and
mechanical properties, all of which have been studied extensively in recent years25, 28, 29. It
is also completely stable in monolayer form, giving researchers new opportunities for
understanding physics at the atomic scale. The most unique feature of monolayer graphene
in the context of this work is its band structure, which about the k and k’ point in the lowenergy limit is linear, E ∝|k|.

Figure 1.5: Calculated band structure of graphene, from [27], with linear dispersion near
the K point highlighted.
Correspondingly, the charge carriers are characterized at massless Dirac fermions. This
results in the unique plasmon dispersion that has been studied in this thesis. We adapt the
formalism developed in ref [30] to model the optical response of monolayer graphene.
Plasmonic modes are identified by inserting the graphene between two dielectric layers at x
= 0, assuming the electric field is of the form:

Ez = Aeikz−K1x , E y = 0, E x = Beikz−K1x , for x> 0
Ez = Ce

ikz+K 2 x

, E y = 0, E x = De

ikz+K 2 x

(1.9a,b)

, for x< 0

and inserting these into Maxwell’s equations and matching the boundary conditions. We
use the surface conductance of graphene σ(ω,k) to define the boundary at x = 0. This gives
us the dispersion relation

εr1
ε ω
k 2 − r1 2

εr 2
ε ω
k2 − r2 2

σ (ω, k)i
ωε 0

which simplifies in the limit of k>>ω/c to

(1.10)

ε +ε
2iω
k ≈ ε 0 r1 r 2
2 σ (ω, k)

(1.11)

where εr1 and εr2 are the optical frequency permittivity of the materials above and below the
graphene sheet, k is the momentum vector of light, ω the frequency, c the speed of light,
and σ the 2D optical conductivity of the graphene.
By utilizing the methods described by Falkovsky in “the Optical Properties of Graphene”31,
32

, we can define the intra- and interband contributions to the optical conductivity of

graphene, which we sum in order to fully describe the material response. The intraband
contribution is expressed as:

σ intra (ω ) =

2ie 2T
ln[2 cosh(µ / 2T )]
π !(ω + iτ −1 )

(1.12)

which takes the form:

σ intra (ω ) =

ie 2 µ
π !(ω + iτ −1 )

(1.13)

for µ >> T. The second component, the interband contribution, is presented as a step
function wherein transitions below 2µ = 2EF are Pauli-blocked and above result in an
optical absorption characteristic of the linear band structure. This is explicitly written as:

σ inter (ω ) =

e2 ⎡
(ω + 2µ )2 ⎤
ln
⎢θ (ω − 2µ ) −
4! ⎣
2π (ω − 2µ )2 ⎦

(1.14)

where we introduce τ the characteristic scattering time of the carriers, and θ(ω-2µ) is a step
function defied by the chemical potential µ of the graphene. It is particularly of note that
the optical conductivity depends strongly on the graphene Fermi energy, indicating a
plasmon dispersion that can be tuned with this parameter. Because graphene is a single
atomic layer thick, we can use an external gate voltage to modulate its carrier concentration
and therefore its optical response. This provides us with new opportunities for realizing

11
actively tunable plasmonics, as the short screening length and high carrier concentration in
bulk plasmonic materials prevents the use of an electric field for modulating this response.
By inserting these optical conductivities into the analytic expression 1.11 above, or into
full-wave simulations, we can accurately map out the plasmon resonances of graphene as a
function of wavelength and of Fermi energy with excellent agreement to experiment.
1.2.2 Black Phosphorus
A newer addition to the 2D materials family, black phosphorus (BP) is the layered allotrope
of phosphorus, possessing a buckled lattice structure that is nominally stable under ambient
conditions.33 However, due to the relatively weak in-plane bonding character of the
material, it is highly sensitive to oxidation and degradation, requiring encapsulation for
device fabrication.
Unlike graphene, with its linear band structure, black phosphorus is a direct band gap
semiconductor. By varying the number of layers of BP, the change in quantum
confinement in the vertical direction widely tunes the band gap energy. In monolayer form,
BP has a band gap of approximately 2 eV, which steadily decreases to the bulk value of 0.3
eV as more layers are added. Unlike transition metal dichalcogenides (TMDCs), which
undergo a direct-to-indirect band gap transition from monolayer to bilayer, the band gap
remains direct at all thicknesses.

Figure 1.6: Lattice structure of black phosphorus (left). Calculated electronic band gap of
black phosphorus as a function of number of layers (right, from [34].)
Black phosphorus is a particularly promising material system for study, then, because it
spans the gap between graphene, a material of greatest relevance in the mid-to-far infrared,
and TMDCs, semiconducting van der Waals materials with band gaps in the visible. While
it does not have the very high electronic mobility of graphene, it has favorable transport
properties with typical mobilities observed in experiments of a few hundred cm2 V-1 s-1,
making it of interest for optoelectronic devices.
In addition to this, BP’s in-plane structural anisotropy makes it a unique materials system
for taking advantage of materials properties that vary with crystal direction. This impacts
its thermal, mechanical, electrical, and optical properties34. It can be thought of as a
naturally occurring quantum well, with the additional interesting feature of large in-plane
anisotropy, something not seen in any other materials. This suggests that electro-optic
effects typically seen in III-V quantum wells, such as the quantum-confined Stark effect35,
should be observed in BP, with different consequences along each crystallographic
direction. Because BP can be easily exfoliated from bulk crystals, and van der Waals
materials can be integrated into devices without lattice-matching constraints or the need for

13
ultra-high vacuum growth chambers, this may be a promising material for future electrooptic modulator devices.
1.3 The Scope of this Thesis
This thesis explores the intersection of the two topics identified above: van der Waals
materials and nanophotonics. By taking advantage of the unique properties of quantumconfined, ultrathin, layered materials, we introduce new functions into existing
nanophotonic designs as well as exploring the unique physics that emerge in the monolayer
limit. We use plasmonic nanostructures to focus infrared light into small volumes, enabling
strong light-matter interactions as the nanoscale. This not only allows use to incorporate
ultrathin materials for electrically tunable structures, but also introduces new types of
coupled quasiparticles not typically observed in bulk materials.
Chapter 2 of this thesis introduces highly confined, electrically tunable graphene plasmons
in nanoresonators. We observe record-breaking confinement factors in nanostructured
monolayer graphene, and utilize an external gate voltage to tune this across the midinfrared, also introducing tunable coupling between plasmons and phonon-polaritons of
another monolayer material, hexagonal boron nitride (h-BN). We also introduce an external
cavity structure for enhancing the light-matter interactions in a monolayer material. Chapter
3 presents work on utilizing graphene plasmons to actively modulate the amplitude and
polarization state of thermal radiation. Due to the reciprocity between absorptivity and
emissivity dictated by Kirchoff’s Law, we tune the emissivity of our graphene structures,
something that is typically thought of as a fixed materials property. Chapter 4 builds on the
ways in which graphene can be used to actively control infrared light by integrating it into a
different type of resonant geometry to modulate reflected phase and realize a
reconfigurable meta-device for beam steering. In this way, we complete the graphene ‘toolkit’ for control of infrared light.
Chapters 5 and 6 focus on the electro-optic effects in few layer black phosphorus (BP). In
Chapter 5, the different mechanisms for the tunable optical response of BP which result
from its narrow band gap and quantum well electronic structure are identified. From this,

14
we suggest the black phosphorus is a promising material for actively tunable infrared
nanophotonics. In Chapter 6, we build on this work, carefully separating the different
contributions to this tunability and their influence on the polarization-dependent optical
response of BP. We observe that this anisotropic tunability is present from the visible to
mid-infrared, something not seen in conventional electro-optic materials.
Finally, in Chapter 7 we discuss the outlook for the emerging field of van der Waals
nanophotonics. We comment on promising research directions for graphene-integrated
structures, including extensions of controlling thermal emission in the near- and far-field,
and the possibility of taking advantage of the fast response time of graphene plasmons to
detect chemical species as they are evolved. We also propose novel nanophotonic designs
that take advantage of the unique optical properties of few-layer black phosphorus. While
more fundamental studies of BP are still needed to design such structures, we suggest that
by taking advantage of the in-plane optical anisotropy, steering of propagating waves and
control of reflected polarization may be realized.
Detailed experimental methods for these works are described in the Appendix.

Ch. 2

kinc

Ch. 3
ksca
Or kemit

Ch.4

hBN

Ch. 5
Ch. 6
Vg

Ch. 7

Figure 1.7: A pictorial representation of this thesis. Chapter 2 presents tightly confined
graphene plasmons. Chapter 3 discusses control of the amplitude and polarization of
thermal emission. Chapter 4 introduces a gate-tunable graphene-gold metasurface for active
beam steering. Chapter 5 examines the electro-optic effects in few-layer black phosphorus,
and Chapter 6 extends this to the polarization-dependent tunable optical response from the
visible to mid-infrared. Chapter 7 proposes future experiments based on graphene and
black phosphorus, including the steering of thermal radiation.

16
Chapter 2

GRAPHENE PLASMONS FOR TUNABLE LIGHT-MATTER
INTERACTIONS
“Graphene is dead; long live graphene”
– Andre Geim (Nobel Laureate who discovered graphene)
“When one dares to try, rewards are not guaranteed, but at least it is an adventure”
– (Also) Andre Geim
Single-layer graphene has been shown to have intriguing prospects as a plasmonic material,
as modes having plasmon wavelengths ∼20 times smaller than free space (λp ∼ λ0/20) have
been observed in the 2−6 THz range, and active graphene plasmonic devices operating in
that regime have been explored. However there is great interest in understanding the
properties of graphene plasmons across the infrared spectrum, where applications in
thermal radiation and molecular sensing are very interesting. We use infrared microscopy
to observe the modes of tunable plasmonic graphene nanoresonator arrays as small as 15
nm. We map the wavevector-dependent dispersion relations for graphene plasmons at midinfrared energies from measurements of resonant frequency changes with nanoresonator
width. By tuning resonator width and charge density, we probe graphene plasmons with λp
≤ λ0/100 and plasmon resonances as high as 310 meV (2500 cm−1, 4 µm) for 15 nm
nanoresonators. Electromagnetic calculations suggest that the confined plasmonic modes
have a local density of optical states more than 106 larger than free space (a record at the
time) and thus could strongly increase light-matter interactions at infrared energies. We
take advantage of this enhancement of light-matter interactions to observe semi-classical
strong coupling between graphene and another monolayer material, hexagonal boron
nitride (h-BN), which supports a surface phonon polariton in the mid-infrared. We then
fabricate graphene resonators on an external cavity (a quarter-wavelength thick dielectric
resonator) to enhance its absorption up to 25%, an improvement of a factor of 10.

17
2.1 Highly Confined Tunable Mid-Infrared Plasmonics in Graphene
Nanoresonators
2.1.1 Introduction
Surface plasmon polaritons (SPPs) are optical modes consisting of a decaying evanescent
wave in a dielectric coupled to an oscillating wave of surface charge (i.e., a surface
plasmon) on the surface of a conductor.36 These modes have remarkable properties
including large wavelength reductions relative to free space, and optical dispersion
relations that can be engineered via metal/dielectric nanoarchitectural design. Such
properties have led to interest in using SPPs for on-chip optical signal routing, visible
frequency metamaterials, and as a means of increasing light-matter interactions.37, 38 While
much progress has been made in achieving these goals, the use of metals as plasmonic
materials has limited the capabilities of the devices. Noble metal films and nanostructures
exhibit high losses due to low carrier mobilities, surface roughness, grain micro-structure
and impurities,39 and the large electronic density of states in metals restricts the possibility
of dynamically tuning the plasmon energy via externally applied electrostatic fields. These
limitations have led to a search for alternative plasmonic materials, including transparent
conducting oxides, transition metal nitrides, superconductors, and graphene.40, 41
Single layer graphene has interesting prospects as a plasmonic material, as discussed in
Chapter 1. It has been shown theoretically and experimentally that SPPs excited in finite
thickness metal films embedded in dielectrics or metal-clad dielectric slots display smaller
mode volumes as the middle layer becomes thinner.42-48 A single atomic layer of material,
such as graphene, represents the ultimate limit of this trend, and theoretical predictions
have shown that the mode volumes of SPPs in graphene can be 106 times smaller than
those in free space.49-51 Furthermore, the optical properties of graphene can be dynamically
tuned by chemical or electrostatic changes to the charge density of the graphene sheet.51, 52
This allows for the creation of SPP-based devices that can be eﬀectively turned on and oﬀ
or tuned to be active at diﬀerent wavelengths. Such devices have recently been
demonstrated in the THz regime on graphene samples patterned at micrometer length
scales, demonstrating plasmonic wavelengths ∼20 times smaller than free space (λp ∼

18
. In the infrared regime some

53-55

λ0/20) and 0.3 decades of tunability in the 2−6 THz range

progress has also been made in imagining plasmons using 10 µm wavelength scattering
NSOM techniques, revealing graphene plasmons 50−60 times smaller than the free space
wavelength56, 57, and very recently graphene nanostructures with ion gel top gates on
indium tin oxide substrates were investigated in the mid- infrared regime.58 However, there
is still great interest in understanding the properties of graphene plasmons across the
infrared spectrum. Some theoretical work has predicted that graphene plasmons in the
infrared should display long lifetimes and high mode confinement,50 while another work
has predicted that graphene is too lossy to exhibit strong plasmonic properties in the midinfrared, especially at energies above the 200 meV optical phonon energy of graphene.41
In this work we use infrared microscopy to measure the plasmon resonances of graphene
nanoresonator arrays patterned down to 15 nm length scales on a back-gated graphene
device. By probing how the resonant frequency changes with nanoresonator width, we are
able to map the wavevector-dependent dispersion relations of graphene plasmons in the
mid-infrared regime. We further show how the graphene plasmon dispersion relation
changes as the charge density is continuously varied, and we find that the mode volume,
intensity, and frequency of plasmon modes depend strongly on the graphene charge
density. By tuning these parameters (nanoresonator width and charge density) we create
and probe plasmons in graphene with λp ≤ λ0/100, and resonant energies as high as 310
meV (2500 cm−1, 4 µm) for 15 nm nanoresonators. By comparing our results to finite
element electromagnetic simulations, we find that these confined plasmonic modes have
mode densities more than 106 larger than free space and thus could serve and an eﬀective
means for increased light−matter interactions. Finally, we observe additional and
unexpected resonances in the graphene nano- resonator spectrum around 110 meV (900
cm−1, 11.1 µm). These features can be eﬀectively modeled as surface plasmon phonon
polaritons (SPPPs),59, 60 new fundamental excitations that arise due to strong coupling
between the graphene plasmons and the optical phonons of the SiO2 substrate.

2.1.2 Experimental Measurement of Tunable Infrared Graphene Plasmons

19
A schematic of our experimental setup is shown in Figure 1a. Our measurements were
performed on graphene grown on 25 µm thick copper foil using established chemical vapor
deposition (CVD) growth techniques.61, 62 After being transferred to SiO2/Si wafers,
nanoresonator arrays were patterned in the graphene using 100 keV electron beam
lithography in PMMA followed by an oxygen plasma etch. Fabrication techniques are
described in depth in Appendix A. Using this process we were able to fabricate graphene
nanoresonators over 80 × 80 µm2 areas with widths varying from 80 nm to 15 nm. These
large area samples are required for measurements performed in a Fourier Transform
Infrared (FTIR) microscope, and are made possible by the use of CVD graphene sheets.
The aspect ratio of the nanoresonators was 5−8:1 and the period was 2−3 × (width). Figure
2.1b shows scanning electron microscope (SEM) and atomic force microscope (AFM)
images of the graphene nanoresonators after fabrication. A typical gate- dependent
resistance curve for one of our devices is shown in Figure 2.1c. The peak in the resistance
corresponds to the charge neutral point (CNP) of the graphene, when the Fermi level is
aligned with the Dirac point and the carrier density is minimized.63 After the CNP for each
device was measured, a capacitor model was used to determine the Fermi level position for
each applied gate voltage.

Figure 2.1: Schematic of experimental device. (a) SEM image of a 80 × 80 um2 graphene
nanoresonator array etched in a continuous sheet of CVD graphene. The graphene sheet
was grounded through Au(100 nm)/Cr(3 nm) electrodes that also served as source−drain
contacts, allowing for in situ measurements of the graphene sheet conductivity. A gate bias
was applied through the 285 nm SiO2 layer between the graphene sheet and the doped Si
wafer (500 um thick). FTIR transmission measurements were taken over a 50 µm diameter
spot. (b) SEM and AFM images of 40 and 15 nm graphene nanoresonator arrays. A
nanoresonator width uncertainty of ±2 nm was inferred from the AFM measurements. (c) A
resistance vs gate voltage curve of the graphene sheet showing a peak in the resistance at
the charge neutral point (CNP), when the Fermi level (EF) is aligned with the Dirac point.

Transmission measurements were done in an FTIR microscope using a 50 µm diameter
spot size and with light polarized perpendicular to the graphene nanoresonators. In order to
probe carrier-dependent optical properties of the graphene nanoresonators all spectra were
normalized to spectra taken at the charge neutral point, isolating the plasmonic response of
the graphene. Figure 2.2a shows normalized spectra taken from nanoresonator arrays with
widths varying from 80 to 15 nm while the Fermi level is held at −0.37 eV, corresponding
to a carrier density of 8.8 × 1012 holes per cm2. These spectra contain two diﬀerent types of
features. The first is a surface plasmon phonon polaritons, labeled SPPP, which is a sharp

21
resonance that appears near 0.12eV for the 80 nm and 50 nm nanoresonators but is not
visible for nanoresonators with widths <40 nm. The second feature is the graphene
plasmon, labeled GP, which is a broader peak that appears for all nanoresonator widths. As
the width of the nanoresonators is decreased, the energy and width of the GP peak increase,
while the intensity of this feature decreases. For example, for 80 nm nanoresonators this
feature appears as a narrow peak at 0.16 eV, while for 15 nm nanoresonators it appears as a
very weak and broad peak at 0.29 eV.
To better understand the origin of these two features, we monitored how they changed as
we varied the carrier density of the graphene sheet. Figure 2.2b shows a series of spectra
taken in this manner from 50 nm nanoresonator arrays. For low carrier densities, when EF
is only 0.22 eV below the Dirac point, both SPPP and GP peaks appear very weakly in the
nanoresonator spectrum, at 0.114 and 0.166 eV, respectively. As more carriers are added to
the graphene sheet, both SPPP and GP peaks gain intensity and shift to higher frequencies,
with the SPPP and GP reaching 0.126 and 0.203 eV, respectively, when EF is increased to
0.52 eV below the Dirac point. In Figure 2.3a we plot the SPPP and GP peak energies for
all nanoresonator widths as a function of EF. Here we observe that the energy of the GP
feature shows a stronger dependence on carrier density for smaller nanoresonator widths.

Figure 2.2: Gate-induced modulation of transmission through graphene nanoresonator
arrays normalized to transmission spectra obtained at the CNP. (a) Width dependence of
optical transmission through graphene nanoresonator arrays with EF = −0.37 eV. The width
of the nanoresonators is varied from 15 to 80 nm. (b) Fermi level dependence of optical
transmission through 50 nm wide graphene nanoresonators, with EF varying from −0.22 to
−0.52 eV. The dotted vertical line in both (a) and (b) indicates the zone-center energy of the
in-plane optical phonons of graphene.
2.1.3 Theoretical Description of Graphene Plasmons
These two experimentally observed resonances can be understood using a simple
Fabry−Perot model of plasmons bound in graphene nanoresonators patterned on SiO2.
When incident light is coupled to a graphene plasmon mode of the wavevector kp, the
plasmon undergoes multiple reflections between the two edges of the nanoresonator.
Constructive interference occurs when the reflected plasmons are in phase, which occurs
when 2 Re(kp)W + 2ϕ = 2mπ, where W is the width of the nanoresonator and ϕ is the phase
shift of the plasmons upon reflection. We estimated ϕ by performing electromagnetic
simulations using a finite element method and for the first-order resonance (m = 1), ϕ is
calculated to be 0.30π to 0.35π depending on the width to period ratio. This implies that the
plasmon wavelength λp = 2π/Re(kp) is almost three times that of the nanoresonator width.

23
Interestingly, we note that ϕ is scale-invariant, as long as the system is in the electrostatic
limit

(kp ≫ ωp/c).64 Recognizing that the wavevector kp can be approximated as

iεωp/[2πσ(ωp)] in the electrostatic limit15, the condition for the first-order plasmon
resonance is reduced to:

ω pW ⎧⎪ ε (ω p ) ⎫⎪
Im ⎨−
⎬ = π −φ
2π
⎩⎪ σ (ω p ) ⎭⎪

(2.1)

Here, ε( ω) = (1 + εSiO2(ω))/2 is the average dielectric function of the air−SiO2 interface.
In our calculations, we used an analytic expression for the graphene conductivity σ(ω)
evaluated within the local random phase approximation,65 and the complex dielectric
function of SiO2, εSiO2(ω), was taken from Palik66. Upon solving eq 2.1 we find that for
some graphene nanoresonator widths multiple first-order plasmon modes can be
supported. This effect is due to the dispersive permittivity of SiO2, which varies greatly
near its transverse optical phonon at 0.13 eV. This results in two separate bands in the
graphene/SiO2 plasmon dispersion relation, both of which can create plasmon resonances
in the patterned graphene. In Figure 2.3a we plot as solid and dashed lines the resonant
energies of these two modes for different nanoresonator widths and EF values, showing
that one of the modes (solid line) has a width and carrier density dependence that
correlates well with the GP feature, while the other mode (dashed line) behaves like the
SPPP feature. We note that, in principle, there can be a third solution to eq 2.1 that would
occur almost right at the SiO2 phonon energy; however, this mode is heavily damped by
the substrate lattice oscillations.

