Modeling the Thermoelectric Properties of Bulk and Nanocomposite Thermoelectric Materials by Austin Minnich Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY [June ao008 May 2008 @ Massachusetts Institute of Technology 2008. All rights reserved. Author .. Department of Mechanical Engineering May 21, 2008 Certified by ...... .... .................... Gang Chen Warren and Townley Rohsenow Professor of Mechanical Engineering Thesis Supervisor .. j I A ccepted by .......................................... Lallit Anand Chairman, Department Committee on Graduate Students OFTEOHNOLOGY JUL 2 9 2008 M•tCHVES LIBRARIES Modeling the Thermoelectric Properties of Bulk and Nanocomposite Thermoelectric Materials by Austin Minnich Submitted to the Department of Mechanical Engineering on May 21, 2008, in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Abstract Thermoelectric materials are materials which are capable of converting heat directly into electricity. They have long been used in specialized fields where high reliability is needed, such as space power generation. Recently, certain nanostructured materi- als have been fabricated with high thermoelectric properties than those of commer- cial bulk materials, leading to a renewed interest in thermoelectrics. One of these types of nanostructured materials is nanocomposites, which are materials with either nanosized grains or particles on the nanometer scale embedded in a host material. Nanocomposites present many challenges in modeling due to their random nature and unknown grain boundary scattering mechanisms. In this thesis we introduce new models for phonon and electron transport in nanocomposites. For phonon modeling we develop an analytical formula for the phonon thermal conductivity using the effec- tive medium approximation, while for electron modeling and more detailed phonon modeling we use the Boltzmann equation to calculate the thermoelectric properties. To model nanocomposites we incorporate a grain boundary scattering relaxation time. The models allow us to better understand the transport processes in nanocomposites and help identify strategies for material selection and fabrication. Thesis Supervisor: Gang Chen Title: Warren and Townley Rohsenow Professor of Mechanical Engineering Acknowledgments This thesis could not have been completed without the help of many people. First, I am grateful to my advisor, Professor Gang Chen, who helped me make the transition to MIT and has helped me learn how to become a more effective researcher. His good advice and technical expertise have been invaluable in allowing me to quickly learn the field and start contributing original research. Second, I am fortunate to have great labmates who have been extremely helpful from the first day I arrived here. The entire lab has given me advice at some point and I am indebted to them. In particular, I would like to thank Hohyun Lee, who has always given good advice and been a great collaborator; Sheng Shen, who is helpful both in problem sets and research discussions; and Qing Hao, with whom I worked extensively for almost a year and still learn from every day. I am also grateful to the Department of Defense for their generous financial support. I would like to thank my family and friends who have supported me and made my time at MIT enjoyable. I am very fortunate to have a wonderful mom, dad, and sister who have always been there for me over the years. Finally, I would like to thank Song-Yi Kim for her love and support. Contents 1 Introduction 15 1.1 Thermoelectric Energy Conversion . .................. 16 1.1.1 Background ............................ 16 1.1.2 Thermoelectric Materials ................... .. 18 1.2 Nanocomposites .............................. 19 2 Phonon Modeling 23 2.1 Effective Medium Approximation ................ ... 24 2.1.1 Classical Theory ......................... 24 2.1.2 Limitations for Nanocomposites . ............. ... 25 2.2 Modified Effective Medium Approximation . .............. 26 2.2.1 Derivation . .. .. .. 26 2.2.2 Results . ....... ...... ... 28 2.3 Sum m ary ................................. 31 3 Modeling Carrier Transport 33 3.1 Boltzmann Transport Equation ................... .. 33 3.1.1 Introduction .......... ......... ......... 33 3.1.2 Scattering Term and RTA .................... 35 3.1.3 Calculating Macroscopic Properties . .............. 38 3.1.4 Application to Thermoelectric Materials . ........... 41 3.2 Modeling Thermoelectric Materials . .................. 44 3.2.1 Non-parabolicity and Anisotropy . ............... 44 3.2.2 Multiple Conduction and Hole Bands ...... 3.3 Scattering Mechanisms .................. 3.3.1 Phonon-Electron Scattering .......... 