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Fall 2014 Dynamic control of plasmonic resonances with graphene based nanostructures Naresh Kumar Emani Purdue University

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DYNAMIC CONTROL OF PLASMONIC RESONANCES

WITH GRAPHENE BASED NANOSTRUCTURES

A Dissertation

Submitted to the Faculty

of

Purdue University

by

Naresh Kumar Emani

In Partial Fulfillment of the

Requirements for the Degree

of

Doctor of Philosophy

December 2014

Purdue University

West Lafayette, Indiana ii

Dedicated to the loving memory of my father – a soldier for “lost causes” and a source of inspiration for everything I am and hope to be. iii

ACKNOWLEDGMENTS

Over the last five years of my PhD studies I have wondered, many times, about how I would feel when I reach the end of this journey. These years have been a tremendous learning experience, both in research and life in general. There are so many people who have helped me along the way, and I am thankful to each of them. First and foremost, I am grateful to my advisor, Prof. Alexandra Boltasseva for her guidance, encouragement and unfailing support. My special thanks to my co-advisor Prof. Vladimir Shalaev who sparked my interest in Nanophotonics, and always inspired me to work harder. I would like to express my sincere gratitude to Prof. Alexander Kildishev for sharing many technical insights and friendly encouragement. I thank Prof. Yong Chen for many stimulating discussions, and graphene samples without which this work would not have been possible. I am thankful to Prof. Minghao Qi, who graciously agreed to serve on my committee and helped me during my research work. A significant portion of my PhD research involved nanofabrication and opto- electrical characterization. I have come to believe that research is 1% ecstasy and 99% perseverance. I cherish the friendship, humour and support of all my co-workers who have made the ‘dull’ part of research so much easier to navigate. I especially thank Jack for the many fruitful collaborations, and all the past and present members of the Nanophotonics team at Purdue for their support. I will cherish and treasure many fond memories I share with them. I also thank the staff members at Birck Nanotechnology Center for creating such an amazing environment. As I come to the end of this lap in my life, I fondly recollect the diverse influences of my friends and teachers at Hyderabad, Parti, IIT Bombay and Taiwan. The last five years have been very eventful times in my life. During the PhD one friendship, with Guru - my friend and brother-in-law, made a lot of impact on iv

my thinking. We spent endless hours absorbed in discussions and arguments over a diverse range of topics - from trivial to deeply philosophical, which I fondly call a PhD within a PhD. Time started to fly by in the last 2 years after my marriage to Brinda. I am grateful for her understanding, unflinching support and (paraphrasing Stefan Maier) the lovely distractions from research. Finally, how can I even begin to express my thoughts about the ones who were there with me from the beginning - my brother, mother and father, who have given so much and asked so little .....! v

TABLE OF CONTENTS

Page LIST OF FIGURES ...... viii SYMBOLS ...... xiii ABBREVIATIONS ...... xiv ABSTRACT ...... xv 1 INTRODUCTION ...... 1 1.1 Current Challenges in Plasmonics ...... 2 1.2 Organization of Dissertation ...... 3 2 FUNDAMENTALS OF PLASMONICS AND GRAPHENE ...... 5 2.1 Optical Properties of Metals ...... 5 2.1.1 From noble metals to dilute and ‘lossless’ metals ...... 6 2.1.2 Plasmonic resonance in a metal nanoparticle ...... 7 2.2 Electronic Bandstructure of Graphene ...... 8 2.3 Optical Properties of Graphene ...... 10 2.4 Graphene as an Alternative Plasmonic Material ...... 13 2.4.1 Qualitative differences in plasmons in 3D vs 2D ...... 13 2.4.2 Loss mechanisms in graphene ...... 14 2.4.3 Conclusions ...... 16 2.5 Nonlinear Optical Properties ...... 16 2.6 Numerical modeling of graphene ...... 17 2.6.1 Validation in frequency domain ...... 17 2.6.2 Validation in time domain ...... 17 2.7 Summary ...... 18 3 DYNAMIC ELECTRICAL CONTROL OF THE PLASMONIC RESO- NANCE WITH GRAPHENE ...... 19 vi

Page

3.1 Experimental Setup ...... 19 3.1.1 Fabrication and Characterization ...... 20 3.1.2 Electrical and Raman Characterization ...... 21 3.1.3 Optical Characterization of Bowtie Antennas ...... 21 3.2 Dependence of tunability on wavelength ...... 23 3.3 Electrical Control of Damping ...... 26 3.4 Discussion ...... 26 3.4.1 Modeling Tunability of a Resonant Structure Using Perturbation Theory ...... 27 3.5 Summary ...... 27 4 TUNABLE FANO RESONANT NANOSTRUCTURES AT NEAR INFRARED WAVELENGTHS ...... 29 4.1 The Fano Resonance in Metallic Nanostructures ...... 29 4.2 Design and Fabrication ...... 30 4.3 Sensitivity of Fano Resonant Structures ...... 31 4.4 Electrical Control of Fano Resonant Nanostructures ...... 32 4.4.1 Electrolytic Top Gate Vs Traditional Si Backgate ...... 33 4.4.2 Comparison Between Experiments and Numerical Simulations 34 4.4.3 Carrier Density near Metallic Nanostructures ...... 35 4.5 Summary ...... 37 5 INVESTIGATION OF THE PLASMON RESONANCES IN MULTILAYER GRAPHENE NANOSTRUCTURES ...... 38 5.1 Motivation ...... 38 5.2 Plasmon Dispersion in 2D Medium ...... 39 5.3 Fabrication and Characterization ...... 41 5.3.1 Electrical characterization of MLG ...... 42 5.3.2 Optical characterization of the substrate ...... 43

5.3.3 Epsilon Near Zero (ENZ) mode near the SiO2 Optical Phonon 44 5.3.4 Impact of Numerical Aperture of FTIR Objective ...... 46 vii

Page 5.3.5 Raman Spectroscopy of Graphene Nanoribbons ...... 46 5.4 Plasmons in Multilayer Graphene ...... 48 5.5 Conclusions ...... 50 6 CONCLUSIONS AND FUTURE OUTLOOK ...... 51 REFERENCES ...... 53 A PROCESS RECIPES FOR NANOFABRICATION ...... 62 A.1 Photolithography for Source/Drain Contacts ...... 62 A.2 Electron Beam Lithography ...... 62 A.3 Reactive Ion Etching of Graphene ...... 64 B LARGE AREA GRAPHENE SYNTHESIS ...... 66 C ESTIMATION OF OPTICAL CONDUCTIVITY OF GRAPHENE USING RANDOM PHASE APPROXIMATION ...... 68 C.1 MATLAB Source Code for Calculating Conductivity ...... 68 VITA ...... 71 viii

LIST OF FIGURES

Figure Page 1.1 (a) The domains in terms of speed and size of different computing tech- nologies. Plasmonics combines the advantages of semiconductor electronics and dielectric photonics on a single platform. Figure adapted from refer- ence [16] with permission from AAAS; (b) The two main types of resonance phenomena encountered in plasmonics - the propagating SPP excited at metal-dielectric interface and the LSP in metallic nanostructures. Figure adapted from reference [17] with permission from Macmillan Publishers Ltd...... 2 2.1 Illustrative example of Drude permittivity calculated using Eq. 2.1 with ωp = 7 eV , γ = 0.07 eV and int = 6.9...... 6 2.2 Electronic bandstructure of graphene (a) Unit cell in reciprocal space showing the basis vectors ~a1 and ~a2 in terms of real space lattice constant a0; (b) The E-K diagram for graphene (eq. 2.3) calculated using the tight binding approximation. The conduction and valance bands meet at the six corners of the hexagon in reciprocal space (known as the Dirac or K points); (c) Simplified representation of bandstructure of graphene using cut-lines along high symmetry directions. The bandstructure is linear close to K points giving rise to many unique properties of graphene; (d) Intraband and interband transitions in graphene; interband transitions occur above a threshold of 2EF...... 8 2.3 Optical absorption of graphene (a) Transmission through a 50 µm aperture showing 2.3% absorption for a SLG; (b) Absorption scales linearly with number of layers in graphene and is spectrally flat at visible wavelengths. Figure adapted from reference [38] with permission from AAAS. .... 10 2.4 Optical transistions in graphene (a) The optical response of graphene is controlled by e-h pair excitations. Photons with energies above 2EF will be absorbed due to transitions into the unoccupied states above the Fermi level; (b) Calculated dielectric functions for carrier densities of 3 × 1011, 1 × 1012, 1 × 1013 cm−2 show a tunable interband threshold. Changes in the imaginary part (dashed lines) of permittivity are accompanied by corresponding changes in the real part (solid lines). The calculations were −13 performed with τ = 1 × 10 s, T = 300 K and tg = 1 nm using the code listed in Appendix C...... 11 ix

Figure Page 2.5 Relative contributions of interband and intraband transitions to optical 11 −2 −14 response of graphene (ng,2D = 7 × 10 cm ,T = 300 K, τ = 3 × 10 s e2 and the y axis are scaled by G0 = 4¯h . (a) Real part of conductivity; (b) Imaginary part of conductivity; (c) Figure of merit calculations indicating that graphene is a good plasmonic materials between 2 µm - 20 µm wavelengths. The plasmonic response can be tuned to NIR wavelengths by increasing carrier density in graphene...... 12 2.6 Dispersion of Plasmons in a solid. (1) Volume Plasmons, (2) Surface Plasmons, (3) Plasmons in 2DEG, (4) Plasmons in 1D system. Note: Upper scale valid for (1) and (2), the scale below for (3) and (4), ll is light line. Figure adapted from reference [50]...... 15 2.7 Validation of numerical modeling of graphene in frequency domain (a) Experimental gate dependent reflection spectra normalized to the Dirac point, (b) Simulated reflection spectra with graphene carrier concentration as a parameter...... 18 3.1 Schematic illustration of the experimental structure for voltage-controlled optical transmission measurements...... 20 3.2 (a) Typical plot of carrier concentration dependence on gate voltage indi- cating a good modulation of carrier concentration. We also observed a very small variation in resistance during optical measurements, which can be attributed to electrochemical redox reactions of adsorbates on graphene [66]; (b) Raman spectroscopy of graphene with and without metal nanostruc- tures shows electron doping caused by the metal [67, 68]. The intensity of the D peak was small (not shown here), indicating the high quality of the graphene. Spectra were averaged from measurements at three different locations on the sample...... 22 3.3 (a) Geometry, dimensions and resonant wavelengths of fabricated bowtie antennas on graphene; (b) Calculated local magnetic field enhancement at the center of bowtie at resonant wavelength. The bowtie plasmonic resonance is thoroughly discussed by Grosjean et al. [62]; (c) Scanning electron micrograph of fabricated bowtie antennas on top of a graphene sheet; (d) Measured optical transmission spectra for bowtie antennas with different periodicities fabricated on graphene...... 23 3.4 The measured transmittance at a particular gate bias (in volts) normalized by the transmittance measured at the Dirac point. The carrier concen- tration in graphene increases as ∆V moves away from zero and leads to a stronger impact on resonance. We observe stronger damping of the plasmonic resonance at mid-infrared wavelengths. Data for bowties #1, #2 and #3 is shown in panels (a), (b) and (c) respectively...... 24 x

Figure Page 3.5 (a) Experimentally observed (solid lines) damping of a plasmonic resonance due to an applied gate voltage. A higher carrier concentration leads to blocking of some interband transitions, and hence leads to a narrower resonance. Full-wave simulations (dashed lines) performed with graphene carrier concentration as a fitting parameter produce an excellent match with the experimental results; (b) Simulated phase delay of E field along the axis of the bowtie. Changes in carrier concentration lead to a simultaneous change in transmission as well as phase since both real and imaginary parts of permittivity of graphene are tuned by electric bias; (c) The narrowing of the width of the resonance with gate bias shows the precise electrical control of the resonance...... 25 4.1 (a) Schematic illustrating the Fano resonant plasmonic antennas fabri- cated on top of SLG used in our experiments. The optical measurements were performed using an FTIR spectrometer with an attached microscope in reflection mode. (b) Geometry of the dolmen structure used in our experiment. When the incident light is polarized along the horizontal rod it excites a dipolar (bright) mode, and simultaneously a quadrupolar (dark) mode is excited in the vertical rod pair. The dimensions in the structure were optimized to achieve overlapping of these modes so that a Fano resonance dip is around 1.9 µm. (c) Scanning electron micrograph showing the sample fabricated using e-beam lithography. The scale bar is shown below the image. Doses in the e-beam lithography were optimized to achieve reliable gaps of 20 and 50 nm required by the design. .... 30 4.2 Measured optical reflectance spectra from Fano resonant antennas at four different locations (two without graphene and two with graphene) showing strong impact of graphene on Fano resonance. In measurements without graphene (red and blue curves), there is perfect overlap, while measurement with graphene (green and turquoise curves) show variations due to spatial inhomogeneities.The dip at 1.8 µm corresponds to the location of the Fano resonance (overlapping dipolar and quadupolar modes in dolmen geometry). We note that in this particular sample the reflection at lower wavelengths does not decrease as expected in Fano line shape due to fabrication imperfections...... 32 4.3 Schematic illustrating the two types of gating techniques for graphene. Traditionally the voltage was applied through the Si back gate, which has limited control of the channel. Alternatively, a liquid electrolytic top gate can create large carrier densities in graphene because of formation of an electric double layer at the interface as shown in the inset...... 33 xi