Figure 2.3: Dispersion of GP and SPPP plasmonic resonances in graphene nanoresonator
arrays. (a) Fermi level dependence of the measured energy of “GP” (open colored symbols)
and “SPPP” (filled colored symbols) features observed in nanoresonators with varying
widths. Solid and dashed colored lines indicate the two solutions to eq. 2.1 using the same
experimental widths and continuously varying EF. (b) Theoretical dispersion of bare
graphene/SiO2 plasmons (solid) and SPPPs (dashed), for diﬀerent EF values. Open and filled
symbols plot the measured energy of “GP” and “SPPP” features (respectively) from graphene
nanoresonators at equivalent EF values. Wavevector values for experimental points are
obtained from AFM measurements of the nanoresonator widths followed by a finite
elements simulation to calculated the wavelength of the first order supported plasmon
modes. The dotted blue lines indicate the theoretical plasmon dispersion of graphene on a
generic, nondispersive dielectric with ε∞ = 2.1, which is the high frequency permittivity of
SiO2. Dashed and dotted black lines in (a) and (b) indicate the energy of the TO optical phonon
of SiO2 and the zone-center energy of the in-plane optical phonons of graphene,
respectively. (c) Mode profile of the GP mode of a 50 nm graphene nanoresonator with
EF = −0.37 eV, obtained from a finite element electromagnetic simulation.
From these calculations, we can now explain the physical origins of the GP and SPPP
features observed in our data. The graphene plasmon mode corresponds to a confined
plasmon excitation of a monolayer graphene sheet in a nearly constant dielectric
environment. As described in previous work,50, 51, 55, 56 when the frequency (ωp) of such
modes are suﬃciently lower than the interband transition energy (2|EF|), ωp should depend
on both carrier density and nanoresonator width through the relationship ωp ∝ |EF|1/2W−1/2.
This behavior is demonstrated by the graphene plasmon mode in Figure 2.3a, although it

25
deviates slightly at lower energies. At energies suﬃciently far from the SiO2 phonon
energy, the dispersion relation of this mode (Figure 2.3b, solid lines) is seen to
asymptotically approach the dispersion of graphene plasmons on a generic and
nondispersive dielectric substrate.
The SPPP modes can be understood by considering that lattice oscillations in the SiO2
lead to a sharp increase in the SiO2 dielectric constant below its phonon energy. Because
the graphene plasmon wavelength depends on the surrounding dielectric environment (see
eq 2.1), the high dielectric constant of the SiO2 within the small energy range below the
phonon can compress graphene plasmons and allow for the graphene nanoresonators to
support additional low energy plasmon oscillations. Thus this mode represents a
composite excitation that consists of a SPP on the graphene coupled to a phonon
excitation in the SiO2, hence the term surface plasmon phonon polariton (SPPP).
Signatures of such plasmon−phonon coupling have previously been observed in NSOM
measurements of graphene on SiO2 surfaces67. In Figure 2.3b we plot the dispersion
relation for this SPPP (dashed lines) for diﬀerent Fermi energies, revealing that the SPPP
mode displays less dispersion than the graphene plasmon mode. Another notable feature
of the SPPP that can be observed in the dispersion is that modes with high k-vectors are
not supported. This can be understood by considering that, while the SiO2 phonon changes
the dielectric function of the substrate, it also introduces loss. Thus as the energy of the
SPPP moves closer to the SiO2 phonon energy, the system becomes too lossy due to
substrate absorption, and the modes can no longer propagate.
The most remarkable feature of both the graphene plasmon and the SPPP resonances is
how small the supported plasmon wavelengths are compared to the free space wavelength
λ0. For example, when EF = -0.22 eV, we observe for the graphene plasmon feature that
λ0/λp = 49 for the 50 nm wide nanoresonators, and λ0/λp becomes as large as 106 in the 20
nm nanoresonators. This factor is seen to decrease as the carrier density of the graphene
sheet is increased and the graphene nanoresonators support higher energy resonances, such
that for EF = -0.41 eV, we measure λ0/λp of 43 and 81 for 50 and 20 nm resonators,

26
respectively. These results are largely consistent with the theoretical predictions of infrared
graphene plasmons.
2.2 Hybrid Surface-Plasmon-Phonon Polariton Modes in Graphene/Monolayer
h‑BN Heterostructures
2.2.1 Introduction
The results presented in Section 2.1 are consistent with the expectation that graphene
plasmons should couple more strongly to their local environment than normal metal
plasmons. In addition to our own work, other experiments performed on graphene devices
on SiO268, 69 and SiC70, 71 substrates have shown that the graphene dispersion relation is
indeed modified due to the substrate phonons, with extra modes appearing due to plasmonphonon coupling which have been described as surface-plasmon-phonon-polaritons, or
SPPPs.68 In those experiments, however, the substrates used were much thicker than the
plasmonic wavelengths, and thus did not test whether the graphene plasmons were
coupling to a large volume of phonons spread throughout the dielectric environment, or
only to the phonons in the immediate vicinity of the graphene sheet. Recently, experiments
have been performed to investigate the coupling between graphene plasmons and thin
layers of PMMA, showing that the PMMA phonon spectral signature can be enhanced
through graphene plasmon coupling for PMMA layers as thin as 8 nm.72 Here we fabricate
graphene nanoresonator devices on a monolayer h-BN sheet in order to test the ability of
graphene plasmons to couple to optical excitations that occupy an atomically thin slice of
volume near the graphene. We find that the small mode volume of the graphene plasmons
combined with the high oscillator strength of the h-BN phonons allows the two modes to
strongly couple, forming two clearly separated hybridized SPPP modes that display an anticrossing behavior.

Figure 2.4: (a) Schematic of device measured and modeled in this paper. Graphene
nanoresonators are fabricated on a monolayer h-BN sheet on a SiO2 (285 nm)/Si wafer.
Gold contact pads are used to contact the graphene sheet and the Si wafer is used to apply
an in situ backgate voltage (VG). Zoom-in shows cartoon of graphene plasmon coupling to
h-BN optical phonon. (b) Optical image of unpatterned area of device where both the
graphene and h-BN monolayers have been mechanically removed. (c) Scanning electron
microscope image of the 80 nm graphene nanoresonators (light regions).
2.2.2 Experimental Measurement of Coupled 2D Phonon-Plasmon Polaritons
A schematic of our experimental device is shown in Figure 2.4. A monolayer h-BN sheet
grown using chemical vapor deposition (CVD) on copper foil (Purchased from Graphene
Supermarket #CVD-2X1-BN) is transferred to a SiO2 (285 nm)/Si wafer and a CVD-grown
graphene sheet is subsequently transferred onto the h-BN. Nanoresonators are patterned
into the graphene surface using 100 keV electron beam lithography in PMMA, followed by
an oxygen plasma etch, as previously (see also Appendix A). Infrared spectroscopy
analysis reveals that the h-BN layer is also degraded in the lithographed areas. The
resonators are patterned into electronically continuous bar array patterns with widths
ranging from 30 nm to 300 nm, and a 1:2 width-to-pitch ratio, as shown if Fig. 2.4c. The
dimensions of patterned nanoresonators are later precisely measured by using atomic force
microscope (AFM). The Si layer was contacted and used as a back-gate electrode, and Cr(2

28
nm)/Au(100 nm) contacts were evaporated onto the nearby graphene surface such that the
conductivity of the graphene could be monitored in situ. The charge neutral (zero carrier
density) point was determined by the applied gate voltage that gave maximum resistance of
the graphene sheet, and the carrier density at different gate voltages was determined by
monitoring the cutoff energy of interband transitions in the graphene, which occurs at
2×EF.73, 74 As observed in previous work,68 the charge neutral point is offset from zero gate
voltage due to impurities introduced during the sample fabrication that hole dope the
sample as well as charges donated by the surface of the SiO2 substrate. The device was then
placed in a Fourier transform infrared spectroscopy (FTIR) microscope and measured in
transmission mode with light polarized perpendicular to the nanoresonators. All graphene
nanoresonator spectra were normalized relative to spectra taken with zero carrier density as
before. For reference, a transmission spectrum was taken on a bare h-BN area of the
sample, as shown at the bottom of Figure 2.5. As can be seen in the figure, the h-BN
spectrum is flat except for a narrow (19 cm-1) resonance near 1370 cm-1, which has been
assigned in previous studies as an in-plane optical phonon of the h-BN.75

Figure 2.5: (Left axis) Normalized transmission spectra of graphene nanoresonators with
width varying from 30 to 300 nm, as well as transmission through the unpatterned
graphene/h-BN sheet. Spectra are measured at carrier densities of 1.0 x 1013 cm−2 and
normalized relative to zero carrier density. For 80 nm ribbons, the four different observable
optical modes are labeled with the symbols used to indicate experimental data points in
Figure 3. (Right axis, bottom spectrum) Infrared transmission of the bare monolayer h-BN
on SiO2 normalized relative to transmission through the SiO2 (285 nm)/Si wafer. The
narrow (∼19 cm−1) peak that occurs at 1370 cm−1 has previously been assigned to an optical
phonon in h-BN. The dotted vertical line indicates this peak position as a reference for the
other spectra.
Figure 2.5 illustrates the dependence of transmission spectra on graphene nanoresonator
width at 1.0 × 1013 cm-2 carrier density. As can be seen in this figure multiple features
appear in the spectra, namely, two distinct set of optical modes can be observed appear
above and below 1200 cm-1. The two modes below 1200 cm-1 have previously been
observed in graphene plasmonic devices on SiO2, and have been assigned to SPPP modes
associated with two SiO2 phonons.68, 69 The two modes above 1200 cm-1, however,
represent new optical features not observed in graphene/SiO2 or graphene/SiC structures,
which contained only a single dispersive mode above 1200 cm-1. A close analysis of these

30
two features reveals an anti-crossing behavior near the 1370 cm optical phonon energy of
-1

the h-BN, with the lower (upper) mode approaching that energy for small (large) ribbon
widths. Furthermore, there is a relative shift in intensity between the upper and lower
modes as the ribbon width varies, with the upper mode being more intense for small ribbon
widths, and vice versa. Significantly, the intensity between the two features drops nearly to
zero for 80 nm resonator widths, when the two features have equivalent intensities.

2.2.3 Modeling of Coupled Plasmon-Phonon Dispersion
In order to better understand the characteristics of each mode, we calculate the transmission
spectrum of graphene nanoresonators for various widths using a finite element method
within a local random phase approximation.76 Here, the in-plane dielectric function of
monolayer h-BN is described using Lorentz oscillator model with parameters fitted from
transmission measurement of the bare h-BN on SiO275, and its thickness is modeled to be
0.34 nm, the interlayer spacing of bulk h-BN. The scale-invariant plasmon phase shift upon
reflection at the nanoresonator edges is calculated to be φ ≈ 0.35π.68 This implies that the
plasmon wavevector kp = (π – φ)/W for the first-order plasmon resonance, with the width,
W, extracted from AFM measurements. The resulting carrier-induced change in
transmission is plotted in Figure 2.6 for varying wavevector and energy at 1.0 × 1013 cm-2
carrier density. The dispersion of the graphene/h-BN/SiO2 nanoresonator optical modes
can be observed in this plot as the maxima in the transmission modulation, −∆T/TCNP.
These features show a strong correspondence with the experimentally measured features,
with modes appearing above and below the h-BN optical phonon energy that display a
clear anti-crossing behavior.

Figure 2.6: Calculated change in transmission for graphene/monolayer h-BN/SiO2
nanoresonators of varying width at a carrier density of 1.0 x 1013 cm−2, normalized relative
to zero carrier density. The wavevector is determined by considering the ribbon width, W,
as well as the phase of the plasmon scattering off the graphene ribbon edge, as described in
the text. Experimental data is plotted as symbols indicating optical modes assigned in
Figure 2.5. The error bars represent uncertainty in the resonator width that is obtained from
AFM measurements. For small k-vectors (large resonators), this uncertainty is smaller than
the symbol size. The dashed line indicates the theoretical dispersion for bare graphene
plasmons, while the dash-dot line indicates the dispersion for graphene/SiO2 The three
horizontal dotted lines indicate the optical phonon energies of h-BN and SiO2.
The behavior displayed experimentally and theoretically in Figures 2.5 and 2.6 is indicative
of a hybridization between the graphene plasmons modes and the h-BN optical phonon
modes that creates two new SPPP modes with dispersion relations that are distinctly
different from the original graphene plasmon dispersion (dashed line, Fig. 2.6) as well as
the graphene/SiO2 dispersion (dashed-dot line, Fig. 2.6).

This hybridization can be

understood through an electromagnetic coupled oscillator model where the local
polarization field created by lattice displacement in the h-BN exerts a force on the free

32
carriers in the overlying graphene resonators via near field interaction, and, likewise, the
polarization due to displaced carriers in the graphene exerts a force on the h-BN lattice.
When this coupling becomes sufficiently strong, the lifetimes and the energies of the two
constitutive optical modes can be significantly shifted and the resulting optical features are
hybrid modes, or SPPPs. These new optical modes contain both plasmon-like and phononlike character, with the relative contribution of each constitutive mode dependent on the
graphene ribbon width and carrier density. Recognizing that each spectrum displayed in
Fig. 2.5 shows the relative difference in transmission while varying the carrier density in
graphene, the relative intensity of two resonances roughly indicates how much the
graphene plasmon contributes to each hybrid SPPP mode. Therefore, we know that the
upper(lower) SPPP mode is more plasmon-like for small(large) ribbon widths from the
relative shift in peak intensity, and that for 80 nm graphene/h-BN resonators, the two
modes are both equally plasmon-like and phonon-like. This behavior is consistent with the
extracted dispersion properties of each mode shown in Fig. 2.6.
In combination with the hybridization behavior described above, we observe a pronounced
minimum in absorption near the h-BN phonon energy for 60, 80, and 100 nm resonators,
for which the bare graphene plasmon mode would typically overlap the h-BN phonon
energy. We interpret this phenomenon as a classical, phonon-based analogue to
electromagnetically induced transparency (EIT) experiments performed on atomic gases.
In this description, it is observed that when the graphene plasmon mode is brought into
resonance with the h-BN phonon, the polarizations of the two modes cancel each other out,
creating a transparency window where no absorption occurs in the plasmonic modes. The
clearly separated resonance peaks also indicate that the coupling between graphene
plasmons and the h-BN phonons enters a classical “strong-coupling” regime, where the
associated electromagnetic interaction can fully transfer energy between the plasmon and
phonon states before decaying via damping. This regime is characterized by a large
splitting between the two hybridized modes, such that the minimum energy separation is
more than the sum of the two linewidths, and the spectral intensity between the two modes
approaches zero.77 For the experimental data shown here, the minimum splitting we

33
observe between the two graphene/h-BN SPPPs is 100 cm (for 80 nm resonators) which is
-1

more than the sum of the two associated peak widths of 25 and 55 cm-1, indicating that the
system is in a strong coupling regime.77 This phenomenon has been explored in
conventional metal plasmonics experiments using molecular vibrations or dyes coupled to
metallic plasmons.78-83 In those experiments, however, a thick (>20 nm) layer of optically
active material was required for strong coupling to be achieved. Here, we observe that the
high confinement of graphene plasmons allows them to strongly couple to optical phonons
in an atomically thin layer.
2.3 Tunable Enhanced Absorption in a Graphene Salisbury Screen
2.3.1 Introduction
While the emergence of the SPPP modes in graphene nanoresonators demonstrates the
strong interaction of the material with its surroundings, the absolute magnitude of these
effects is limited by the amount of light absorbed by the graphene sheet, which is typically
2.3% at infrared and optical frequencies84, 85 – a small value that reflects the single atom
thickness of graphene. To increase the total graphene-light interaction, a number of novel
light scattering and absorption geometries have recently been developed. These include
coupling graphene to resonant metal structures86-90 or optical cavities where the
electromagnetic fields are enhanced91-93, or draping graphene over optical waveguides to
effectively increase the overall optical path length along the graphene94, 95. While those
methods rely on enhancing interband absorption processes, we are interested in enhancing
the absorption in graphene plasmon modes to take advantage of their unique properties and
high confinement factors. These modes have been shown to display large absorption when
embedded in liquid salts or by sandwiching dopants between several graphene layers96-98.
However without blocking the transmission of light, it is not possible to achieve unity
absorption in these previously demonstrated geometries96-98. Moreover, in order to access
nonlinear or high frequency modulation as well as the high confinement factors
characteristic of graphene plasmons, device geometries with open access to the graphene
surface that operate with field effect gating at low doping are desirable.

34
Plasmonically active metallic and semiconductor structures can achieve near-perfect
absorption of radiation at specified frequencies using a resonant interference absorption
method.99-103 The electromagnetic design of these structures derives in part from the
original Salisbury screen design104, but with the original resistive sheet replaced by an array
of resonant metal structures used to achieve a low surface impedance at optical frequencies.
The high optical interaction strength of these structures has made them useful in such
applications as chemical sensing,101, 105 and it was recently proposed that similar devices
could be possible using graphene to achieve near perfect absorption from THz to MidIR.106, 107 Such a device would offer an efficient manner of coupling micron-scale freespace light into nanoscale plasmonic modes, and would further allow for electronic control
of that in-coupling process. In this work, we construct a device based on that principle,
using tunable graphene nanoresonators placed a fixed distance away from a metallic
reflector to drive a dramatic increase in optical absorption into the graphene.
2.3.2 Experimental Demonstration of Enhanced Absorption
A schematic of our device is shown in Figure 2.7a. A graphene sheet grown using chemical
vapor deposition on copper foil is transferred to a 1 µm thick low stress silicon nitride
(SiNx) membrane with 200nm of Au deposited on the opposite side that is used as both a
reflector and a backgate electrode. Nanoresonators with widths ranging from 20-60 nm are
then patterned over 70 × 70 µm2 areas into the graphene using 100 keV electron beam
lithography. An atomic force microscope (AFM) image of the resulting graphene
nanoresonators is shown in the inset of Fig. 2.7b. The device was placed under a Fourier
transform infrared (FTIR) microscope operating in reflection mode, with the incoming light
polarized perpendicular to the resonators. The carrier density of the graphene sheet was
varied in situ by applying a voltage across the SiNx between the gold and the graphene, and
the resulting changes in resistance were continuously monitored using source and drain
electrodes connected to the graphene sheet (Fig 2.7b). The carrier density of the graphene
nanoresonators was determined from experimentally measured resonant peak frequencies.

200nm

Figure 2.7: (a) Schematic of experimental device. 70 × 70 µm2 graphene nanoresonator
array is patterned on 1 µm thick silicon nitride (SiNx) membrane via electron beam
lithography. On the opposite side, 200 nm of gold layer is deposited that serves as both a
mirror and a backgate electrode. A gate bias was applied across the SiNx layer in order to
modulate the carrier concentration in graphene. The reflection spectrum was taken using a
Fourier Spectrum Infrared (FTIR) Spectrometer attached to an infrared microscope with a
15X objective. The incident light was polarized perpendicular to the resonators. The inset
schematically illustrates the device with the optical waves at the resonance condition. (b)
DC resistance of graphene sheet as a function of the gate voltage. The inset is an atomic
force microscope image of 40 nm nanoresonators.
The total absorption in the device – which includes absorption in the SiNx and the graphene
resonators – is determined from the difference in the reflected light from the nanoresonator
arrays and an adjacent gold mirror. For undoped and highly doped 40 nm nanoresonators,
the total absorption is shown in Figure 2.8a, revealing large absorption at frequencies
below 1200 cm-1, as well as an absorption peak that varies strongly with doping at 1400
cm-1 and a peak near 3500 cm-1 that varies weakly with doping. In order to distill
absorption features in the graphene from the environment (i.e., SiNx and Au back reflector),
we plot the difference in absorption between the undoped and doped nanoresonators, as
shown in Figure 2.8b for 40 nm nanoresonators. This normalization removes the low
frequency feature below 1200 cm- 1, which is due to the broad optical phonon absorption in
the SiNx and is independent of graphene doping. The absorption feature at 1400 cm-1,

36
however, shows a dramatic dependence on the graphene sheet carrier density, with
absorption into the graphene nanoresonators varying from near 0% to 24.5% as the carrier
density is raised to 1.42 × 1013 cm-2. Because the absorption increases with carrier density,
we associate it with resonant absorption in the confined plasmons of the nanoresonators.30,
97, 108, 109

a 40

carrier density
( 1013 cm-2)
0. (CNP)
1.42

(%)

1000
25

2000

3000

4000

carrier density
( 1013 cm-2)

0.32
0.66
0.95
1.42
1.42 (bare)

15
10
10

1000
25

2000

4000

20nm
30nm
40nm
50nm
60nm

(%)

3000

1000

2000

3000

4000

Frequency (cm-1)

Figure 2.8: (a) The total absorption in the device for undoped (red dashed) and highly hole
doped (blue solid) 40 nm nanoresonators. Absorption peaks at 1400 cm-1 and a peak at
3500 cm-1 are strongly modulated by varying the doping level, indicating these features are
originated from graphene. On the other hand, absorption below 1200 cm-1 is solely due to
optical phonon loss in SiNx layer. (b) The change in absorption with respect to the
absorption at the charge neutral point (CNP) in 40 nm wide graphene nanoresonators at
various doping levels. The solid black curve represents the absorption difference spectrum

37
of bare (unpatterned) graphene. (c) Width dependence of the absorption difference with the
carrier concentration of 1.42 × 1013 cm-2. The width of the resonators varies from 20 to 60
nm. The dashed curve shows the theoretical intensity of the surface parallel electric field at
SiNx surface when graphene is absent. Numerical aperture of the 15X objective (0.58) is
considered.
In Figure 2.8b we also see that absorption at 3500 cm-1 exhibits an opposite trend relative
to the lower energy peak, with graphene-related absorption decreasing with higher carrier
density. This higher energy feature is due to interband graphene absorption where
electronic transitions are Pauli blocked by state filling at higher carrier densities.74 For
spectra taken from the bare, gate-tunable graphene surface, this effect leads to ~8%
absorption, roughly twice the intensity observed from patterned areas. Finally, in Figure
2.8c, we investigated the graphene nanoresonator absorption as the resonator width is
varied from 20 to 60 nm at fixed carrier density. This figure shows that the lower energy,
plasmonic absorption peak has a strong frequency and intensity dependence on resonator
width, with the maximum absorption occurring in the 40 nm ribbons.
The observed resonance frequency varies from 1150 - 1800 cm-1, monotonically increasing
with larger carrier densities and smaller resonator widths. The plasmon energy
asymptotically approaches ~1050 cm-1 due to a polar phonon in the SiNx that strongly
reduces the dielectric function of the substrate at that energy.110 This coupling between the
substrate polar phonon and the graphene plasmon has also been previously observed in
back-gated SiO2 devices and was commented on in Chapter 2.1.109, 111
2.4 Conclusions and Outlook
In summary, this chapter has presented results on the gate-tunable plasmonic response of
monolayer graphene. We have observed that by utilizing an applied gate voltage, it is
possible to tune the plasmonic absorption across the mid-infrared. In addition, this tuning
allows us to actively control the coupling between the graphene and its environment,
including the presence of composite surface plasmon-phonon polaritons. These modes are
observed in bulk substrates (e.g. SiO2) as well as in the monolayer limit (e.g. h-BN).
Finally, we have demonstrated that by matching the plasmon resonance of the graphene to

38
an external cavity resonance – a quarter wavelength thick Salisbury Screen design – we can
enhance the absorption in the graphene to 24.5%. These results provide insights into tightly
confined quasiparticles in the monolayer limit, as well as suggesting that nanophotonic
devices based on graphene plasmons could be useful as tunable ‘perfect absorber’ devices,
with implications for thermal emission that will be discussed in Chapter 3. Finally, we
suggest that the highly confined nature and resulting ultra-small mode volume of graphene
plasmons may enable strong Purcell enhancement of emitters in the mid-infrared that could
be actively controlled.

