UNIVERSITY OF OKLAHOMA GRADUATE COLLEGE HIGH-PERFORMANCE INAS-BASED INTERBAND CASCADE LASERS A DISSERTATION SUBMITTED TO THE GRADUATE FACULTY in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY By YUCHAO JIANG Norman, Oklahoma 2016 HIGH-PERFORMANCE INAS-BASED INTERBAND CASCADE LASERS A DISSERTATION APPROVED FOR THE SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING BY ______________________________ Dr. Rui Q. Yang, Chair ______________________________ Dr. Michael B. Santos ______________________________ Dr. Zhisheng Shi ______________________________ Dr. Matthew B. Johnson ______________________________ Dr. James Sluss © Copyright by YUCHAO JIANG 2016 All Rights Reserved. To my mother, Zi-Zhen Huang Acknowledgements Life is like a cascade of transitions: in each stage, I accumulate my energy with the help of others and make the final jump, emitting the wave that resonates with my soul. Each “degree” is a new challenge. In retrospect, it was in overcoming various barriers that I obtained a deeper insight into the world. I like what Albert Einstein said, “a hundred times a day I remind myself that my inner and outer life depend on the labors of other men, living and dead, and that I must exert myself in order to give in the measure as I have received and am still receiving.” First and foremost, I would like to thank my advisor, Prof. Rui Q. Yang. He provided me a precious opportunity to learn how an original concept was developed into practical devices. He was generous to offer his knowledge and experience for me to complete various daunting projects. I have acquired both theoretical understanding and experimental skills that are crucial to my future career. His foresight and high standard have driven me out of a student’s comfort zone to think more thoroughly and act more professionally. I also thank him for giving me freedoms to explore my thoughts and ideas, which is the most intriguing part of scientific research. I am very appreciative of the efforts made by my group members and collaborators. I would like to thank Lu Li and Hao Ye, who performed the material growth and fabrication, for providing reliable devices presented in this work. I learned a lot from their responsible attitudes and attentions to detail. I would like to thank Hossein Lotfi for his insightful questions. I was inspired by his carefulness when we did some experiments together. I would also like to thank Zhaobing Tian, Robert Hinkey, iv Zhuowei Yin, Lin Lei, SM Shazzad Rassel, Tetsuya Mishima, James Gupta, David Jui- Yang Feng and Prof. Fow-Sen Choa for their help in the research. I would like to thank Prof. Matthew Johnson and Prof. Michael Santos for constructive conversations and for providing resources and expertise in device fabrication and material growth. I also thank Prof. Zhisheng Shi and Prof. James Sluss for serving on my committee. The last miles are always the toughest. I am deeply thankful to my friends for illuminating me to walk through the darkest time in this final year. I would like to thank my running pals Echo and Holly for their enthusiastic encouragements. I enjoyed every weekend training and three marathon races, which blew away my worries and recharged my spirit. I would like to thank Dr. Michele Eodice and William Dower for organizing a writing group to improve my writing. Special thanks go to Ying Lan for setting a writing camp, a neat and undisturbed heaven for me to concentrate on my dissertation and nourish my thoughts. I want to express my deepest gratitude to Prof. Chang-Zhi Guo. Before I came to U.S., he planted a seed of curiosity of laser research in my mind during my master’s study. He was so patient to make detailed comments on each of my misunderstanding in the homework and was always encouraging when I stepped further. I learned the basic modeling skills from him, and he was kind enough to show me his Matlab codes at his apartment. I also thank Prof. Gang Yu for encouraging me to study abroad. Lastly, I would like to thank my family for their unconditional love and support over the years. v Table of Contents Acknowledgements ......................................................................................................... iv List of Tables ................................................................................................................... xi List of Figures ................................................................................................................ xiv Abstract .......................................................................................................................... xix Chapter 1 Introduction ...................................................................................................... 1 1.1 Lasers .................................................................................................................... 1 1.2 Semiconductor lasers ............................................................................................ 3 1.3 Mid-IR semiconductor lasers ............................................................................... 5 1.4 Brief history of IC lasers ...................................................................................... 8 Chapter 2 Fundamentals of interband cascade lasers ..................................................... 13 2.1 Basis in laser operation ....................................................................................... 13 2.1.1 Gain analysis ............................................................................................. 13 2.1.2 Rate equation ............................................................................................. 17 2.2 Gain coefficient in semiconductor materials ...................................................... 22 2.2.1 Probability inversion ................................................................................. 22 2.2.2 Quasi-Fermi levels in bulk and QW material ............................................ 23 2.2.3 Gain coefficient ......................................................................................... 27 2.3 Active region material and band structure .......................................................... 29 2.3.1 Type-II QW materials ................................................................................ 30 2.3.2 Band structure modeling ............................................................................ 31 2.3.3 Two-band model and formalism ............................................................... 35 2.3.4 Kane’s two-band model ............................................................................. 37 vii 2.4 Optical wave modeling ....................................................................................... 38 2.4.1 Optical wave equations .............................................................................. 38 2.4.2 Light propagating in a multilayer structure ............................................... 40 2.4.3 Waveguide mode ....................................................................................... 45 2.4.4 Far-field patterns ....................................................................................... 47 Chapter 3 Material growth, fabrication and laser characterizations ............................... 49 3.1 Material growth .................................................................................................. 49 3.2 Device fabrication .............................................................................................. 51 3.3 Laser characterizations ....................................................................................... 52 3.3.1 Light-current-voltage characteristic .......................................................... 52 3.3.2 Double-modulation technique in pulse spectra ......................................... 55 3.3.3 Pulse power calibration ............................................................................. 59 3.3.4 Gain spectrum ............................................................................................ 61 3.3.5 Thermal resistance ..................................................................................... 65 Chapter 4 Far-field patterns and beam qualities of plasmon-enhanced waveguide interband cascade lasers ..................................................................................... 70 4.1 Waveguide modeling .......................................................................................... 70 4.1.1 Plasmon-enhanced waveguide ................................................................... 70 4.1.2 Calculation of refractive index .................................................................. 73 4.1.3 Device structure and waveguide simulation .............................................. 79 4.2 Far-field pattern measurement ............................................................................ 83 4.2.1 Experimental setup .................................................................................... 83 4.2.2 Experimental and simulated results ........................................................... 84 viii 4.3 Beam quality ....................................................................................................... 89 4.3.1 Gaussian beam ........................................................................................... 90 4.3.2 Brightness .................................................................................................. 92 4.3.3 Beam quality factors