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Computational Simulations of Thermoelectric Transport Properties

  • Ryu, Byungki (Thermoelectric Conversion Research Center, Creative and Fundamental Research Division, Korea Electrotechnology Research Institute (KERI)) ;
  • Oh, Min-Wook (Department of Advanced Materials Engineering, Hanbat National University)
  • Received : 2016.04.23
  • Accepted : 2016.05.12
  • Published : 2016.05.31

Abstract

This review examines computational simulations of thermoelectric properties, such as electrical conductivity, Seebeck coefficient, and thermal conductivity. With increasing computing power and the development of several efficient simulation codes for electronic structure and transport properties calculations, we can evaluate all the thermoelectric properties within the first-principles calculations with the relaxation time approximation. This review presents the basic principles of electrical and thermal transport equations and how they evaluate properties from the first-principles calculations. As a model case, this review presents results on $Bi_2Te_3$ and Si. Even though there is still an unsolved parameter such as the relaxation time, the effectiveness of the computational simulations on the transport properties will provide much help to experimental scientist researching novel thermoelectric materials.

Keywords

References

  1. K. F. Hsu, S. Loo, F. Guo, W. Chen, J. S. Dyck, C. Uher, T. Hogan, E. K. Polychroniadis, and M. G. Kanatzidis, "Cubic $AgPb_mSbTe_{2+m}$: Bulk Thermoelectric Materials with High Figure of Merit," Science, 303 [5659] 818-21 (2004). https://doi.org/10.1126/science.1092963
  2. G. J. Snyder and E. S. Toberer, "Complex Thermoelectric Materials," Nature Mater., 7 [2] 105-14 (2008). https://doi.org/10.1038/nmat2090
  3. J. P. Heremans, V. Jovovic, E. S. Toberer, A. Saramat, K. Kurosaki, A. Charoenphakdee, S. Yamanaka, and G. Snyder, "Enhancement of Thermoelectric Efficiency in PbTe by Distortion of the Electronic Density of States," Science, 321 [5888] 554-57 (2008). https://doi.org/10.1126/science.1159725
  4. Y. Pei, X. Shi, A. LaLonde, H. Wang, L. Chen, and G. J. Snyder, "Convergence of Electronic Bands for High Performance Bulk Thermoelectrics," Nature, 473 [7345] 66-9 (2011). https://doi.org/10.1038/nature09996
  5. P. F. P. Poudeu, J. D. Angelo, A. D. Downey, J. L. Short, T. P. Hogan, M. G. Kanatzidis, "High Thermoelectric Figure of Merit and Nanostructuring in Bulk p-type $Na_{1-x}Pb_mSb_{y-}Te_{m+2}$," Angew. Chem. Int. Ed., 45 [23] 3835-39 (2006). https://doi.org/10.1002/anie.200600865
  6. G. K. H. Madsen and D. J. Singh, "BoltzTraP. A Code for Calculating Band-Structure Dependent Quantities," Comput. Phys. Commun., 175 [1] 67-71 (2006). https://doi.org/10.1016/j.cpc.2006.03.007
  7. P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka, and J. Luitz, WIEN2k, An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties, Vienna University of Technology, Austria, 2001.
  8. G. Kresse and J. Furthmuller, "Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set," Phys. Rev. B, 54 [16] 11169-86 (1996). https://doi.org/10.1103/PhysRevB.54.11169
  9. G. Kresse and J. Furthmuller, "Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set," Comput. Mater. Sci., 6 [1] 15-50 (1996). https://doi.org/10.1016/0927-0256(96)00008-0
  10. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L Chiarotti, M. Cococcioni, I. Dabo, A. D. Corso, S. Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos1, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari1, and R. M. Wentzcovitch, "QUANTUM ESPRESSO: a Modular and Open-Source Software Project for Quantum Simulations of Materials," J. Phys.: Condens. Matter, 21 [39] 395502 (2009). https://doi.org/10.1088/0953-8984/21/39/395502
  11. G. Pizzi, D. Volja, B. Kozinsky, M. Fornari, and N. Marzari, "BoltzWann: A code for the Evaluation of Thermoelectric and Electronic Transport Properties with a Maximally-Localized Wannier Functions Basis", Comp. Phys. Comm., 185 [1] 422-29 (2014). https://doi.org/10.1016/j.cpc.2013.09.015
  12. G. S. Nolas, J. Sharp, and H. J. Goldsmid, Thermoelectrics: Basic Principles and New Materials Developments, Springer-Verlag, Heidelberg, 2001.