Figure Page 4.4 (a) Experimentally measured modulation of the resonance using backgating through SiO2. The measurements were performed in hole doping regime where carrier concentration was reduced with the applied voltage increase. (b) Experimentally measured optical spectra on the same device using ion-gel top electrolyte gating. The scans were taken in the electron dop- ing regime where carrier concentration increases as the applied voltage increases...... 34 4.5 (a) The measured optical reflectance spectra with ion-gel top electrolyte. (b) 3D FE simulations using experimental geometry and graphene sheet carrier density as an input parameter. We observe a qualitative agreement with experimental results. These simulations do not take into account the ion-gel,the thickness and index of which are challenging to determine in the experiment. This explains the difference in the experimentally measured and simulated wavelength of the Fano dip...... 35 4.6 Scanning photocurrent measurements across a graphene FET structure with 532 nm laser. The sharp changes in photocurrent at the source and drain contacts is due to the built in field at the respective junctions (as illustrated on the right). Since the E field is directed in opposite directions at contacts we see a reversal in measured photocurrent...... 36 5.1 (a) Optical conductivity of AB stacked SLG and BLG (b) Evolution of optical conductivity of FLG samples with increase in number of layers. (Figures adapted with permission from Mak et.al., 107, 34, PNAS (2010); reference [97] in bibliography; ©2010 National Academy of Sciences). 39 5.2 Schematic of interface between two dielectrics with a 2D sheet charge at the interface. The incident electromagnetic wave can excite charge oscillations at the interface illustrated by the dashed line...... 40 5.3 The measured sheet resistance of MLG samples indicated that up to 3 layers there is large tuning of resistance even though mobility is reduced. 42 5.4 (a) Schematic illustration of the sample used for studying plasmon resonance in graphene nanostructures; (b) SEM Micrograph of the fabricated GNRs. 43

5.5 (a) Reflectance from Si substrate with a 300 nm SiO2 substrate. (b) Initial fit with a lorentz oscillator in WVASE software which was later proven to be inaccurate...... 44 5.6 (a) Spectroscopic ellipsometry measurements of lightly doped Si with 300 nm thermal oxide for 25◦ incidence angle; (b) The extracted permittivity around SiO2 optical phonon using gaussian oscillators ...... 45 xii

Figure Page 5.7 (a) Angular dependence of the reflection dip at 8 µm calculated using 2D full wave FEFD simulations in COMSOL Multiphysics; (b) The calculated reflection, transmission and absorption spectra at an angle of incidence of 20◦; (c) Numerical simulations of enhanced absorption at higher angles of incidence...... 45

5.8 (a) Modulation of IR reflectivity of CVD graphene on Si/300 nm SiO2 sub- strate as a function of sheet carrier density. Measurements were performed using a Fourier Transform Infrared (FTIR) Spectrometer with microscope accessory (Objective: 15X, N.A. 0.58 Reflectochromat); measurements are normalized to RCNP (b) 2D full wave FEFD simulations with COMSOL Multiphysics using a surface current model for graphene; carrier scattering rate (τ) is the only parameter used in simulations...... 47 5.9 Raman spectroscopy of unpatterned SLG and GNRs. Patterning causes an additional D peak to appear while simultaneously decreasing the I2D/IG ratio from 3.18 to 2.08. All measurements were performed under identical conditions with 532 nm, 1 mW , circularly polarized laser source and 100X objective. Resolution of spectrometer is 1.3 cm-1 ...... 48 5.10 Modulation of IR reflectivity of graphene nanoribbons, which were fab- ricated using few layer CVD graphene on Si/300 nm SiO2 substrate, as a function of sheet carrier density. Measurements were performed using a Fourier Transform Infrared (FTIR) Spectrometer with microscope ac- cessory (Objective: 15X, N.A. 0.58 Reflectochromat); measurements are normalized to RCNP . Panels shows measured data on for SLG, double layer graphene and triple layer graphene. The width and period of GNRs were fixed at 50 nm and 150 nm respectively...... 49 5.11 2D full wave FEFD simulations of GNRs with COMSOL Multiphysics using a surface current model for graphene; carrier scattering rate (τ) is the only parameter used in simulations...... 50 A.1 Main processing steps used to fabricate experimental devices used in this dissertation. Steps (a)-(d) are used for fabricating graphene-antenna hybrid devices (Chapters 3 and 4) and steps (a),(b) and (e) were used for fabricating devices used in Chapters 5...... 63 A.2 SEM images of the graphene nanoribbons (Period 150 nm and Width 50 nm) fabricated by ebeam lithography. It should be noted that the patterns are very sensitive to ebeam dose...... 65 xiii

SYMBOLS

−31 me Mass of electron = 9.1 × 10 kg −12 0 Vacuum permittivity = 8.85 × 10 F/m 6 vF Fermi velocity of electrons =1 × 10 m/s e Charge of electron =1.602 × 10−19 C h¯ Reduced Planck’s constant =1.054 × 10−34 Js

−23 kB Boltzmann constant = 1.38 × 10 J/K eV Electron-volt 1 eV = 1.602x10−19 J sccm Standard cubic centimeter per minute 1 sccm = 16.67 standard mm3/s T orr Pressure 1 T orr = 133.28 P a or 1 P a ≈ 7.5 mT orr ◦ ◦ A Angstrom 1 A = 10−10 m

1 Real part of dielectric permittivity

2 Imaginary part of dielectric permittivity γ Drude damping rate µm Micrometers 1 × 10−6 m nm Nanometers 1 × 10−9 m xiv

ABBREVIATIONS

AFM Atomic force microscope CVD Chemical vapor deposition CMOS Complementary metal oxide semiconductor FDTD Finite difference time domain FTIR Fourier transform infrared FEFD Finite element frequency domain EM Electromagnetic LSPR Localized surface plasmon resonance GNR Graphene nanoribbon MEMS Micro electro mechanical systems MIR Mid-infrared NSOM Near-field scanning optical microscope NIR Near-infrared RPA Random phase approximation SHA Spatial harmonic analysis SP Surface plasmon SPP Surface plasmon polariton SEM Scanning electron microscope SRR Split ring resonator SLG Single layer graphene FLG Few layer graphene MLG Multiple layer graphene THz Tera-hertz xv

ABSTRACT

Emani, Naresh Kumar PhD, Purdue University, December 2014. Dynamic Control of Plasmonic Resonances with Graphene Based Nanostructures . Major Professors: Alexandra Boltasseva and Alexander V. Kildishev.

Light incident on a metallic structure excites collective oscillations of electrons termed as plasmons. These plasmons are useful in control and manipulation of information in nanoscale dimensions and at high operating frequencies. Hence, the field of plasmonics opens up the possibility of developing nanoscale optoelectronic circuitry for computing and sensing applications. One of the challenges in this effort is the lack of tunable plasmonic resonance. Currently, the resonant wavelength of plasmonic structure is fixed by the material and structural parameters. Post-fabrication dynamic control of a plasmonic resonance is rather limited. In this thesis we explore the combination of optoelectrical properties of graphene and plasmon resonances in metallic nanostructures to achieve dynamic control of plas- mon resonances. First, we show that it is possible to use the highly tunable interband transitions in graphene to effectively control the plasmonic resonance in mid-infrared (MIR) wavelengths. We then outline the current challenges in achieving modulation in the technologically relevant near-infrared (NIR) wavelengths. One potential solution is to combine Fano resonances in metallic structures with graphene to realize a higher degree of tunability at NIR wavelengths. In addition to modulating resonances in metallic nanostructures, graphene itself supports highly confined and tunable plasmons in MIR wavelengths. We report experimental studies on the plasmonic resonance in multilayer graphene, and the interaction of graphene plasmons with the substrate phonons. Finally, we conclude with the current challenges and present directions for further improvements so as to enable practical devices. 1

1. INTRODUCTION

The current information revolution is driven by relentless advances in computing capacities enabled by nanoelectronics, and progress in long distance optical com- munications enabled by photonics. In the last decade there have been increasing difficulties in scaling the clock speed of processing chips [3]. Fundamental RC delay and power dissipation considerations limit the processing speed of electronic chips to a few GHz. On the other hand, photonics offers huge advantages in bandwidth and speeds, but is limited to relatively bulky components. Nanophotonics is the science of control and manipulation of light at the nanoscale, and offers a potential path for revolutionary advances in optical information processing. One of the most promising directions in nanophotonics is to use free charge oscillations in metal nanostructures known as surface plasmons (SPs) for control and manipulation of optical signals [4,5]. Surface plasmons exhibit a resonant behavior at a particular wavelength, when the electrostatic restoring force equals the Lorentz force caused by an incident field. At such a resonance the electromagnetic energy is confined to subwavelength length scales in close vicinity of the nanostructures. Thus, plasmonics effectively combines the sub-wavelength (nanoscale) functionality of electronics and high (THz) bandwidth of photonics as shown in Fig. 1.1. This interplay between electromagnetic waves and the optoelectronic properties of materials provides a rich platform for both fundamental studies and practical applications. Plasmonic resonances can be broadly divided into two classes - Surface plasmon polaritons (SPP) and Localized surface plasmons (LSP), which are excited when light is incident of metal films and metallic nanoparticles respectively. Several promising integrated optical components have been demonstrated in the last decade using

This dissertation contains some text and figures which have been adapted with permission from the author’s research publications especially references [1,2] (© 2012, 2013 American Chemical Society). 2

SPPs [6,7]. LSPs have been used in a array of applications like like surface plasmon assisted lithography [8], data storage [9], enhanced chemical reaction rates [10, 11], improved photovoltaic devices [12], particle trapping [13,14] and bio-sensing [15].

Fig. 1.1. (a) The domains in terms of speed and size of different comput- ing technologies. Plasmonics combines the advantages of semiconductor electronics and dielectric photonics on a single platform. Figure adapted from reference [16] with permission from AAAS; (b) The two main types of resonance phenomena encountered in plasmonics - the propagating SPP excited at metal-dielectric interface and the LSP in metallic nanostruc- tures. Figure adapted from reference [17] with permission from Macmillan Publishers Ltd.

1.1 Current Challenges in Plasmonics

At present, there are two main challenges in realizing the full promise of plasmonics. Firstly, the traditional noble metals (gold and silver) used in plasmonics exhibit relatively high intrinsic optical loss. They are also not fully CMOS compatible and hence cannot be integrated with electronic components. In recent years a number of significant breakthroughs were made in identifying alternative plasmonic materials [18,19]. Naik et. al. demonstrated that doped semiconductors and intermetallics can be used to lower losses and thereby improve the performance of plasmonic devices [19,20]. The second major challenge in plasmonics is the lack of post fabrication dynamic 3

control of plasmonic resonance. Currently the resonant wavelength of plasmonic nanostructures is dependent on their size, shape and material properties [4,5]. In the literature we find that a number of phenomena like phase transitions [21], electrical carrier injection in semiconductors [22, 23], ultra-fast optical pumping [24], liquid crystals [25] and mechanical stretching of elastic membranes [26–28] have been used to tune plasmonic resonances. The magnitude and speed of change in resonance and wavelength of operation are important criteria in evaluating the merits of these approaches for specific applications. For example, molecular alignment in liquid crystals, which exhibits strong refractive index variation at visible wavelengths with electric field and temperature, has a very slow response time and does not provide linear tunability. Mechanical stretching and Micro Electro Mechanical Systems (MEMS) have been used at THz frequencies, but these approaches are not scalable to visible and NIR wavelengths because of fabrication difficulties. There is very little work on tunable plasmonic resonance at visible and NIR wavelengths because of the challenging nature of the problem, and in this work we demonstrate a new technique to tackle this issue. Our approach is based on combining the exceptional optoelectrical properties of graphene and plasmon resonances in metallic nanostructures to realize electrically modulated plasmonic resonance. In our approach the optical response is controlled by electrical signals which is essential for on-chip applications. During the course of this research there has been a lot of contemporary research exploring other aspects of these problems from several leading groups in the world, which can potentially lead to applications like modulators, photodetectors and sensors in NIR and MIR wavelength ranges.