39
Chapter 3

GRAPHENE-BASED ACTIVE CONTROL OF THERMAL
RADIATION
“In this house we obey the laws of thermodynamics!”
– Homer Simpson
Chapter 3.1
1. Victor W. Brar, Michelle C. Sherrott, Min Seok Jang, Laura Kim, Mansoo Choi,
Luke A. Sweatlock, Harry A. Atwater, “Electronic modulation of infrared radiation in
graphene plasmonic resonators”, Nature Communications, 6, 7032 (2015)
DOI: 10.1038/ncomms8032
All matter at finite temperatures emits electromagnetic radiation due to the thermally
induced motion of particles and quasiparticles. Dynamic control of this radiation could
enable the design of novel infrared sources; however, the spectral characteristics of the
radiated power are dictated by the electromagnetic energy density and emissivity, which
are ordinarily fixed properties of the material and temperature. Here we experimentally
demonstrate tunable electronic control of blackbody emission from graphene plasmonic
resonators. It is shown that the graphene resonators produce antenna-coupled blackbody
radiation, which manifests as narrow spectral emission peaks in the mid-infrared. By
continuously varying the nanoresonator carrier density, the frequency and intensity of these
spectral features can be modulated via an electrostatic gate. We extend this work to show
that we can control not just the spectral distribution of thermal radiation, but also its
polarization state. This opens the door for future devices that may control blackbody
radiation at timescales beyond the limits of conventional thermo-optic modulation. Multipixel devices composed of the deep-sub-wavelength graphene resonators may enable
‘designer’ thermal radiation profiles that can be switched at MHz speeds or faster89.

40
3.1 Electronic Modulation of Thermal Radiation in a Graphene Salisbury Screen
3.1.1 Introduction
Thermal radiation is commonly viewed to be broadband, incoherent and isotropic, with a
spectral profile and intensity that are dependent on the emissivity of a material, and that
vary only with changes in temperature. Recent experiments on nanoengineered structures,
however, have begun to challenge these notions, showing that blackbody emission can be
coherent and unidirectional, with narrow spectral features. These structures have included
patterned gratings on metal or silicon carbide surfaces that can control the directionality
and coherence of thermal radiation,112, 113 as well as photonic crystals,114 size-tunable Mie
resonances,115 and frequency selective meta-surfaces116 which can tune the spectral profile.
Progress has also been made in demonstrating dynamic control of thermal radiation
through in situ modification of material emissivity. This has been achieved with devices
that

incorporate

phase

change

materials

which

display

temperature-dependent

emissivities,117 as well as electronically controlled devices, where injected charges are used
to overdampen polariton modes in quantum wells.118 These results suggest that careful
control of both the photonic and electronic structure of metasurfaces could allow for
thermal emitters that have continuously variable frequency and directionality control, and
that can operate at speeds much faster typical thermal cycling times, potentially
approaching speeds of modern telecommunication devices.
Graphene provides a unique platform for studying and controlling thermal radiation at
infrared wavelengths. The optical absorptivity/emissivity of graphene depends on two
carrier density dependent terms: an intraband contribution that is characterized by a large
Drude-like peak in the DC to far-IR range, and an interband contribution that manifests as a
step-like feature in the absorption in the far to near-IR at 2 x EF.73, 74, 85, 119-121 Additionally,
the linear bandstructure and two-dimensional nature of graphene allow for it to support
plasmonic modes that have a unique dispersion relation, discussed in the previous
chapter.122-125 These plasmonic modes have been proposed as a means of efficiently
coupling to THz radiation,126-128 and they have been shown to create strong absorption
pathways in the THz to mid-IR when the graphene is patterned to form plasmonic Fabry-

58, 69, 129, 130

Perot resonances.

41
The intensity and frequency of the plasmonic modes in

graphene are carrier density dependent, and they display extremely large mode
confinement, which allows them to efficiently couple to excitations (e.g. phonons) in their
environment and create new optical modes.68, 69, 72, 129 As the graphene sheet is heated up,
these different infrared absorption pathways become thermal emission sources, with
contributions that vary with the graphene carrier density and surface geometry. The
graphene plasmons are particularly interesting as thermal emitters because their small mode
volumes allow for extremely efficient thermal energy transfer in the near field131, 132, and
also lead to large Purcell factors that can enhance the emission rate of emitters within the
plasmon mode volume133. These large Purcell factors suggest that electronic control of the
graphene plasmonic modes could potentially control thermal radiation at time scales much
faster than the spontaneous emission rate for conventional light emitting diodes and
classical blackbody emission sources.
3.1.2 Experimental Realization of Dynamically Tuned Thermal Radiation
In this work, we experimentally demonstrate the dynamic tuning of blackbody emission
through electronic control of graphene plasmonic nanoresonators on a silicon nitride
substrate at temperatures up to 250°C. Our device is based on field effect tuning of the
carrier density in nanoresonators, which act as antennas to effectively outcouple thermal
energy within the resonator mode volume. We show that through this mechanism the
thermal radiation generated by substrate phonons and inelastic electron scattering in
graphene can be tuned on and off. By varying the charge carrier density of the graphene
from ~ 0 - 1.2 × 1013 cm-2, with resonator widths from 20 – 60 nm, we show that a narrow
bandwidth emission feature may be tuned in intensity and varied in frequency across the
mid-IR, from approximately 1200 – 1600 cm-1.
A schematic of the measurement apparatus and device geometry are shown in Figure 3.1a.
The device consists of 20 – 60 nm wide graphene nanoresonators patterned into a graphene
sheet on a 1 µm SiNx layer with a gold back reflector that also serves as a back gate
electrode. This device geometry was previously used as a gate-tunable absorber in the mid-

42
IR, described in Chapter 2.3, where a large enhancement in absorption was observed when
the graphene plasmonic resonance was matched to the energy of the 𝜆 4𝑛

!"#

‘Salisbury

Screen’ resonance condition in the 1 µm SiNx layer, which occurred at 1360 cm-1.134, 135 In
those experiments, the polarized absorption (aligned to the confined dimension of the
graphene resonator) in the graphene nanoresonators could be tuned from 0 to up to 24.5%
for large carrier densities. In this work, a similar sample displayed up to 3% total
absorption when probed using our apparatus. This smaller number reflects the use of nonpolarized light, the higher numerical aperture objective of the apparatus, the effect of the
window of the vacuum stage, and the lower carrier densities used due to the onset of PooleFrenkel tunneling in the SiNx at higher temperatures and high gate biases.134, 136

Figure 3.1: Device and experimental set-up (a) Schematic of experimental apparatus. 70 ×
70 µm2 graphene nanoresonator arrays are placed on a 1 µm thick SiNx membrane with 200
nm Au backreflector. The graphene was grounded through Au(100 nm)/Cr(3 nm)
electrodes that also served as source-drain contacts. A gate bias was applied through the
SiNx membrane between the underlying Si frame and graphene sheet. The temperature
controlled stage contains a feedback controlled, heated silver block that held a 2mm thick

43
copper sample carrier, with a 100 µm thick sapphire layer used for electrical isolation. The
temperature was monitored with a thermocouple in the block, and the stage was held at a
vacuum of 1 mtorr. A 1mm thick potassium bromide (KBr) window was used to pass
thermal radiation out of the stage, which was collected with a Cassegrain objective and
passed into an FTIR with an MCT detector. (b) A representative SEM image of 30 nm
graphene nanoresonators on a 1µm thick SiNx membrane. (c) Source-drain resistance vs
gate voltage curve of the device. The peak in the resistance occurs at the charge neutral
point (CNP), when the Fermi level (EF) is aligned with the Dirac point.
Figure 3.2 (left axis) shows the emitted radiation at 250°C from a black soot reference
sample and from a 40 nm graphene nanoresonator array at 250°C under doped (1.2 × 1013
cm-2) and undoped conditions. On the right axis of Fig. 3.2 we plot the change in emissivity
corresponding to the observed change in emitted light from the undoped to doped graphene
resonators. This change in emissivity is calculated assuming unity emissivity at all
frequencies for the black soot reference and normalizing accordingly. This accounts for the
non-idealities of the FTIR optics as well as giving us an accurate temperature calibration.
As can be seen in the figure, increasing the carrier density of the graphene nanoresonators
leads to increases in emissivity near 730 cm-1 and 1400 cm-1.

Figure 3.2: Experimental emission results (left axis) Emitted thermal radiation at 250°C
from soot (black dotted line) and 40 nm graphene nanoresonators at zero (red) and 1.2 ×
1013 cm-2 (green) carrier density. (right axis, blue line) Change in emissivity of 40 nm
nanoresonators due to increase in carrier density. Soot reference is assumed to have
emissivity equal to unity.
In order to explore these gate-tunable emissivity features, we investigate their behavior as
the nanoresonator doping and width is varied, as shown in Figures 3.3a and 3.3b, as well as
their polarization dependence (Fig. 3.3c). These results indicate that the intensity, width,
and energetic position of the thermal radiation feature near 1360 cm-1 are widely tunable,
and that this feature is strongly polarized. The energy of this feature increases as the
nanoresonator width is decreased and as the carrier density is increased, while the intensity
of this feature increases with carrier density, and is largest in 40 nm resonators, when it
occurs closest to the 𝜆 4𝑛

!"#

resonance condition of the SiNx at 1360 cm-1. Because

Kirchoff’s Law dictates that thermal emissivity is equal to absorptivity, these observations

45
are consistent with previously reported absorption measurements performed on identical
samples that showed a narrow absorption feature near 1360 cm-1,134

Figure 3.3: Emissivity tunability (a) Carrier
density dependence of change in emissivity
with respect to the CNP for 40 nm graphene
nanoresonators at 250°C. (b) Width
dependence of change in emissivity for 20,
30, 40, 50 and 60 nm wide nanoresonators
at 250°C and for a carrier density of 1.2 ×
1013 cm-2. (black line) Emissivity change
for a nearby region of bare, unpatterned
graphene at the same carrier density and
temperature. (c) Polarization dependence of
the emissivity change for 40 nm graphene
nanoresonators at 250°C, for a carrier
density of 1.2 × 1013 cm-2.

46
The lower energy emissivity modulation feature near 730 cm shows different behavior
-1

than the higher energy peak. Namely, the low energy feature shows extremely weak
polarization dependence, and also shows no noticeable dependence on graphene
nanoresonator width. As the carrier density is increased, there is a small, non-monotonic
increase in intensity for this feature, but it shows no spectral shift. Finally, unlike the higher
energy peak, the lower energy peak is also observed in the bare, unpatterned graphene,
where it appears as a slightly narrower feature. The absorption properties of this device
near the energy range of the lower energy feature were not discussed in previously reported
work in Chapter 2 due to the low energy cutoff of the detector used in that work.
3.1.3 Theoretical Interpretation of Results
We explain the above phenomena as electronic control of thermal radiation due to a
combination of plasmon-phonon and plasmon-electron interactions, Pauli-blocking of
interband transitions, and non-radiative transfer processes between the SiNx and the
graphene sheet. While Kirchoff’s law dictates that the thermal equilibrium emissivity must
be equal to the absorptivity for any material, the precise, microscopic mechanisms of
thermal emission are dramatically modified in inhomogeneous artificial photonic materials
with highly confined optical modes relative to homogeneous materials.
We attribute the prominent spectral feature at 1360 cm-1 to a Fabry-Perot plasmonic
resonance from the patterned graphene. The width and doping dependence of the 1360 cm-1
feature follows the behavior expected for graphene plasmonic modes, and is consistent with
reflection measurements.134 Specifically, the graphene plasmon resonant frequency should
vary as ωp ∝ n1/4W-1/2, where n is the carrier density and W refers to the resonator width.
This relationship was explored in depth in Chapter 2, and results from the unique
dispersion relation of graphene plasmons due to their two-dimensional nature and the linear
band structure of graphene. This behavior is in accord with the emission spectra in which
we observe a blue shift of the plasmonic resonance at increased doping and decreased
graphene nanoresonator width. The intensity of the higher energy peak increases with
graphene carrier density, an effect that results from the increased polarizability of the

47
resonant plasmonic modes. Finally, this feature is strongly polarization dependent – as we
would expect for laterally confined graphene plasmonic resonant modes – and vanishes
quickly as we rotate the polarization of the probing radiation from 90° to 0° relative to the
nanoresonator axis. This suggests that graphene nanoresonators may be an interesting
platform for light sources with controllable polarization, to be discussed in Chapter 3.2.
In order to understand the source of thermally excited plasmons in graphene
nanoresonators, we note that the microscopic processes that lead to plasmonic loss in
graphene should by reciprocity correspond to plasmon-generating processes when the
sample is heated. For the case of the 1360 cm-1 feature we observe here, the plasmonic loss
(and corresponding plasmon generating) processes are attributed to the factors that limit the
electron mobility of the graphene, such as defect scattering, impurity scattering, and
inelastic electron-electron and electron-phonon interactions.68, 69, 123, 134, 137

Additionally,

plasmons have been shown to decay via loss channels associated with the edges of
graphene nanostructures, and by coupling to substrate phonons.68, 69 For a bare graphene
sheet, the plasmons generated by thermal emission do not couple well to free space and are
thus non-radiative. Upon patterning the graphene, however, the plasmonic resonances can
effectively serve as antennas that out-couple radiation, and the plasmon decay processes
give rise to free-space thermal emission by exciting resonant plasmonic modes, which then
radiate.
The resonant enhancement of emission from plasmon generating processes is in
competition with the blocking of interband transitions that act as thermal emitters in the
undoped graphene, but are forbidden due to Pauli blocking when the sheet is doped.73, 74
The role of interband transitions can be seen most clearly in the bare graphene emissivity
spectra in Fig. 3.3b where there is a broad decrease in emissivity near 1360 cm-1 at higher
carrier densities. While interband transitions should occur across a wide range of
frequencies, in the back reflector geometry we use here, thermal emission from the surface
can either constructively or destructively interfere with itself and is thus most prominent at
1360 cm-1 , the 𝜆 4𝑛
frequency of the SiNx layer. For patterned graphene areas,
!"#

48
however, we find that doping the graphene allows for the resonant plasmonic modes to
create an emission enhancement that outweighs the decrease in emission due Pauli
blocking, and thus we get a net increase in emission near 1360 cm-1.

Figure 3.4: Finite element power density simulations (a) Finite element electromagnetic
simulation of ∇ ⋅ S (electromagnetic power density) in graphene/SiNx structure for 40 nm
graphene nanoresonators on 1 µm SiNx with a gold backreflector. The simulation is
performed at 1357 cm-1 (on plasmon resonance) at a carrier density of 1.2 × 1013 cm-2. The
dotted white line indicates the mode volume of the plasmon. (b) Integrated power density
absorbed in the 40 nm graphene nanoresonator, the SiNx within the plasmon mode volume
(Top SiNx), and the remaining bulk of the SiNx (Bulk SiNx) for carrier densities of 1.2 ×
1013 cm-2 and ~ 0 cm-2 (the charge neutral point).
As mentioned above, in addition to out-coupling of radiation due to plasmon loss
mechanisms in the graphene, the plasmonic resonators also interact with vibrations in the
SiNx substrate. When the SiNx is heated, the plasmonic modes act as antennae to enhance
the spontaneous thermal radiation from the nearby SiNx. The enhancement of the
spontaneous emission radiative rate and of the quantum efficiency arising from dipole
emitters’ proximity to a dipole optical antenna is well known,138-140 and is attributed to
increasing the probability of radiative emission by modification of the photonic mode
density.141 The rate enhancement is correlated to the strong polarizability of the graphene at
its plasmonic resonance that enhances the out-coupling of thermal radiation from the SiNx.

49
In particular, the radiative rate is expected to be most strongly amplified within the mode
volume of the resonant graphene plasmon, which for 40 nm resonators at 1.2 × 1013 cm-2
roughly corresponds to the area within 10 nm of the resonator (see Fig. 3.4a). We therefore
assign the net increase of thermal emission near 1360 cm-1 to a combination of thermal
excitations in the graphene as well as thermal phonons in the SiNx that are out-coupled
through the confined plasmonic modes in the graphene nanoresonators.
In contrast to the high-energy feature, which is due to plasmons in the graphene, the low
energy feature at 730 cm-1 is related to an optically active phonon in the SiNx substrate.
This phonon mode is strongly absorbing (emitting) and is typically located near 850 cm-1.
The large divergence in the SiNx permittivity due to this phonon, however, creates an
additional 𝜆 4𝑛

!"#

condition in the structure that leads to a destructive interference effect,

resulting in an absorption (emission) maximum at 730 cm-1. When graphene is placed on
top of the SiNx, the intraband and interband transitions in the graphene act to modify the
surface impedance of the device. The result is that increasing the doping in the graphene
leads to a stronger destructive interference effect, which manifests as larger emission from
the SiNx layer (see Fig. 3.4b). In addition to direct emission from the SiNx phonon, the
graphene plasmons can couple to the SiNx phonons to create new surface phonon plasmon
polariton modes (SPPPs).68, 69, 129, 142 The formation of these modes leads to a modification
of the plasmonic dispersion relation, and additional absorption (emission) pathways near
and below the energy of the SiNx phonon. Emission from the SPPP modes, however,
should display some polarization dependence, which was not observed in Fig. 3.3b, and
thus an increase in direct emission from the SiNx layer likely plays the dominant role in
creating the feature at 730 cm-1.
To better understand and quantify the emission features observed in the graphene-SiNx
structure, we used a finite element method to calculate the electromagnetic power density
(∇ ∙ 𝐒) associated with plane waves incident on 40 nm graphene nanoresonators on an
SiNx/Au substrate. The parameters for our computational model were equivalent to those
described in Chapter 2.3, where the optical absorption of the device was modeled.134

50
Because ∇ ∙ 𝐒 reveals where power is absorbed, it therefore also indicates where far field
thermal emission originates, and an increase in ∇ ∙ 𝐒 indicates an enhancement of the
spontaneous emission intensity of the thermally excited dipoles.134 The results of these
simulations are shown in Fig. 3.4a at 1357 cm-1, corresponding to the resonant energy of
the graphene plasmon mode when the carrier density is set to 1.2 × 1013 cm-2. It can be seen
in this figure that there is a marked increase in the amplitude of ∇ ∙ 𝐒 near the graphene
nanoresonator. On resonance, there is a significant amount of power absorbed directly into
the graphene, and it can also be seen that there is a large amount of absorption in the SiNx
in the immediate vicinity of the nanoresonator, where the fields of the graphene plasmon
mode extend. To further distinguish the relative contributions to thermal emission, we
integrate the power densities at 1357 cm-1 over the graphene, the SiNx within the plasmon
mode volume, and the remaining SiNx. We calculate the mode volume of our structure as

Veff = ∫ udV / u0 , where the numerator is the total stored energy and u0 is the
electromagnetic-energy density at the emitter position, chosen to be sitting directly atop the
resonator. We define the boundary of the mode to be centered about the graphene resonator
along a contour of constant electric field (Ex). In Fig. 3.4b, we show results for undoped
and doped nanoresonators. For undoped graphene, we observe weak power absorption in
the SiNx near the graphene nanoresonator, and we see only interband transitions
contributing to absorption in the graphene itself. As the carrier density is increased to 1.2 ×
1013 cm-2, absorption in the graphene and the nearby SiNx increases due to excitation of the
confined plasmonic mode. The absorption in the bulk of the SiNx layer shows little
dependence on graphene carrier density, except at low frequencies, near 730 cm-1, where
absorption decreases with carrier density due to changes in the reflection coefficient at the
surface, as described above. We note that our finite element model does not account for the
non-radiative processes discussed in other work.143 Our model indicates how graphene
plasmons interact with a homogenous, lossy medium but not the manner in which
individual dipoles interact with the graphene sheet, which is another source of nonradiative quenching.

