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Thesis-Franckie-FINAL Modeling Quantum Cascade Lasers Modeling Quantum Cascade Lasers: The Challenge of Infra-Red Devices by Martin Franckié Thesis for the degree of Doctor of Philosophy Thesis advisors: Prof. Andreas Wacker, Dr. Claudio Verdozzi Faculty opponent: Prof. Gerhard Klimeck To be presented, with the permission of the Faculty of Science of Lund University, for public criticism in the Rydberg lecture hall (Rydbergsalen) at the Department of Physics on Friday, the 13th of May 2016 at 13:00. Organization Document name LUND UNIVERSITY DOCTORAL DISSERTATION Department of Physics Date of disputation Box 118 2016-05-13 221 00 LUND Sponsoring organization Sweden Author(s) Martin Franckié Title and subtitle Modeling Quantum Cascade Lasers: The Challenge of Infra-Red Devices Abstract The Quantum Cascade Laser (QCL) is a solid state source of coherent radiation in the tera- hertz and mid-infrared parts of the electro-magnetic spectrum. In this thesis, I have used a non-equilibrium Green’s function (NEGF) model to theoretically investigate the quantum nature of the device operation, and compared simulation results to experiments. As simula- tions with the NEGF model are time-consuming, especially for mid-infrared QCLs owing to their large state space, the program has been parallelized to run on large computer clusters. Additional challenges of mid-infrared QCLs are increased interface roughness scattering and non-parabolicity effects, which have been included into the existing NEGF model. With this new model, simulation results in close agreement with experimental data has been produced for terahertz and mid-infrared lasers employing various design schemes. DOKUMENTDATABLAD enl SIS 61 41 21 Key words quantum cascade lasers, non-equilibrium Green’s function theory, cluster computations Classification system and/or index terms (if any) Supplementary bibliographical information Language English ISSN and key title ISBN 978-91-7623-778-6 (print) 978-91-7623-779-3 (pdf) Recipient’s notes Number of pages Price 184 Security classification I, the undersigned, being the copyright owner of the abstract of the above-mentioned disser- tation, hereby grant to all reference sources the permission to publish and disseminate the abstract of the above-mentioned dissertation. Signature Date 2016-04-04 Modeling Quantum Cascade Lasers: The Challenge of Infra-Red Devices by Martin Franckié Thesis for the degree of Doctor of Philosophy Thesis advisors: Prof. Andreas Wacker, Dr. Claudio Verdozzi Faculty opponent: Prof. Gerhard Klimeck To be presented, with the permission of the Faculty of Science of Lund University, for public criticism in the Rydberg lecture hall (Rydbergsalen) at the Department of Physics on Friday, the 13th of May 2016 at 13:00. Cover illustration: Free interpretation of this work by Bernt Franckié Grünewald Funding information: The thesis work was financially supported by the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no 317884, the collaborative Integrated Project MIRIFISENS and the Swedish Research Council (VR). c Martin Franckié 2016 Faculty of Science, Department of Physics Paper I c 2013 Society of Photo-Optical Instrumentation Engeneers (SPIE) Paper II c 2013 American Institute of Physics Paper III c 2013 Institute of Electrical and Electronics Engineers (IEEE) Paper IV c 2014 American Institute of Physics Paper V c 2015 The Optical Society (OSA) Paper VI c 2015 American Institute of Physics isbn: 978-91-7623-778-6 (print) isbn: 978-91-7623-779-3 (pdf) Printed in Sweden by Media-Tryck, Lund University, Lund 2016 Till Fleur Contents List of publications . iii List of Acronyms . v Acknowledgements . vi Popular summary in English . vii Populärvetenskaplig sammanfattning på svenska . viii 1 Introduction 3 1.1 Motivation and structure of the Thesis . 5 1.2 Operation principles . 6 1.3 Material systems . 11 1.4 Approaches to QCL modeling . 13 2 Theory 15 2.1 Hamiltonian . 15 2.2 Envelope functions . 17 2.3 Bloch functions of a periodic heterostructure . 18 2.4 Wannier functions . 19 2.5 The Wannier-Stark Basis . 20 2.6 The NEGF model . 20 2.7 Temporal response . 23 2.8 Current density . 28 2.9 Gain from complex conductivity . 29 2.10 Gain from Fermi’s Golden Rule . 30 2.11 Gain clamping and output power . 30 3 The two-band model 33 3.1 Current density in the two-band model . 35 3.2 Interface roughness in the two-band model . 37 3.3 Comparison of one- and two-band model simulations . 38 4 Parallelization 43 4.1 Computation scheme . 43 4.2 Single node computations . 46 4.3 Cluster computations . 47 ii CONTENTS 5 Mid-infrared QCLs 51 5.1 Role of interface roughness scattering . 52 5.2 Multi-stack device . 54 5.3 Strain compensated InGaAs/InAlAs/AlAs structures . 56 5.4 Optimization of short wavelength and low dissipation act- ive region . 58 6 Terahertz QCLs 63 6.1 Injection schemes in THz QCLs . 64 6.2 Two-quantum well designs . 71 7 Conclusions and outlook 81 Scientific publications 93 Author contributions . 