Dynamic Control of Plasmonic Resonances with Graphene Based Nanostructures Naresh Kumar Emani Purdue University

Purdue University Purdue e-Pubs Open Access Dissertations Theses and Dissertations Fall 2014 Dynamic control of plasmonic resonances with graphene based nanostructures Naresh Kumar Emani Purdue University Follow this and additional works at: https://docs.lib.purdue.edu/open_access_dissertations Part of the Electrical and Computer Engineering Commons, Nanoscience and Nanotechnology Commons, and the Optics Commons Recommended Citation Emani, Naresh Kumar, "Dynamic control of plasmonic resonances with graphene based nanostructures" (2014). Open Access Dissertations. 265. https://docs.lib.purdue.edu/open_access_dissertations/265 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. ÿ ÿÿ !"# ÿ%%&'&'%()ÿ 012314ÿ16784297@Aÿ B2C31C@4ÿ9DEFFGÿ @HIPQPR3QPPISTUTQVWÿCXXIYTUWXIÿ àbÿabÿÿ acdÿÿÿbabeabbafÿggÿ hdÿhjihj hk ifaÿÿ ÿmhkqrjepehkqhqdktjhzhfhjiqij mqjpkez ÿÿpÿcÿÿÿ qbÿggrÿsdÿÿcafÿtafafpÿ auÿ ÿn ÿnmnnuu norqhkj n nm mu orqhkj tn nmunn ÿÿÿÿÿdefgÿhfÿhÿifjfÿÿÿifÿkÿÿklmkjhkÿngjoÿ piekqhkÿmehoÿhfÿrjkkqhklmkqehkjÿstjhfihÿuqeÿvjÿwxyoÿkÿklfkjhkÿÿ hfjÿÿÿÿzj{kkÿÿpijfiÿ|k{jk}ÿ~pekqÿÿgjkÿkÿhjqÿhfÿÿiÿÿ ÿqzjkgfÿhjkheÿ n nmnnuu norqhkj vggrÿsdÿwxÿycbbb)uÿÿ ÿÿÿÿÿÿÿÿÿ ÿvggrÿsduhehjkh llx ÿcÿÿ#!"# "ÿÿypÿ ÿÿÿ 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 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 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 !p = 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)

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