AN ABSTRACT OF THE DISSERTATION OF Andrew Stickel for the degree of Doctor of Philosophy in Physics presented on August 10, 2016. Title: Terahertz Induced Non-linear Electron Dynamics in Nanoantenna Coated Semiconductors at the Sub-picosecond Timescale Abstract approved: Yun-Shik Lee This dissertation is an exploration of the material response to Terahertz (THz) radiation. Specifically we will explore the ultrafast electron dynamics in the non- perturbative regime in semiconductors that have been patterned with nanoantenna arrays using broadband, high intensity, THz radiation. Three main semiconductor materials will be studied in this work. The first is VO2 which undergoes a phase transition from an insulator, when it is below 67◦ C, to a metal, when it is above 67◦ C. The second and third materials are Si and GaAs which are two of the most commonly used semiconductors. We study the insulator to metal transition (IMT) of VO2 and its response to high field THz radiation. The near room temperature IMT for VO2 makes it a very promising material for electrical and photonic applications. We demonstrate that with high field THz the IMT transition can be triggered. This transition is induced on a sub-cycle timescale. We also demonstrate a THz field dependent reduction in the transition temperature for the IMT when transitioning from both below Tc to above as well as from above Tc to below. This transition is not equal for the above and below cases and leads to a narrowing of the hysteresis curve of the IMT. The thin film Fresnel coefficients, along with a phenomenological model developed for the nanoantenna patterned VO2, are also used to calculate the sheet conductivity of the VO2 sample. We show, using this sheet conductivity and its relation to the band gap, that the bang gap in the insulating phase has a strong dependence on the incident THz radiation with larger fields reducing the band gap from 1.2 eV at low incident THz fields to 0.32 eV at high incident THz fields. The ultrafast, non-equilibrium, electron dynamics of GaAs and Si were also explored. GaAs and Si are the two most prevalent semiconductors in use today and with the decrease in size and increase in clock speeds of transistors a deep understanding of the ultrafast high field electron dynamics of these materials is of vital importance. Using THz time domain spectroscopy we investigate the transition rates of electrons excited by a 800 nm optical pump. We show that the optically induced transition for GaAs happens on a shorter timescale than that of Si. We also investigate the THz transmission dependence on the indecent THz field. We show that intense THz fields enhance the transmission through the sample. The increase in transmission is due to intervalley scattering which increases the effective mass of the electrons resulting in a decrease in the conductivity the sample. c Copyright by Andrew Stickel August 10, 2016 All Rights Reserved Terahertz Induced Non-linear Electron Dynamics in Nanoantenna Coated Semiconductors at the Sub-picosecond Timescale by Andrew Stickel A DISSERTATION submitted to Oregon State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Presented August 10, 2016 Commencement June 2017 Doctor of Philosophy dissertation of Andrew Stickel presented on August 10, 2016. APPROVED: Major Professor, representing Physics Chair of the Department of Physics Dean of the Graduate School I understand that my dissertation will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of my dissertation to any reader upon request. Andrew Stickel, Author ACKNOWLEDGEMENTS First and foremost I would like to thank Professor Yun-Shik Lee. For Advising me throughout the my 6 years of working for him. I would also like to thank Dr. Zack Thompson for working with me, teaching how to tighten a bolt, and not punching me in the face as much as he had the right to. I would also like to thank Dr. Byounghwak Lee and Ali Mousavian for their input and support during my work. All of my friends and faculty in the physics department that have listened to me whine...I mean helped me out. Specifically I would like to thank Dr. KC Walsh for being a mentor, friend, and all around amazing help who gave me important insights into grad school and helped me out immensely. I would like to thank my teachers Mr. Day, Mr. Morales, and Dr. Deal for encouraging my passion for science and guiding me when I needed it. Also I need to thank Dr. Ritter and Ms. Wise without who this 137 page document would be a dribbling pile of non-sense. Finally, and most importantly, I would like to thank my parents Bryan Stickel and Carol Ernst. From the beginning of my life they have done nothing but support my dreams and put up with my 19,762 questions. They kept me from killing myself, even when those cool metal disks on the oven seemed REALLY fun to play with. Mom, Dad, I love you both. TABLE OF CONTENTS Page 1 Terahertz Radiation and Applications1 1.1 History...................................2 1.2 Sources...................................2 1.3 Detection.................................4 1.4 Applications................................6 2 Theoretical Foundations for Terahertz Spectroscopy of Semiconductors8 2.1 Maxwell's Equations and Electromagnetic Radiation..........8 2.1.1 Electromagnetic Plane Waves................. 