93 Paper I: Injection Schemes in THz Quantum Cascade Lasers Un- der Operation . 93 Paper II: An indirectly pumped terahertz quantum cascade laser with low injection coupling strength operating above 150 K 93 Paper III: Nonequilibrium Green’s Function Model for Simula- tion of Quantum Cascade Laser Devices Under Operating Conditions . 93 Paper IV: Comparative analysis of quantum cascade laser model- ing based on density matrices and non-equilibrium Green’s functions . 94 Paper V: Impact of interface roughness distributions on the oper- ation of quantum cascade lasers . 94 Paper VI: Influence of Interface Roughness in Quantum Cascade Lasers . 94 Paper I: Injection Schemes in THz Quantum Cascade Lasers Under Operation . 95 Paper II: An indirectly pumped terahertz quantum cascade laser with low injection coupling strength operating above 150 K . 107 Paper III: Nonequilibrium Green’s Function Model for Simulation of Quantum Cascade Laser Devices Under Operating Conditions . 123 Paper IV: Comparative analysis of quantum cascade laser modeling based on density matrices and non-equilibrium Green’s functions 137 Paper V: Impact of interface roughness distributions on the operation of quantum cascade lasers . 143 Paper VI: Influence of Interface Roughness in Quantum Cascade Lasers 157 Appendix: Tables with details for simulated structures 165 List of publications iii List of publications This thesis is based on the following publications, referred to by their Roman numerals: i Injection Schemes in THz Quantum Cascade Lasers Under Operation M. Lindskog, D. O. Winge, and A. Wacker Proc. SPIE, 8846:884603 (2013) ii An indirectly pumped terahertz quantum cascade laser with low injection coupling strength operating above 150 K S. G. Razavipour, E. Dupont, S. Fathololoumi, C. W. I. Chan, M. Lind- skog, Z. R. Wasilewski, G. Aers, S. R. Laframboise, A. Wacker, Q. Hu, D. Ban, and H. C. Liu Journal of Applied Physics 113, p. 203107 (2013) iii Nonequilibrium Green’s Function Model for Simulation of Quantum Cascade Laser Devices Under Operating Conditions A. Wacker, M. Lindskog, and D. O. Winge IEEE Journal of Selected Topics in Quantum Electronics 19, p. 1200611 (2013) iv Comparative analysis of quantum cascade laser modeling based on density matrices and non-equilibrium Green’s functions M. Lindskog, J. M. Wolf, V. Trinité, V. Liverini, J. Faist, G. Maisons, M. Carras, R. Aidam, R. Ostendorf, and A. Wacker Applied Physics Letters 105, p. 103106 (2014) v Impact of interface roughness distributions on the operation of quantum cascade lasers M. Franckié, D. O. Winge, J. M. Wolf, V. Liverini, E. Dupont, V. Trinité, J. Faist, and A. Wacker Optics Express 23, p. 5201-5212 (2015) iv CONTENTS vi Influence of Interface Roughness in Quantum Cascade Lasers K. Krivas, D. O. Winge, M. Franckié, and A. Wacker Journal of Applied Physics 118, p. 114501 (2015) All papers are reproduced with permission of their respective publishers. Paper III reprinted with permission from A. Wacker, M. Lindskog, and D. O. Winge c 2013 IEEE. Publications not included in this thesis: Non-linear response in Quantum Cascade Structures D. O. Winge, M. Lindskog, and A. Wacker Appl. Phys. Lett. 101(21), p. 211113 (2012) Microscopic approach to second harmonic generation in quantum cascade lasers D. O. Winge, M. Lindskog, and A. Wacker Optics Express 22, pp. 18389-18400 (2014) A phonon scattering assisted injection and extraction based tera- hertz quantum cascade laser E. Dupont, S. Fathololoumi, Z. R. Wasilewski, G. Aers, S. R. Laframboise, M. Lindskog, S. G. Razavipour, A. Wacker, D. Ban, and H. C. Liu J. Appl. Phys. 111(7), p. 73111 (2012) Superlattice gain in positive differential conductivity region D. O. Winge, M. Franckié, and A. Wacker preprint arXiv:1601.00915 Simple electron-electron scattering in non-equilibrium Green’s function simulations D. O. Winge, M. Franckié, C. Verdozzi, A. Wacker, and M. F. Pereira preprint arXiv:1602.03997 List of Acronyms v List of Acronyms ac Alternating Current CBO Conduction Band Offset dc Direct Current DM Density Matrix FCA Free-carrier absorption FCG Free-carrier gain FGR Fermi’s Golden Rule IFR Interface Roughness IR Infra-Red laser Light Amplification by Stimulated Emission of Radiation LLS Lower Laser States LO Longitudinal Optical (phonon) MBE Molecular Beam Epitaxy MOCVD Metal-Organic Chemical Vapour Deposition MPI Message Passing Interface NDR Negative Differential Resistance NEGF Non-Equilibrium Green’s function OMP OpenMP (Open Multi-Processing) QCL Quantum Cascade Laser RE Rate Equation RP Resonant phonon SA Scattering Assisted THz Terahertz (1012 Hz) ULS Upper Laser State vi CONTENTS Acknowledgements Physics has always been the subject that interest me the most, and so doing a PhD in this field has truly been a dream come true. I would like to first thank my supervisor Andreas Wacker for being an inspiration to go into the field of solid state theory and quantum optics.
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