1.2 Organization of Dissertation

This dissertation is organized into six chapters. Chapter 2 discusses the relevant background for understanding the plasmon resonance in metal nanostructures and also fundamental optoelectrical properties of graphene. Chapter 3 discusses the 4

experimental results with modulation of plasmon resonance in Bow-tie antennas in MIR wavelengths. In chapter 4 we identify the path to realize dynamic control of plasmon resonance in NIR wavelengths, and present our experimental results in Fano resonant metal nanostructures. While chapters 3 and 4 deal with plasmon resonance in metal nanostructures, chapter 5 describes intrinsic plasmon resonance in graphene itself. Here the current challenges in research are presented, and in that context our work on plasmon resonance in multilayer graphene nanoribbons (GNR) is discussed. Finally, chapter 6 provides a brief summary and provides some directions for further research. 5

2. FUNDAMENTALS OF PLASMONICS AND GRAPHENE

The interaction of electromagnetic waves with materials can be described in the classical framework by Maxwell’s equations [5, 29]. The electric and magnetic fields in an electromagnetic (EM) wave induce corresponding electric and magnetic polarizations in the material. However, at optical frequencies the magnetic polarization is usually negligible, and the material properties are typically represented in the Maxwell’s equations using a complex dielectric function (dielectric permittivity) denoted by (ω)

0 00 =  + i = 1 + i2. 1 and 2 represent the real and imaginary parts of dielectric function, and must satisfy Kramers-Kronig (KK) relations [29]. The real part of

permittivity (1) represents the strength of polarization and the imaginary part of

permittivity (2) represents the dissipation or loss of polarization in the medium. In an insulating medium such as glass the optical loss is usually very small, and hence it

is represented only by the 1.

2.1 Optical Properties of Metals

The electrons in metals are free to move in response to EM fields. According to the classical Drude model, which treats metals as 3-dimensional free electron gas, the permittivity of metals is given by [30]

ω 2 (ω) =  + i =  − p 1 2 int ω(ω + iγ) ω 2 ω 2γ =  − p + i p (2.1) int ω2 + γ2 (ω2 + γ2)γ

2 2 ∗ where ωp = Ne /m 0, int is the contribution of inner electrons and sometimes the interband transition contribution, ω is the frequency of light, γ is the Drude 6

damping coefficient and m∗ is the effective mass of electrons. We should note that γ can take different values for bulk metals and nanostructures metals because of additional scattering losses at the surface of nanostructures. The Drude permittivity calculated using Eq. 2.1 for a typical metal is shown in Fig. 2.1. A key feature to note is that the real part of permittivity changes sign from positive to negative around crossover wavelength of 472 nm. Further, if we consider another metal with smaller

carrier density, then ωp would be smaller leading to longer crossover wavelength. Typically in the IR wavelength range, noble metals are very lossy as indicated by the increasing imaginary part of the permittivity.

Fig. 2.1. Illustrative example of Drude permittivity calculated using Eq. 2.1 with ωp = 7 eV , γ = 0.07 eV and int = 6.9.

2.1.1 From noble metals to dilute and ‘lossless’ metals

Noble metals are ’good’ plasmonic materials at visible wavelengths. However, if we were to consider telecommunications wavelength of 1.5 µm then the losses, which scale with carrier density N, are too high. It could be advantageous to move to dilute metals with lower carrier density to lower losses. This is a topic of active research in the last five years, wherein a number of materials like doped semiconductors and intermetallics have been proposed as alternative plasmonic materials [18–20,31–33]. In fact it has been theoretically proposed that by engineering lattice spacing we might be able to engineer a designer ’lossless’ metal [34]. We should note that this very 7

intriguing idea would work practically only for a range of wavelengths but not all the wavelengths.

2.1.2 Plasmonic resonance in a metal nanoparticle

Let us consider a homogeneous nanoparticle of radius a within a dielectric medium of

permittivity (d) and static electric field (E). The electric field causes charge separation and hence induces a dipole moment within the nanoparticle. The polarizability (α), which is defined as a ratio of induced dipole moment to the electric field that induces dipole moment, can be shown to be [29]

 −  α = 4πa3 d m (2.2) d + 2m

If the permittivity of the surrounding dielectric d = 1, then at a wavelength where

m = -0.5 the polarizability shows a singularity leading to a resonant response. This phenomenon is referred to as localized surface plasmon (LSP) in the literature. At the resonant wavelength the electric field near the nanoparticle is enhanced compared to the free space. The resonant wavelength is extremely sensitive the changes in the

dielectric environment (d). Physical picture: A physical intuition into the plasmon resonance can be gained by approaching from energy conservation point of view. In a normal electromagnetic mode confined to resonator size greater than λ the electromagnetic energy is stored

as both electric and magnetic energy in equal measure, UE = UM [29], where UE

and UM are electric and magnetic energies respectively. It would oscillate indefinitely between electric and magnetic energies experiencing no losses. However, if the mode is confined to sub-wavelength volumes then in the quasi-static limit it can be shown

2 that UM /UE ∼ (πna/λ) . Since the magnetic component of EM energy is very small, it is confined near nanoresonator for one-quarter of a period as electric energy, and for another one quarter it will radiate out into the surrounding environment [35]. We can 8

conclude that subwavelength confinement, as in the case of a plasmonic resonance, will always be lossy and hence is relatively broad in the spectral domain.

2.2 Electronic Bandstructure of Graphene

Fig. 2.2. Electronic bandstructure of graphene (a) Unit cell in reciprocal space showing the basis vectors ~a1 and ~a2 in terms of real space lattice constant a0; (b) The E-K diagram for graphene (eq. 2.3) calculated using the tight binding approximation. The conduction and valance bands meet at the six corners of the hexagon in reciprocal space (known as the Dirac or K points); (c) Simplified representation of bandstructure of graphene using cut-lines along high symmetry directions. The bandstructure is linear close to K points giving rise to many unique properties of graphene; (d) Intraband and interband transitions in graphene; interband transitions occur above a threshold of 2EF. 9

Graphene is a hexagonal lattice of sp2 hybridized carbon atoms arranged in a single monolayer [36]. In the reciprocal space, the unit cell can be described by two

basis vectors ~a1 and ~a2 as shown in Fig. 2.2. Starting from these basis vectors and using the tight binding approximation [36] it can be shown that the bandstructure can be described using the equation [30,36]

s √ 3k a k a k a E(~k) = 1 + 4cos x 0 cos y 0 + 4cos2 y 0 (2.3) 2 2 2 The conduction and valance bands touch each other at the six corners of the reciprocal lattice known as the K points. Close to the K points the dispersion relation for graphene is linear (see Fig. 2.2(c)) and is given by

√ EF =hv ¯ F πng,2D (2.4) where ng,2D is the carrier concentration in the 2 dimensional graphene sheet, vF is the Fermi velocity (∼ 1 × 106 m/s). This linear dispersion implies that charge carriers in graphene behave as massless Dirac fermions. This is the underlying reason for many novel electronic and optical properties of graphene like large carrier mobility (and hence low dc scattering rate), and allowed interband transitions in a broad range of frequencies [37,38]. It can easily be shown that this linear dispersion results in a linear increase in electronic density of states around the Dirac point which is given by

kF ω DOS(kF ) = = 2 (2.5) πhv¯ F πhv¯ F Therefore, undoped graphene is extremely sensitive to small external perturbations especially at IR frequencies. This leads to highly nonlinear current change close to the Dirac point [39]. This is clearly different from a conventional 2D electron gas, with

∗ 2 parabolic dispersion, where the density of states is constant (m /πh¯ ). Further, ng,2D can be electrically tuned by electrostatic gating using a field effect transistor (FET)

In the crystalline phase the electronic configuration of Carbon is 1s, 2s, 2px, 2py, 2pz. The 2s and 2p orbitals can mix with each other in three possible ways giving rise to sp, sp2 and sp3 hybridizations forming different carbon based molecules. 10 structure. Hence, due to these fascinating electrical properties, graphene was initially considered as an alternative to silicon for nanoelectronics.

2.3 Optical Properties of Graphene

The electronic properties and optical properties of graphene are very closely related. In undoped graphene at 0K, optical absorption is frequency independent — determined only by the universal absorbance, A(ω) = πe2/hc¯ = πα(≈ 2.3%) (see Fig. 2.3). This is due to cancellation of frequency dependent terms in the three important parameters

2 2 determining optical absorption— the square of transition matrix element ∝ vF /ω , 2 the joint density of states (∝ ω/hv¯ F) and the photon energy (∝ ω) [40].

Fig. 2.3. Optical absorption of graphene (a) Transmission through a 50 µm aperture showing 2.3% absorption for a SLG; (b) Absorption scales linearly with number of layers in graphene and is spectrally flat at visible wavelengths. Figure adapted from reference [38] with permission from AAAS.

The optical absorption in doped graphene depends strongly on the sheet carrier density. There are two types of possible transitions — an intraband transition where the initial and final states of the electron are within the same band, and an interband transition where the incident photon excites an electron in valence band into the conduction band (see Fig. 2.4(a)). Further-more, an interband transition can generate 11

an electron-hole (e-h) pair only if the energy of the incident photon is greater than

2EF. These transitions can be analytically expressed in terms of optical conductivity of graphene derived under the so-called local limit of Random Phase Approximation (RPA) as [41,42]:

Fig. 2.4. Optical transistions in graphene (a) The optical response of graphene is controlled by e-h pair excitations. Photons with energies above 2EF will be absorbed due to transitions into the unoccupied states above the Fermi level; (b) Calculated dielectric functions for carrier densities of 3×1011, 1×1012, 1×1013 cm−2 show a tunable interband threshold. Changes in the imaginary part (dashed lines) of permittivity are accompanied by corresponding changes in the real part (solid lines). The calculations were −13 performed with τ = 1 × 10 s, T = 300 K and tg = 1 nm using the code listed in Appendix C.

2    2e ωT i ωF σ(ω) = −1 log 2cosh πh¯ ω + iτ 2ωT  ∞  2 Z ω0
ω
e ω  2ω H − H 0 + H + i 2 2 dω  where, 4¯h 2 π ω2 − ω02 0 sinh(ω/ω ) H (ω) = T (2.6) cosh(ωF /ωT ) + sinh(ω/ωT ) 12

ω is the frequency of incident light, tg is the graphene thickness, e is the charge

of an electron, τ is the Drude relaxation rate, T is the temperature, kB is the

Boltzmann constant, ωF = EF/h¯ and ωT = kBT/h¯. The first term represents the free carrier response of graphene arising due to the intraband transitions. The intraband response is dominant at MIR frequencies and beyond. The second term describes the contribution of interband transitions, which are dominant above a threshold determined by the the carrier density. The calculated effective dielectric functions at three different carrier concentrations are shown in Fig. 2.4(b). There is a strong variation of dielectric function around the interband transition threshold. An increase in carrier concentration leads to shifting of interband edge to lower wavelength. The calculations were performed by modeling graphene as an effective

medium of thickness tg = 1 nm (see also section 2.6 and Appendix C). For realistic sheet carrier densities in the range 1011 − 1013 cm−2, the interband threshold can be continuously tuned up to NIR frequencies. Further, as can be seen in Fig. 2.5, at visible frequencies the interband contribution to conductivity dominates and has a constant value of e2/4h¯. The predicted optical conductivity is consistent with experimental measurements [38,43,44].