51
3.1.4 Radiated Power and Device Considerations
In order to quantify the thermally radiated power of this structure, we consider Planck’s
law for spectral radiance using the black soot as a reference with ɛ = 1, and including our
50 x 50 µm2 collection area and the 1.51 steradians covered by the 0.65 NA objective. This
calculation yields a maximum thermal power modulation of 50 pW/cm-1 at 1360 cm-1 (7.1
µm) for 40 nm resonators at 250°C doped to a carrier density of 1.2 × 1013 cm-2. These
calculations indicate that a 1 x 1 mm2 device could act as an electronically controllable
mid-IR source that would modulate 2 µW of power over 100 cm-1 of bandwidth. This
compares favorably to commercial mid-IR LEDs at 7 µm, which emit 1.25 µW over similar
bandwidths (IoffeLED, Ltd. OPLED70Sr). The percent change in emitted power at the
resonant plasmonic frequency is 7.5%, a value that reflects the large background
contribution due to SiNx phonons as well as the low mobility of the graphene sheet, the
polarization of the plasmon-assisted radiation, and the low dielectric strength of the SiNx at
elevated temperatures. Figure 3.4 shows that while the SiNx phonons play some role in
contributing to the plasmon-assisted radiation, the majority originates in the graphene sheet
itself. Thus, by choosing a substrate with a low optical phonon density at the resonant
plasmon frequency, such as diamond-like carbon (DLC),69 the background signal could be
reduced without significantly suppressing the plasmon-assisted radiation, leading to a
larger modulation depth of the emitted power. We also note that the maximum temperature
and gate bias applied in these experiments was not limited by the graphene but by the SiNx
dielectric, which is known to exhibit Poole-Frenkel tunneling at high temperatures.136 By
choosing a dielectric that can withstand higher temperatures, such as SiO2 or DLC, devices
displaying larger power modulation could be fabricated. Finally, devices fabricated with
higher mobility graphene, less edge roughness and with circular resonator geometries (i.e.
non-polarized)

have

been

predicted

theoretically135

exhibit

tunable

absorptivity/emissivity that can vary from 0 to 1 (i.e. zero to total absorption) within a
narrow frequency range. Such devices would display changes in absorptivity that equal or
exceed those provided by electrochromic devices,144 while also providing potential for
more operation cycles, and higher temperature and higher speeds of operation.

52
In addition to providing utility as a tunable mid-IR source, the physics by which this device
operates is distinctly different from conventional laser or LED sources. Because thermal
radiation is a form of spontaneous emission, the emission rate is increased by the presence
of the plasmonic cavity, with the degree of rate enhancement is dictated by the ratio
between the Q factor and mode volume of the optical cavity (i.e. the Purcell factor).145
This effect has been explored as a means of increasing LED switching rates by placing the
semiconductor emitting layer within either a plasmonic or photonic cavity.146-150 For the
case of graphene plasmonic nanoresonators that have highly confined mode volumes, the
Purcell factor has been shown to be extremely high, approaching 107, and thus, the
modulation rate of thermal emission from our device could be exceedingly fast, beyond
what has been demonstrated with plasmonically enhanced LEDs or lasers.151 For the device
demonstrated here, where the switching and detection speeds are limited by a large
electrical RC time constant, and the slow operation speeds of our FTIR-based detector, kHz
switching speeds can be demonstrated, presented in Figure 3.5. However, careful device
design, where the capacitance is minimized and lower resistance contacts are used, could
allow for the creation of a mid-IR emitter with ultrafast switching times and a broad range
of tunability.

53
Applied Gate Voltage
Emission from 50 nm ribbons (250°C)

Figure 3.5: kHz modulated emission signal. Temporal waveform of applied voltage signal
(black line) and detector signal of emission from 50 nm ribbons at 250°C (green line). A
voltage of 60 V corresponds to a doping level of 1.2 × 1013 cm-2, resulting in a positive
detector signal. A voltage of 0 V corresponds to the charge neutral point of the graphene
and therefore the measurement of an ‘off’ signal.
3.2 Electronic Control of Polarized Emission
3.2.1 Introduction
In order to gain full, active control over emitted infrared light, one would like to control not
just amplitude, as discussed in the previous section, but additionally polarization and phase
(the latter of which will be addressed in Chapters 4 and 7). With this additional layer of
control, metasurface polarizers that filter or emit specific polarization states of light may be
realized, which can be modulated in real time.
Metasurfaces have recently been utilized to selectively reflect or absorb specific
polarization states of light, as well as to convert the polarization state of light152-161.
However, none of these structures have been demonstrated to actively modulate the

54
polarization state of light using electrostatic gating, limiting their ultimate utility in
reconfigurable photonic devices. In this work, we demonstrate that by taking advantage of
the gate-tunability of graphene plasmons, and the two free parameters (width and Fermi
energy), active control of the polarization state of light may be achieved in a single
structure.
3.2.2 Design of Dual-Resonant Structure for Polarization Control
We design a resonant cavity inspired by the Salisbury Screen concept described in Chapter
2, wherein graphene nanoresonators of different widths are fabricated on a thick silicon
cavity terminated with a gold back reflector, on which a thin insulating layer is transferred
to allow active gate-tunability, shown schematically in Figure 3.6. Unlike the Salisbury
screen, which takes advantage of the λ

dielectric resonance (where n is the index of

refraction of the cavity), we implement a design based on a thicker, high-index external
cavity that supports higher order resonances that span the mid-infrared. In this way, we
achieve two goals: the first to narrow the peak width of the resonance, and the second to
decrease the free spectral range, both of which scale inversely with cavity thickness.

kinc

ksca
Or kemit
VG

hBN

Figure 3.6: Schematic illustration of graphene-dielectric dual resonant structure for
controlling the polarization state of reflected or emitted infrared light. A 7.5 µm thick Si
cavity with Au back-reflector results in enhanced absorption in the graphene
nanoresonators at the surface.
By carefully selecting the carrier concentration and width of the graphene resonators, it is
possible to match different resonators to the mλ

dielectric resonances of the cavity,

where m is an integer and n the cavity index of refraction, for which simulation results are
shown in Figure 3.7 (See Appendix B for simulation parameters). We use 7.5 µm thick Si
as the lossless dielectric for the mid-infrared, with a 7 nm thick hexagonal boron nitride (hBN) gate dielectric sandwiched between the graphene nanoresonators and Si. 200 nm Au
serves as a near-ideal back-reflector. The use of a thin h-BN layer allows for electrostatic
modulation of the graphene plasmon, in addition to providing a substrate with a decreased
density of surface charges, which may increase the graphene mobility.162, 163

Δ Abs (%)

56
45
40
35
30
25
20
15
10
-5

30 nm

40 nm

90 nm

60 nm

Wavelength (μm)
Figure 3.7: Graphene absorption at EF = 0.4 eV normalized to EF = 0 eV for different
nanoresonator widths. High order dielectric resonances of the silicon cavity are matched to
the plasmon resonances.
Of most interest in this geometry is the selective enhancement of absorption for different
resonator widths matched to specific cavity modes. This enables excellent spectral control
of absorption with narrow absorption/emission features that can be switched on and off on
demand. Moreover, due to the strong dependence of the graphene plasmon frequency on
carrier concentration described in previous chapters, it is possible to identify multiple
conditions of enhanced absorption by taking advantage of the relations ω p ∝W

−1

and

ω p ∝ EF 2 . An example of this is shown in Figure 3.8, wherein a graphene resonator of 60
nm is well-matched to the external cavity resonance ( 11λ

) for EF = 0.45 eV, but poorly

matched to this for EF = 0.3 eV. The exact opposite trend is observed for a resonator width
of 40 nm: for EF = 0.45 eV, minimal absorption is observed, but for EF = 0.3 eV, the
plasmon absorption is strongly enhanced. This suggests that we may establish a
“switching” behavior between 40 nm and 60 nm ribbons by changing the graphene Fermi
energy.

60 nm,EFEF==0.3eV
0.3 eV
40nm,

40 nm,EFEF==0.45eV
0.3 eV
40nm,
40 nm,EFEF==0.3eV
0.45 eV
60nm,

20
18
16

60 nm,EFEF==0.45eV
0.45 eV
60nm,

60 nm

45
40
35
30
25
20
15
10
-5
8.5

EF = 0.45 eV

12
10
50nm

50nm

9.0

9.5

10.0

Wavelength (μm)

10.5

40 nm

Δ Abs (%)

EF = 0.3 eV

25nm

Figure 3.8: (a) Tunable absorption in graphene resonators of selected widths (40 and 60
nm) and Fermi energies (0.3 and 0.45 eV) for selectively enhanced absorption. (b – e) Field
profiles for each width/EF combination at a wavelength of 9.34 µm.
We can therefore take advantage of this Fermi energy tuning to realize active polarization
control of infrared light: by designing a crossed structure comprised of 40 and 60 nm
resonators, absorption (and therefore emission) can be enhanced in each arm by switching
the graphene Fermi energy from 0.3 to 0.45 eV, shown in Figure 3.9. Moreover, by
carefully selecting the dimensions of the unit cell, amplitude compensation can be done to
create approximately equal ‘on’ and ‘off’ states for Ex and Ey polarizations.

58
b.

Δ Absorp)on (%)

95 nm
40 nm

60 nm

175 nm

20
18
16
14
12
10

Ex, EF = 0.3 eV
Series2

Ey, EF = 0.3 eV
Series3

Ex, EF = 0.45 eV
Series4

Ey, EF = 0.45 eV
Series1

8500
8.5

9000
9.0

9500
9.5

10000
10.0

10500
10.5

Wavelength (μm)

Figure 3.9: (a) Geometry of graphene crosses for polarization switching and corresponding
absorption, (b), normalized to EF = 0 eV for X and Y polarizations as defined in the
reference frame of the schematic.
Samples are now being fabricated to experimentally realize these designs. Silicon-oninsulator (SOI) wafers are purchased from Ultrasil with 7.5 µm thick device layers, 200 nm
SiO2 (as an etch stop layer), and 300 µm thick handles. Electron beam lithography is used
to expose a window on the backside of the handle, and XeF2 is used to etch through to the
SiO2. Hydrofluoric acid (HF) is used to remove the SiO2 layer, leaving a suspended Si
membrane. Au is then deposited on the backside and h-BN is transferred on the top.
Graphene is then transferred on top of the h-BN and 100 keV electron beam lithography is
used to pattern the ribbon or crossed structures.
3.3 Conclusions and Outlook
In conclusion, we have demonstrated that by combining the width- and carrier
concentration-dependent plasmon resonance of graphene nanoresonators with external
cavity designs, active control of the spectral intensity and polarization state of absorbed and
emitted light may be realized. We experimentally demonstrate kHz modulation of emitted
intensity in the mid-infrared and present simulations and calculations to explain the
emission control as arising from antenna-coupled enhancement based on graphene

59
plasmons. We have shown that by taking advantage of dual-resonant structures, it is
possible to create devices with ‘designer’ thermal radiation profiles, useful for thermal
camouflage or infrared light sources. In future works, it may be of interest to additionally
control the phase of emitted radiation for emission-type metasurfaces. Moreover, these
experiments suggest that graphene may also be a very interesting material for controlling
near-field heat transfer.

60
Chapter 4

PHASE MODULATION AND ACTIVE BEAM STEERING WITH
GRAPHENE-GOLD METASURFACES
"To invent, you need a good imagination and a pile of junk."
– Thomas Edison
Chapter 4.1
1. Michelle C. Sherrott*, Philip W. C. Hon*, Katherine T. Fountaine, Juan C. Garcia,
Samuel M. Ponti, Victor W. Brar, Luke A. Sweatlock, Harry A. Atwater, “Experimental
Demonstration of >230° Phase Modulation in Gate-Tunable Graphene-Gold
Reconfigurable Mid-Infrared Metasurfaces”, Nano Lett., 2017, 17 (5), pp 3027–3034
(*Equal author contributors)
DOI: 10.1021/acs.nanolett.7b00359
Metasurfaces offer significant potential to control far-field light propagation through the
engineering of amplitude, polarization, and phase at an interface. We report here phase
modulation of an electronically reconfigurable metasurface and demonstrate its utility for
mid-infrared beam steering. Using a gate-tunable graphene-gold resonator geometry, we
demonstrate highly tunable reflected phase at multiple wavelengths and show up to 237°
phase modulation range at an operating wavelength of 8.50 µm. We observe a smooth
monotonic modulation of phase with applied voltage from 0° to 206° at a wavelength of
8.70 µm. Based on these experimental data, we demonstrate with antenna array calculations
an average beam steering efficiency of 23% for reflected light for angles up to 30° for this
range of phases, confirming the suitability of this geometry for reconfigurable mid-infrared
beam steering devices. By incorporating all non-idealities of the device into the antenna
array calculations, including absorption losses which could be mitigated, 1% absolute
efficiency is achievable up to 30°. We design and fabricate a 28-pixel meta-device based on
this design for realizing active beam steering.

61
4.1
Experimental Demonstration of >230° Phase Modulation in Gate-Tunable
Graphene-Gold Reconfigurable Mid-Infrared Metasurfaces
4.1.1 Introduction
Metasurfaces have been demonstrated in recent years to be powerful structures for a
number of applications including anomalous reflection164, focusing/lensing4, 5, and more
complex functionalities such as polarization conversion, cloaking, and three-dimensional
image reconstruction12-16, among others11, 17-21. These functionalities are accomplished
through careful engineering of phase fronts at the surface of a material, where geometric
parameters of resonant structures are designed to scatter light with a desired phase and
amplitude. However, all of these structures have functions that are fixed at the point of
fabrication, and cannot be transformed in any way. Therefore, significant effort has been
made in the community to develop metasurfaces that can be actively modulated. There
exist numerous examples of metasurface designs which enable active control of reflected or
transmitted amplitude, taking advantage of different technologies including MEMS, fieldeffect tunability, and phase change materials89, 165-168, discussed further in recent reviews of
the state-of-the-art in metasurfaces20, 169-172.
For mid-infrared (mid-IR) light, graphene has been demonstrated as an ideal material for
active nanophotonic structures for a number of reasons, including its low losses in the midIR and its intermediate carrier concentration (1012 - 1013 cm-2), placing its plasma frequency
in the IR – THz regime68, 173-176. Additionally, since it is atomically thin and has a linear
density of electronic states, its charge carrier density can be easily modulated via
electrostatic gating in a parallel plate capacitor configuration63, 177-179. Its corresponding
complex permittivity can therefore be modulated over a wide range, potentially at GHz
speeds. Recent works have demonstrated that the incorporation of graphene into resonant
gold metasurfaces can also be used to significantly modulate absorption profiles, operating
at MHz switching speeds89. This has been accomplished by either the un-assisted
modulation of the graphene dielectric constant, or by exploiting the strong confinement of
light by a graphene plasmon excited between metal edges to enhance the sensitivity of the
design to the graphene’s optical constants.88, 167 Additional examples have used the tunable

62
permittivity of graphene to modulate the transmission characteristics of a variety of
waveguide geometries94, 180.
Despite the significant progress that has been made, an important requirement for power
efficient, high-speed, active metasurfaces is electrostatic control of scattered phase at
multiple wavelengths, which has not been adequately addressed experimentally in the midIR. In gaining active control of phase, one can engineer arbitrary phase fronts in both space
and time, thereby opening the door to reconfigurable metasurface devices. This is
particularly necessary as classic techniques for phase modulation including liquid crystals
and acousto-optic modulators are generally poorly-suited for the IR due to parasitic
absorption in the materials used181, 182, in addition to being relatively bulky and energyexpensive in comparison to electrostatic modulators. Similarly, though 60° phase
modulation based on a VO2 phase transition has been demonstrated at 10.6 µm, the phase
transition occurs over relatively long time scales and the design is limited in application
due to the restricted tunability range183. Finally, recent works on the electrostatic control of
phase in the mid-IR using graphene-integrated or ITO-integrated resonant geometries are
limited to only 55° electrostatic phase tunability at 7.7 µm184 and 180° tunability at 5.95
µm185, respectively. In this work, we overcome these limitations and experimentally
demonstrate widely-tunable phase modulation in excess of 200° with over 250 nm
bandwidth using an electrostatically gate-tunable graphene-gold metasurface (see Figure
4.1). We highlight a smooth phase transition over 206° at 8.70 µm and sharper, but larger,
phase modulation of 237° at 8.50 µm, opening up the possibility of designing high
efficiency, reconfigurable metasurface devices with nanosecond switching times. By
measuring this active tunability over multiple wavelengths in a Michelson interferometer
measurement apparatus, we present evidence that this approach is suitable for devices that
can operate at multiple wavelengths in the mid-IR.

Figure 4.1: Tunable resonant gap-mode geometry. (a) Schematic of graphene-tuned
antenna arrays with field concentration at gap highlighted. Resonator dimensions: 1.2 µm
length by 400 nm width by 60 nm height, spaced laterally by 50 nm. SiNx thickness 500
nm, Au reflector thickness 200 nm. (b, c) Field profile in the antenna gap shows detuned
resonance at different EF at a wavelength of 8.70 µm. Scale bar is 50 nm. (d) Simulated
tunable absorption for different graphene Fermi energies. (e) Simulated tunable phase for
different graphene Fermi energies. (f) Phase modulation as a function of Fermi energy for
three different wavelengths – 8.2 µm, 8.5 µm, 8.7 µm.
4.1.2 Design of Resonant Phase-Shifting Structure
Our tunable phase metasurface design is based on a metasurface unit cell that supports a
gap plasmon mode, also referred to as a patch antenna or ‘perfect absorber’ mode, which
has been investigated previously by many groups100, 186-188, shown schematically in Figure
1a. Absorption and phase are calculated as a function of Fermi energy (EF) using COMSOL
FEM and Lumerical FDTD software (see Appendix B). A 1.2 µm length gold resonator on
graphene is coupled to a gold back-plane, separated by 500 nm SiNx. At the appropriate
balance of geometric and materials parameters, this structure results in near-unity
absorption on resonance, and a phase shift of 2π. This may be considered from a theoretical
perspective as the tuning of parameters to satisfy critical coupling to the metasurface187.
This critical coupling occurs when the resistive and radiative damping modes of the
structure are equal, thereby efficiently transforming incoming light to resistive losses and

64
suppressing reflection. This condition is possible at subwavelength spacing between the
gold dipole resonator and back-plane, when the resonator is able to couple to its image
dipole moment in the back-reflector, generating a strong magnetic moment. The magnetic
moment, in turn, produces scattered fields that are out of phase with the light reflected from
the ground plane, leading to destructive interference and total absorption. This may be
considered the plasmonic equivalent of the patch antenna mode.
In order to enhance the sensitivity of the structure to the tunable permittivity of the
graphene, these unit cells are arrayed together with a small (50 nm) gap size to result in
significant field enhancement at the position of the graphene, as shown in Figures 4.1b and
4.1c. This is critical for enhancing the in-plane component of the electric field to result in
sensitivity to the graphene’s optical response. Therefore, as the Fermi energy of the
graphene is modulated, changing both the inter- and intra-band contributions to its complex
permittivity, the resonant peak position and amplitude are shifted, as shown in Figures 1d
and 1e. Specifically, the intraband contribution to the permittivity is shifted to higher
energies as the plasma frequency of the graphene, ωp increases with the charge carrier

density as ω p ∝ n 4 . Additionally, as EF increases, Pauli blocking prevents the excitation of
interband transitions to energies above 2EF, thereby shifting these transitions to higher
energy. The net effect of these two contributions is a decrease of the graphene permittivity
with increasing carrier density, leading to a shift of the gap mode resonance to shorter
wavelengths.
By taking advantage of graphene’s tunable optical response, we obtain an optimized design
capable of a continuously shifted resonance peak from 8.81 µm at EF = 0 eV or Charge
Neutral Point (CNP) to 8.24 µm at EF = 0.5eV; a peak shift range of 570 nm.
Correspondingly, this peak shift indicates that at a fixed operation wavelength of 8.50 µm,
the scattered phase can be modulated by 225°, as seen in Figure 1f. This trend persists at
longer wavelengths, with greater than 180° modulation achieved between 8.50 and 8.75
µm. At shorter wavelengths, such as 8.20 µm, minimal tuning is observed because this falls
outside of the tuning range of the resonance. It is noteworthy that this phase transition

65
occurs sharply as a function of EF at 8.50 µm because it falls in the middle of our tuning
range, and becomes smoother at longer wavelengths. We therefore illustrate this smooth
resonance detuning at a wavelength of 8.70 µm in Figure 4.1b and 4.1c, wherein we plot
the magnitude of the electric field at different Fermi energies of the graphene. On
resonance (Figure 4.1b), the field is strongly localized to the gap, and then as the Fermi
energy is increased (Figure 4.1c), this localization decreases as the gap mode shifts to
shorter wavelengths. These different responses are summarized at three wavelengths (8.2,
8.5, and 8.7 µm) in Figure 4.1f, where the phase response is plotted as a function of EF.
4.1.3 Experimental Demonstration of Phase Modulation
We experimentally demonstrate the tunable absorption and phase of our designed structure
using Fourier-Transform Infrared Microscopy and a mid-IR Michelson interferometer,
respectively, schematically shown in Figure 4.2a. Graphene-gold antenna arrays are
fabricated on a 500 nm free-standing SiNx membrane with a gold back-plane. A Scanning
Electron Microscope (SEM) image of the resonator arrays is presented in Figure 4.2b. An
electrostatic gate voltage is applied between the graphene and gold reflector via the doped
silicon frame to modulate the Fermi energy. Tunable absorption results are presented in
Figure 4.2c demonstrating 490 nm of tunability from a resonance peak of 8.63 µm at the
CNP of the graphene to 8.14 µm at EF = 0.42 eV, corresponding to voltages of +90 V and 80V. This blue-shifting is consistent with the decrease in graphene permittivity with
increasing carrier concentration, and agrees well with simulation predictions. Discrepancies
between simulation and experiment are explained by fabrication imperfections, as well as
inhomogeneous graphene quality and minor hysteretic effects in the gate-modulation due to
the SiNx and atmospheric impurities189. The shoulder noted especially at longer
wavelengths is a result of the angular spread of the FTIR beam, wherein the use of a 15X
Cassegrain objective results in off-normal illumination of the sample. We note that the
processing of our sample in combination with the surface charge accumulated as a result of
the SiNx surface results in a significant hole-doping of the graphene, as has been observed
in previous experiments190. Due to this heavy doping, we are unable to experimentally
observe the exact CNP of the graphene using standard gate-dependent transport

66
measurement techniques, and therefore determine this by comparison to simulation. We
then calculate the Fermi energy at each voltage using a standard parallel plate capacitor
model.

kinc

ksca

ϕ = ϕ0 + Δϕ(VG)

Nitride
Silicon
Frame
Gold

CNP
EF = 0.10 eV
EF = 0.23 eV
EF = 0.25 eV
EF = 0.31 eV
EF = 0.38 eV
EF = 0.42 eV
EF = 0.44 eV

Wavelength (μm)

Figure 4.2: (a) Schematic of a gate-tunable device for control of reflected phase. (b) SEM
image of gold resonators on graphene. Scale bar indicates 1 µm. (c) Tunable absorption
measured in FTIR at different gate voltages corresponding to indicated Fermi energies. A
peak shift of 490 nm is measured.
To experimentally characterize the phase modulation of scattered light achievable in our
graphene-gold resonant structure, we use a custom-built mid-IR, free-space Michelson
Interferometer, for which a schematic is presented in Figure 4.3a and explained in depth in
the Appendix D. The integrated quantum cascade laser source, MIRcat, from Daylight
Solutions provides an operating wavelength range from 6.9 µm to 8.8 µm, allowing us to
characterize the phase modulation from our metasurface at multiple wavelengths. The
reference and sample legs of the interferometer have independent automated translations in
order to collect interferograms at each wavelength as a function of gate voltage.

