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Pattern-Integrated Interference Lithography PATTERN-INTEGRATED INTERFERENCE LITHOGRAPHY: SINGLE-EXPOSURE FORMATION OF PHOTONIC-CRYSTAL LATTICES WITH INTEGRATED FUNCTIONAL ELEMENTS A Thesis Presented to The Academic Faculty by Guy Matthew Burrow In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Electrical and Computer Engineering Georgia Institute of Technology August 2012 PATTERN-INTEGRATED INTERFERENCE LITHOGRAPHY: SINGLE-EXPOSURE FORMATION OF PHOTONIC-CRYSTAL LATTICES WITH INTEGRATED FUNCTIONAL ELEMENTS Approved by: Professor Thomas K. Gaylord, Advisor Professor Muhannad S. Bakir School of Electrical and Computer School of Electrical and Computer Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Professor Miroslav M. Begovic Dr. Donald D. Davis School of Electrical and Computer School of Electrical and Computer Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Professor Zhuomin Zhang Date Approved: 29 May 2012 School of Mechanical Engineering Georgia Institute of Technology ACKNOWLEDGEMENTS Over the course of nearly three years at Georgia Tech, numerous people have impacted my life and proven instrumental to the research presented in this thesis. It is with great appreciation and humility that I acknowledge their support and contributions. First and foremost, I want to express my sincere thanks to my advisor, Professor Thomas K. Gaylord. I am grateful to have had the chance to learn and develop under his expert guidance. Having served for more than 20 years in the Army, I have found no better example of a true professional. Thank you, sir, for being such a great mentor and leader to us all. I would also like to recognize the other members of my thesis committee: Professor Muhannad S. Bakir, Professor Miroslav M. Begovic, Dr. Donald D. Davis, and Professor Zhuomin Zhang. Your participation and guidance throughout this process were invaluable. Knowing the busy schedule that you all keep, I sincerely appreciate your time and consideration. I am also grateful to have worked alongside the other outstanding members of the Georgia Tech Optics Laboratory. Whether problem-solving with Dr. Mike Hutsel, receiving cleanroom instruction from Jon Maikisch, developing laboratory procedures with Joe Kummer, or asking Matthieu Leibovici for one more simulation using his Fourier model, I could not have anticipated the level of teamwork and support that I have experienced in this group. For our Friday lunch discussions and other words of wisdom, I would also like to thank the other group members, past and present, including Dr. Chien-I Lin, Micah Jenkins, Lorelyn Kilby, Prof. Amy Sullivan, LTC(R) Greg Kilby, iii Prof. Stephen Schultz, David Davis, Jacob Block, Melissa Meister, Laney Hall, and, of course, Dr. Justin Stay, from whom I inherited this well-developed line of research. From the Georgia Tech Machine Shop, I would like to thank Louis Boulanger for his expert fabrication of the custom components for the experimental configuration. I would also like to thank my family and friends who have helped me throughout my life: my mother Debbie, my father Guy, my sister Kathryn and her family, and my brother John and his family. I want to specifically acknowledge my grandmother, Iona Hardison, for developing both my scientific and creative mind through everything from science fairs to art lessons. Of course, there are countless educators from grade school through grad school who provided me with the knowledge and motivation for this research. For this, I thank you all. Most importantly, I want to thank my wife, Dee Ann, for her love and support during this process. I am grateful for your patience as I often worked late into the evening and occasionally through the weekend. Seeing your smile at the end of the day remains my greatest motivation and source of happiness. Finally, I thank God for taking me down this path. For this and for all of you who have supported me in this endeavor, I am forever grateful. G. MATT BURROW Georgia Institute of Technology May 2012 iv TABLE OF CONTENTS Page ACKNOWLEDGEMENTS ............................................................................................iii LIST OF FIGURES ……………………………………………………………….….... ix LIST OF TABLES ……………………………………………………………….……. xii LIST OF ACRONYMS AND ABBREVIATIONS ………………………………… xiv SUMMARY …………………………………………………………………….….….. xv CHAPTER 1 INTRODUCTION ……………………………………………………. 1 1.1 Background .............................................................................................................2 1.1.1 Multi-Beam Interference ............................................................................... 2 1.1.2 Multi-Beam Interference Configurations .................................................... 16 1.1.3 Interference Lithography ............................................................................ 22 1.2 Research Objectives and Contributions ................................................................27 1.3 Thesis Overview ...................................................................................................30 CHAPTER 2 MUTI-BEAM INTERFERENCE APPLICATION AREAS …….… 32 2.1 Nano-Electronics ...................................................................................................32 2.2 Photonic Crystals ..................................................................................................33 2.3 Metamaterials ........................................................................................................34 2.4 Subwavelength Structures .....................................................................................36 2.4.1 Guided-Mode Resonant Elements .............................................................. 37 2.4.2 Synthesized-Index Elements ....................................................................... 37 2.4.3 Form-Birefringent Polarization Elements ................................................... 38 2.4.4 Field-Emission Devices .............................................................................. 39 v 2.4.5 Plasmonic Structures ................................................................................... 40 2.4.6 Surface Texturing ........................................................................................ 40 2.4.7 Magnetic Nanostructures ............................................................................ 41 2.5 Biomedical Structures ...........................................................................................42 2.6 Optical Trapping ...................................................................................................44 CHAPTER 3 TWO-DIMENSIONAL MOTIF GEOMETRIES ……………….….. 47 3.1 Motif Geometry Modeling ....................................................................................47 3.1.1 Circle to Square: p4m Plane-Group Symmetry .......................................... 49 3.1.2 Ellipse to Rhombus: pmm Plane-Group Symmetry .................................... 53 3.1.3 Ellipse to Hexagon: p6m, p4m and cmm Plane-Group Symmetries ........... 56 3.2 Experimental Demonstration ................................................................................61 3.3 Summary ...............................................................................................................64 CHAPTER 4 CONSTRAINED PARAMETRIC OPTIMIZATION …….………...66 4.1 Parametric Constraints ..........................................................................................68 4.1.1 Amplitude Constraints ................................................................................ 70 4.1.2 Polarization Constraints .............................................................................. 72 4.2 Constrained Optimization Results ........................................................................74 4.2.1 Amplitude Constraints ................................................................................ 75 4.2.2 Polarization Constraints .............................................................................. 76 4.3 Summary ...............................................................................................................77 CHAPTER 5 PATTERN-INTEGRATED INTERFERENCE LITHOGRAPHY... 80 5.1 Pattern-Integrated Interference Exposure System ................................................81 5.1.1 System Design ............................................................................................ 84 vi 5.1.2 Zemax System Optimization ....................................................................... 88 5.1.3 Predicted System Performance ................................................................... 91 5.2 System Model .......................................................................................................94 5.2.1 Mask Function ............................................................................................ 95 5.2.2 Pupil Function ............................................................................................. 96 5.2.3 Aerial Optical-Intensity Distribution Simulation ........................................ 97 5.3 Pattern Metrics ......................................................................................................99 5.3.1 Intensity Performance Metrics .................................................................. 101 5.3.2 Lattice-Vector Performance Metrics ......................................................... 102 5.4 Summary .............................................................................................................104
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