Fig. 2.5. Relative contributions of interband and intraband transitions 11 −2 to optical response of graphene (ng,2D = 7 × 10 cm ,T = 300 K, τ = −14 e2 3 × 10 s and the y axis are scaled by G0 = 4¯h . (a) Real part of conductivity; (b) Imaginary part of conductivity; (c) Figure of merit calculations indicating that graphene is a good plasmonic materials between 2 µm - 20 µm wavelengths. The plasmonic response can be tuned to NIR wavelengths by increasing carrier density in graphene. 13

2.4 Graphene as an Alternative Plasmonic Material

In the near future we envision plasmonics to effectively bridge information between fiber based long-haul networks and nanoscale integrated electronics. However, the best plasmonic materials, namely, silver and gold exhibit relatively high losses of 0.02 eV and 0.071 eV respectively [18,19]. Graphene exhibits large mobility (indicating low losses) and large tunability. Hence, it is interesting to see if graphene can serve as a better plasmonic material at telecommunication wavelength of ∼ 0.8 eV. In view of the unique electrical and optical properties of graphene it could be an ideal platform for coupling electronic and optical functionalities by excitation of plasmons. Indeed graphene has been proposed as a platform for integrated optoelectronics and transformation optics [42,45,46]

2.4.1 Qualitative differences in plasmons in 3D vs 2D

Plasmon resonance arises from the collective motion of electrons in response to incident field. There are important differences between plasmon behavior in 3D and 2D primarily because of differences in restoring force in the two cases. In graphene the induced charges are confined to 2D plane while the restoring force is in 3D. Therefore, the 2D confined charges can be treated as a line charges, and the force between them is position dependent. This is significantly different from the 3D where the restoring force originates from electric field between two charged plates and is position independent. Considering the force experienced by an electron between two line charges we can see that the resonance frequency (similar to x¨ = −ω2x) will be position dependent. Using the rigorous RPA the dispersion relations can be derived as shown in eq. 2.7 [47]. 14

s 2 parabolic n3De ωp,3D = m0 s 2 parabolic n2De 1/2 ωp,2D = q m0

linear √ 1/4 1/2 ωp,2D = rsgπn2D vF q (2.7) where, rs is dimensionless fine structure constant, g is degeneracy factor (4 for graphene), q is the in-plane wavevector. Experimental measurements in semiconductor inversion layers, which have parabolic electronic dispersion, show a quadratic wavevec- tor dependence given by the above relations [48,49]. Some of the consequences of the above relations are:

ˆ 2D plasmon frequency goes to zero in the local approximation (λ → 0 and q → 0), and it is strongly perturbed by the shape and dielectric constant of the material in it’s vicinity

ˆ 2D plasmons are excited at much lower than 3D plasmons (see Fig. 2.6 adapted from [50])

ˆ In graphene the dispersion is explicitly non-classical and shows much weaker carrier concentration dependence

ˆ The carrier density in graphene needs to be unrealistically large for exciting visible/NIR plasmons. However, at longer wavelengths plasmon can indeed be excited in graphene.

2.4.2 Loss mechanisms in graphene

Since graphene can in principle support plasmons it is interesting to further explore the loss mechanisms in graphene. The large mobility of graphene indicates that the scattering losses will be low. However, a more careful investigation reveals that the main processes that contribute to loss in graphene are: 15

Fig. 2.6. Dispersion of Plasmons in a solid. (1) Volume Plasmons, (2) Surface Plasmons, (3) Plasmons in 2DEG, (4) Plasmons in 1D system. Note: Upper scale valid for (1) and (2), the scale below for (3) and (4), ll is light line. Figure adapted from reference [50].

ˆ Scattering Accounts for scattering losses because of electron-impurity, electron- defect and electron-electron interactions. This is the dominant loss mechanism for frequencies below 0.2 eV (Optical Phonon Energy), and can be estimated from traditional current voltage measurements. A typical value for losses by this mechanism is 6-10 meV .

ˆ Interband Transitions Interband transitions contribute to significant losses

for frequencies above 2EF as shown in Fig. 2.5. Since the Fermi energy is √ dependent on carrier concentration as EF = hv¯ F πng,2D we can avoid interband contribution by increasing doping. Considering the fact the interband transitions show smearing at higher temperature, we need a carrier concentration of atleast 3 × 1013cm−2 to push interband threshold to 1.28 eV (beyond our desired operation frequency of 0.8 eV). Practically, a still higher concentration of up to 1.2 × 1014cm−2 might be needed if we take momentum dependence of interband 16

threshold. This seems unlikely with current technological limitations. At lower concentrations we would have loss contribution from interband transistions.

ˆ Electron-phonon coupling Even below the interband threshold the plasmon lose energy by phonon assisted interband transitions. This effect would be strong just below the interband threshold and weaker at longer wavelengths.

2.4.3 Conclusions

Graphene could serve as an alternative plasmonic material below the optical phonon at 0.2 eV (6.4 µm). Indeed there have been experimental demonstrations of real space imaging and gate tuning of plasmons with scattering NSOM at 10 µm wavelength [51,52]. Further, gate tuning of T Hz plasmons has also been demonstrated [53]. In the visible and near-IR frequencies, however, the interband loss becomes large and makes graphene unattractive as a plasmonic material [18,54].

2.5 Nonlinear Optical Properties

The linear conductivity of graphene given by Eq. 2.6. However, if the energy

acquired by a particle under electric field in one cycle, qEv/ω, is larger than the EF then the linear approximation breaks down [55]. Under intense laser illumination this leads to nonlinear response which can be described by:

1 2 3 j(ω) = σ (ω)E1(ω) + σ (ω)E1(ω)E2(ω) + σ (ω)E1(ω)E2(ω)E3(ω) + ... (2.8)

The higher order terms in surface conductivity σ(ω) produce higher order harmonics under intense illumination. Further, nonlinearity is strong in a material around a resonance. Since graphene has allowed interband transitions at all frequencies, the nonlinearity can expected to be strong. Indeed, χ(3) ≈ 1.5 × 10−7 e.s.u has been reported in literature [56]. Tunable properties of graphene in principle can lead to active control of parametric processes. This would be useful for applications where 17

tunable phase mismatch is desired to compensate for fabrication variations. However, recent calculations indicate that the nonlinearity in graphene will saturate rather quickly because of linearly increasing density of state [39].

2.6 Numerical modeling of graphene

To develop useful devices with graphene it is essential to develop accurate models for numerical simulations. Graphene being a vanishingly thin monolayer poses unique challenges for numerical treatment. There are two main approaches for numerical implementation of graphene (i) treat graphene as an effective medium with finite

thickness tg and permittivity given by Eq. 2.9, and (ii) describe graphene with a surface current given by σ(ω) in Eq. 2.6. The second approach is more suited for grid-based, full-wave finite element frequency domain (FEFD) simulation methods using for example commercial tools such as COMSOL Multiphysics or CST Studio.

iσ(ω) (ω) = 1 + where, (2.9) ω0tg tg is the effective thickness of graphene.

2.6.1 Validation in frequency domain

Fig. 2.7 shows comparison between experimentally measured IR reflectivity data normalized to reflectivity at charge neutral point (CNP) and numerical simulations. The fit is remarkably close considering that experiments were performed using Chemical Vapor Deposition (CVD) grown with up to 20% inhomogeneity. Further details can be found in the section 5.3.2.

2.6.2 Validation in time domain

The RPA model cannot be used directly in time domain simulations because the interband conductivity does not have a simple time domain form. Several groups 18

Fig. 2.7. Validation of numerical modeling of graphene in frequency domain (a) Experimental gate dependent reflection spectra normalized to the Dirac point, (b) Simulated reflection spectra with graphene carrier concentration as a parameter.

report time domain simulations by either ignoring interband contribution or assuming asymptotic conditions [57]. These approximations are not valid at optical wavelengths or room temperature. We recently developed an accurate, multivariate time domain model for graphene using two Pad`eapproximant terms, which accurately captures the time domain response of graphene from visible to IR wavelengths [58,59]. This model has been already tested by combining critical-point approach [58, 59] with a surface-current enabled FDTD [60].

2.7 Summary

In this chapter we discussed fundamental aspects of plasmonics and graphene. These form the basis for understanding the experiments described in the next few chapters. 19

3. DYNAMIC ELECTRICAL CONTROL OF THE PLASMONIC RESONANCE WITH GRAPHENE

Surface plasmons confine the incident electromagnetic energy into a sub-wavelength volume where it interacts strongly with the local dielectric environment. Electrical control of plasmonic resonances has been demonstrated at T Hz frequencies [21,22,61] by electrically modulating the local dielectric environment. Similar dynamic switching of plasmonic resonances at NIR and MIR wavelengths could open up many exciting possibilities for many applications like integrated modulators, switches and sensors. Here we show that it is indeed possible to electrically control the width of the plasmonic resonance in metal nanostructures fabricated on top of a sheet of graphene. As discussed in chapter 2.3 the dielectric function of graphene exhibits strong variation around the interband transition.The calculated effective dielectric functions at three different carrier concentrations was shown in Fig. 2.4. An increase in carrier concentration leads to shifting of interband peak to lower wavelength. The calculations were performed by modeling graphene as an effective medium of thickness tg = 1 nm (see also section 2.6). For realistic sheet carrier densities in the range 1011 − 1013 cm−2, the interband threshold can be continuously tuned up to near-IR frequencies.

3.1 Experimental Setup

To investigate the impact of graphene on plasmonic resonances we fabricated bowtie antennas, which exhibit a strong resonance in the IR wavelength range [62], on top of graphene sheet as illustrated in Fig. 3.1. If the plasmonic resonance frequency is above the graphene interband threshold, then the resonance decays by direct emission of e-h pairs. This gives us a route to create tunable plasmonic resonances. A gate voltage

(VG) is applied through the silicon back-gate to change the carrier concentration in 20

graphene sheet, which is monitored by measuring the resistance between the source

and drain terminals (RSD).

Fig. 3.1. Schematic illustration of the experimental structure for voltage- controlled optical transmission measurements.

3.1.1 Fabrication and Characterization

The devices were fabricated on a 300 µm thick double side polished Si wafer with low doping density (1-10 Ohm cm). The source drain contacts were defined by photolithography (Processing details are provided in A), followed by e-beam evaporation of 10 nm Ti / 60 nm Au. The lift-off process was carried out by soaking in Acetone solution followed by squeeze bottle spray. A large-area graphene sheet, which was initially grown on 25 µm copper foil by atmospheric pressure chemical vapor deposition (CVD) [63], was transferred onto the sample substrate while ensuring good electrical connections with both the source and the drain contacts. Next, bowtie structures were fabricated by electron beam lithography, metallization (2 nm Ti and 30 nm Au), and subsequent lift-off processes. 21

3.1.2 Electrical and Raman Characterization

The electrical characteristics of the fabricated devices were obtained using Keithley 2400 Source Measure Unit (SMU) at gate terminal, and Agilent 31101A to measure the source drain resistance. Typical modulation of carrier concentration in graphene with gate voltage is shown in Fig. 3.2(a). We define ∆V = VG − VDP, where VG is the

gate voltage applied and VDP is the gate voltage for which graphene exhibits a peak

in source drain resistance (RSD) referred to as Dirac point. Raman spectroscopy is a widely used tool to characterize the quality of graphene sheet. The main features of graphene Raman spectrum are the so-called G peak appearing at 1582 cm−1 and the 2D (or G’) peak appearing around 2700 cm−1 using a laser excitation at 2.41 eV (or 514 nm). Additionally if there is disorder in graphene or at the edge of the sample, we can also find another peak at 1350 cm−1 which is referred to as D peak [64,65]. A typical Raman spectrum measured on a bare graphene device is shown in Fig. 3.2(b). We observe sharp 2D and G peaks and the ratio

of their intensities I2D/IG is about 2 indicating that our devices consist of mostly monolayer graphene. Since the resonant structures are in contact with the graphene, they could have an impact on the electronic properties of the graphene. To investigate possible effects from the metal nanostructures, we performed Raman spectroscopy on graphene with metal nanostructures as well. We observed changes in the graphene carrier concentration caused by additional electron doping due to the metal (see Fig. 3.2(b)). At the same time, the electrical characteristics remained qualitatively similar to those of bare graphene except for a shift in the Dirac point.

3.1.3 Optical Characterization of Bowtie Antennas

To investigate the impact of graphene on metal nanostructures at different resonant frequencies, we fabricated bowtie antennas of different dimensions as shown in Fig. 3.3(a). Bowties 1-3 were fabricated on the same graphene device, and bowtie 4 was fabricated on a different device. A scanning electron micrograph of a fabricated 22

Fig. 3.2. (a) Typical plot of carrier concentration dependence on gate voltage indicating a good modulation of carrier concentration. We also observed a very small variation in resistance during optical measurements, which can be attributed to electrochemical redox reactions of adsorbates on graphene [66]; (b) Raman spectroscopy of graphene with and without metal nanostructures shows electron doping caused by the metal [67,68]. The intensity of the D peak was small (not shown here), indicating the high quality of the graphene. Spectra were averaged from measurements at three different locations on the sample.

sample with plasmonic structures on top of the graphene sheet is shown in Fig. 3.3(c). It is clearly seen that the CVD graphene is mostly uniform, although some folds and domain discontinuities can be observed. A Fourier Transform Infrared (FTIR) spectrometer with a microscope was used to optically characterize the plasmonic resonance behavior. All the optical measurements were performed in ambient air at room temperature. The experimentally measured optical transmission spectra of the 23

resonant structures on top of the graphene are shown in Fig. 3.3(d). We observe a strong resonance which exhibits a red shift in resonant wavelength with increasing dimensions.

Fig. 3.3. (a) Geometry, dimensions and resonant wavelengths of fabri- cated bowtie antennas on graphene; (b) Calculated local magnetic field enhancement at the center of bowtie at resonant wavelength. The bowtie plasmonic resonance is thoroughly discussed by Grosjean et al. [62]; (c) Scanning electron micrograph of fabricated bowtie antennas on top of a graphene sheet; (d) Measured optical transmission spectra for bowtie antennas with different periodicities fabricated on graphene.