CNP
EF=0.18 eV
EF=0.44 eV

Position (μm)
CNP
EF =0.15 eV
EF =0.16 eV
EF =0.18 eV
EF =0.22 eV
EF =0.31 eV
EF =0.38 eV
EF =0.44 eV

100
90
80
70
60
50

Increase EF

40
30

Reflectance (%)

20
10

Position (μm)

Figure 4.3: (a) Schematic of a Michelson interferometer used to measure reflection phase
modulation. (b) Representative interferometer measurements for different Fermi energies
with linear regression fits at a wavelength of 8.70 µm. (c) Interferometry data fitted for all
EF at 8.70 µm. (d) Extracted phase modulation as a function of EF at 8.70 µm
demonstrating 206° tuning and corresponding reflectance between 1.5 and 12%.
A comparison of the relative phase difference between interferograms taken for different
sample biases is conducted to capture the phase shift as a function of EF. At each Fermi
energy, an interferogram for different reference mirror displacements is taken. Due to the
different absorptivity at each doping level, each biases’ interferogram is normalized to its
own peak value. We then take the midpoint of the normalized interferogram amplitude as a
reference, and a relative phase shift from one bias to the other is calculated by recording the

68
displacement between the two interferograms at the reference amplitude. Factoring that the
sample leg is an optical double pass, the relative phase difference is given by equation 4.1:
∆𝜙 =

!"#∆!

(4.1)

where ΔΦ is the phase difference between different sample responses in degrees, Δx is the
displacement between interferograms, and λ is the wavelength of operation. Data collected
for three Fermi energies at 8.70 µm and fitted to a linear regression for extracting phase
based on the above equation are presented in Figure 4.3b. For straightforward comparison,
the phase modulation is presented relative to zero phase difference at EF = 0 eV. Linear
regression fits to the data for all Fermi energies measured at 8.70 µm are presented in
Figure 4.3c, and the extracted phase as a function of EF is presented in Figure 4.3d.
Discrepancies between the experimental data and fits, particularly at CNP, can be
explained by the decreased reflection signal from the sample due its strong absorption on
resonance. We additionally plot the reflectance as a function of Fermi energy in Figure
4.3d. This relatively low reflectance is primarily a result of the large losses in the SiNx
substrate and low mobility graphene, and additionally arises from the resonant mode used
to attain a large phase shift. However, this mode has been utilized to design high efficiency
tunable and static metasurfaces14, 191, and the high losses are not fundamental to its
implementation in phase modulation. We suggest that by using lossless silicon as the
dielectric instead of SiNx, and an insulating layer of h-BN (which is also lossless at the
wavelengths considered here) to improve the mobility of the graphene, much higher
reflection efficiencies could be realized.
To further highlight the broad utility of our device, phase modulation results are presented
in Figure 4.4a at multiple wavelengths: 8.20, 8.50, and 8.70 µm. At an operating
wavelength of 8.70 µm, continuous control of phase is achieved from 0° relative at CNP to
206° at EF = 0.44 eV with excellent agreement to simulation. At 8.50 µm, this range
increases to 237°, much greater than any observed in this wavelength range previously,
though as noted above, the transition is very sharp. At the shorter wavelength of 8.20 µm, a
modulation range of 38° is achieved, with excellent agreement to simulation,

69
demonstrating the different trends in phase control this structure presents at different
wavelengths. Simulation parameters are presented in Appendix B. Deviation is primarily
due to hysteresis effects in the nitride gate dielectric and sample inhomogeneity (e.g.,
bilayer graphene patches, polymer residue from fabrication, and cracks in the graphene).
We summarize the experimental and simulation results at all wavelengths between 8.15 µm
and 8.75 µm in Figure 4.4b, wherein we plot the tuning range at each wavelength, defined
as the maximum difference of scattered phase between CNP and EF = 0.44 eV. This Fermi
energy range is limited by electrostatic breakdown of the SiNx gate dielectric. By using
high-k dielectric materials, such as HfO2, this range could be improved. We can therefore
highlight two features of this structure: at longer wavelengths, we observe experimentally a
smooth transition of phase over more than 200°, and at slightly shorter wavelengths, we
can accomplish a very large phase tuning range with the tradeoff of a large transition slope.
It is also noteworthy that more than 200° active tunability is achieved between 8.50 µm and
8.75 µm, which is sufficient for active metasurface devices in the entire wavelength range.

λ=8.2 μm
λ=8.5 μm
λ=8.7 μm

λ (μm)

Figure 4.4: Demonstration of phase modulation over multiple wavelengths. (a) Phase
modulation at wavelengths of 8.2 µm, 8.50 µm, and 8.7 µm (circles – experiment, line –
simulation). (b) Maximum phase tuning achievable at wavelengths from 8.15 um to 8.75
um, simulation and experiment indicating up to 237° modulation.
4.1.4 Beam Steering Calculations

70
To illustrate the applicability of our design to reconfigurable metasurfaces, we calculate the
efficiency of beam steering to different reflected angles as a function of active phase range
for a linear array of independently gate-tunable elements as shown schematically in Figure
4.5a. We choose a linear array with polarization orthogonal to the steering direction to
ensure minimal coupling between neighboring elements and a pitch of 5.50 µm to suppress
spurious diffracted orders at a wavelengths of 8.50 µm. To quantify the beam steering
feasibility of this metasurface, we frame the analysis in the formalism of antenna array
theory, where the array can be considered as a discretized aperture. The far-field radiation
pattern of such a discretized aperture can be analytically calculated by independently
considering the physical array configuration (radiating element layout) and the radiating
element properties, such as its amplitude, phase, and element far-field radiation pattern. For
a general two-dimensional array, the far-field radiation pattern is given by the array factor
weighted by the element’s radiation pattern. The element pattern can be considered a
weighting factor in the calculation of the far-field radiation pattern, where the array factor
is only a function of the element placement and assumed isotropic radiators with a complex
amplitude and phase. For relatively omnidirectional radiating elements, as in our case, the
array factor captures the primary radiation pattern features, such as the main beam
direction, main beam half power beam width (angular width of the main beam noted at half
the main beam peak intensity), and major side lobes, reasonably well. The array factor for a
general two-dimensional configuration is given as:192

𝐼!" 𝑒 !!!" 𝑒 !!!"

𝐴𝐹 𝜃, 𝜑 =

(4.2)

!!! !!!
𝛼!" = −𝛽 𝑥!"
sin 𝜃! cos 𝜑! + 𝑦!"
sin 𝜃! sin 𝜑!

(4.3)

𝛾!" = 𝛽𝑟 ∙ 𝑟!"
= 𝛽 𝑥!"
sin 𝜃 cos 𝜑 + 𝑦!"
sin 𝜃 sin 𝜑

(4.4)

where θ0 and ϕ0 are the elevation and azimuthal values of the main beam pointing direction,
respectively, αmn represents the element imparted phase that controls the beam direction,
γmn represents the path length phase difference due to the element position 𝑟!"
and the unit

vector 𝑟 from the array center to an observation angle, 𝜃, 𝜑. β is the free space propagation

71
constant, Imn is the complex element amplitude and the double summations represent the
row and column element placement of a general two-dimensional array.

Eﬃciency (%)

5.55 μm

25
20

360° Phase
237° Phase

Reflection Angle (°)

d4
Eﬃciency (%)

Eﬃciency (%)

Element Tuning Range (°)

Reflection Angle (°)

Figure 4.5: Calculation of proposed reconfigurable metasurface based on experimentally
realized design. (a) Schematic of beam steering device, where each of the 69 unit cells is
assigned a different EF. (b) Steering efficiency, η, for a 69 element metasurface with a
lattice spacing of 5.55 µm illuminated with a plane wave at 8.60 µm. (c) Steering efficiency
calculated for 360° and 237° phase modulation with unity reflectance. (d) Steering
efficiency for 215° phase modulation incorporating simulated absorption losses.
Considering only the array factor, we can analytically capture the beam steering
characteristics of a metasurface as a function of the achievable element phase tuning range.
In the microwave regime, where the achievable element phase tuning range is greater than
270°, beam attributes such as its pointing direction and side lobe levels, can be quantified
as a function of the phase discretization; the phenomenon is known as quantization error193.
Independent of quantization errors, it is informative to understand the consequence of an
element phase tuning range well below the desired ideal 360°. We define a figure of merit,
the beam efficiency η, to be the ratio of the power in the half power beam width (of the
steered main beam) for a given phase tuning range relative to the total power of the entire
beam from -90 to 90° for unity amplitude and 360° phase tunability, which gives the total
power possible from the aperture. In our analysis we consider maximum phase tuning
ranges as low as 200° and desired scan angles up to +/-30° relative to surface normal. For

72
phase ranges below 200°, the undesirable side lobes will equal or exceed the intensity of
the primary beam and main beam pointing errors exceeding one degree can exist; therefore,
we restrict our analysis for phase ranges greater than 200°. In a simplified analysis, a onedimensional array is assumed (Fig. 4.5a). Since the focus of the analysis is only on the
consequence of a limited element phase tuning range, the element amplitude is initially
assumed to be equal and unity. Assuming a fine enough gating step size, a virtually
continuous sampling of a given element phase tuning range, is possible and therefore
quantization error is not an issue. In this analysis, for a calculated element phase value that
was unachievable, the closest phase value achievable was assigned. Namely, either an
element phase value of 0° or the maximum phase for the considered element phase tuning
range. As shown in Figure 4.5b, regardless of the element phase tuning range, the main
beam scanning direction of zero degrees represents the trivial case where a zero difference
in beam efficiency is expected because all elements exhibit the same reflected phase (zero
phase gradient along the metasurface). The analysis illustrates the trade space and allows us
to quantitatively assess the effect of the experimentally verified phase range of 237° at 8.50
µm. For consideration of the influence of a non-ideal phase range, we present in Figure
4.5c a comparison of the steering efficiency of our designed metasurface with 360° and
237° phase tuning ranges, showing a small decrease due to the limited range up to 30°
steering angle. Up to ±30°, an efficiency greater than 18% is calculated, with an average
efficiency of 23%. Below this phase range, lower efficiency steering is observed; however,
we note that down to 200°, the steered main beam signal still exceeds the intensity in the
other lobes. We note that the fluctuating trends observed as a function of reflection angle
are a result of the incomplete phase range, which manifests differently depending on the
deviation from the ideal phase gradient needed.
This clearly illustrates the necessity of achieving at least 200° in active phase control in
order to create viable reconfigurable metasurfaces. In addition, it is noteworthy that this
calculation includes an assumption of all intermediate phase values being available,
meaning that a smoothly varying phase response as a function of gate voltage is necessary,
as demonstrated in our device. This highlights the potential applications of our structure to

73
metasurface devices, in which independently gateable elements can be used to generate
arbitrary phase gradients in time and space.
To further analyze the applicability of our structure to real beam steering applications, we
calculate the steering efficiency incorporating the absorption losses of our measured device.
We perform this calculation using simulated reflectance and phase at a wavelength of 8.6
µm due to the smoothly varying phase observed here; although a larger phase range is
predicted at shorter wavelengths, its sharp transition translates to a difficult realization of
intermediate phase values, and therefore we sacrifice some phase modulation in exchange
for necessary smoothness. The achievable efficiency is on average 1% up to ±30°,
presented in Figure 4.5d. We note that all calculations presented in Figure 4.5 were
calculated for an operation wavelength of 8.6 µm for ease of comparison.
4.2 Multi-Element Graphene-Gold Meta-Device for Active Beam Steering
The realization of active modulation of phase in graphene-gold metasurfaces exceeding
180° presented in the previous section opened an unprecedented capability to realize fully
electrically reconfigurable meta-devices for beam steering. In this section, we design and
fabricate a 28-element tunable meta-device for beam steering in the mid infrared, based on
the unit cell presented above. We use 28 elements for ease of experimental realization. An
optical image of the completed is presented in Figure 4.6a below. Multi-stage aligned
electron beam lithography is used to define the graphene-gold resonators and then
electrically isolate each pixel by using an oxygen reactive ion etch to remove the graphene
between them (See Appendix A for details). 750 nm spacing is used to minimize
electrostatic cross talk between elements, as shown in an SEM image in Figure 4.6b. A
final aligned lithography step is used to define 5 nm Ti/250 nm Au electrical contacts to
each isolated element.

74
a.

Graphene

Top 14 Contacts
750 nm
Electrical
Isola5on

50 nm
Gap

Graphene

Metasurface
Device

Reference Pads
400 μm

1 μm

No
Graphene

Figure 4.6: Fabricated tunable metadevice. (a) Optical microscope image of completed
device with 28 independently gate-tunable elements. Other dark regions correspond to
additional metasurface devices fabricated for performing a dose array to optimize the
design. Gold reference pads are included for measurement ease. (b) Zoomed in SEM image
of fabricated device showing gold resonators spaced by 50 nm and the electrical isolation
between pixels.
We take advantage of a blazed grating style metasurface, using linear phase gradients of
different pitches to redirect the reflected beam. These phase gradients approximate the saw
tooth shape of a conventional blazed grating, wherein the reflection angle is selected by
varying the pitch of the saw tooth. In the simplest implementation, we use the grating
equation:
d (sin α + sin β ) = mλ

(4.5)

where d is the pitch of the repeat unit, α the incident angle (normal incidence for cases
considered here), β the diffraction angle, λ the wavelength of incident light, and m the
diffraction order (here we seek the first order peak).
This allows us to easily switch between reflection angles by varying the voltages applied to
each pixel, and is more robust against phase errors (i.e., a phase range less than 2π). Two
examples of designs being experimentally pursed currently are presented in Figure 4.7.

10 μm

0°

25°

Intensity (a.u.)

18°
0° 105° 204°

64° 132° 204°

10 μm

Steering Angle (°)

Figure 4.7: Beam steering designs for reconfigurable meta-device. (a) A three-element
blazed grating style reflectarray with three phases of 0°, 105°, and 204° repeated across all
28 pixels. Steers to approximately 25°. (b) A four-element blazed grating style reflectarray
with four phases of 0°, 64°, 132°, and 204° repeated across 28 pixels. Steers to
approximately 18°. (c) Calculated steering angles for each configuration (a) and (b).

For the three-pixel repeat cell (d = 3 x 6.6 µm, λ = 8.5 µm) the grating equation yields a
steering angle of 25°. For the four-pixel repeat cell, (d = 4 x 6.6 µm, λ = 8.5 µm), the
grating equation yields a steering angle of 18°. These are in very good agreement with the
results of full wave simulations presented in Figure 4.7c. We utilize the full range of
achievable phases at 8.5 µm, with approximately equal spacing from 0° to 204°,
corresponding to Fermi energies between 0 eV and 0.5 eV that we experimentally realized
in the prior section with electrostatic gating. It is worth noting that, as discussed previously,
for phase ranges below 180°, it is not possible to realize a steered beam of greater intensity
than the side-lobes with steering error less than 1°.
Experimental work is ongoing with collaborators at Northrop Grumman to complete the
characterization of the electrically reconfigurable metadevice that I have fabricated.

76
4.3 Conclusions and Outlook
In conclusion, we have demonstrated for the first time electrostatic tunability of phase from
graphene gold antennas of 237° at a wavelength of 8.5 µm, more than 55° greater than has
been demonstrated in the mid-IR in a different materials system. We additionally
demonstrate phase modulation at multiple wavelengths, exceeding 200° from 8.50 to 8.75
µm. By calculating from antenna theory the fraction of power reflected to the desired angle
as opposed to spurious side-lobes, we show that this design will enable beam steering with
acceptable signal to noise ratio. We therefore conclude that this design is feasible for
reconfigurable metasurfaces. We fabricate a 28-element tunable meta-device based on this
design and present calculations for experimentally realizable beam steering configurations.
These are particularly interesting for applications to LIDAR, a portmanteau of light and
RADAR, which uses optical wavelengths to spatially map the environment with higher
spatial resolution than is possible using radio waves. In LIDAR systems currently used in
self-driving cars, a number of fixed-mount lasers and detectors are required to map the
car’s surroundings with sufficient speed and areal coverage. This results in very high costs.
By using reconfigurable meta-devices, a much faster and less expensive form of LIDAR
could be realized by electrically scanning reflected light over a wide angular range.

77
Chapter 5

FIELD EFFECT OPTOELECTRONIC MODULATION OF
QUANTUM-CONFINED CARRIERS IN BLACK PHOSPHORUS
“[Quantum mechanics] describes nature as absurd from the point of view of common
sense. And yet it fully agrees with experiment. So I hope you can accept nature as She is absurd.”
-- Richard Feynman
1. William S. Whitney*, Michelle C. Sherrott*, Deep Jariwala, Wei-Hsiang Lin, Hans A.
Bechtel, George R. Rossman, Harry A. Atwater, “Field Effect Optoelectronic Modulation
of Quantum-Confined Carriers in Black Phosphorus”, Nano Lett., 2017, 17 (1), pp 78–84
(*Equal author contributors)
DOI: 10.1021/acs.nanolett.6b03362
Few-layer black phosphorus is an appealing emerging van der Waals material, behaving
like a naturally occurring quantum well with large in-plane anisotropy. In this chapter, we
report measurements of the infrared optical response of thin black phosphorus under fieldeffect modulation. We interpret the observed spectral changes as a combination of an
ambipolar Burstein-Moss (BM) shift of the absorption edge due to band-filling under gate
control, and a quantum confined Franz-Keldysh (QCFK) effect, phenomena which have
been proposed theoretically to occur for black phosphorus under an applied electric field.
Distinct optical responses are observed depending on the flake thickness and starting carrier
concentration. Transmission extinction modulation amplitudes of more than two percent
are observed, suggesting the potential for use of black phosphorus as an active material in
mid-infrared optoelectronic modulator applications.
5.1 Introduction
The emergence of a variety of two-dimensional materials has spurred tremendous research
activity in the field of optoelectronics194-197. While gapless graphene can in principle exhibit
an optoelectronic response at wavelengths ranging from the far infrared to the ultraviolet,
its optoelectronic behavior is limited by a lack of resonant absorption and poor optical
modulation in the absence of one-dimensional confinement. On the other hand, the

78
semiconducting molybdenum- and tungsten-based transition metal dichalcogenides have
shown considerable prospects for visible frequency optoelectronics.

Yet while these

materials promise exciting new directions for optoelectronics and nanophotonics in the
visible range, they have limited response for lower energy, infrared light.
The isolation of atomically thin black phosphorus in recent years has bridged the
wavelength gap between graphene and transition metal dichalcogenides, as black
phosphorus is an emerging two-dimensional semiconductor material with an infrared
energy gap and typical carrier mobilities between those of graphene and transition metal
dichalcogenides.198-202 Since the first isolation of black phosphorus and demonstration of a
field effect device, numerous reports investigating the synthesis and optoelectronic
properties of this material have emerged, appropriately summarized in recent reviews.198,
199, 203-205

Likewise a number of reports have also appeared on the applications of black

phosphorus in fast photodetectors206, polarization sensitive detectors,207 waveguide
integrated devices208, multispectral photodetectors209, visible to near-infrared absorbers210
and emitters, 211-214 heterojunction215 and split gate p-n homojunction photovoltaics216,
gate-tunable van der Waals heterojunctions for digital logic circuits217, 218 and gigahertz
frequency transistors in analog electronics219. A majority of the studies on both the
fundamental optical properties of black phosphorus and applications in optoelectronic
devices have explored only the visible frequency range220-223. Therefore, little is known
about the intrinsic optical response of black phosphorus in the infrared range. As a narrow
band-gap semiconductor, much of the potential for black phosphorus lies in these infrared
optoelectronic applications – ranging from tunable infrared emitters224 and absorbers for
waste heat management/recovery225 to thermophotovoltaics226 and optical modulators for
telecommunications227. Theoretical investigations of black phosphorus have suggested
novel infrared optical phenomena, such as anisotropic plasmons228, 229, field-effect tunable
exciton stark shifts230, and strong Burstein-Moss231 and quantum-confined Franz-Keldysh
effects232 that promise to open new directions for both fundamental nanophotonics research
and applications. In this work, we report the first experimental observations of the infrared
optical response of ultrathin BP samples under field effect modulation. We observe

79
modulation of oscillations in the transmission spectra, which we attribute to a combination
of an ambipolar Burstein-Moss shift and quantum-confined Franz-Keldysh behavior.
5.2 Experimental Design
Measurements were performed on black phosphorous flakes that were mechanically
exfoliated in a glove box onto a 285 nm SiO2/Si substrate. We analyzed three flakes of 6.5
nm, 7 nm, and 14 nm thickness, determined by Atomic Force Microscopy (AFM), and
lateral dimensions of approximately 10 µm x 10 µm. A schematic of our experimental
setup is shown in Figure 5.1a. Standard electron beam lithography and metal deposition
methods were used to define Ni/Au electrodes to each exfoliated BP flake, described in
Appendix E. The samples were then immediately coated in 90 nm PMMA for protection
against environmental degradation. Once encapsulated in PMMA we observe minimum
degradation of our samples to ambient exposure as verified by Raman spectroscopy233 and
reported in literature precedent234. Transmission measurements were obtained via Fourier
Transform Infrared (FTIR) Spectroscopy. All optical measurements were done in a Linkam
cryo-stage at a pressure of 3 mTorr and a temperature of 80 K. First, a room-temperature
gate-dependent source-drain current was measured to extract approximate carrier densities
as a function of gate bias. Transmission spectra were then gathered at different gate
voltages applied between the flake and lightly doped Si substrate. We note that in our
setup, the silicon substrate is grounded and BP experiences the applied voltage, so the sign
of the applied voltages is reversed from the more common convention. In order to probe
the electric field- and charge-carrier-dependent optical properties of the BP, all spectra
were normalized to the zero-bias spectrum. The measured infrared optical properties result
primarily from the unique band structure of thin BP, schematically depicted in Figure 5.1b.
Quantized inter sub-band transitions provide the primary contribution to its zero-field
optical conductivity.

