Growth of Graded Quantum Wells for Thz Polaritonics
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Growth of graded quantum wells for THz polaritonics by Chris Deimert A thesis presented to the University of Waterloo in fulllment of the thesis requirement for the degree of Doctor of Philosophy in Electrical and Computer Engineering Waterloo, Ontario, Canada, 2021 © Chris Deimert 2021 Examining Committee Membership The following served on the Examining Committee for this thesis. The decision of the Examining Commit- tee is by majority vote. External Examiner: Gottfried Strasser, Professor, Electrical Engineering and Information Technology, Vienna University of Technology (TU Wien) Supervisor: Zbigniew R. Wasilewski, Professor, Electrical and Computer Engineering, University of Waterloo Internal Member: Dayan Ban, Professor, Electrical and Computer Engineering, University of Waterloo Internal Member: Na Young Kim, Associate Professor, Electrical and Computer Engineering, University of Waterloo Internal-External Robert Hill, Associate Professor, Member: Dept. of Physics and Astronomy, University of Waterloo ii Author’s Declaration I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required nal revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. iii Abstract Rectangular quantum wells have long dominated the landscape of layered nanostructures. They exhibit a rich variety of physics and can be reliably grown with techniques such as molecular beam epitaxy. Rectangular wells represent only a fraction of the possible design space, however: much less explored have been alternative structures with continuously varying potential proles. This is not for want of applications. Parabolic quantum wells (PQWs), wells with a quadratically varying prole, have been recently identied as a potential key ingredient for terahertz (THz) polaritonic devices. The development of THz devices remains an important challenge with myriad applications that are only just beginning to be unlocked. We aim toward this important challenge by developing THz polaritonics based on PQW active regions, bringing to bear the fascinating physics of polariton quasiparticles – part light, part matter – and one of the most ubiquitous elements in physics, the harmonic oscillator. Using non-square quantum wells comes with challenges, however. Growing these structures with molecular beam epitaxy requires time-varying ux from the eusion cells, which is dicult to produce reliably due to the slow thermal response of the cells. While this problem can sometimes be bypassed through the use of digital alloys, there are limits on the quality of material that can be produced in this way. We develop an approach for growing smoothly graded quantum wells with molecular beam epitaxy, compensating for the eusion cell’s thermal behaviour via a simple linear dynamical model. We further provide an iterative scheme to correct for any lingering errors. With this technique, we demonstrate the ability to grow smoothly graded Alx Ga1 – x As PQWs for THz polaritonics, with a root- mean-square Al composition (x) error of just 0.0018. This accuracy is achieved at the standard growth rates (0.15–0.25 nm=s) necessary for thick structures± of several micrometres or more. The approach is quite generally applicable beyond Alx Ga1 – x As PQWs, and could be used for other materials or composition proles, or for other situations where precise time-dependent ux control is required. We further study the properties of continuously graded Alx Ga1 – x As PQWs grown in this manner, both theoretically and experimentally. Theoretically, we pull together existing work in the literature to build a numerical semiclassical model of quantum well absorption, which includes the multi-subband plasmonic interactions that appear at the doping levels required for THz polaritonics. This, combined with electromagnetic modelling allows us to study the design aspects of THz quantum wells relevant to polaritonic devices. We explore the possibility of studies on polariton-polariton scattering, and examine the quality of quantum well active region necessary for such studies. We further explore the possibility of new active region designs incorporating half parabolic quantum wells. Experimentally, we probe PQWs grown with the continuous grading method, using reection mea- surements in a metal-insulator-metal cavity and absorption measurements in a multipass geometry. We demonstrate robust oscillation at 2.1 THz and 3 THz for structures containing 8, 18, and 54 PQWs. Ab- sorption at room temperature is achieved, which is as expected from a parabolic potential but would typically be impossible with square quantum wells in the THz. Linewidths below 12 % of the central frequency are obtained up to 150 K in two of the samples, with a very small 3.9 % linewidth obtained in one sample at 4 K. Furthermore, we show that the system correctly displays an absence of nonlinearity despite electron-electron interactions – analogous to the Kohn theorem. The high quality of these structures already opens up several new experimental vistas. iv Acknowledgements First and foremost, I would like to thank my supervisor, Prof. Zbig Wasilewski. Your support, guidance, and experience have been invaluable during my time in Waterloo. I am inspired by your curiosity and passion for science, and I have always been struck by your ability to remain calm in the face of challenges and setbacks. I truly hope that I can carry some piece of that forward. I would like to thank Profs. Gottfried Strasser, Rob Hill, Na Young Kim and Dayan Ban for the time they’ve dedicated to serving as my committee members. I would especially like to thank Prof. Kim and her post-doc Dr. Taehyun Yoon for their work on the photoluminescence excitation measurements in this thesis. Thanks to both Prof. Kim and Prof. Ban for many good discussions and collaborations over the years. I would like to thank Dr. Wojtek Pasek for his tireless eorts in plasmon modelling, and for his patience in guiding us experimentalists through the dark jungles of k p theory. I would like to thank the folks at the Centre for Nanoscience· and Nanotechnology in Paris – particularly Dr. Raaele Colombelli, Dr. Jean-Michel Manceau and soon-to-be-Dr. Paul Goulain – who were kind enough to host me there for several trips and who were heavily involved in the many of the designs and experiments presented throughout this thesis. I certainly could not have done this on my own, and it was a pleasure to work with all of you. I should also thank the folks at École normale supérieure, with particular thanks to Jacques Hawecker who not only helped us with time domain spectroscopy measurements, but who kindly lent me his guitar while I stayed in Paris. I feel I must give special thanks to my dog, Sterling, who has frequently encouraged me to take breaks from writing my thesis to play and go on walks. She is always selessly looking out for my mental well- being. More seriously though, I would like to thank my parents, who always encouraged my sense of curiosity. And I would like to thank all of my colleagues and friends and family who have supported me both in my work and in my life outside of research. I started listing your names, but there are just far too many of you. Believe me that each one of you has made a lasting impact. Doing a PhD is no easy task, and life has a way of surprising us with diculties and trials. Many of you have helped me through the dicult times: probably more than you realize. This – my whole life in the last ve and a half years in Waterloo – really wouldn’t have been possible without you. v Table of Contents List of Figures ix List of Abbreviations xvi 1 Overview 1 2 Background: a short survey of THz devices3 2.1 Applications of THz devices........................................3 2.1.1 THz communications.......................................3 2.1.2 Quantum information.......................................4 2.1.3 THz imaging and spectroscopy.................................4 2.2 Challenges in THz devices........................................5 2.3 Broadband THz sources..........................................6 2.3.1 Photoconductive antennas....................................6 2.3.2 Optical rectiers..........................................6 2.4 Continuous wave sources.........................................7 2.4.1 Photomixers............................................7 2.4.2 Dierence frequency generation................................7 2.4.3 Gas lasers..............................................7 2.4.4 P-type germanium lasers.....................................8 2.4.5 Microwave multiplication....................................8 2.4.6 Backwards wave oscillators...................................8 2.4.7 Free electron lasers........................................8 2.4.8 Quantum cascade lasers.....................................8 2.5 Final observations............................................. 10 3 Background: exciton polariton lasers 12 3.1 What are polaritons?............................................ 12 3.1.1 Quasiparticles........................................... 13 3.1.2 Exciton polaritons......................................... 14 3.2 Exciton polariton condensation..................................... 16 3.3 Exciton polariton lasers.......................................... 17 3.4 Exciton polaritons in the THz...................................... 18 vi 4 THz devices with intersubband polaritons 20 4.1 The active region.............................................