3.2 Dependence of tunability on wavelength

The carrier concentration of graphene can be realistically tuned between 1 ×

12 −2 13 −2 10 cm and 3 × 10 cm , and hence EF can be varied in the range of 0.12 - 0.64 eV . Therefore, we can expect a significant impact from the gate voltage on the resonances at IR wavelengths. To investigate this dependence we compared the optical 24

transmission spectra from three structures (Bowtie 1-3) fabricated on the same device. We found that the effect of the gate voltage on the resonance increases as the resonant frequency shifts further into the IR as shown in Fig. 3.4. We observed that the change for graphene with bow-tie antennas was much higher than the approximately 1% change in a bare graphene device (see Fig. 2.7). This is consistent with the results reported in the published literature [53], confirming that plasmonic structures do indeed enhance the interaction of light with graphene.

Fig. 3.4. The measured transmittance at a particular gate bias (in volts) normalized by the transmittance measured at the Dirac point. The carrier concentration in graphene increases as ∆V moves away from zero and leads to a stronger impact on resonance. We observe stronger damping of the plasmonic resonance at mid-infrared wavelengths. Data for bowties #1, #2 and #3 is shown in panels (a), (b) and (c) respectively.

To gain further insight into the experimentally obtained spectra, we performed full-wave numerical simulations using 3D Spatial Harmonic Analysis (SHA) [69]. The sample was modeled with four layers: silicon, silicon dioxide, graphene, and gold bowtie antennas with corresponding material properties and geometries taken from experiments. We treated graphene as an effective medium with a thickness of 1 nm, and we calculated its dielectric function using the optical conductivity of graphene (Eqs. 2.6, 2.9). To investigate the impact of gate voltage, we used the carrier concentration of the graphene sheet as a fitting parameter in our numerical simulations. 25

Fig. 3.5. (a) Experimentally observed (solid lines) damping of a plasmonic resonance due to an applied gate voltage. A higher carrier concentration leads to blocking of some interband transitions, and hence leads to a narrower resonance. Full-wave simulations (dashed lines) performed with graphene carrier concentration as a fitting parameter produce an excellent match with the experimental results; (b) Simulated phase delay of E field along the axis of the bowtie. Changes in carrier concentration lead to a simultaneous change in transmission as well as phase since both real and imaginary parts of permittivity of graphene are tuned by electric bias; (c) The narrowing of the width of the resonance with gate bias shows the precise electrical control of the resonance. 26

3.3 Electrical Control of Damping

The optical transmission spectrum for a resonance at 4.5 µm is shown in Fig. 3.5(a) where we see an observable variation of transmittance with gate voltage. At the Dirac point (∆V = 0), the interband transitions are allowed at all frequencies, leading to a broader resonance. However, with increasing carrier concentration (∆V < 0) some of the interband transitions are forbidden, leading to narrower line width. The asymmetric influence of graphene on the line shape reflects the changes in the dielectric function plotted in Fig. 2.4(b). The full-wave numerical electromagnetic simulations show remarkable agreement with the experimental results using only the carrier concentration in graphene as a fitting parameter. We observe up to 210 nm decrease in resonance line width with applied bias. Further, in addition to the damping that is expected from the absorption due to graphene, we also see a small blue shift in the resonance. This is not surprising as the changes in the real part of permittivity lead to change in the resonant wavelength.

3.4 Discussion

It should be noted that despite the early promise up to 25% peak change in transmission at a 5 µm wavelength (see Fig. 3.5) the bow-tie antennas show negligible spectral tunability. One main reason for this could be that the incident electromagnetic energy interacts strongly with graphene only in the narrow (80 nm × 80 nm) neck region of the bow-tie antenna. In fact, for any dipole antenna at resonance the electromagnetic energy is confined only to the small regions around the edges of the antenna. Therefore, these geometries will not be very sensitive to changes in graphene and are not strongly tunable. An improved design for tunable resonance in MIR frequencies was proposed by Yao et. al., where they incorporated ideas from Metal- Insulator-Metal (MIM) waveguides into the antenna geometry [70–72]. In a clever design they stagger two adjacent nanorod antennas so that the electric field is confined 27

to regions between the nanorods similar to a bonding mode in a MIM waveguide. They report improved tuning range of ∼1100 nm at 6.5 µm wavelength [71].

3.4.1 Modeling Tunability of a Resonant Structure Using Perturbation Theory

There are a wide variety of graphene-plasmonic antenna hybrid systems being studied in different groups. Perturbation theory is a useful tool to estimate the impact of graphene in different resonant plasmonic systems. According to this theory for small material perturbations the change in resonance frequency is given by [73,74]

h i RRR ↔ ~ ~ ∗ ↔ ~ ~ ∗ (∆µ · H0) · H0 + (∆ · E0) · E0 ∆ω dV ∆Wm + ∆We = − h i = − (3.1) ω0 RRR ↔ ~ ~ ∗ ↔ ~ ~ ∗ Wm + We µ · H0 · H0 +  · E0 · E0 dV ~ ~ where, ω0 is the resonance frequency, E0 and H0 are unperturbed electric and magnetic fields, ↔ and ↔µ are changes in permittivity and permeability respectively. This expression clearly shows that the maximum contribution to tunability occurs when graphene is close to strongly confined electric and magnetic fields. Further, the fractional change in resonance frequency is simply proportional to fractional changes in electromagnetic energy. This analysis gives a quantitative handle to analyze newer geometries, and has been verified for dipole antennas [75] and Fano resonant metasurfaces [76] in MIR wavelengths.

3.5 Summary

In this chapter we showed that graphene can be used to electrically control the damping of plasmonic resonances in the MIR part of the spectrum. The framework developed in this work will be useful to further explore designs to achieve stronger damping and tuning of plasmonic resonances. MIR wavelengths constitute an extremely important wavelength range with applications like molecular vibration sensors [77] 28 and compact and ultrafast MIR modulators [72]. We can be cautiously optimistic that further progress in this area could lead to practically useful devices. 29

4. TUNABLE FANO RESONANT NANOSTRUCTURES AT NEAR INFRARED WAVELENGTHS

In the preceding chapter we showed that graphene can be used to modulate the plasmonic resonance in MIR wavelengths. This is a very exciting technology win- dow with many practical applications. If the modulation can be extended to NIR wavelengths then plasmonic structures can be integrated into on-chip devices working at telecommunications wavelength. However, this is an extremely challenging task with most of the research of tunable plasmonics with graphene being confined to MIR wavelengths. In this chapter we discuss our approach to integrate graphene with Fano resonant metallic structures to realize tunable device operating at 2 µm wavelength.

4.1 The Fano Resonance in Metallic Nanostructures

The most commonly encountered resonance lineshape in physical phenomena is γ2 a Lorentzian given by I ∝ 2 2 , where ω0 is the resonant frequency and γ is (ω−ω0) +γ the damping factor. This type of resonance is exhibited by many diverse systems such as mass on a spring, electron bound to an nucleus, cavity modes in a laser, etc. However, in a system where there are many closely spaced resonances the modes can mutually interfere to produce more complex lineshape. While analyzing auto-ionizing systems Ugo Fano discovered a new type of resonance - now called as Fano resonance, wherein a distinct asymmetric lineshape is produced by the interference of a discrete line with a continuum of states [78]. This asymmetric line shape of Fano resonance is

2 (F γ+ω−ω0) given by I ∝ 2 2 , where F is the so-called Fano factor [79]. Fano resonance has (ω−ω0) +γ recently been observed in plasmonic systems, where the dipolar mode (broad) and quadrupolar modes (narrow) interfere to give an asymmetric lineshape [80–83]. This can also be understood as a plasmonic analogue of the well-known electromagnetically 30

induced transparency [84]. Dipolar mode is readily excited in metal nanostructures because of coupling to incoming radiation. However, higher order modes can be excited only by breaking the symmetry in the system through proper design of geometrical parameters of metal structures. If these two modes are designed to overlap at particular wavelength we will observe Fano resonance, which inherently sensitive to local dielectric environment due to the interference phenomenon. Indeed, Fano resonant structures have been shown to be extremely sensitive to presence of glucose [85].

4.2 Design and Fabrication

Fig. 4.1. (a) Schematic illustrating the Fano resonant plasmonic antennas fabricated on top of SLG used in our experiments. The optical mea- surements were performed using an FTIR spectrometer with an attached microscope in reflection mode. (b) Geometry of the dolmen structure used in our experiment. When the incident light is polarized along the horizontal rod it excites a dipolar (bright) mode, and simultaneously a quadrupolar (dark) mode is excited in the vertical rod pair. The dimensions in the structure were optimized to achieve overlapping of these modes so that a Fano resonance dip is around 1.9 µm. (c) Scanning electron micrograph showing the sample fabricated using e-beam lithography. The scale bar is shown below the image. Doses in the e-beam lithography were optimized to achieve reliable gaps of 20 and 50 nm required by the design. 31

Fig. 4.1(b) shows the dimensions of the fabricated plasmonic antennas which were optimized to achieve a resonance at a 2 µm wavelength using full-wave 3D full wave FEFD simulations (with COMSOL Multiphysics). The antennas were fabricated on a graphene FET by e-beam lithography using 100 nm ZEP 520A (Zeon Chemicals) as a resist. The fabrication of the 20 nm and 50 nm gaps close to large features with dimensions around 100’s of nm, as required by the present design is challenging in ebeam lithography due to the so-called proximity effect. In the present experiment, the doses applied to individual antennas were varied and optimized to realize the final fabricated structure as shown in Fig. 4.1(c) (see Appendix A for additional details). This was followed by e-beam evaporation of 2 nm Ti/20 nm Au and subsequent lift-off processes. The SEM micrograph in Fig. 4.1; (c) shows representative dimensions of the fabricated sample. The optical studies of the samples were performed using a Fourier Transform Infrared Spectrometer (FTIR) in the reflection mode.

4.3 Sensitivity of Fano Resonant Structures

One of the earliest reports of the extraordinary sensitivity of Fano resonances to presence of graphene was reported in split-ring resonators [86,87]. However, in that work the influence of carrier density and the exact nature of the interaction between resonance and metallic structures was not discussed. To verify the hypothesis that Fano resonant structures interact strongly with SLG, we measured the reflectance from the antennas at four different locations with and without an underlying SLG as shown in Fig. 4.2. We observe a strong impact of the graphene on the spectra measured and also the characteristic the Fano dip in line shape around 1.8 µm. Further, the spectra measured from the antennas fabricated on the graphene at different locations show small deviations, while spectra from antennas fabricated on bare substrate are identical. This can be easily explained by the spatial inhomogeneities of carrier density due to topographic corrugations [88] and electron and hole puddles [89] that lead to changes in the optical properties. It should be noted that while this strong impact of 32

graphene on the Fano resonance agrees with other studies [76,86,90], it is only the first step in the realization of a practical device with large dynamic tunability.

Fig. 4.2. Measured optical reflectance spectra from Fano resonant antennas at four different locations (two without graphene and two with graphene) showing strong impact of graphene on Fano resonance. In measurements without graphene (red and blue curves), there is perfect overlap, while measurement with graphene (green and turquoise curves) show variations due to spatial inhomogeneities.The dip at 1.8 µm corresponds to the location of the Fano resonance (overlapping dipolar and quadupolar modes in dolmen geometry). We note that in this particular sample the reflection at lower wavelengths does not decrease as expected in Fano line shape due to fabrication imperfections.

4.4 Electrical Control of Fano Resonant Nanostructures

It can be seen from Fig. 2.5 that large changes in conductivity in NIR frequencies occur when the carrier density in graphene is greater than 1 × 1013 cm−2. Typically carrier densities lower than > 7 × 1012 cm−2 are only reported in conventional Si

back-gate due to possibility of gate oxide breakdown. For a SiO2 dielectric to function as a gate dielectric it should be free of defects, since defects can form a conducting 33

path (so-called percolation path) through which the gate current can flow leading to

shorting of gate voltage to channel. Alternative high-k gate dielectrics like Al2O3 and

HfO2 can increase the maximum obtainable carrier density [91]. In our experiments we found liquid electrolytic gate to be a effective solution as shown below.

4.4.1 Electrolytic Top Gate Vs Traditional Si Backgate

A simple yet effective method of achieving large carrier densities is to use an electrochemical top gate [67,92,93], wherein the gate voltage is applied to an electrolyte deposited on top of a graphene sheet (see Fig 5a). In a electrochemical gate the applied voltage falls across an extremely thin electrical double layer (EDL) or Debye layer at the interface with graphene leading to a much higher gate capacitance (∼ 2 µF/cm2).

