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Electronic Structure and Thermoelectric Properties of Narrow Band Gap Semiconductors and Pseudo-Gap Systems

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Electronic Structure and Thermoelectric Properties of Narrow Band Gap Semiconductors and Pseudo-Gap Systems ELECTRONIC STRUCTURE AND THERMOELECTRIC PROPERTIES OF NARROW BAND GAP SEMICONDUCTORS AND PSEUDO-GAP SYSTEMS By Dat Thanh Do A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Condensed Matters Physics - Doctor Of Philosophy 2013 ABSTRACT ELECTRONIC STRUCTURE AND THERMOELECTRIC PROPERTIES OF NARROW BAND GAP SEMICONDUCTORS AND PSEUDO-GAP SYSTEMS By Dat Thanh Do The direct energy conversion from heat to electricity without any moving part using the thermo- electric effects is attractive and has many promising applications in power generation and heat pumping (refrigeration) devices. However, the wide use of thermoelectric materials in daily life is still not practical due to its low efficiency. Presently, there has been renewed interest in thermo- electrics with new strategies for improving the efficiency, mostly by controlling the morphology and dimensionality, and manipulating the electronic structure of novel complex systems. There are new questions arise and several old questions have not yet been answered. My group at Michi- gan State University has been actively working on narrow band gap semiconductors and pseudo- gap systems including BiTe, BiSe, SbTe, AgPbmSbTem+2 (LAST), III-VI compounds, Mg2Si, Cu3SbSe4, Fe2VAl, ZrNiSn, etc. , focusing on their thermoelectrics related properties. This dis- sertation tries to address some of the fundamental questions on the electronic structure and related thermoelectric properties of narrow band gap semiconductors and pseudo-gap systems, employ- ing the state-of-art density functional theory (DFT) and Boltzmanns transport equation. I focuses on some well-known materials including Heusler compound, Fe2VAl, tetrahedrally bonded com- pounds (Cu3SbSe4 and related systems) and a newly reported novel nanocomposite system of Half-Heusler–Heusler (ZrNiSn–ZrNi2Sn). For the first two systems (Heusler and tetrahedrally co- ordinated systems), the effects of correlated electrons in the system containing d-electrons, valency of sp-elements, and the role of lone-pair electrons in band gap formation and effects on thermoelec- tric properties are fully investigated. For the third system, Half-Heusler–Heusler nanocomposite, I report a detailed energetics analysis of the nanostructure formation and its effects on the electronic structures of the interested systems. Copyright by DAT THANH DO 2013 To my family iv ACKNOWLEDGEMENTS I am extremely grateful to those who in anyway contribute to my work at Michigan State University (MSU). First of all, I would like to express my sincere thanks to my supervisor Prof. S. D. Mahanti for helping me become a theoretical physicist, for his patient, understanding and inspiration. Over last five year, he has dedicated countless amount of time and effort to support me in my research as well as in writing this dissertation. I would like to thank Prof. Donald Morelli,Prof. Carlo Piermarocchi,Prof. Wayne Repko, and Prof. Chong-Yu Ruan for serving on my guidance committee and for providing useful advices when I needed. I would also like to thank my collaborations, Prof. Donald Morelli’s Group (MSU), Prof. Christopher Wolverton’s Group (Northwestern University – NWU), Prof. Vidvuds Ozoline’s (Uni- versity of California at Los Angeles – UCLA), Prof. Mercouri G. Kanatzidis’s (NWU), especially to those who I have been directly working with, Dr. Eric Skoug, Dr. Chang Liu (MSU), Dr. Yong- sheng Zhang, Dr. Daniel Shoesmaker, Dr. Thomas Chasapi, Dr. Utpal Chatterjee (NWU), for their valuable contributions. My gratitude also goes to the past members of my group at MSU, Dr. Khang Hoang, Dr. Rak Zsolt, Dr. Mal-Soon Lee, for stimulus and useful discussions. Special thanks goes to my family, my friends for always being by my side and supporting me when I needed the most. I would like to acknowledge the Energy Frontier Research Center (EFRC) of at MSU, Revo- lutionary Materials for Solid State Energy Conversion, a research center of the U.S. Department of Energy, for funding my research and providing an extremely active networking environment, giving me chance to work with and learn from people from different disciplines. Last but not least, I would like to thank Vietnam Education Foundation (VEF) for giving me scholarship to study at MSU. v TABLE OF CONTENTS LIST OF TABLES .......................................viii LIST OF FIGURES ...................................... ix LIST OF SYMBOLS AND ABBREVIATIONS .......................xiv CHAPTER 1 INTRODUCTION ............................ 1 1.1 Thermoelectrics .................................... 1 1.1.1 Brief history of thermoelectrics ........................ 