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Terahertz Quantum Cascade Lasers Benjamin S. Williams Terahertz quantum cascade lasers by Benjamin S. Williams Submitted to the Department of Electrical Engineering and Computer Science in partial ful¯llment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY August 2003 c Massachusetts Institute of Technology 2003. All rights reserved. ° Author . ............................................................ Department of Electrical Engineering and Computer Science August 22, 2003 Certi¯ed by. ....................................................... Qing Hu Professor Thesis Supervisor Accepted by . ..................................................... Arthur C. Smith Chairman, Department Committee on Graduate Students 2 Terahertz quantum cascade lasers by Benjamin S. Williams Submitted to the Department of Electrical Engineering and Computer Science on August 22, 2003, in partial ful¯llment of the requirements for the degree of Doctor of Philosophy Abstract The development of the terahertz frequency range (1{10 THz, ¸ 30{300 ¹m) has long been impeded by the relative dearth of compact, coherent radiation¼ sources of reasonable power. This thesis details the development of quantum cascade lasers (QCLs) that operate in the terahertz with photon energies below the semiconductor Reststrahlen band. Photons are emitted via electronic intersubband transitions that take place entirely within the conduction band, where the wavelength is chosen by engineering the well and barrier widths in multiple-quantum-well heterostructures. Fabrication of such long wavelength lasers has traditionally been challenging, since it is di±cult to obtain a population inversion between such closely spaced energy levels (¹h! 4{40 meV), and because traditional dielectric waveguides become extremely lossy¼ due to free carrier absorption. This thesis reports the development of terahertz QCLs in which the lower radiative state is depopulated via resonant longitudinal-optical phonon scattering. This mech- anism is e±cient and temperature insensitive, and provides protection from thermal back¯lling due to the large energy separation ( 36 meV) between the lower radiative state and the injector. Both properties are important» in allowing higher tempera- ture operation at longer wavelengths. Lasers using a surface plasmon based waveg- uide grown on a semi-insulating (SI) GaAs substrate were demonstrated at 3.4 THz (¸ 88 ¹m) in pulsed mode up to 87 K, with peak collected powers of 14 mW at 5K,and4mWat77K.¼ Additionally, the ¯rst terahertz QCLs have been demonstrated that use metal- metal waveguides, where the mode is con¯ned between metal layers placed immedi- ately above and below the active region. These devices have con¯nement factors close to unity, and are expected to be advantageous over SI-surface-plasmon waveguides, especially at long wavelengths. Such a waveguide was used to obtain lasing at 3.8 THz (¸ 79 ¹m) in pulsed mode up to a record high temperature of 137 K, whereas sim- ilar¼ devices fabricated in SI-surface-plasmon waveguides had lower maximum lasing temperatures ( 92 K) due to the higher losses and lower con¯nement factors. » This thesis describes the theory, design, fabrication, and testing of terahertz quan- tum cascade laser devices. A summary of theory relevant to design is presented, 3 including intersubband radiative transitions and gain, intersubband scattering, and coherent resonant tunneling transport using a tight-binding density matrix model. Analysis of the e®ects of the complex heterostructure phonon spectra on terahertz QCL design are considered. Calculations of the properties of various terahertz waveg- uides are presented and compared with experimental results. Various fabrication methods have been developed, including a robust metallic wafer bonding technique used to fabricate metal-metal waveguides. A wide variety of quantum cascade struc- tures, both lasing and non-lasing, have been experimentally characterized, which yield valuable information about the transport and optical properties of terahertz devices. Finally, prospects for higher temperature operation of terahertz QCLs are considered. Thesis Supervisor: Qing Hu Title: Professor 4 Acknowledgments I would like to ¯rst thank my advisor Qing Hu for giving me the opportunity to work on this project and for teaching and advising me along the way. Although this research often proved quite di±cult with no assurance of success, Qing's persistence and relentless determination in the pursuit of terahertz lasing was motivating for my own e®orts. I feel lucky to be engaged in such fast-paced research that is at once stimulating and challenging. A large part of the success of this project is due to the excellent MBE growths obtained ¯rst from Michael Melloch at Purdue, and