Fig. 4.3. Schematic illustrating the two types of gating techniques for graphene. Traditionally the voltage was applied through the Si back gate, which has limited control of the channel. Alternatively, a liquid electrolytic top gate can create large carrier densities in graphene because of formation of an electric double layer at the interface as shown in the inset.

In our experiments electrochemical gating was achieved with DEME-TFSI (Di- ethylmethyl (2-methoxyethyl) ammonium bis(trifluoromethylsulfonyl) imide) as a top electrolyte. Fig. 4.4 shows measurements performed using the same device via back 34

Fig. 4.4. (a) Experimentally measured modulation of the resonance using backgating through SiO2. The measurements were performed in hole doping regime where carrier concentration was reduced with the applied voltage increase. (b) Experimentally measured optical spectra on the same device using ion-gel top electrolyte gating. The scans were taken in the electron doping regime where carrier concentration increases as the applied voltage increases.

gating and ion-gel gating. We clearly see that introduction of the ion-gel causes the resonance to be red-shifted. At the same time, the tunability of the resonance increases considerably. Fig.4.5(a) shows optical measurements using ion-gel gating measured on one of the fabricated devices which shows a similar trend as in Fig. 4.4(b).

4.4.2 Comparison Between Experiments and Numerical Simulations

To verify the experimental observations we performed numerical simulations using 3D FE modeling of SLG as a transition boundary condition wherein the surface current depends on the conductivity given by Eq. 2.6. The simulation results which are shown in Fig. 4.5(b) show qualitative agreement with experimental results. We note that the peak to the left of Fano dip shows less modulation than the peak to the right of Fano dip. This is consistent with our previous results [1] showing the impact of graphene to be stronger at longer wavelengths. Further, the measured data show a saturation effect, wherein the spectra do not significantly change at large carrier 35

Fig. 4.5. (a) The measured optical reflectance spectra with ion-gel top electrolyte. (b) 3D FE simulations using experimental geometry and graphene sheet carrier density as an input parameter. We observe a qualitative agreement with experimental results. These simulations do not take into account the ion-gel,the thickness and index of which are challenging to determine in the experiment. This explains the difference in the experimentally measured and simulated wavelength of the Fano dip.

concentrations. This differs from our simulation results which assume an ideal scenario of increasing carrier concentration.This clearly indicates that the graphene carrier concentration around the gold antennas shows a much smaller degree of variation than the changes expected from free standing graphene. This can result from the work function mismatch leading to contact resistance between the graphene and gold nanostructures [94–96]. This can be minimized by introducing thin intermediate metals and is beyond the scope of this work. Another potential direction for improving the tunability of the plasmonic resonance is using several layers of graphene which have higher optical conductivity [97], therefore leading to stronger impact on plasmonic resonance.

4.4.3 Carrier Density near Metallic Nanostructures

It is well known that the metal-graphene interface plays a critical role in charge transport properties, and presence of a work function mismatch can lead to contact 36 resistance. It has been reported that Ni or P d show low contact resistance, while T i, Cr and Al contacts show high contact resistance [98]. Further, presence of surface defects can lead to Fermi level pinning at the interface [99]. Mueller et.al., report that the metal contact induced doping of graphene not only occurs under the contact, but also extends 200-300 nm into the graphene sheet [95]. Our previous Raman scattering measurements also indicated that nanostructures indeed cause electron doping of graphene [1]. Scanning photocurrent measurement technique offers a simple method to characterize the variations in the potential profile. Fig. 4.6 shows the measured photocurrent as a 532 nm laser spot (∼ 10 µm diameter) is scanned across from source to drain contacts. We see a sharp rise in photocurrent at the interface between graphene and source/drain contacts (5 nm Ti/ 50 nm Au). A optical chopper was introduced into the light path to modulate the light beam and provide a reference to lock-in amplifier.

Fig. 4.6. Scanning photocurrent measurements across a graphene FET structure with 532 nm laser. The sharp changes in photocurrent at the source and drain contacts is due to the built in field at the respective junctions (as illustrated on the right). Since the E field is directed in opposite directions at contacts we see a reversal in measured photocurrent.

While there have been a number of studies on bulk junctions, the diffusion length of carriers in the case of nanostructured metal antennas in contact with graphene is presently unclear. This needs to be investigated carefully for optimizing the tunability of plasmon resonance. 37

4.5 Summary

In summary, we discussed efficient dynamic control of Fano resonances in plasmonic structures at NIR wavelengths using graphene [2]. Stronger modulation can be achieved by optimizing the graphene nanostructure contact resistance, and by use of multilayer graphene. This demonstration paves the way for development of tunable elements for next generation of plasmonic and hybrid nanophotonic on-chip devices such as sensors and detectors. 38

5. INVESTIGATION OF THE PLASMON RESONANCES IN MULTILAYER GRAPHENE NANOSTRUCTURES

In the preceding chapters we focused on the interaction of graphene with plasmons in metal nanostructures. However, graphene itself supports intrinsic plasmons in IR frequencies [54]. In the recent years there were numerous demonstrations of tunable intrinsic graphene plasmons in graphene ribbons [53], tapered graphene [51,52], nano- disks [100–102] and rectangular hole arrays [103]. Graphene plasmon wavelength has been shown to be 20-60 times smaller than free space wavelength, and can be tuned over a large wavelength range by electrical gating [51,52,102,103]. If tunable graphene plasmons can be extended to NIR wavelengths there could be many potential applications in optical signal processing. However, this currently a major challenge due to the maximum achievable carrier density in graphene, and the scattering due to rough edges in nanopatterned graphene.

5.1 Motivation

Currently the amplitude of graphene plasmon resonance is small (< 10%) due to the small optical conductivity of SLG. Optical studies of AB stacked bilayer using a synchrotron light source reveal that the optical conductivity of multi layer graphene is higher than single layer graphene as shown in Fig. 5.1. The optical conductivity of SLG is consistent with the prediction of the RPA model (cf. Fig. 2.5). However, the spectrum of bilayer graphene shows a sharp resonance at 0.37 eV due to alteration of

There are important differences between plasmon behavior in 3D and 2D primarily because of differences in restoring force in these two cases. In graphene the restoring force is in 3D while the induced charges are confined to 2D plane. Therefore, the restoring force arises from electric field between two line charges and is position dependent. This is in contrast to the 3D case, where the restoring force originates from electric field between two charged plates and is position independent. This manifests as a wavevector dependence in plasmon dispersion for 2D systems. 39 low energy 2D bandstructure [97]. With further increase in number of layers the optical conductivity spectrum becomes more complex, but the general trend of increasing optical conductivity is maintained. Only SLG was used in all the investigations of plasmons in graphene till date. Clearly there is a need for a systematic study of plasmon resonance in multilayer graphene, which is the objective of this study.

Fig. 5.1. (a) Optical conductivity of AB stacked SLG and BLG (b) Evolution of optical conductivity of FLG samples with increase in number of layers. (Figures adapted with permission from Mak et.al., 107, 34, PNAS (2010); reference [97] in bibliography; ©2010 National Academy of Sciences).

Here we begin by calculating the plasmon dispersion in 2D sheet at an interface between 2 dielectrics, and show how this can be used to estimate plasmon resonance in graphene nanoribbons (GNR). We then discuss our studies on plasmon resonance in multilayer CVD grown graphene.

5.2 Plasmon Dispersion in 2D Medium

Let us consider a 2D sheet charge at an interface between 2 dielectrics with permittivity 1 and 2 respectively as shown in Fig. 5.2. To understand the behavior of the TM waves at this interface we can apply Maxwell’s equations. For harmonic time

The discussion in this section closely follows derivation for SPPs at the interface between dielectric and metal except for the boundary conditions [5]. 40

∂ ∂ dependence ( ∂t = −iω), assuming uniformity in y direction ( ∂y = 0) and considering only TM modes (Hx = Hz = Ey = 0; Hy 6= 0; Ex 6= 0 and Ez 6= 0), Maxwell’s equations simplify the following set of equations

∂E ∂E x − z = −iωH (5.1a) ∂z ∂x y ∂H y = iωE (5.1b) ∂z x ∂H y = −iωE (5.1c) ∂x z

Fig. 5.2. Schematic of interface between two dielectrics with a 2D sheet charge at the interface. The incident electromagnetic wave can excite charge oscillations at the interface illustrated by the dashed line.

Now, let us assume that a surface wave is propagating along x-direction given by

iβx k1z Hy1 (z) = A1e e (5.2a) 1 iβx k1z Ex1 (z) = −iA1 k1e e (5.2b) ω1 β iβx k1z Ez1 (z) = −A1 e e for z > 0 (5.2c) ω1 41

and

iβx −k2z Hy2 (z) = A2e e (5.2d) 1 iβx −k2z Ex2 (z) = iA2 k2e e (5.2e) ω2 β iβx −k2z Ez2 (z) = −A2 e e for z < 0 (5.2f) ω2

The boundary condition imposed by the 2D sheet charge is Hy1 − Hy2 = σEx, where σ is the surface conductivity. Differentiating Hy w.r.t z, and using 5.1b we iω find that Hy = k Ex. Substituting this back into boundary condition we obtain the dispersion relation for TM modes supported by the current sheet as [54]

r1 r2 iσ q − q = General case (5.3a) 2 ω
2 2 ω
2 ω0 β − r1 c β − r2 c iω β ≈  ( +  ) Non-retarded regime q >> ω/c (5.3b) 0 r1 r2 σ (ω, β)

where, β is the plasmon wavevector, ω is the frequency, σ(ω, β) is the frequency

dependent optical conductivity, and r is the dielectric permittivity of the environment. When graphene is patterned in nanoribbons it can support plasmon standing waves when the condition Re(β) W = π + φ, where W is the width of the Graphene Nanoribbon Ribbon (GNR), and φ is an arbitrary phase shift introduced by the reflection at GNR edge.

5.3 Fabrication and Characterization

SLG was grown on Cu foils using standard CVD process [104]. We then sequentially transferred one, two and three layers of CVD grown graphene on three separate silicon substrates with 300 nm thermal oxide. Subsequently a 500 µm × 500 µm active area, and source drain contacts were defined by photolithography on each sample. The active area was patterned into GNRs (50 nm width and 150 nm period) using electron beam lithography. Further nanofabrication details can be found in Appendix A. 42

5.3.1 Electrical characterization of MLG

We first verified that the source drain sheet resistance of MLG sheets can be modulated by applying gate voltage. We found that SLG exhibits highest dynamic range of variation of electrical resistance as shown in Fig. 5.3, followed by two layer and three layer graphene respectively. It is also widely believed that increasing number of graphene layers leads to decrease in mobility due to alteration of graphene bandstructure. While some other studies of the screening and inter layer coupling in exfoliated multilayer graphene transistors suggested that the linear bandstructure model works up to 4 layers [105].

Fig. 5.3. The measured sheet resistance of MLG samples indicated that up to 3 layers there is large tuning of resistance even though mobility is reduced.

In graphene plasmonics there are two main quantities of interest, the optical conductivity and mobility which together determine the strength of plasmon resonance. When we move from SLG to few layer graphene (FLG) the mobility will most likely be degraded. However, graphene plasmons are observed only at high carrier densities where the mobility can be expected to be poor (µ ∝ 1 ). Experimental studies of EF plasmon resonance in graphene nanoribbons will help in uncovering the most critical influence. 43

Fig. 5.4. (a) Schematic illustration of the sample used for studying plas- mon resonance in graphene nanostructures; (b) SEM Micrograph of the fabricated GNRs.

5.3.2 Optical characterization of the substrate

The optical measurements were performed using a FTIR (Nicolet Magna-IR 850) with a microscope accessory (Nicplan IR Scope, 15X NA 0.58 Reflectochromat). The incoming beam was polarized with electric field perpendicular to ribbons using a wire grid polarizer to excite TM modes in GNRs. Graphene plasmons occur in the wavelength range 7 µm − 10 µm range for ribbon width ∼ 50 nm and typical carrier density (1 × 1012 − 7 × 1012 cm−2). Since free carrier absorption becomes strong around 10 um wavelength in highly doped silicon substrates, we chose a silicon substrate with

low doping (1-10 Ohm − cm). Further, since SiO2 has a phonon in this wavelength range we initially performed reflectance measurements using a FTIR to characterize the phonon optical properties. The measured data was fit with Lorentz and ionic oscillator models using WVASE software (J. A. Woollam Co.) as shown in Fig. 5.5. We can see that there was an anomalous and very narrow dip at 8 µm wavelength in reflection which could not be fit initially without unphysical oscillator parameters. The

magnitude of SiO2 in our fitting is too large for a phonon in amorphous substrate like

SiO2. We first verified that this was not an artifact by making the measurements in 44

two different FTIR instruments. We then hypothesized that it was some form of modal interference effect, and concluded that additional data was required to accurately

characterize the SiO2 phonon properties.