Figure 5.1: (a) Schematic illustration of transmission modulation experiment. Broadband
mid-IR beam is transmitted through black phosphorus sample. Variable gate voltage
applied across SiO2 modulates transmission extinction. (b) Schematic band diagram of fewlayer black phosphorus with subbands arising from vertical confinement
5.3 Tuning of Infrared Absorption in Few-Layer BP
5.3.1 BP Thickness #1
We first present results for the 7 nm thick BP flake, in Figure 5.2. An optical image is
shown in Figure 5.2e. FTIR spectra were taken using a Thermo Electron iS50 FTIR
spectrometer and Continuum microscope for which the light source is a broadband,
unpolarized tungsten glow-bar. To improve signal/noise and minimize spatial drift, we
surrounded the sample with a 150 nm thick gold reflector which also served as the gate
electrode. The extinction modulation results are presented in Figure 5.2a. We observe two
major features in this flake at energies of 0.5 eV (I) and 0.9 eV (II). The dip in extinction at
0.5 eV is present for both positive and negative gate voltages, as the sample is increasingly
hole or electron doped, respectively. It grows in strength as the doping is further increased
at larger gate-biases. The same trend is true for the feature at 0.9 eV, where a smaller peak
in extinction modulation is observed for both polarities of voltage. This peak also is
strengthened as the gate voltage is increased to +/- 120V. To gain insights into this
behavior, we measure gate-dependent transport, using a scheme in which a positive bias

81
induces hole-doping, and a negative bias introduces electron-doping. We observe
ambipolar transport at room temperature and atmospheric conditions, as shown in Figure
5.2b. Similar results have been shown in the literature with on/off ratios of ~104 for flakes
thinner than the one considered here, at low temperature.215, 235 From this, the CNP is
observed to be at 20 V, and, using a standard parallel plate model the unbiased, n-type
carrier concentration is estimated to be 1.5·1012 cm-2.

Figure 5.2: Gate modulation of lightly doped 7 nm flake. (a) FTIR transmission
extinction vs photon energy normalized to zero bias. (b) Source-drain current vs gate
voltage. Ambipolar conduction is seen. (c) Calculated optical conductivity of a 4.5 nm
thick BP flake at different carrier concentrations, normalized to the universal conductivity
of graphene. No field effects included. (d) Schematic of electronic band structure and
allowed interband transitions at different voltages. (e) Optical microscope image of flake.
Scale bar is 10 µm.
We can interpret our spectroscopic results with consideration of a Burstein-Moss shift,
which is a well-known phenomenon in chemically doped narrow-band gap semiconductor
materials. This effect, which changes the optical band gap of a semiconductor, results from
band-filling. As the charge carrier density is increased and the Fermi level moves into the
conduction or valence band, there are fewer unoccupied electronic states available, and

82
optical transitions to the occupied states are disallowed. This results in a decrease in the
optical conductivity of the material at the energy of the transition, and is manifest in
measurements as a decrease in absorption236, 237. Because this flake exhibits ambipolar
transport behavior, we can explain both features (I) and (II) as arising from an ambipolar
BM effect. At zero applied bias, the flake is very lightly doped, and all optical transitions
are allowed. As a positive gate voltage is applied and the sample becomes hole doped,
lower energy optical transitions become disallowed and the absorption of the flake
decreases. Feature (I) corresponds to the band filling effect of the E11 intersubband
transition, and feature (II) corresponds to the blocking of the E22 intersubband transition,
shown schematically in Figure 2d. For a negative gate voltage, as the sample is electrondoped and the Fermi level moves into the conduction band, the E11 and E22 transitions are
again blocked due to band filling, resulting again in a decrease in absorption. To support
this explanation, we calculate the optical conductivity for the flake, as shown in Figure 5.2c
to identify the appropriate energies of the intersubband transitions. To do so, we use the
Kubo method described by Tony Low, et al.231 The observed transitions energies are
consistent with theoretical models that predict an increase in band gap energy from the bulk
0.3 eV value as the material thickness decreases to several layers or less.222 This deviation
from the bulk band gap indicates the influence of vertical confinement of charge carriers, a
feature of the two-dimensionality of the material. We note that these transition energies
suggest that the true thickness of our sample is thinner than 7 nm, at approximately 4.5 nm.
This apparent variation between true and observed thickness from AFM topography is a
result of surface oxidation, as has been recently reported.238 The surface oxide on our
samples is expected to be between 1-2 nm on either side, which appears inevitable despite
following best practices, and is stable with no measurable degradation over an ambient
exposure of > 18 hrs in ambient. It is noteworthy that we observe extinction modulation at
relatively high photon energies, indicative of very large charge modulation taking place in
the fraction of the BP nearest to the silicon oxide interface, with an accumulation/depletion
layer that decays over the remainder of the flake. This is consistent with in-depth
calculations of charge screening in BP using the Thomas-Fermi model done previously,
reported by Tony Low, et al.228 We estimate this screening length to be of order 3 nm for

83
our devices. This ambipolar, gate-modulated Burstein-Moss shift is the first observed in a
two-dimensional semiconductor, to the best of our knowledge.
5.3.2 BP Thickness #2
We next present data for a BP flake of 14 nm thickness in Figure 5.3. An optical image is
shown in Figure 3e. Extinction measurements are again taken with an iS50 FTIR
spectrometer and Continuum microscope for which the light source is a tungsten glowbar.
These results are presented in Figure 5.3a. Four prominent features are observed to
modulate under application of a gate voltage, at energies of 0.35 eV, 0.41 eV, 0.55 eV, and
0.75 eV. As in the previous sample, they grow in strength with increased magnitude of the
gate voltage, regardless of polarity. To better understand this behavior, we again measure
gate-dependent transport, reported in Figure 4b. We observe ambipolar transport
characteristics as in the previous flake, centered about a conductance minimum at
approximately 20 V. Again using a parallel-plate capacitor model, we estimate an unbiased
n-type carrier density of 1.5·1012 cm-2 for a 20 V CNP.

Figure 5.3: Gate modulation of lightly doped 14 nm flake. (a) FTIR transmission
extinction vs photon energy normalized to zero bias (b) Source-drain current vs gate

84
voltage. Ambipolar conduction is seen. (c) Calculated optical conductivity of a 10 nm
thick BP flake at different carrier concentrations, normalized to the universal conductivity
of graphene. No field effects included. (d) Schematic of electronic band structure and
allowed interband transitions at different voltages. (e) Optical microscope image of flake.
Scale bar is 10 µm.
We propose that the optical modulation for this sample also results from an ambipolar
Burstein-Moss effect. In this case, as the Fermi energy is moved into the conduction band
of the BP under negative bias, transitions become disallowed and the transmission is
increased at each of the E11 – E44 energies. Under positive bias, as the Fermi energy is
moved into the valence band, the band-filling effect of opposite charge carrier type results
in negative extinction modulation peaks at the same energies of transitions E11 – E44. As in
the previous sample, we estimate an oxide layer of 1-2 nm has grown on our BP on either
surface. Based on optical conductivity calculations presented in Figure 3c, we again
estimate the adjusted thickness of our flake to be less than that measured by AFM, at
approximately 10 nm. We further note that for this sample, the measurement extended
beyond the area of the flake, to cover the flake and an area of bare silicon oxide roughly
eight times the flake are. We thus suggest that the true modulation strength of this device is
of order six percent, not the 0.75 percent indicated by the modulation of the entire area.
5.3.3 BP Thickness #3
Finally, results for the 6.5 nm thick flake are reported in Figure 5.4, for which an optical
image is shown in Figure 5.4e. Unlike the previous two flakes, transmission measurements
for this sample were taken using a Nicolet Magna 760 FTIR spectrometer coupled to a NicPlan infrared microscope on infrared Beamline 1.4.3 at the Advanced Light Source (ALS)
at Lawrence Berkeley National Laboratory. This allowed us to perform measurements
using a high brightness, diffraction-limited infrared beam, which is beneficial for
accurately analyzing the small-area BP samples attainable by mechanical exfoliation. In
contrast to the previous measurements, the incident light was elliptically polarized due to
the synchrotron source, with an intensity ratio of two to one.

85
Figure 5.4a shows the primary result of this experiment, which is the modulated extinction
of the sample at different voltages, normalized to the zero-bias extinction spectrum. Three
prominent features are observed in these spectra. First, under negative applied bias (i.e.:
when the sample is being depleted of holes), a negative peak (I) appears in transmission
near 0.45 eV, which grows in amplitude and broadens to lower energies as the magnitude
of the bias increases. Second, under positive applied bias (i.e., when the sample is being
increasingly hole-doped), a positive peak (II) appears in transmittance near 0.5-0.7 eV.
Lastly, these two effects, which we propose to depend on the Fermi level, are superimposed
with an oscillatory feature (III) that varies with the magnitude of the applied field, but not
its polarity, and which is most clearly visible in the negative bias spectra in the 0.5 - 0.7 eV
range.

Figure 5.4: Gate modulation of a heavily doped 6.5 nm flake. (a) FTIR transmission
extinction vs photon energy normalized to zero bias (b) Source-drain current vs gate
voltage. Only hole-type conduction is seen. (c) Schematic of electronic band structure
and allowed interband transitions at different voltages. (d) Schematic representation of
quantum confined Franz-Keldysh Effect (e) Calculated optical conductivity of a 6.5 nm
thick BP flake at different carrier concentrations, normalized to the universal conductivity
of graphene. No field effects included (f) Optical microscope image of flake. Scale bar is
10 µp.

86
To better understand these results, transport measurements were again taken at room
temperature under ambient conditions, as shown in Figure 5.4b. The gate dependence of
the conductance indicates that, unlike the previous samples, this BP flake was initially
heavily hole-doped, as ambipolar transport is not observed and only hole-type conduction
is seen even at large negative bias.
Due to the distinct character of each feature and their relation to the transport
measurements, we can understand the overall spectral shifts as arising from a combination
of a Burstein-Moss (BM) shift and a quantum confined Franz-Keldysh (QCFK) effect, both
of which have been predicted theoretically for gated BP flakes of this thickness.232 In the
bulk limit, the Franz-Keldysh effect refers to electron and hole wavefunctions leaking into
the band gap, as described by Airy functions. This behavior introduces oscillatory features
to the interband absorption spectrum, and redshifts the band edge. In confined systems, the
quantum-confined Franz-Keldysh effect similarly modulates intersubband transitions.239
As confinement becomes stronger and excitonic effects dominate, this phenomenon
eventually gives way to the quantum-confined Stark effect. Because our flake exceeds a
thickness of ~4 nm, we expect excitonic effects to be weak and therefore will not focus our
discussion on the quantum-confined Stark effect or a normal-to-topological phase transition
in our analysis.222, 223, 230
We suggest that peak (I) at 0.45 eV can be described by the onset of j = 1 intersubband
transitions as the material is depleted of holes at negative gate voltages and the valence
band is un-filled, in agreement with our transport measurements. We further suggest that
peak (II) can be described primarily by the suppression of j = 2 inter sub-band transitions as
more holes are accumulated in the flake at positive gate voltages. This behavior is shown
schematically in Figure 4d, and is again supported by calculations of the optical
conductivity of the flake for various doping levels, shown in Figure 4e. Our experimental
results correspond to modulation of the calculated intersubband transitions only in part,
suggesting that a simple Burstein-Moss shift is insufficient to explain this measurement.
From these results, we assign the band gap energy of our flake to be approximately 0.4 eV.

87
Unlike our previous samples, the optical data indicates minimal oxide formation, as the E11
and E22 transition energies match well to theory for a 6.5 nm thick BP quantum well.
Given we do not see the charge neutral point in transport, we do not assign a carrier density
to this flake, but can say that with a charge neutral point of greater than -80 V, its p-type
carrier density must be greater than 6·1012 cm-2.
We suggest that quantum-confined Franz-Keldysh effects lead to the appearance of the
additional oscillatory spectral features we observe.

Specifically, we point to the

oscillations in the negative voltage extinction curves at energies above 0.5 eV – where
Burstein-Moss considerations would predict zero modulation – and in the positive voltage
extinction curves both in that same range – where Burstein-Moss behavior would predict
only a single dip in extinction centered at the 0.575 transition energy – and at 0.45 eV.
This oscillatory modulation increases with bias magnitude, but does not depend
significantly on the sign of the bias – behavior which is consistent with shifting of the
overlap of the first and second conduction and valence sub-band wavefunctions, as
described by the quantum-confined Franz-Keldysh effect. This behavior is investigated
theoretically for gated BP by Charles Lin, et al.232 In addition, under a sufficiently strong
electric field, hybrid optical transitions between sub-bands of different index (eg: Ev1 to
Ec2) that are nominally forbidden at zero field become allowed. In total, quantum-confined
Franz-Keldysh effects in thin BP are expected to lead to behavior including redshifting of
intersubband transitions, modification of intersubband selection rules (allowing hybrid
transitions), or oscillatory, Airy function modulation of the absorption edge, all of which
can be considered as consistent with our experimental observations. However, further
theoretical work is needed to understand this effect satisfactorily; the same authors provide
evidence in a more recent, experimental report that hybrid transitions may occur with zero
applied field as well.240 Interestingly, we see no evidence of a tunable plasma edge;
investigations in the long-wave infrared wavelength range with larger samples would likely
be needed to observe this feature. We suggest that far-infrared measurements on
nanoresonators fabricated in few-layer BP might reveal gate-tunable plasmons, as was seen
in monolayer graphene samples in Chapter 2.

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The clear appearance of the QCFK effect in this measurement distinctly differs from our
previous two samples, indicating that BP quantum wells of similar thickness may have very
different optical responses. We suggest that the primary reason for this is that this flake is
very heavily doped under zero bias, whereas our previous measurements were performed
on nearly intrinsic flakes. In particular, in the intrinsic case, field strength and carrier
concentration vary proportionally (i.e., under larger bias, there is a larger carrier
concentration, and vice-versa). To the contrary, in our heavily doped sample, this
proportionality is absent, leading to potentially competing effects and the clear emergence
of oscillatory features. It is also worth noting that, while we see no clear evidence of the
QCFK effect in our first two experiments, it is possible that the large BM shift is simply
dominant over the QCFK effect, making the latter effect difficult to observe, or that our
increased noise prevents the effect from obviously manifesting. A complete theoretical
framework that addresses the interplay between zero-bias carrier concentration and fieldeffect has not yet been developed, and is beyond the scope of this paper. We also note that,
while we see no clear evidence of excitonic effects, and it has been suggested theoretically
and experimentally that such effects should not be present in flakes of this thickness, we do
not rule out the possibility that they may be influencing our results.
We note that because of the complicated polarization state of incident light from the
synchrotron, and because a previous study has extensively studied this effect
experimentally241, we do not address in detail the anisotropic optical properties of BP.
However, due to the primary contribution to the optical conductivity arising from the σxx
component, we argue that the only effect of elliptically polarized light is to scale the
observed modulation.
5.4 Conclusions and Outlook
In conclusion, we have demonstrated experimentally that ultra-thin black phosphorus
exhibits widely tunable, quantum well-like optical properties at mid-infrared wavelengths.
In 7 and 14 nm, lightly doped flakes, we observe for the first time an ambipolar BursteinMoss shift of intersubband transitions, which also varies with thickness as these transition

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energies are changed. In a heavily doped 6.5 nm thick BP flake, modulation of infrared
transmission takes place as a result of both a Burstein-Moss shift and additional, quantumconfined Franz-Keldysh effects. While our results verify some of the recent theoretical
predictions about the electro-optical effects in few-layer BP, they also report new behavior
and serve as motivation to further understand the BP optical response as function of sample
thickness, doping and field. Our results indicate that BP is both an interesting system for
exploring the fundamental behavior of quantum-confined carriers in two-dimensional
semiconductors under field-effect modulation, and a promising candidate for tunable midinfrared optical devices. While we do not see evidence of a plasma edge in the BP, we
suggest that this should be present at lower energies; by adapting the nanoresonator
geometry in Chapter 2, this may be measured. Moreover, due to the different effective
masses along each crystallographic axis, these plasmons should appear at different
wavelengths. It is possible that for certain carrier concentrations, the permittivity of the BP
will be positive along one axis and negative along the other, supporting hyperbolic plasmon
polaritons.

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Chapter 6

ELECTRICAL CONTROL OF LINEAR DICHROISM IN BLACK
PHOSPHORUS FROM THE VISIBLE TO MID-INFRARED
“Thoroughly conscious ignorance is the prelude to every real advance in science.”
– James Clerk Maxwell

1. Michelle C. Sherrott*, William S. Whitney*, Deep Jariwala, George R. Rossman,
Harry A. Atwater, “Electrical Control of Linear Dichroism in Black Phosphorus from the
Visible to Mid-Infrared”, (*Equal author contributors)
arXiv:1710.00131
The incorporation of electrically tunable materials into photonic structures such as
waveguides and metasurfaces enables dynamic control of light propagation by an applied
potential. While many materials have been shown to exhibit electrically tunable
permittivity and dispersion, such as transparent conducting oxides (TCOs) and III-V
semiconductor quantum wells, these materials are all optically isotropic. In this chapter, we
report the first known example of electrically tunable linear dichroism, observed here in
few-layer black phosphorus (BP). Building on results in Chapter 5, we measure active
modulation of the linear dichroism from the mid-infrared to visible frequency range,
suggesting BP is an ideal material system for actively controlling the complex polarization
state of light – or even the propagation direction of surface waves – over a broad range of
wavelengths. This novel phenomenon is driven by anisotropic quantum-confined Stark and
Burstein-Moss effects and field-induced forbidden-to-allowed optical transitions, which we
carefully separate via different gating schemes (something not addressed in the previous
chapter). Moreover, we observe that these effects generate near-unity modulation of BP
absorption for certain material thicknesses and photon energies. This suggests BP is a
promising material for active infrared (and visible) nanophotonics.

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6.1 Introduction
As photonic structures for controlling the near- and far-field propagation of light become
increasingly complex and compact, the need for new materials that can exhibit unique,
strong light-matter interactions in the ultra-thin limit is growing rapidly. Ultrathin van der
Waals materials are especially promising for such applications, as they allow for the control
of light at the atomic scale, and have properties that can be modulated actively using an
external gate voltage56, 242. Of these, few-layer black phosphorus (BP) is particularly
noteworthy due to its high electronic mobility, and a direct band gap that can be tuned as a
function of thickness from 0.3 eV to 2 eV34, 243. This has enabled the realization of
numerous optoelectronic devices with high performance, including photodetectors that can
be easily integrated with other photonic elements such as waveguides208, 244-248. In addition
to this static control, recent works using electrostatic gating and potassium ions have shown
that the electronic band gap of BP may be tuned by an electric field. 249-251
One of the most salient features of BP is its large in-plane structural anisotropy, leading to a
polarization-dependent optical response229, 252, 253 as well as mechanical254, thermal255, and
electrical transport characteristics256,

257

that vary with in-plane crystallographic

orientation258. This optical anisotropy corresponds to a large, broadband birefringence259,
wherein the distinct optical index of refraction along each axis leads to a phase delay
between polarization states of light. Moreover, mirror-symmetry in the x-z plane forbids
intersubband optical transitions along the zigzag axis, and as a result, BP exhibits
significant linear dichroism, wherein the material absorption depends strongly on the
polarization state of exciting light253, 260.
6.2 Experimental Isolation of Electro-Optic Effects
In this work, we experimentally demonstrate that the application of a static electric field
enables the modulation of the linear dichroism of few-layer black phosphorus (BP). This
response – which approaches near-unity modulation of the BP oscillator strength for some
thicknesses and photon energies – is achieved by active control of quantum-confined Stark
and Burstein-Moss effects, and of quantum-well selection rules. We observe anisotropic

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modulation from the visible to mid-infrared (mid-IR) spectral regimes, behavior not seen in
traditional electro-optic materials such as graphene261, transparent conducting oxides262, 263,
silicon264, and quantum wells265. This opens up the possibility of realizing novel photonic
structures in which linear dichroism in the van der Waals plane can be continuously tuned
with low power consumption, because the switching is electrostatic in nature. By
controlling optical losses in the propagation plane, for example, efficient in-plane beam
steering of surface plasmon polaritons or other guided modes is enabled. Moreover, a
tunable polarizer could be realized by the tuning of the polarization state of light absorbed
in a resonant structure containing BP. Because this modulation is strongest at infrared
wavelengths, it could also enable control of the polarization state of thermal radiation266-268.
In order to probe and distinguish the electro-optical tuning mechanisms evident in fewlayer BP, we used a combination of gating schemes wherein the BP either floats in an
applied field or is contacted, as shown in Fig. 6.1a and described further in Appendix E.
Polarization-dependent optical measurements are taken aligned to the crystal axes, in order
to probe the structural anisotropy shown in Fig. 6.1b. This enables us to isolate the
contribution of charge-carrier density effects – i.e., a Burstein-Moss shift – and external
field-effects – i.e., the quantum-confined Stark effect and control of forbidden transitions in
the infrared – to the modulation of linear dichroism, qualitatively illustrated in Figures 6.1c
and 6.1d231, 249, 269, 270. In the anisotropic Burstein-Moss (BM) shift, the optical band gap of
the material is changed as a result of band filling and the consequent Pauli-blocking of
intersubband transitions. As the carrier concentration of the sample is changed, the Fermi
level moves into (out of) the conduction or valence band, resulting in a decrease (increase)
of absorptivity due to the disallowing (allowing) of optical transitions271, 272. Because
intersubband optical transitions are only allowed along the armchair axis of BP, this
modulation occurs only for light polarized along this axis. In the quantum-confined Stark
Effect, the presence of a strong electric field results in the leaking of electron and hole
wave functions into the band gap as Airy functions, red-shifting the intersubband
transitions energies35. In quantum well structures, this red-shifting is manifested for
multiple subbands, and therefore can be observed over a wide range of energies above the

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band gap. To assess the gate-tunable anisotropy of the optical response of BP, the armchair
and zigzag axes, illustrated in Fig. 6.1b, of the samples considered are identified by a
combination of cross-polarized visible microscopy, described in Appendix E, and either
polarization-dependent Raman spectroscopy or infrared measurements, described below.
Representative Raman spectra are presented for the visible frequency sample on SrTiO3 in
Figure 6.1e. The optically active armchair axis exhibits a maximum intensity of the Ag2
resonant shift at 465 cm-1, whereas this is a minimum for the zigzag axis273.