10 2.1.2 Electromagnetic Waves at a Boundary............ 16 2.2 Non-linear Optics............................. 23 2.2.1 Second Order Non-linear Effects................ 24 2.2.2 The χ(2) tensor......................... 26 2.2.3 Phase Matching......................... 28 2.3 Ultrafast Optics.............................. 30 2.3.1 Mode Locking.......................... 31 2.3.2 Pulse Width and Dispersion.................. 34 2.4 Band Theory of Semiconductors..................... 36 2.4.1 The Simple 1-D Chain..................... 37 2.4.2 Beyond the 1-D Chain..................... 39 2.5 THz Field Enhancement by Nanoantennas............... 41 2.5.1 Nanoantenna Enhanced Electric Fields for Long Wavelength Radiation............................ 42 TABLE OF CONTENTS (Continued) Page 2.5.2 Nanoantenna Arrays...................... 44 3 Terahertz Generation and Detection 46 3.1 THz Generation.............................. 46 3.1.1 ZnTe and Optical Rectification................. 46 3.1.2 LiNbO3 THz Generation.................... 48 3.2 THz Detection.............................. 51 3.2.1 Pyroelectric Detectors..................... 52 3.2.2 The Bolometer......................... 53 3.3 Experimental Setup and Procedures................... 55 3.3.1 The Laser System........................ 55 3.3.2 Layout of Experimental Setup................. 56 3.3.3 Experimental Designs...................... 58 4 Vanadium Dioxide Field Induced Transition 65 4.1 Mott Insulators.............................. 65 4.1.1 The Hubbard model...................... 65 4.1.2 Conductivity and the band gap................ 68 4.1.3 Mott Criterion.......................... 71 4.2 Insulator to Metal transition in VO2 .................. 72 4.2.1 The structural phase transition of VO2 and its consequences on conductivity......................... 72 4.3 The Sample................................ 74 4.4 THz Dependent Transmission...................... 76 TABLE OF CONTENTS (Continued) Page 4.5 Frequency Response........................... 80 4.6 THz dependent Hysteresis Narrowing.................. 84 4.7 THz Dependent Sheet Conductivity................... 89 4.8 Time Dependent Transmission of the THz Beam and Real Time Fluc- tuations of the Conductivity....................... 94 4.9 Conclusion................................. 98 5 High Field Electron Dynamics at Sub-picosecond Timescale in GaAs and Si 99 5.1 Intervalley Scattering Induced by Strong THz Fields.......... 99 5.1.1 Intervalley Scattering in GaAs................. 101 5.1.2 Intervalley Scattering in Si................... 104 5.2 Nanoantenna Patterned Samples.................... 104 5.3 Optical Free Carrier Driven Conductivity................ 106 5.4 Temporal Evolution of Optically Excited Free Carriers........ 112 5.5 THz Induced Transparency Via Intervalley Scattering......... 120 5.5.1 Time Domain Spectroscopy Investigation of THz Intensity Dependent Transmission.................... 121 5.5.2 Power Transmission Detection of THz Induced Transparency 127 5.6 Induced Sheet Conductivity....................... 133 5.7 Conclusion................................. 135 6 Conclusion 137 TABLE OF CONTENTS (Continued) Page Appendix 139 A Derivation of Index of Refraction Vs Wavelength............ 140 LIST OF FIGURES Figure Page 1.1 The electromagnetic spectrum with the THz region highlighted in blue...................................1 2.2 A schematic of all of the internal reflections inside a bulk, lossy, dielectric................................. 20 2.3 A schematic of all of the internal reflections inside a bulk, lossy, dielectric coated with a thin film.................... 21 2.4 A plot a cavity where N=200 modes have a) random phase (inco- herent) b) uniform phase (coherent).................. 32 2.6 A cartoon plot of a nanoantenna array (left) with an SEM images of an actual nanoantenna (right).................... 44 3.1 Three time steps in the generation of the THz pulse via optical rectification............................... 48 3.2 Cartoon setup of the LiNbO3 based THz generation. The dark lines within the optical pulse represent the the pulse front......... 50 3.3 The basic circuit diagram for the