Fig. 5.5. (a) Reflectance from Si substrate with a 300 nm SiO2 substrate. (b) Initial fit with a lorentz oscillator in WVASE software which was later proven to be inaccurate.

The samples were sent over to J. A. Woollam Co. for accurate IR Spectroscopic ellipsometric characterization. These measurements were performed at the lowest possible angle to simulate the normal incidence measurements in FTIR. The measured reflectance for s and p polarizations, and extracted permittivity is shown in Fig. 5.6.

The SiO2 phonon leads to strong absorption (large Im SiO2) in the 8 µm − 10 µm wavelength range. Also, note the dip at 8 um which was also seen in our FTIR measurements.

5.3.3 Epsilon Near Zero (ENZ) mode near the SiO2 Optical Phonon

A close examination of the dielectric function in Fig. 5.6b reveals that the real part

of SiO2 crosses zero at exactly 8 µm wavelength, and the corresponding imaginary

part of SiO2 is 0.3. When the angle of incidence is increased the effect seems to be stronger as shown in Fig. 5.7a. Further, 2D full wave FEFD simulations in COMSOL

I am very much thankful to Tom Tiwald from J. A. Woollam Co. for his help in measuring and fitting this data. Discussions with him were very helpful in understanding our FTIR measurements. 45

Fig. 5.6. (a) Spectroscopic ellipsometry measurements of lightly doped Si with 300 nm thermal oxide for 25◦ incidence angle; (b) The extracted permittivity around SiO2 optical phonon using gaussian oscillators

Multiphysics reveal that the dip in reflection is accompanied by dip in reflection and enhanced absorption as seen in Fig. 5.7b.

Fig. 5.7. (a) Angular dependence of the reflection dip at 8 µm calculated using 2D full wave FEFD simulations in COMSOL Multiphysics; (b) The calculated reflection, transmission and absorption spectra at an angle of incidence of 20◦; (c) Numerical simulations of enhanced absorption at higher angles of incidence.

There is some controversy in the literature regarding the exact origin of this feature. Berreman observed a dip in transmission of p polarized light in LiF films, and attributed it to coupling to longitudinal optical (LO) phonons [106]. Later this 46

explanation was proved to be incorrect, and an alternative explanation of excitation of a surface wave was proposed [107,108]. Using the recent ENZ related literature [109] we can explain this mode as ENZ enhanced absorption. When light is incident on an interface the normal component of displacement field (D) should be continuous across the interface. This implies that when the dielectric permittivity of a medium is close to 0, the electric field in that medium should be proportionally higher. This increased concentration of electric field leads to stronger absorption due to non-zero

imaginary part of SiO2. At normal incidence the normal component of E is zero, and it progressively increases for higher angles of incidence. This explains the increased absorption for p-polarized light when compared to s-polarized light observed in Fig. 5.7.

5.3.4 Impact of Numerical Aperture of FTIR Objective

Based on the analysis in the last section it is clear that the FTIR is collecting some light at off-normal angle of incidence, leading to a dip in reflection at 8 µm. FTIR is routinely used by many groups to study graphene plasmons, and it is surprising that the impact of off-normal angle of incidence is not discussed. In fact, since the objective lens is a 15X NA 0.58 Reflectochromat, the acceptance angle can be calculated to be asin(0.58) ∼ 35◦. The exact contribution of each angle is difficult to determine, and hence we chose to average simulations over a range of angles of incidence (0◦− 30◦) and compare with experiments. The results are presented in Fig. 5.8.

5.3.5 Raman Spectroscopy of Graphene Nanoribbons

When single layer graphene is pattered the edges of graphene ribbons can be expected to have defects. As previously noted in section 3.1.2, the presence of disorder in graphene will lead to a peak in Raman spectra at 1350 cm−1 which is referred to as D peak [64, 65]. Raman spectroscopy performed to verify the extent of defects in bare graphene and graphene nanoribbons is shown in Fig. 5.9. The analysis of different 47

Fig. 5.8. (a) Modulation of IR reflectivity of CVD graphene on Si/300 nm SiO2 substrate as a function of sheet carrier density. Measurements were performed using a Fourier Transform Infrared (FTIR) Spectrometer with microscope accessory (Objective: 15X, N.A. 0.58 Reflectochromat); measurements are normalized to RCNP (b) 2D full wave FEFD simulations with COMSOL Multiphysics using a surface current model for graphene; carrier scattering rate (τ) is the only parameter used in simulations. peaks (parameters listed in table 5.1) reveals that in patterned graphene there is a

−1 new peak at 1350 cm as expected. Futher, the I2D/IG ratio which is indicative of quality of graphene is greater than 2. Therefore, we can conclude that patterning has not completely destroyed the physical properties of graphene.

Table 5.1. Analysis of the Raman spectra for unpatterned graphene and graphene nanoribbons

Freq [cm−1] FWHM [cm−1] Intensity [a.u]

G (SLG) 1588 15 116.35 2D (SLG) 2680 28 370.35

G (GNR) 1589 19 49.61 2D (GNR) 2680 15 103.35 D (GNR) 1343 25 52.57 48

Fig. 5.9. Raman spectroscopy of unpatterned SLG and GNRs. Patterning causes an additional D peak to appear while simultaneously decreasing the I2D/IG ratio from 3.18 to 2.08. All measurements were performed under identical conditions with 532 nm, 1 mW , circularly polarized laser source and 100X objective. Resolution of spectrometer is 1.3 cm-1

5.4 Plasmons in Multilayer Graphene

The experimental measurements on plasmons in one, two and three layer graphene are shown in Fig. 5.10. The measurements are performed with the input beam polarized perpendicular to the graphene ribbons (TM mode). There are two main peaks observed in the measured data – one above and another below the optical phonon wavelength. The peak above the phonon shows a smaller shift with carrier density when compared to peak below the optical phonon. This behavior could be easily explained by the plasmon hybridization model wherein the graphene plasmon hybridizes with the optical phonon in the substrate. To verify the experimental results we performed full wave frequency domain numerical simulations in COMSOL Multiphysics after carefully accounting for the influence of substrate as described in 49

the previous sections. The simulation results are shown in Fig. 5.11 which qualitatively agrees with the experimental results. A closer scrutiny of the experimental and simulation results shows that the width of the plasmon resonance is larger in simulation when compared to experiments. This could be due to fact that the optical conductivity used in simulations was derived for graphene sheets but not graphene ribbons. It is well known that patterning graphene into ribbons introduces a bandgap in graphene which will reduce the optical loss at IR wavelength [110]. The extent of this bandgap is independent of orientation of GNR in the presence of edge disorder [111]. Further analysis of this interesting phenomenon is ongoing and would be published at a later date.

Fig. 5.10. Modulation of IR reflectivity of graphene nanoribbons, which were fabricated using few layer CVD graphene on Si/300 nm SiO2 substrate, as a function of sheet carrier density. Measurements were performed using a Fourier Transform Infrared (FTIR) Spectrometer with microscope accessory (Objective: 15X, N.A. 0.58 Reflectochromat); measurements are normalized to RCNP . Panels shows measured data on for SLG, double layer graphene and triple layer graphene. The width and period of GNRs were fixed at 50 nm and 150 nm respectively. 50

Fig. 5.11. 2D full wave FEFD simulations of GNRs with COMSOL Multiphysics using a surface current model for graphene; carrier scattering rate (τ) is the only parameter used in simulations.

5.5 Conclusions

CVD grown graphene, which can yield large sample area, has been predominantly used in graphene plasmon studies due to ease of optical characterization. However, the growth kinetics of CVD grown graphene on copper foil result in polycrystalline films with domain boundaries, and hence poorer physical properties compared to epitaxial films [104]. Our experimental results indicate that plasmons are indeed supported by few layer graphene. However, the strength of plasmon peak did not scale with the number of layers mainly due to the inhomogeneities in CVD graphene. Clearly, there is a lot of room for further improvements in fabrication and exploration in the quest for improved performance. 51

6. CONCLUSIONS AND FUTURE OUTLOOK

In this dissertation we summarize our research progress in the areas of plasmonic antenna - graphene hybrid devices, and the intrinsic 2D plasmons in graphene. When it started this work was mainly exploratory in nature due to the fact that hardly any literature was available on graphene plasmons. There was remarkable progress in all areas of graphene plasmonics — fundamental physics, numerical modeling, experi- mental techniques and fabrication methods, which were essentially contemporaneous with this work. In our work we build upon some of these advances, and demonstrate that graphene is an excellent platform for dynamic control of optical phenomena. The tunable optical properties of graphene could be used to electrically modulate plasmonic resonances in MIR and NIR wavelengths. We observed up to 210 nm decrease in the resonance line width and very strong amplitude modulation at 4.5 um and ∼2.0 um wavelengths respectively. We showed that the modulation will be stronger be at longer wavelengths, and identified possible directions for further improvements. We have also investigated intrinsic graphene plasmons in graphene nanoribbons and find that the substrate phonons couple to strongly to graphene plasmons. The strength of plasmon resonance could be improved significantly using stacked AB graphene rather than CVD graphene. In any exciting research we begin by asking questions and go about looking for answers. At what seems like the end of this dissertation we find ourselves asking many more questions, and looking into many uncharted paths. Some of the main directions of further research in the author’s — perhaps biased opinion are:

ˆ Scanning photocurrent measurements indicate that the interface between graphene and metal has strong field gradients indicating presence of defects and/or Fermi 52

level pinning. Further optimization of this interface needs to be performed to improve the tunability of plasmonic resonance.

ˆ A fundamental limitation is that a single monolayer of graphene will only have a finite impact. Tunability can be improved to some extent by using bernal stacked few layer graphene (FLG) which was shown to have higher optical conductivity [97]. The current large area fabrication methods like CVD only produce disordered graphene which is not suitable for multilayer studies. Some preliminary experiments similar to SLG [51, 52] with scattering NSOM on MLG could help in further understanding.

ˆ Alternative approaches like optical pumping of electrons [112] into conduction band can help in improving the modulation speed and enable of ultrafast devices.

ˆ Currently the edge roughness in nanopatterened graphene leads to very short carrier lifetime of τ ∼ 1 × 10−14 secs. High resolution patterning tools like Helium Ion lithography [113], epitaxial graphene on SiC [114] and/or bottom up approaches to grow cleaner nanostructures are essential to make graphene plasmons a viable alternative at NIR wavelengths.

ˆ Our analysis of intrinsic plasmons in alternative 2D materials indicates that they have poorer performance when compared to graphene. However, they are also known to exhibit many other unique phenomena such as room temperature excitons. We can hope that further research on these materials can lead to some potentially novel hybrid devices.

In light of many dramatic improvements demonstrated in this research area in the last few years we can be cautiously optimistic that there will be practical devices in the near future. REFERENCES 53

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A. PROCESS RECIPES FOR NANOFABRICATION

The nanofabrication of the various devices described in this dissertation has been carried out at the Birck Nanotechnology Center at Purdue University. This chapter summarizes the processing recipes for some specific devices. Additional guidelines that could help ‘easy’ reproduction of devices are also provided where appropriate.

A.1 Photolithography for Source/Drain Contacts

Photolithography was used to define large (1 mm × 500 µm ) contact pads of graphene devices in chapters 3, 4 and 5. A Mask Aligner (Suss MJB-3) with 365 nm exposure, 10 mW/cm2 output, and AZ 1518 (Microchemicals GmbH) resist were used in the fabrication.

1. Spin Coating: 3000 rpm for 60 secs followed by postbake at 80 C for 2 mins

2. Exposure Conditions: Mask was placed in contact with resist surface and softcontact mode was used

3. Development: A diluted AZ developer was used to develop the patterns. The

dilution ratio was 1:3 of AZ Developer:H2O. The timing was adjusted to clear the photoresist and was typically 40-50 seconds.

A.2 Electron Beam Lithography

An ultra-high resolution wide-field electron beam lithography tool, Leica VB6 at 100 kV, was used to pattern most of the nanostructures in this thesis. The resist used was ZEP520A which is a positive tone ebeam resist from Zeon Chemicals. Some important parameters used in ebeam processing are listed below: 63

Fig. A.1. Main processing steps used to fabricate experimental devices used in this dissertation. Steps (a)-(d) are used for fabricating graphene-antenna hybrid devices (Chapters 3 and 4) and steps (a),(b) and (e) were used for fabricating devices used in Chapters 5.

1. Spin Coating All the samples were spin-coated at 2000 rpm for 30 secs followed by postbake at 180 C for 2 mins

2. ZEP 520A Dilution To obtain thinner films original resist was diluted using a solvent Anisole by weight ratio defined as Dilution Ration (DR)

OriginalResist(g) + Solvent(g) DilutionRatio(DR) = (A.1) OriginalResist(g)

Undiluted ZEP gives a film thickness of 500 nm, while DR 2.4 would gives films of thickness of 110 nm, and DR 4 gives 80 nm thick films.