Figure 6.1: Anisotropic electro-optical effects in few-layer BP. (a) Schematic figure of
infrared modulation devices. Few-layer BP is mechanically exfoliated on 285 nm SiO2/Si
and then capped with 45 nm Al2O3 by ALD. A semitransparent top contact of 5 nm Pd is
used to apply field (VG1) while the device floats and 20 nm Ni/200 nm Au contacts are used
to gate (VG2) the contacted device. (b) Crystal structure of BP with armchair and zigzag
axes indicated. (c) Illustration of quantum-confined Stark effect and symmetry-breaking
effect of external field. Under zero external field, only optical transitions of equal quantum
number are allowed. An external field tilts the quantum well-like energy levels, causing a
red-shifting of the optical band gap and allowing previously forbidden transitions. (d)
Illustration of anisotropic Burstein-Moss shift in BP. Intersubband transitions are blocked
due to the filling of the conduction band. Along the ZZ axis, all optical transitions are
disallowed regardless of carrier concentration. (e) Raman spectra with excitation laser
polarized along AC and ZZ axes. The strength of the Ag2 peak is used to identify crystal
axes.

94
To illustrate the mechanisms of tunable dichroism of BP in the mid-infrared, we measure
modulation of transmittance using Fourier-Transform Infrared (FTIR) microscopy as a
function of externally (VG1) or directly applied bias (VG2), presented for a 3.5 nm thick
flake, as determined from atomic force microscopy (AFM), in Figure 6.2. Fig. 6.2a presents
the raw extinction of the flake along the armchair axis at zero bias, obtained by normalizing
the armchair axis to the optically inactive zigzag axis. A band edge of approximately 0.53
eV is measured, consistent with a thickness of 3.5 nm. A broad, weak shoulder feature is
observed at approximately 0.75 eV. The corresponding calculated optical constants for the
flake are presented in Figure 6.2c for comparison.

Figure 6.2: Electrically tunable linear dichroism: quantum-confined Stark and BursteinMoss effects and forbidden transitions. (a) Optical image of fabricated sample. (b) Zerobias infrared extinction of 3.5 nm flake, polarized along armchair (AC) axis. (c) Calculated
index of refraction for 3.5 nm thick BP with a Fermi energy at mid-gap. (d) Modulation of
BP oscillator strength with field applied to floating device, for light polarized along the AC
axis. (e) Corresponding modulation for light polarized along the zigzag (ZZ) axis. (f)
Modulation of BP oscillator strength with gating of contacted device, for light polarized
along the AC axis. (g) Corresponding modulation for light polarized along the ZZ axis.

95
Figures 6.2d and 6.2e illustrate the influence of an external field on the extinction of BP
with carrier concentration held constant (i.e., the BP is left floating). The extinction data for
each voltage is normalized to the zero bias case and to the peak BP extinction seen in
Figure 6.2b, to obtain a modulation strength percentage that quantifies the observed
modulation of the BP oscillator strength. We note that this normalization scheme
underestimates modulation strength away from the band edge, where BP extinction is
maximal. Along the armchair axis, presented in Fig. 6.2d, two modulation features are
measured near photon energies of 0.5 and 0.8 eV. We explain the first feature at 0.5 eV as
arising from a shifting of the BP band edge due to the quantum-confined Stark effect. At
negative bias, the band gap effectively shrinks and this is manifest as a redistribution of
oscillator strength near the band edge to lower energies. As a result, an increase in
absorptance is measured below the zero-bias optical band gap, and a decrease is seen above
it. At positive bias, this trend is weakened and reversed. We propose two explanations for
this asymmetry: the first is the influence of electrical hysteresis, and the second is the
presence of a small internal field in the BP at zero bias, which has been observed in
previous works on the infrared optical response of few-layer BP253.
The second, higher energy feature observed in the measured spectrum does not correspond
to any predicted intersubband transition. Rather, we propose it arises due to the allowing of
an optical transition that was previously forbidden by quantum-well selection rule
constraints dictated by symmetry (i.e., only transitions of equal quantum number are
allowed under zero field231). We note that this feature is present in the 0 V extinction
spectrum, consistent with a zero-bias internal field. As the symmetry is further broken with
an externally-applied electric field, this transition is strengthened. Under positive bias, the
internal and external fields are in competition, resulting in minimal change. This
suppressed modulation can also be attributed to hysteresis, as before.
In Figure 6.2e, no modulation is measured for any applied bias for light polarized along the
zigzag axis. This can be well understood due to the dependence of the Stark effect on the
initial oscillator strength of an optical transition; because no intersubband optical transitions

96
are allowed along this axis, the field effect is weak. Similar behavior has been observed in
excitons in ReS2 based on an optical Stark effect274. Moreover, while the externally applied
field can allow ‘forbidden’ transitions along the armchair axis by breaking the out-of-plane
symmetry of the quantum well, in-plane symmetry properties and thus the selection rule
precluding all zig-zag axis intersubband transitions are unaffected. This selection rule and
the corresponding symmetry properties have been previously described 257.
In Figures 6.2f and 6.2g, we present the complementary data set of tunable dichroism
measurements due to a directly applied gate bias with electrical contact made to the BP in a
standard field-effect transistor (FET) geometry. Here, we observe modulation dominated
by carrier concentration effects. At the band gap energy of approximately 0.53 eV, a simple
decrease in absorptance is observed at negative and large positive biases, consistent with an
ambipolar BM shift. Unlike the results of applying field while the BP floats, no modulation
of the forbidden transition at 0.75 eV is observed; this is explained in part due to the
screening of the electric field due to the carrier concentration modulation. We additionally
may consider the possibility that this optical transition is disallowed by Pauli-blocking
effects, negating the symmetry-breaking effect of the directly applied field. As in the case
for the floating BP measurement, no modulation is observed along the zigzag axis.
6.3 Thickness-Dependent Tunability of Optical Response
The anisotropic electro-optical effects described above change character rapidly as the BP
thickness – and hence band gap and band structure – is varied. Figure 6.3 presents
analogous results on a flake of 8.5 nm thickness, determined by AFM, for which an optical
image is presented in Fig. 6.3a. Due to the increased thickness, the energy separation
between subbands is smaller, resulting in a narrower free-spectral range between
absorptance features measured in the zero-bias spectrum, presented in Fig. 6.3b and for
which corresponding calculated optical constants are presented in Fig. 6.3c. Results for
modulation by an external field with the BP left floating are presented in Fig. 6.3d. As in
the thin flake, substantial modulation of the absorptance at each intersubband transition is
observed due to the QCSE red-shifting the energy of the subbands. Due to the large Stark

97
coefficient in BP – which increases with thickness in the few-layer limit – absorption is
nearly 100% suppressed, resulting in an approximately isotropic optical response from the
material251, 275. Unlike the previous sample, modulation of forbidden transitions is not
apparent; all features correspond to transitions measured in the 0 V normalization scheme
as well as the calculated optical constants for a thickness of 8.5 nm. As before, no
modulation is seen along the zigzag axis. In Fig. 6.3e, the modulation for directly gated,
contacted BP is shown. The observed modulation – a reduction in extinction centered at
each of the calculated intersubband transition energies – is relatively weak and does not
persist to high photon energies. This suggests that the dominant modulation mechanism is
the ambipolar BM shift, rather than the QCSE.

Figure 6.3: Variation of modulation with BP thickness. (a) Optical image of fabricated 8.5
nm sample. (b) Zero-bias extinction of 8.5 nm flake, polarized along AC axis. (c)
Calculated index of refraction for 8.5 nm thick BP. (d) Modulation of BP oscillator strength
with field applied to floating device, for light polarized along the AC axis. (e) Modulation
of BP oscillator strength with gating of contacted device, for light polarized along the AC
axis.
Additional data at lower energies is presented in Figure 6.4, more clearly illustrating the
tuning of the band gap energy of this sample around 0.35 eV. This was done using a KBr
beamsplitter instead of CaF2 that was used for the rest of the measurements, allowing a
better measurement at lower energies.

Figure 6.4: Lower photon energy spectra for the 8.5 nm flake. Modulation of BP oscillator
strength with field applied to floating device, for light polarized along the AC axis,
normalized to the maximum oscillator strength as previously.
6.4 Visible-Frequency Gate-Tunability
Finally, in Figure 6.5 we present results of gate-tunable dichroism at visible frequencies in
a 20 nm thick flake, comparable to those considered for infrared modulation. A new device
geometry is used to enable transmission of visible light, shown schematically in Fig. 6.5a
and in an optical image in Fig. 6.5b. In this configuration, a SrTiO3 substrate is utilized to
allow transmission-mode measurements at visible wavelengths. A symmetric gating
scheme is devised based on semi-transparent top and back gate electrodes of 5 nm Ni, as
described in Appendix E. Only an applied field, floating BP measurement is utilized, as
band-filling effects should be negligible at this energy range. In Fig. 6.5c, we present
modulation results from 1.3 to 2 eV. Due to the QCSE, modulation is observed up to 1.8
eV, corresponding to red light. Thus we demonstrate that electro-optic modulation of
linear dichroism is possible across an extraordinarily wide range of wavelengths in a single
material system, enabling multifunctional photonic devices with broadband operation.

100

Figure 6.5: Modulation in the visible. (a) Schematic figure of visible modulation device.
Few-layer BP is mechanically exfoliated on 45 nm Al2O3/5 nm Ni on SrTiO3 and then
coated with 45 nm Al2O3. A 5 nm thick semitransparent Ni top contact is used. (b) Optical
image of fabricated sample with 20 nm thick BP. Dashed white line indicates the boundary
of the top Ni contact. (c) Modulation of extinction with field applied to floating device, for
light polarized along the AC axis. (d) Corresponding modulation for light polarized along
the ZZ axis. (e) Calculated index of refraction for 20 nm thick BP for the measured
energies. (f) Calculated imaginary index of refraction of several thicknesses of BP from the
infrared to visible.
6.5 Conclusions and Outlook
The decay of BP intersubband oscillator strength at higher photon energies provides a
spectral cutoff for QCSE-based modulation, but for 5 nm BP or thinner this oscillator
strength is strong through the entire visible regime, as illustrated in Fig. 6.5f. We thus
suggest that in very thin BP, strong modulation of absorption and dichroism is possible to
even higher energies. By selecting a flake of 2 nm, for example, tunable linear dichroism is
possible up to 3 eV from the band gap energy of 0.75 eV. A higher density of features,
beginning at lower energies, may be introduced by utilizing a thicker flake, with slightly
decreased modulation strength, as seen for 5 and 10 nm thickness flakes. We also note that

101
by substituting graphene top and bottom contacts or utilizing nanophotonic techniques to
focus light in the BP, higher absolute modulation strength could be easily realized.
This phenomenon is in stark contrast to the gate-tunability of the optical response of other
2D materials, where substantial modulation is typically constrained to the narrowband
energy of the primary exciton, as in MoS2 and WS2242, 276. In another van der Waals
materials system, monolayer graphene, tunability is accessible over a broader wavelength
range due to the Pauli-blocking of optical transitions at 2EF; however, this is limited to the
range over which electrostatic gating is effective, typically between EF ~ 0 to EF ~ 0.5 eV56,
277

. Moreover, these materials are not dichroic or birefringent in-plane, and so BP offers a

novel phenomenon that can be taken advantage of to realize previously challenging or
impossible photonic devices. The same restriction is true of bulk tunable materials such as
quantum wells, transparent conducting oxides, and transition metal nitrides.
In summary, we have demonstrated broadly tunable linear dichroism in few-layer black
phosphorus. We can explain this modulation as arising from a combination of quantumconfined Stark effects, ambipolar Burstein-Moss effects, and the allowing of forbidden
optical transitions by the symmetry-breaking effects of the applied electric field. We
identify the different physical mechanisms governing this tunability by comparing the
modulation response from a dual gate wherein the BP is left floating to a single gate
directly applied to the BP, leading to modulation of carrier concentration. By varying the
thickness, and therefore band structure of the BP, we see that it is possible to control the
spectroscopic modulation as well as the dominant physical mechanisms of modulation. We
suggest that this phenomenon is a promising platform for controlling the in-plane
propagation of surface or waveguide modes, as well as for polarization-switching,
reconfigurable far-field metasurfaces. These applications are particularly promising in light
of our observation that BP absorption can be modulated from anisotropic to nearly isotropic
in-plane. Because van der Waals materials can be easily integrated into photonic devices,
this promises to introduce new functionalities that cannot be realized by conventional
electro-optic materials.

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Chapter 7

PERSPECTIVE AND FUTURE WORKS
"No man should escape our universities without knowing how little he knows."
– J. Robert Oppenheimer
In this thesis, we have commented on two van der Waals materials, graphene and few-layer
black phosphorus, as promising materials for active nanophotonic devices in the midinfrared. We have made progress to create a complete ‘tool-kit’ for controlling all aspects
of infrared light in absorption, reflection, and emission using graphene nanostructures. We
have additionally introduced few-layer black phosphorus as a promising new material for
actively tunable nanophotonic structures from the visible to mid-infrared based on its
natural quantum well electronic band structure. We also explored the in-plane optical
anisotropy of BP, which yields a tunable linear dichroism, the first material to show such a
feature to the best of our knowledge. In this chapter, we extend these concepts and present
some future directions for research on van der Waals materials for nanophotonics. We
additionally make a brief comment on the long-term viability of both materials in
commercial technology. Finally, we note that these nanophotonic approaches are applicable
to other van der Waals systems, including semiconducting transition metal dichalcogenides
(TMDCs), and present a method for enhancing absorption in monolayer WS2.
7.1 Graphene Research
Fundamental research on graphene at the lab scale has largely moved beyond the basic
physics problems into more applied topics, as well as the development of heterostructures
that take advantage of graphene’s unique properties in combination with other van der
Waals materials (semiconducting, superconducting, and insulating). This is allowing for an
in-depth study of van der Waals/low-dimensional quasiparticles, their coupling, and their
response to an external bias278. Moreover, graphene can be easily incorporated as a semitransparent electrical contact in many devices based on other van der Waals materials,

103
which may be useful for integrated optoelectronic devices (e.g. LEDs and photovoltaics
may benefit from such a device geometry)279. As new methods for growing large-scale 2D
materials, such as metal-organic chemical vapor deposition for transition metal
dichalcogenides, mature, there will be new opportunities for commercialization of devices
based on such heterostructures280, 281. So, as the research on other van der Waals materials
matures, new opportunities for graphene may emerge.
In addition, the tunable optical properties of graphene in the mid-infrared discussed in this
thesis may lend it to applications in a number of spaces. Because graphene can be utilized
to control amplitude, phase, and polarization in the infrared, it may enable new functions
for tunable sensors (biological or chemical because of the well-defined infrared signatures
of molecular species) and thermal radiation control in the near- and far-field. It is also
possible that these topics may be merged, enabling multifunctional devices in the infrared.
Comments on another exciting potential application for phase control, LIDAR, were made
in Chapter 4.
7.1.1 Control of Far-Field Thermal Radiation
In this thesis, we discussed the control of the amplitude and polarization of thermal
radiation in the far-field. We additionally demonstrated active modulation of reflected
phase using graphene-gold nanoantennas. It would be of great interest to consider the
combination of such projects, enabling active control of the phase of emitted thermal
radiation. Based on the reciprocity between absorptivity and emissivity, it stands to reason
that the phase relation between two different resonant elements would be preserved when
the exciting field is thermal oscillations (such as from the substrate on which they are
fabricated) instead of an incident light source (typically required to be a laser). If we could
then engineer the phase profile at a surface into a metasurface using these tunable resonant
elements, we could create a self-contained tunable metasurface device that provides both
the light source and the optical functionality (e.g., focusing, steering, etc). For this to be
realized, we require spatial coherence to be preserved, such that the phase fronts from each
position can interfere in the far-field. Works from J. J. Greffet et al. have shown that

104
coherence can be preserved in thermally excited surface phonon polaritons over long
distances, up to 10s of µms in polar dielectrics.282 So, by taking advantage of this, we could
realize a proper emission-type reconfigurable metasurface.

Figure 7.1: A conceptual representation of the steering of thermal radiation using a
metasurface with a linear phase gradient on a heated polar substrate for steering of
radiation. Active control could be incorporated by using graphene as a tunable dielectric
environment.
7.1.2 Control of Near-Field Heat Transfer
Near-field heat transfer has become an exciting research topic over the past decade as it
allows us to exceed the Stefan-Boltzmann law that restricts the power density of thermal
radiation in proportion to T4 in the far field. As we move into the near-field, where we are
operating at length scales comparable to the wavelength of the emitted light, the coupling
of surface modes between objects leads to radiative heat transfer that significantly exceeds
the Stefan-Boltzmann law283. This has interesting implications for new types of energyharvesting devices such as thermo-photovoltaics that operate based on thermal emission, or
using radiative heat transfer for refrigeration.
A remaining challenge in this field is how to actively control near-field heat transfer
(NFHT) with rapid switching speeds, typically not accessible with the slow time scales
needed for heating and cooling bulk objects. By using the electrically tunable plasmons and
coupled plasmon-phonon polaritons supported by graphene on a polar substrate, it should

105
be possible to control the near-field heat transfer between two graphene sheets with rapid
switching speeds. This operates based on the principle that when the spectral overlap
between surface waves is large, near-field heat transfer is efficient, and when there is no
overlap, the NFHT is suppressed, schematically shown in Figure 7.2. So, by electrically
tuning the graphene plasmon resonance using an external gate, the degree of spectral
overlap can be controlled, and therefore the NFHT can be modulated at speeds
characteristic of carrier relaxation times in graphene.

Graphene, EF1
Graphene, EF2

SiO2
Si

b.
Im[r]

EF1 ≠ EF2

Wavelength (μm)

c.
Im[r]

EF1 = EF2

Wavelength (μm)

Figure 7.2: (a) Schematic of experimentally realistic structure for tunable near-field heat
transfer. (b) Spectral absorption coefficients for unequal Fermi energies on the top and
bottom sheets, minimizing heat transfer. (c) Spectral absorption coefficients for equal
Fermi energies, maximizing NFHT. Electrostatic gating can be used to tune the Fermi
energies to be matched/unmatched.
There have been a number of theoretical works on this topic284, 285; however, the
experimental realization of such a structure has remained elusive, in part because many of
the theoretical works neglect important features such as substrate contributions and the

106
challenges associated with placing two objects in very close proximity (~100s of nm).
Along with collaborators Nate Thomas and Prof. Austin Minnich, we suggest that by using
a straightforward planar geometry of two graphene sheets on SiO2/Si substrates, this
experiment could be done.
7.1.3 Graphene-Based Sensors
Because graphene plasmons are active in the mid-infrared, their coupling to molecular
vibrations can produce a very strong optical signal. This was shown in a recent publication
from D. Rodrigo et al., where the plasmon resonance of graphene nanoribbons was
modified by the presence of different molecular species and the active tunability of the
plasmon gave an additional degree of sensitivity286. Moreover, because of the strong field
enhancement in the near-field of the graphene resonators, it is suggested that very small
concentrations of molecules may be detected. One application space where this might be
interesting is in tracking the time evolution of different chemical reactions. Because the
response time of graphene carriers is very fast, its time-dependent optical response could
give new insights into the different molecules present throughout the course of a chemical
reaction, such as the important and complex process of CO2 reduction, of interest in the
Department of Energy Joint Center for Artificial Photosynthesis. By better understanding
the different species that are evolved over time, more efficient photocatalysts could be
developed that target the specific intermediate steps observed. Such experiments would
necessitate ultrafast detection schemes, but would be consistent with time scales achievable
for graphene charge carriers.
7.1.4 Graphene Devices in the High-Carrier Concentration Limit
For many years, a major goal of the graphene community has been the realization of
tunable plasmon devices in the technologically important telecommunications band (1550
nm), or higher energies. There exist two major barriers to realizing this: this first being the
achievement of sufficiently high carrier concentrations, and the second being the
fabrication of nanoresonators of sufficiently small dimensions, as the plasmon frequency of

107

graphene (as noted previously) has a dependence as ω p ∝ n 4 , ω p ∝

. Therefore, in

order to measure plasmons in the near-infrared, nanoresonators widths down to ~5 nm are
needed, as well as carrier concentrations on the order of 1014 cm-2.

Telecommunications band

Ionic gel gating

Electrostatic gating

Figure 7.3: A map of the thickness and carrier concentration dependence of the plasmon
resonance of graphene, illustrating the importance of small resonators and high carrier
concentration to reach high energies.
To date, using electron beam nanolithography, we have been able to obtain plasmon
resonance spectra from graphene nanoribbons as small as 15 nm. These nanoresonators
have displayed resonant frequencies across the mid-IR, to wavelengths as short as 4 µm,
and, notably, above the graphene optical phonon energy at 200 meV.
To address this challenge, we suggest the possibility of extending the range of these
graphene nanoresonators by patterning them to the 3-5 nm length scale in order to achieve
near-infrared resonances, and to explore Fermi level modulation gating techniques that will
allow for higher charge densities and thus access to a larger plasmon frequency range.