1 1.1.2 Mechanisms of thermoelectric effects .................... 4 1.1.3 Thermoelectric applications ......................... 5 1.1.4 Figure of merit and device efficiency ..................... 8 1.2 Theoretical aid in pursuing better figure of merit (ZT) . 11 1.3 Narrow band gap semiconductors and pseudo-gap systems . 13 1.4 Outline of the dissertation ............................... 16 CHAPTER 2 THEORETICAL METHODOLOGY . 17 2.1 Basic equations .................................... 17 2.2 Independent-electron – Hartree and Hartree-Fock approximation . 20 2.2.1 Hartree approximation ............................ 20 2.2.2 Hartree-Fock approximation (HFA) ..................... 22 2.3 Exchange and correlation ............................... 25 2.4 Fundamentals of density functional theory (DFT) . 26 2.5 Functionals for exchange and correlation ....................... 30 2.5.1 Local (spin) density approximation (LSDA) and the gradient correction (GGA) ..................................... 33 2.5.2 Local treatment of strongly correlated electron systems: LDA+U . 34 2.5.3 Non-local treatment of exchange-correlation in correlated electron sys- tems: Hybrid functional theory ........................ 37 2.6 Boltzmann’s equation for transport .......................... 39 2.7 Computational details ................................. 42 CHAPTER 3 HEUSLER COMPOUND – Fe2VAl: EFFECTS OF ON-SITE COULOMB REPULSION ........................ 44 3.1 Introduction ...................................... 44 3.2 Computational details ................................. 48 3.3 Electronic structure: Pseudo-gap versus real gap ................... 49 3.4 Thermoelectric properties ............................... 56 3.4.1 GGA calculation ............................... 56 3.4.2 GGA+U calculation : the effect of finite band gap . 59 3.4.3 Comparison with experiment and other theoretical results . 60 vi 3.5 Summary ....................................... 64 CHAPTER 4 DIAMOND-LIKE TERNARY COMPOUNDS . 66 4.1 Introduction ...................................... 66 4.2 Crystal structures of Famatinite and Enargite ..................... 69 4.3 Electronic structure of Cu3SbSe4: band gap formation and the role of Sb lone pairs and non-local exchange effect .......................... 71 4.3.1 GGA calculation and indication of the existence of Sb lone pair electrons . 74 4.3.2 Failure of local exchange approximation – Effect of non-local exchange interaction ................................... 77 4.3.3 Unphyscal value of U and its meaning .................... 81 4.4 Bond and band gap in the a class of I3-V-VI4 Famatinite and Enargite compounds . 83 4.4.1 Atomic energy levels of constituents and some schematic studies. 84 4.4.2 Results obtained using local approximations . 85 4.4.3 Effect of non-local exchange ......................... 92 4.5 Thermopower calculation of Cu3SbSe4 ........................ 92 4.6 Summary ....................................... 96 CHAPTER 5 HALF-HEUSLER–HEUSLER COMPOSITE . 98 5.1 Introduction ...................................... 98 5.2 Methods of electronic structure calculation and modeling nanostructures . 103 5.3 Results and Discussions ................................105 5.3.1 Formation energy and energetics of clustering . 105 5.3.1.1 HH with excess Ni . 105 5.3.1.2 FH with deficient Ni . 108 5.3.2 Electronic structure ..............................112 5.4 Summary and Conclusion ...............................117 CHAPTER 6 CONCLUSION AND OUTLOOK . 119 BIBLIOGRAPHY .......................................123 vii LIST OF TABLES Table 2.1: Summary of approximations used in DFT ..................... 32 Table 3.1: Summary of experimental studies of energy gap in Fe2VAl . 44 Table 3.2: Summary of previous theoretical studies on Fe2VAl electronic structure . 45 Table 3.3: Summary of Fe2VAl band gap using different methods . 54 Table 4.1: Summary of crystal structures of Cu3AB4 ..................... 71 Table 4.2: Nearest neighbor distances (Å) and band gaps (eV) with different exact ex- change ratios .................................... 80 Table 4.3: Atomic energies of the s and p valence electrons for different constituents and for the monovalent Cu, the energy of Cu d-level is included . 84 Table 4.4: Effect of different V element substitutions on the band gap of Cu3SbSe4 with and without ionic relaxation ............................ 90 Table 5.1: Formation energies (eV) of HH-FH systems (for the lowest energy configurations)105 Table 5.2: Ground state energy as a function of Ni3’s relative position with respect to Ni1-Ni2 .......................................106 viii LIST OF FIGURES Figure 1.1: Schematic diagram of a simple thermo-couple made of two conductors A and B with junction 1 and 2 kept in a heat sink and heat source respectively. (For interpretation of the references to color in this and all other figures, the reader is referred to
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