later from John Reno at Sandia. I also wish to thank my many colleagues and research group-mates. I am partic- ularly indebted to Bin Xu, from whom I inherited this research project. Bin Xu, and Jurgen Smet before him built the foundations of this research in our group. Much of my early training in this ¯eld came from Bin as well as Ilya Lyubormirsky. I am also grateful to my current colleagues on this project: Hans Callebaut, Sushil Kumar, and Stephen Kohen. As well pouring many long hours into this research performing experiments and simulations, they have contributed to the friendly and intellectually stimulating atmosphere in the lab. I also am grateful to many other colleagues for their help and useful conversations including Konstantinos Konistis, Noah Zamdmer, Farhan Rana, Mathew Abraham, Gert de Lange, Brian Riely, and Juan Montoya. Erik Duerr in particular has been a good friend to joke with as well as someone who was always willing to answer all my terahertz questions. I appreciate all the help given to me by the sta® at MTL, CMSE, and RLE. I am indebted to Amanda Gruhl, who provided no end of support during this e®ort, and kept me going throughout it all. She was good enough not to drag me out of lab at every opportunity, but also good enough to drag me out periodically to keep me sane. I promise to repay her patience when it is her turn. I want to thank my brother Peter, for all of his physics \knowledge." I can only hope he has paid similar attention to my take on law. Of course I want to thank my parents for all of their love and support throughout not only this, but two previous theses, many science 5 reports, and many basketball games. I couldn't imagine having better teachers, role models, and friends. Thanks to all of my family and friends who I haven't mentioned. I couldn't have done it without you. 6 Contents 1 Introduction 35 1.1 Terahertz applications .......................... 36 1.2 Terahertz sources ............................. 39 1.2.1 Microwave upconversion ..................... 41 1.2.2 Tubes ............................... 41 1.2.3 Photomixing and downconversion ................ 41 1.2.4 Terahertz lasers .......................... 42 1.3 Intersubband transitions and quantum cascade lasers ......... 44 1.3.1 Mid-infrared quantum cascade lasers .............. 45 1.3.2 Terahertz quantum cascade lasers ................ 48 1.3.3 Survey of terahertz QCL active regions ............. 52 1.4 Thesis overview .............................. 55 2 Intersubband laser theory and modeling 57 2.1 Introduction ................................ 57 2.2 Electronic states in heterostructures ................... 57 2.3 Intersubband radiative transitions and gain ............... 61 2.3.1 Spontaneous emission lifetime .................. 63 2.3.2 Stimulated emission ........................ 65 2.3.3 Intersubband gain ......................... 66 2.4 Nonradiative inter- and intra-subband transitions ........... 67 2.4.1 Polar longitudinal optical (LO) phonon scattering ....... 70 2.4.2 Electron-electron scattering ................... 74 7 2.5 Resonant tunneling transport and anticrossings ............ 79 2.5.1 Semiclassical \coherent" model ................. 80 2.5.2 Tight-binding density matrix approach ............. 81 2.6 Summary ................................. 95 3 Heterostructures and optical-phonons 97 3.1 Introduction ................................ 97 3.2 Complex phonon calculation ....................... 101 3.3 Optimized design of three-level structure ................ 108 3.4 Conclusion ................................. 115 4 Waveguide design 117 4.1 Introduction ................................ 117 4.2 One-dimensional mode solver ...................... 118 4.3 Free carrier e®ects ............................ 120 4.3.1 Drude model ........................... 123 4.3.2 Propagation in lightly doped regions .............. 124 4.3.3 Propagation in MQW active region ............... 125 4.4 Phonon coupling e®ects .......................... 128 4.5 Terahertz waveguides ........................... 129 4.5.1 Plasmon waveguide ........................ 130 4.5.2 Metal-metal waveguide ...................... 132 4.5.3 Semi-insulating-surface-plasmon waveguide ........... 135 4.5.4 Waveguide comparison ...................... 137 5 Experimental Setup and Fabrication 139 5.1 Experimental setup ............................ 139 5.2 Fabrication ................................ 148 5.2.1 Etching .............................. 149 5.2.2 Non-alloyed ohmic contacts ................... 152 5.3 Metal-metal waveguide fabrication .................... 153 8 5.3.1 Wafer bonding .......................... 155 5.3.2 Substrate removal ......................... 158 5.3.3 Metal-metal fabrication results ................. 160 6 Survey
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