3. Exposure Conditions for Bow-tie Antennas ZEP 520A DR 2.4, Dose 260 - 280 µC/cm2 64

4. Exposure Conditions for Dolmen Antennas As noted earlier, the fabrication of the 20 nm and 50 nm gaps close to large features with dimensions around 100’s of nm, as required by the dolmen design is challenging in ebeam lithography due to the so-called proximity effect. The easiest work around is to use Proximity Correction software such as GenISys Layout Beamer. Since this tool was not available during fabrication a process of ’trial and learn’ was adopted. As the dose was varied uniformly, we found that either the 50 nm or 20 nm gap would be patterned accurately in the actual sample after metallization. Therefore, it was decided that the doses applied to individual antennas should be fixed to realize the final fabricated structure. In the final structure, ZEP 520A DR 2.4 was used and a dose of 190 µC/cm2 for quadrupole antenna, and a dose of 260 µC/cm2 was fixed for dipolar antenna. The SEM image of the fabricated sample was shown in Fig. 4.1. Further, due to the issues with liftoff process in small gaps the thickness of antennas was limited to 20 nm.

5. Sub-100 nm Graphene Ribbons ZEP 520A DR 4 was used to fabricate sub-100 nm features since thinner resist will not fall/crash during development. The dose was found to be a very critical parameter in fabricating these structures as can be seen in Fig. A.2.

A.3 Reactive Ion Etching of Graphene

1. Blanket removal of SLG on Copper before transfer: Plasmatech RIE machine with source 60 W (200 units on dial), 20 sccm, 42 units of time ( ∼ 18 secs) on dial.

2. Removal of SLG on Si/SiO2 substrate to define active area: Plasmatech RIE machine with source 50 W (170 units on dial), 10 sccm, 30 units of time ( ∼ 10 secs) on dial. 65

Fig. A.2. SEM images of the graphene nanoribbons (Period 150 nm and Width 50 nm) fabricated by ebeam lithography. It should be noted that the patterns are very sensitive to ebeam dose.

3. Patterning GNR after ebeam lithography Panasonic RIE machine with source 60 W , Bias 30 W , 20 sccm, 2 P a chamber pressure and 12-15 secs of duration. 66

B. LARGE AREA GRAPHENE SYNTHESIS

The graphene used in this thesis was grown by atmospheric pressure (AP) CVD process. The synthesis procedure is described by Ting-Fung Chung, et. al., in International Journal of Modern Physics B 27, 1341002 (2013), and is reproduced below for accuracy and completeness (©2013 World Scientific Publishing Company). The typical process parameters described below were sometimes slightly modified to obtain high quality films.

A 25 µm thick Cu foil substrate (99.8 % purity, Alfa Aesar) was cleaned by acetone and isopropanol (IPA) followed by diluted hydrochloric acid to remove native oxide on the surface. The cleaned Cu foil was thoroughly dried by a nitrogen gas and then loaded into an APCVD system. The reaction chamber was evacuated to ∼ 10 25 mT orr, and then filled back to ambient

pressure with a forming gas (5 % H2/Ar). After this, the temperature was increased to ∼ 1050 oC with flowing forming gas of 460 sccm. The Cu foil

was annealed for 30 120 minutes before flowing methane (500 ppm CH4

diluted by Ar) for 90 120 minutes. After the growth, the CH4 flow was turned off and the Cu foil was cooled down naturally [104].

Transferring as-grown graphene film from the Cu substrate to an Si/SiO2 substrate is a critical step for fabricating electronic devices. PMMA as- sisted transfer technique is commonly used because of its simplicity and repeatability [115]. In a typical transfer, a graphene film on Cu substrate is coated with PMMA (950PMMA-A4, MicroChem) by spin-coating (3000 rpm), then dried on a hotplate at 120 oC. The graphene on the reverse side (not covered by PMMA) of Cu was removed by oxygen plasma etching.

Many thanks to Ting-Fung Chung who developed the process flow and synthesized graphene for the work reported in this thesis. 67

The PMMA-graphene-Cu stack was floated on a copper etchant (0.25 g/mL FeCl3 in water in initial experiments and later ammonium persulfate ∼0.4 g in 50 mL) overnight. After copper etching, the PMMA-graphene mem- brane was scooped out and transferred to several baths of DI water and SC solutions for rinsing [116]. It was then scooped out again with a target

Si/SiO2 substrate and dried in air several hours before immersion in a bath of acetone to dissolve the PMMA, followed by rinsing in IPA and drying with nitrogen gas flow. 68

C. ESTIMATION OF OPTICAL CONDUCTIVITY OF GRAPHENE USING RANDOM PHASE APPROXIMATION

The optical properties of noble metals are commonly described using the Drude model, which captures the scattering events using a phenomenological scattering time constant (τ). A more accurate description is provided by the semi-classical Thomas-Fermi model which takes into account the screening effects. In the Lindhard theory the screening effects are further generalized and an electron is assumed to move in a total potential which is sum of external perturbation and screened potential from other electrons, which yields a self consistent Lindhard dielectric function [30, 117]. This is the commonly used starting point for calculating the dielectric function of graphene. Usually to simplify the dielectric function into an analytic expression the random phase approximation (RPA) is used [42]. The optical conductivity of graphene is given by Eq. 2.6, which takes into account both the intraband scattering (which is similar to metals), and also the interband transitions. Here we list the MATLAB source code used in the our numerical calculations.

C.1 MATLAB Source Code for Calculating Conductivity

function [sigma] = GrapheneRPA(lam0,ns,tg,param) %{ Initial script written by Naresh based on Koppens et. alNL(2011) andL Falkovsky IOP 2008 in June 2012. Modified by Ludmila Prokopeva 69 to fix the intergration limits issue at Inf Introduced quadgk function and zero loss approximation for better convergence Inputs modified to allow variation in scattering rate by Naresh %} lam = lam0; % Constants e0 = 8.854187817620e-12;% permittivity in vacuum,[F/m] c = 299792458;% speed of light,[m/s] kB = 8.61733247800e-05;% Boltzmann constant,[eV/K] h = 6.58211928150e-16;% reduced Planck constant,[eV *s] e = 1.60217656535e-19;% electron charge,[C] s0 = e/4/h ;% conductivity of undoped zero-T graphene,[S] vf = 1e6;% inm/s % Parameters T = 300*kB;% temperature,[eV] %G= 11e-3;% 1/(1e-13) *h ;% scattering rate,[eV] %11 meV corresponds to ~1e13 G = 1/(param)*h ;% scattering rate,[eV] %m=0.6;% chemical potential,[eV] ns = ns*1e4; m = h *vf*sqrt(pi*ns);

% Wavelength range % lam= linspace(0.01,4,1500) *1e-6;% wavelength range,[m] w = h *2*pi*c./lam;% frequency range,[eV]

% INTRABAND Conductivity/s0 sig1 = 8i/pi * T./(w+1i*G) * log(2*cosh(m/T/2));

% INTERBAND Conductivity/s0(zero loss,PV of real integral) g = @(x) tanh(0.5*(x-m)/T) + tanh(0.5*(x+m)/T); handle = @(W) quadgk( @(e) (g(e)-g(W/2))./(W.ˆ2-4*e.ˆ2), 0,inf,'AbsTol',0); [integral,err] = arrayfun(handle,w); sig2 = g(w/2)/2 + 2i/pi*w.*integral; 70

%max(err)

% INTERBAND Conductivity/s0(finite loss, contour integral, bypass pole) handle2 = @(W) quadgk( @(e) g(e)./(4*e.ˆ2-(W+1i*G).ˆ2), 0,inf,'AbsTol',0); [integral,err] = arrayfun(handle2,w); sig3 = -2i/pi*(w+1i*G).*integral; sigma = s0*(sig1+sig3);

% Estimate total relative permittivity % tg=1e-9;% graphene thickness,[m] epsr = 1+s0*(sig1+sig3)./(1i*e0*(w/h )*tg); VITA 71

VITA

Naresh Kumar Emani received his M.Sc. degree in Physics from Sri Sathya Sai University (India) in 2005 and MTech degree in Electrical Engineering from the Indian Institute of Technology Bombay (India) in 2007. During 2007-2009 he worked in the area of CMOS reliability in MOSFETs at Taiwan Semiconductor Manufacturing Company (Taiwan). He is currently working towards his Ph.D. degree in Electrical Engineering at Purdue University, USA. His broad research interests are in the areas of Nanophotonics, Plasmonics and Metamaterials. He has authored or co-authored 10 journal publications and delivered several conference talks including one invited talk at SPIE Optics + Photonics 2014. In December 2009 Naresh will join Data Storage Institute (ASTAR), Singapore as a research scientist.

Naresh Emani’s publications from his research at Purdue University in reverse chronological order are:

Journal Articles during PhD

8. Naresh K. Emani, Di Wang, Ting-Fung Chung, Alexander V. Kildishev, Vladimir M. Shalaev, Yong P. Chen, Alexandra Boltasseva, “Investigation of plasmon resonance in CVD grown multilayer graphene”, Manuscript in preparation.

7. Naresh Kumar Emani, Alexander V. Kildishev, Vladimir M. Shalaev and Alexan- dra Boltasseva, “Graphene: A Dynamic Platform for Nanophotonics”, Manuscript submitted. 72

6. Carl Pfeiffer, Naresh Kumar Emani, Amr M. Shaltout, Alexandra Boltasseva, Vladimir M. Shalaev, and Anthony Grbic, Efficient Light Bending with Isotropic Huygens Surfaces, Nano Letters, 14, 5 (2014).

5. Naresh K. Emani, Ting-Fung Chung, Alexander V. Kildishev, Vladimir M. Sha- laev, Yong P. Chen, Alexandra Boltasseva, “Electrical modulation of fano reso- nance in plasmonic nanostructures using Graphene”, Nano Letters 14 78 (2014).

4. J. Kim, G. V. Naik, N. K. Emani, U. Guler, and A. Boltasseva, “Plasmonic resonances in nanostructured transparent conducting oxide films”, IEEE Journal Of Selected Topics in Quantum Electronics 19 (2013).

3. Naresh K. Emani, T. F. Chung, X. Ni, A. V. Kildishev, Y. P. Chen, and A. Boltas- seva, “Electrically Tunable Damping of Plasmonic Resonances with Graphene”, Nano letters 12, 5202-5206 (2012).

2. Xingjie Ni, Naresh K. Emani, Alexander V. Kildishev, Alexandra Boltasseva, and Vladimir M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas”, Science 335 (2011).

1. P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials”, Laser Photonics Reviews 4, 795-808 (2010).

Selected Conference Proceedings during PhD

7. Naresh K Emani, Ting-Fung Chung, Alexander Kildishev, Yong P. Chen, Vladimir M. Shalaev and Alexandra Boltasseva, “Graphene as a platform for dynamically controlled plasmonics”, SPIE Optics+Photonics August 17th-22th 2014, San Diego, CA.

6. Ludmila Prokopeva, Naresh Emani, Alexander Kildishev and Alexandra Boltas- seva, “Tunable Pulse Shaping with Gated Graphene Nanoribbons”, CLEO/QELS June 8th-13th 2014, San Jose, CA. 73

5. N. K. Emani, T. F. Chung, L. Prokopeva, A. Kildishev, Y. Chen, and A. Boltas- seva, “Tuning Fano Resonances with Graphene”, CW3O.4, CLEO/QELS June 8-14, 2013, San Jose, CA.

4. L. J. Prokopeva, N. K. Emani, A. Boltasseva, and A. Kildishev, “Time Domain Modeling of Tunable Response of Graphene”, QTh1A.8 CLEO/QELS June 8-14, 2013, San Jose, CA.

3. N. K. Emani, T. F. Chung, X. Ni, A. Kildishev, Y. P. Chen, and A. Boltas- seva, “Electrically Tunable Plasmonic Resonances with Graphene”, JTu1M.2, CLEO/QELS May 2012, San Jose, CA.

2. X. Ni, N. K. Emani, A. Kildishev, A. Boltasseva, V. Shalaev, “Symmetry-breaking plasmonic metasurfaces for broadband light bending”, QM3F.1 CLEO/QELS 2012, San Jose, CA.

1. G. V. Naik, J. Kim, N. K. Emani, P. R. West, A. Boltasseva, “Plasmonic meta- materials: Looking beyond gold and silver”, 6th International Congress on Ad- vanced Electromagnetic Materials in Microwaves and Optics: Metamaterials 2012, September 17-22, 2012, St. Petersburg, Russia.