3.3.1.1 Acoustic Phonon Scattering ...... 3.3.1.2 Non-polar Optical Phonon Scattering . 3.3.1.3 Polar Optical Phonon Scattering . 3.3.1.4 Piezoelectric scattering ......... 3.3.1.5 Intervalley Scattering .......... 3.3.2 Ionized Impurity Scattering . ......... 3.3.3 Alloy Scattering . ............... 3.3.4 Summary of Scattering Mechanisms ....... 3.4 Phonon Thermal Conductivity . ............. 3.5 Summary ................... 4 Modeling Bulk and Nanocomposite Thermoelectric Materials 63 4.1 Validation with Bulk Materials ............ 63 4.1.1 SiGe x . ............ 64 4.1.2 G aA s .. ........ ........ ..... 66 4.1.3 InSb ........... ............ 69 4.1.4 In -l_Ga, As ................... 72 4.2 M aterials Search .................... 75 4.3 Modeling Nanocomposites ............... 77 4.3.1 Grain Boundary Scattering for Electrons . 78 4.3.2 Grain Boundary Scattering for Phonons . .. 79 4.3.3 Results ...... ........ ... 80 4.3.3.1 Nano-SiGe ...... ....... 80 4.3.3.2 Nano-GaAs .............. 83 4.3.4 Summary of Grain Boundary Scattering Analy sis, • .•.. ..° 84 5 Conclusion 5.1 Summary . 5.2 Future Work ................................ 88 A Material Properties 91 List of Figures 1.1 Example demonstration of thermoelectric power generation. ...... 17 1.2 Thermoelectric refrigeration. .................. .... 18 1.3 Diagram of a nanocomposite. ...................... 20 2.1 Unmodified and modified effective medium approximation with spher- ical inclusions............... .. .............. .. 29 2.2 Unmodified and modified effective medium approximation with cylin- drical inclusions. ............................. 30 3.1 Schematic of electron-phonon scattering. Phonons compress and ex- pand the lattice, changing the local lattice constant and scattering electrons. ................................. 51 4.1 Thermoelectric properties of Si80Ge 20 versus T for several different dop- ing concentrations; ND increases as the electrical conductivity increases. 66 4.2 Mobility of intrinsic GaAs versus temperature with high and low tem- perature approximations for the POP relaxation time (data from Ref. [52], Fig. 1).................... ............ 67 4.3 Mobility of intrinsic GaAs versus temperature, showing the effects of multiple band transport; the top set of curves only incorporate one band (data from Ref. [52], Fig. 1) ..................... 68 4.4 Mobility of GaAs versus temperature, ND = 5 x 1015 cm -3 (high tem- perature data from Ref. [41]; low temperature data from Ref. [48]). 69 11 4.5 Seebeck coefficient of GaAs versus doping concentration, T = 300K (data and literature calculation from Ref. [52], Fig. 4). ... ..... 70 4.6 Mobility of intrinsic InSb versus temperature (data from Ref. [53], Fig. 1).................................... 70 4.7 Seebeck coefficient and electrical conductivity of InSb versus tempera- ture, ND = 2x10 14 cm-3 (data from Ref. [55]) . ............ 72 - 3 4.8 Mobility of In.53Ga.47As versus temperature, ND = 3.5x 1014 cm (data from Ref. [48]; also in Ref. [56], Fig. 2). .......... 73 4.9 Mobility of In.53Ga.47As versus doping concentration, T=300K (data from Ref. [57], Fig. 1). ...... ........... ....... 73 4.10 Mobility of In-lGaAs versus composition x, T=300K, ND = 1.0 x 1016 cm - 3 (data from Ref. [58], Fig. 1). .................... 74 4.11 Seebeck coefficient of InGaAs versus temperature (data from Ref. [59], Fig. 6) ..... .. ................ .......... 75 4.12 Figure of merit ZT versus temperature for several materials. ...... 76 4.13 PFT versus temperature for several materials. ............. 77 4.14 Thermoelectric properties of nano-SiGe with a 35nm grain size, 20% volume fraction. ................... ........... 81 4.15 Thermoelectric properties of nano-SiGe with various grain sizes, 20% volume fraction. ................... .......... .. 82 4.16 Thermoelectric properties of GaAs with 20nm inclusions, 20% volume fraction, ND = 2x 1019 cm - 3 , for several different barrier heights. The bulk case is shown for reference. ................... .. 83 4.17 ZT of GaAs with 10 and 20nm inclusions for several different volume fractions; Ug = 0.3 eV. ................... ....... 85 List of Tables 2.1 Material properties used in the modified effective medium approximation. 28 A.1 Fitting parameters used in the lattice thermal conductivity calculation. 92 A.2 Temperature and composition dependence of the band gap between the lowest lying conduction band edge and the valence band. ...... 92 A.3 Material parameters used in the Boltzmann equation calculation. 93 Chapter 1 Introduction Energy has become one of the most critical current issues. The need for sources of energy other than fossil fuels,