108

Figure 7.4: Suspended graphene nanoresonator of 5 nm width and an aspect ratio of 60:1
fabricated by He ion FIB. From Zeiss white paper., ref [289]
We will employ the use of ionic liquids as well as high static permittivity and ferroelectric
substrates (e.g., SrTiO3 and BaTiO3) in order to achieve these goals. In particular, we will
explore the use of materials with extremely high DC permittivities for gate dielectrics. A
recent report demonstrated that only 15 V is needed across a 500 µm thick gate dielectric of
single-crystal SrTiO3 to dope graphene from its charge neutral point (CNP) to a carrier
density of 4x1012 cm-2 at low temperatures, due to the divergent dielectric constant of
SrTiO3 (~20,000 at a temperature of 4K).287 Higher carrier concentrations have not yet
been achieved due to the charged surface states of the SrTiO3 pinning the Fermi energy of
the graphene.288 We suggest that by employing a geometry consisting of graphene
nanoresonators on 100 µm thick SrTiO3 substrates passivated by 10 nm Al2O3 films
deposited by atomic layer deposition, carrier concentrations of close to 1015 cm-2 could be
reached, an order of magnitude larger than has been achieved to date in solid-state systems.
In addition, we will take advantage of the ultra-high resolution patterning of monolayer
materials enabled by He+ ion focused ion beam lithography (Zeiss Orion FIB). By using the
shorter de Broglie wavelength of high energy 30 keV He+ ions it is possible to directly
pattern resonators into monolayer materials which weakly back-scatter the incident ions.

109
Use of the Zeiss Orion FIB instrument for fabrication of graphene nanoribbons with 5 nm
feature sizes has been demonstrated, as seen in Fig. 15.289
7.2 Graphene-Integrated Devices (Commercialization)
While the excitement surrounding graphene has dimmed since its initial discovery in 2004,
it now has reached a level of maturity where we can assess the real opportunities for
incorporating it into devices, and its longer-term potential. The Graphene Flagship project
in Europe has set ambitious goals to commercialize graphene-based products, such as
photodetectors and biosensors, investing €1 billion to bring lab-scale research to market.
So far, no major company has emerged that is competing with the state of the art; however,
it appears possible that niche markets will emerge in which graphene’s high conductivity
and mechanical flexibility could make it the superior material for devices, and a number of
start-up companies have launched. This is particularly interesting for wearable technologies
and implantable devices. As growth and roll-to-roll transfer processes become more
sophisticated and less expensive, it is possible that graphene will eventually live up to its
hype. If we consider graphene in the context of the ‘Gartner Hype Cycle’, Figure 7.5
below, it looks like the field has survived the ‘trough of disillusionment’ that came not long
after the Nobel Prize in Physics was awarded in 2010 for its discovery, and may move into
a comfortable ‘plateau of productivity’. By throwing out our expectations that graphene
would revolutionize all realms of technology, there may be real opportunities for it to make
an impact, though none have yet come to fruition.

110

Figure 7.5: Gartner Hype Cycle. A visualization of the phases of maturity of new
technologies, useful (if not scientifically validated) for understanding the life cycle of
graphene to date. Adapted from [290]
7.3 Black Phosphorus Research and Development
Unlike graphene, black phosphorus is in a much earlier stage of research, and indeed its
most fundamental optical properties are still not fully characterized. While our works have
attempted to answer some of these questions, one of the major limitations is the absence of
large-area samples needed for measurements like infrared ellipsometry to determine the
complex index of refraction. Efforts in a number of labs are ongoing to grow large-scale
BP; however, these are often nanocrystalline in nature, and therefore the electronic quality
is low, and the in-plane anisotropy – one of black phosphorus’ most desirable properties –
is lost. The primary challenge here is that black phosphorus is the high-temperature and
high-pressure phase of phosphorus, and therefore its growth relies on extremely high
temperatures and pressures, introducing safety hazards and preventing economical growth
conditions from being realized. It is possible that there will be major breakthroughs in
growth in the future; however, until this time, BP will remain an exciting material at the lab
scale only. Optimistically, one might imagine that if a unique application for BP is realized,
there will be sufficient motivation in the academic community to develop exotic new

111
growth schemes for large are black phosphorus films. Below, we comment on a few
interesting nanophotonic structures using black phosphorus.
7.3.1 Black Phosphorus for In-Plane Beam Steering
One of the most interesting properties of black phosphorus is that it is optically inactive
along one axis (absorption pathways are forbidden), and, by using an external gate, its
oscillator strength along the other axis can be completely suppressed at a given energy
corresponding to one of its intersubband transitions. This means that BP can effectively be
tuned from optically anisotropic to isotropic in plane. One consequence of this is it may
enable in-plane beam steering by changing the local dielectric environment of a plasmonic
material such as gold or silver. By changing the degree of anisotropy of the BP, the
propagation of a surface plasmon polariton could be redirected, as shown schematically in
Figure 7.6, below.

Output gra*ng

Surface
Plasmon

Input gra*ng

Output gra*ng

Surface
Plasmon

Input gra*ng

Figure 7.6: A schematic proposal of using black phosphorus as an active dielectric material
for steering of surface plasmons. (a) When BP is optically isotropic, the surface plasmon
propagates in a straight line from input to output gratings. (b) When the optical anisotropy
of the BP is increased, the surface plasmon is redirected. In this case, we simply use this as
a switch; multiple gratings or multiple branches of a slot waveguide mode could be used to
route light.
In its simplest configuration, this could be utilized as a switch, redirecting light away from
the output grating on a plasmonic surface. However, by carefully designing different

112
branches of a waveguide structure (e.g. silicon slab or slot waveguides), it is possible that
the preferential propagation through each branch could be achieved. By taking advantage
of the anisotropy of BP, we may open up an interesting new design space for integrated
photonics. To date, BP has never been experimentally integrated into a nanophotonic
structure/device; we suggest that this is a promising avenue to explore.
7.3.2 Black Phosphorus for Far-Field Polarization Control
One of the simplest ways to take advantage of the anisotropic optical response of BP is by
integrating it into an external cavity for efficiently switching the absorbed polarization state
of light. On its own, black phosphorus only interacts with a small fraction of light due to its
deep subwavelength thickness; photonic design is required to realize highly efficient
modulators. An isotropic resonant structure could be used, taking advantage of the BP to
introduce varying degrees of anisotropy. The simplest way to approach this would be to
incorporate BP into a ‘perfect absorber’ or gap mode based on a square array of gold disks
aligned with the two axes of the BP, schematically presented in Figure 7.7. In this way, the
polarization component of light absorbed depends on the differential absorption between
the two axes of the BP, enhanced by the resonant design. This is a very straightforward
design; more complex designs that include phase and polarization control could likely be
realized through careful design and optimization.

113

Figure 7.7: A schematic representation (top-down) of a nanophotonic structure that could
be used for actively controlling the polarization of absorbed (or thermally emitted) light
using the tunable linear dichroism of BP.
7.4 Nanophotonics and other van der Waals Materials
In addition to black phosphorus and graphene, other van der Waals materials are of great
interest in nanophotonic designs, highlighted in a recent review from F. Xia et al.197 In this
chapter we briefly describe designs for enhancing the absorption in a monolayer van der
Waals semiconductor in the visible. Other works from our group have tackled the problem
of absorption in few-layer TMDCs279, 291; however, to maintain the high external quantum
efficiency in these materials, devices that operate with monolayer samples (which are direct
band gap materials, whereas in the few layer limit, TMDCs are indirect band gap
semiconductors) are desirable.
We take advantage of a dual-resonant cavity based on high index TiO2 resonators
fabricated on monolayer TMDCs. The second resonance is introduced by a Ag backreflector separated by 20 nm from the TMDC, as shown in Figure 7.8 below.

114

TiO2 resonator
TMDC

300nm

SiO2
Ag
Figure 7.8: Schematic of resonant geometry designed for enhancing absorption in
monolayer TMDCs. Insert in upper right is a SEM image of fabricated TiO2 resonators.
By using different TMDCs, and varying the dimension of the TiO2 dielectric resonators, it
is possible to target narrow- or broad-band absorption (and therefore luminescence)
enhancement, depending on the goal. For designing a highly efficient emitter, we use
monolayer WS2 as our TMDC, and a resonator width of 350 nm, spaced by 100 nm.
Because of the low losses of the TiO2, almost all the enhancement of absorption is into the
WS2, shown in Figure 7.9 below.
0.9

Absorption

0.8

Total Absorp7on
WS2 Absorp7on

0.7
0.6
0.5
0.4
0.3
0.2
0.1

400

500
600
Wavelength (nm)

700

Figure 7.9: Simulated absorption of TiO2/WS2 resonant structure. 85% of absorption is into
the monolayer WS2 at its exciton peak of 625 nm.

115
This geometry is of interest in particular because it is known that the excitonic emission of
TMDCs can be controlled with an external gate voltage292, enabling an electrically
switched emitter.
In considering designs for a photovoltaic device, broadband absorption into a monolayer
TMDC is desirable. In this case, we take advantage of the variation in peak absorption in
the TiO2 resonators with resonator width combined with WSe2, which absorbs light
strongly across the visible, unlike WS2 with a narrow exciton absorption line. By sweeping
the width of the resonators from 135 to 295 nm, WSe2 absorption can be enhanced across
the visible. We can then imagine designing a trapezoid structure based on this range of
widths in order to enhance the absorption across that entire range, analogous to the
broadband perfect absorber developed by K. Aydin et al using silver trapezoid absorbers.186
The simulated WSe2 absorption is presented in Figure 7.10, below.

0.9

WSe2 Absorption

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
400

500
600
Wavelength (nm)

700

Figure 7.10: Simulated absorption in WSe2 using TiO2 resonators on an Ag back reflector,
with varying width of the TiO2 and a fixed separation between resonators of 100 nm.
There are many exciting opportunities for incorporating TMDCs into photovoltaic devices,
particularly because of their very high luminescence quantum yield in monolayer form293,

116
and band gap energies that would make them an excellent tandem partner to silicon based
on the Shockley Quissier limit. The further exploration of nanophotonic designs to
optimize these devices may be a research topic of great interest in the future.
7.5 Endless Opportunities
As more 2D materials are discovered and explored, the opportunities to combine them with
different nanophotonic designs will expand greatly. Even now, with the recent discovery of
monolayer magnetic materials and the excitement surrounding layered topological
insulators, we can imagine exotic new physics will emerge that we can exploit for new
photonic functions. The challenges of large-scale integration remain; however great
progress is being made in this field, and roll-to-roll manufacturing of some of these
materials is not out of reach. Van der Waals materials give us an amazing set of properties
that we can combine together at will, and by incorporating them with nanophotonics, the
possibilities for new devices and emergent physics are immense.

117

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131
Appendix A

GRAPHENE FABRICATION METHODS
Graphene Transfer (Chapters 2 – 4)
Following CVD graphene growth (or purchasing from Graphenea or Graphene
Supermarket), the Cu foil is etched in iron chloride solutions, and the graphene is
transferred to double-side polished oxidized Si wafers with 285 nm SiO2 on 10
Ohm-cm Si using a poly(methyl methacrylate) (PMMA) transfer technique:
PMMA 950 A4 is spin coated on the graphene/Cu foil at 3000 rpm for 1 minute,
and then baked at 180°C for 2 minutes and 30 seconds to evaporate the solvent. The
graphene/Cu foil is then cut using a razor blade into squares slightly smaller than 1
cm x 1 cm. This process is done utilizing two razor blades: the first holds the foil in
place (by vertically pressing it down at the position where the cut will be made),
and the second cuts the foil by carefully and in slow steps making cuts working
from the inside out with the corner of the blade. The foil is then placed on top of the
ferric chloride etchant solution (Transene, CE-100) for approximately 20 minutes
until the copper is fully removed, leaving the graphene/PMMA film floating on the
surface. A plastic spoon is then used to scoop up the graphene/PMMA film and
place it into a water bath, typically a 3 in diameter shallow dish. The graphene is
left for ~5 minutes in the first bath, and then moved into a second for 10 minutes,
and a third for 10 more minutes. Finally, the graphene is transferred by spoon into a
smaller beaker of water for 20 minutes, after which it is scooped up onto the
substrate of choice (in this case, 285nm SiO2/Si chips). The water is baked off of
the chip for at least 8 hours at 40 - 50°C) and then the PMMA is removed in
acetone or Remover PG (Microchem) for 45 minutes. If needed, the
acetone/Remove PG may be heated to 40°C to more completely remove the PMMA
residue.

132
Electron Beam Lithography and Graphene Etch (Chapters 2 and 3):
Nanoresonator arrays are patterned in the graphene using 100 keV electron beam
lithography (Raith EBPG 5000+ in Caltech’s Kavli Nanoscience Institute) on 90
nm thick 950 A2 PMMA (MicroChem). The 950 A2 PMMA is spin-coated at 3000
rpm for 1 minute, and then baked for 2 minutes and 30 seconds. For very small
features, a longer bake time (5 minutes) may be used. The exposed PMMA is
developed in 3:1 isopropanol (IPA):methyl isobutyl ketone (MIBK) for 45 s
followed by a rinse step with IPA for several seconds. The freezer in the Atwater
Group labs (251a) is used to keep the MIBK cold and improve the resolution of the
patterning. The pattern is etched into the graphene using oxygen plasma at 20
mTorr, a flow rate of 10 sccm, and power of 80 W for 15 s. If the plasma strikes to
a high DC voltage (in excess of 50 V within 8 seconds), the etch is stopped after 11
seconds. In order to tune and monitor the carrier density of our device in situ,
source and drain contacts (3 nm Cr, 100 nm Au) are deposited on the bare graphene
areas adjacent to the nanoresonator arrays using a shadow mask (purchased from
Photo Etch Technology), and the sample is connected in a field effect transistor
(FET) configuration, with the Si layer acting as the backgate electrode.
Graphene-Gold Resonator Fabrication (Chapter 4):
Cu foil was etched away in iron chloride solution, and the graphene was transferred
to a suspended SiNx membrane obtained commercially from Norcada, part
#NX10500E. A back-reflector/back-gate of 2 nm Ti/200 nm Au was evaporated on
the back of the membrane by electron beam deposition. 100 keV electron beam
lithography was then used to fabricate the device. First, arrays of gold resonators
were patterned in 300 nm thick 950 PMMA (MicroChem) developed in cold 3:1
isopropanol:methyl isobutyl ketone (MIBK) for one minute. The sample was then
etched for five seconds in a RIE oxygen plasma at 10 sccm, 20 mTorr, and 80 W to
partially remove the exposed graphene and enable easier liftoff. 3 nm Ti/60 nm Au
was then deposited by electron beam evaporation in the CHA (small gap sizes
require a long throw distance provided only by this tool in the KNI), and liftoff was

133
done in acetone heated to 45°C. A second electron beam lithography step was used
to define contacts of 10 nm Ti/150 nm Au. Wire bonding was done to electrically
address the electrode.
For the multi-pixel device, as described in Chapter 4.2, additional aligned
lithography steps are used to electrically isolate each array of gold antennas (RIE
for 15 seconds, three times – not a single 45 second etch, as the striking time of the
plasma is significant) and then define contacts of 10 nm Ti/150 nm Au to each
pixel. Alignment marks are defined as “p20” in the EBPG: typically 10 nm Ti/100
nm Au thick, 20 µm on a side squares spaced by 1500 µm. Alignment errors are
typically ~100 nm using this approach.

134
Appendix B

GRAPHENE ELECTROMAGNETIC SIMULATIONS
Throughout this thesis two different simulation methods have been used for
graphene:
1) For most 2D simulations, we rigorously solve Maxwell’s equation by using
the finite element method (commercially available software, COMSOL).
We model graphene as a thin film of the thickness δ and impose the relative
permittivity εG = 1 + 4πiσ/ωδε0. σ(ω) is the complex optical conductivity of
graphene evaluated within the local random phase approximation from 31. δ
is chosen to be 0.1 nm which shows good convergence with respect to the δ
→ 0 limit. The complex dielectric function of SiO2, εSiO2 (ω), was taken
from Palik.294 The complex dielectric constant of SiNx was fit using IR
ellipsometry based on the model in ref [295].
2) For larger, three-dimensional simulations such as those presented in Chapter
4, we use finite difference time domain (FDTD) simulations (commercially
available software, Lumerical). Graphene is modeled as a surface
conductivity adapted again from ref [174]. We use a scattering rate of 20 fs
for the graphene, which provides the optimum fit to experimental results
and is consistent with previous experimental works using patterned CVD
graphene on SiNx.190
The agreement between approaches is excellent, and agreement to experiment is
good.

135
Appendix C

BLACKBODY EMISSION MEASUREMENTS
For blackbody emission measurements, the device was connected to a temperaturecontrolled stage (Linkam) consisting of a 100 µm thick layer of sapphire on 2 mm
copper on a heated silver block that can vary in temperature from room temperature
to 250°C. The stage temperature was monitored via a thermocouple mounted in the
silver block, and the temperature on the SiNx membrane was confirmed to be no
more than 15°C less than the thermocouple temperature by placing a series of
temperature indicating laquers (Omegalaq®) on an equivalent SiNx membrane. The
device and stage were held at a pressure of 1-2 mTorr during emission
measurements. Gate-dependent emission spectra were measured using a Fourier
transform infrared (FTIR) microscope operating such that emitted light from the
heated device passes through a KBr window and is collected in a Cassegrain
objective, collimated, and passed through the interferometer in the FTIR before
being focused on a liquid nitrogen-cooled HgCdTe detector. For polarization
dependent measurements a wire grid polarizer was placed in the collimated beam
path. As a reference a SiNx/Au membrane was coated with an optically thick layer
of black soot deposited using a candle. Soot is known to be a thermal emitter that
approximates an ideal blackbody with emissivity approaching unity across the midIR.117

136
Appendix D

INTERFEROMETRY MEASUREMENTS
A custom built mid-IR, free-space Michelson interferometer built with
collaborators at Northrop Grumman Corporation (Philip Hon, Juan Garcia) was
used to characterize the electrically tunable optical reflection phase from the
graphene-gold metasurface. The integrated quantum cascade laser source, MIRcat,
from Daylight Solutions provided an operating wavelength range from 6.9 µm to
8.8 µm, which was a sufficiently large enough wavelength range to characterize the
absorption spectra and phase of the designed metasurface. A ZnSe lens with a focal
length of 75 mm was used to focus the beam onto the sample. The near-field beam
waist was 2.5 mm and the far-field beam waist was 90 µm and was measured with a
NanoScan beam profiler. The reference and sample legs have independent
automated translations, namely, the reference mirror is mounted on a Newport VP25XA automated linear translation stage with a typical bi-directional repeatability
of +/- 50 nm and the sample stage is automated in all three dimensions to give
submicron alignment accuracy with the Newport LTA-HS. The propagating beams
from the sample and reference legs combine after a two inch Germanium beam
splitter. Two ZnSe lenses, one with a focal length of 100 mm and another with
1000 mm image the beam at the sample plane with a ~10 times expansion. Control
of the source, translation stages, pyroelectric power detector, and the Keithley
source used to bias the metasurface is conducted through a Labview automation
script.

137
Appendix E

BLACK PHOSPHORUS EXFOLIATION AND FABRICATION
METHODS
Infrared Sample Preparation (Chapters 5 and 6)
Samples for infrared measurements are fabricated by mechanically exfoliating fewlayer BP onto double-side polished 285 nm SiO2/Si chips in a glove box
environment. Contacts of 20 nm Ni/200 nm Au are fabricated by electron beam
lithography, electron beam evaporation, and liftoff. Alignment of the contacts to the
flakes is done by the patterning of four reference marks of 5nm Ti/100 nm Au in a
square around the flake typically separated by 100 µm. Metal thickness for the
reference marks doesn’t matter as long as they are visible in the microscope with
well-defined edges. An image is then taken in a confocal microscope at 50 or 100X
magnification. The image is imported into AutoCAD and used as the basis for
creating the contact files for electron beam lithography.
To prevent sample degradation in air (BP is sensitive to light, oxygen, and water),
two different capping layers have been used:
1) PMMA 950 A8 is spin-coated at 3000 rpm for 1 minute on top of the BP
and fabricated contacts in a glove box environment. 1 minute 30 seconds
baking time at 180°C is sufficient to remove the solvent and protect the BO.
Electrical access to the contacts is made by exposing the PMMA using
electron beam lithography on top of the contacts and then wire-bonding.
2) A top gate dielectric or capping layer of 45 nm Al2O3 is deposited by atomic
layer deposition (ALD) following the technique in ref[14]. This entails an
initial 10 pulses of the Al2O3 precursor to saturate the surface (and protect it
from the H2O pulse that follows) followed by the deposition of 5 nm Al2O3
at 50°C following standard ALD procedures. The sample and chamber are
then heated up to 150°C for the remaining 40 nm, again with standard
conditions.

138
When top-gating is used, a semi-transparent top contact of 5 nm Ni is deposited by
electron beam evaporation and liftoff. A second lithography step is used to fabricate
a thicker top contact of 20 nm Ni/150 nm Au in electrical contact with the first, but
with the bond pad far away from the sample that can then be wire-bonded.
Visible Sample Preparation:
Samples for visible measurements are fabricated by depositing a 5 nm thick semitransparent back contact of Ni, followed by 45 nm Al2O3 by ALD on a 0.5 mm
thick SrTiO3 substrate. Few-layer BP is then mechanically exfoliated and a top gate
and electrical contacts are fabricated as above.
Black Phosphorus Calculations:
Calculations of the optical constants of BP are based on the formalism developed in
ref[231]. Optical conductivity σ is calculated using the Kubo formula within an
effective low-energy Hamiltonian for different thicknesses. The permittivity is
calculated as ε(ω) = ε∞ + iσ/ωδ, where δ is the thickness of the BP, and the highfrequency permittivity ε∞ is taken from ref[296]
Identification of Crystal Axes of BP:
The x (armchair) and y (zig-zag) crystal lattice directions are determined by
polarization-dependent visible reflectance measurements.

At each angle of

polarization an image is recorded, and pixel RGB values are sampled from both the
BP flake and nearby substrate. The ratio of green channel values from flake to
substrate is averaged over three sample positions, and plotted as a function of
polarization angle in Figure E1.

Maxima and minima in green reflectance

determine the armchair and zig-zag directions, respectively.297

139

Figure E1: Intensity of the green channel of light reflected from BP flakes as the
linear polarization of the incident light is rotated for the 6.5 nm flake from Chapter
5. In both cases, the polarization angle is defined as the angle between the x
(armchair) crystal axis and the linear polarizer. The green component of the pixel
RGB of the flakes is normalized to that of the adjacent substrate.