  13. M. W. Oh, D. M. Wee, S. D. Park, B. S. Kim, and H. W. Lee, "Electronic Structure and Thermoelectric Transport Properties of AgTlTe: First-Principles Calculations," Phys. Rev. B, 77 [16] 165119 (2008). https://doi.org/10.1103/PhysRevB.77.165119
  14. G. Jeffrey and T. S. Ursell, "Thermoelectric Efficiency and Compatibility," Phys. Rev. Lett., 91 [14] 148301 (2003). https://doi.org/10.1103/PhysRevLett.91.148301
  15. S. J. Youn and A. J. Freeman, "First-Principles Electronic Structure and its Relation to Thermoelectric Properties of $Bi_2Te_3$," Phys. Rev. B, 63 [8] 851121 (2001).
  16. P. Larson, S. D. Mahanti, and M. G. Kanatzdis, "Electronic Structure and Transport of $Bi_2Te_3$ and $BaBiTe_3$," Phys. Rev. B, 61 [12] 8162 (2000). https://doi.org/10.1103/PhysRevB.61.8162
  17. T. J. Scheidemantel, C. Ambrosch-Draxl, T. Thonhauser, J. V. Badding, and J. O. Sofo, "Transport Coefficients from First-Principles Calculations," Phys. Rev. B, 68 [12] 125210 (2003). https://doi.org/10.1103/PhysRevB.68.125210
  18. B.-L. Huang and M. Kaviany, "Ab Initio and Molecular Dynamics Predictions for Electron and Phonon Transport in Bismuth Telluride," Phys. Rev. B, 77 [12] 125209 (2008). https://doi.org/10.1103/PhysRevB.77.125209
  19. S. Lee and P. von Allmen, "Tight-Binding Modeling of Thermoelectric Properties of Bismuth Telluride," Appl. Phys. Lett., 88 [2] 022107 (2006). https://doi.org/10.1063/1.2162863
  20. S. K. Mishra, S. Satpathy, and O. Jepsen, "Electronic Structure and Thermoelectric Properties of Bismuth Telluride and Bismuth Selenide," J. Phys. Cond. Matter., 9 [2] 461 (1997). https://doi.org/10.1088/0953-8984/9/2/014
  21. P. Larson, and W. R. L. Lambrecht, "Electronic Structure and Magnetism in $Bi_2Te_3$, $Bi_2Se_3$, and $Sb_2Te_3$ Doped with Transition Metals (Ti-Zn)," Phys. Rev. B, 78 [19] 195207 (2008). https://doi.org/10.1103/PhysRevB.78.195207
  22. P. Larson, "Effect of $p_{1/2}$ Corrections in the Electronic Structure of $Bi_2Te_3$ Compounds," Phys. Rev. B, 68 [15] 1551211 (2003).
  23. B. Yu. Yavorsky, N. F. Hinsche, I. Mertig, and P. Zahn, "Electronic Structure and Transport Anisotropy of $Bi_2Te_3$ and $Sb_2Te_3$," Phys. Rev. B, 84 [16] 165208 (2011). https://doi.org/10.1103/PhysRevB.84.165208
  24. N. F. Hinsche, B. Yu. Yavorsky, I. Mertig, and P. Zahn, "Influence of Strain on Anisotropic Thermoelectric Transport in $Bi_2Te_3$ and $Sb_2Te_3$," Phys. Rev. B, 84 [16] 165214 (2011). https://doi.org/10.1103/PhysRevB.84.165214
  25. M. Kim, A. J. Freeman, and C. B. Geller, "Screened Exchange LDA Determination of the Ground and Excited State Properties of Thermoelectrics: $Bi_2Te_3$," Phys. Rev. B, 72 [3] 035205 (2005). https://doi.org/10.1103/PhysRevB.72.035205
  26. P. Pecheur and G. Toussaint, "Electronic Structure and Bonding in Bismuth Telluride," Phys. Lett. A, 135 [3] 223-26 (1989). https://doi.org/10.1016/0375-9601(89)90267-3
  27. P. Pecheur and G. Toussaint, "Tight-binding Studies of Crystal Stability and Defects in $Bi_2Te_3$," J. Phys. Chem. Solids., 55 [4] 327-38 (1994). https://doi.org/10.1016/0022-3697(94)90229-1
  28. B. Ryu, B. S. Kim, J. E. Lee, S. J. Joo, B. K. Min, H. W. Lee, S. D. Park, and M. W. Oh, "Prediction of the Band Structures of $Bi_2Te_3$-Related Binary and Sb/Se-Doped Ternary Thermoelectric Materials," J. Kor. Phys. Soc., 68 [1] 115-20 (2016). https://doi.org/10.3938/jkps.68.115
  29. M. W. Oh, B. Ryu, J. E. Lee, S. J. Joo, B. S. Kim, S. D. Park, B. K. Min, and H. W. Lee, "Electronic Structure and Seebeck Coefficients of $Bi_2Te_3$, $Sb_2Te_3$, and $(Bi_{0.25}Te_{0.75})_2Te_3$: A First-Principles Calculation Study," J. Nanoelec. Optoelec., 10 [3] 391-96 (2015). https://doi.org/10.1166/jno.2015.1756
  30. S. Nakajima, "The Crystal Structure of $Bi_2Te_{3-x}Se_x$," J. Phys. Chem. Solids., 24 [3] 479 (1963). https://doi.org/10.1016/0022-3697(63)90207-5
  31. M. W. Oh, J. H. Son, B. S. Kim, S. D. Park, B. K. Min, and H. W. Lee, "Antisite Defects in n-type $Bi_2(Te,\;Se)_3$: Experimental and Theoretical Studies," J. Appl. Phys., 115 [13] 133706 (2014). https://doi.org/10.1063/1.4870818
  32. J. P. Perdew, K. Burke, and M. Ernzerhof, "Generalized Gradient Approximation Made Simple," Phys. Rev. Lett., 77 [18] 3865 (1996). https://doi.org/10.1103/PhysRevLett.77.3865
  33. G. A. Thomas, D. H. Rapkine, R. B. Van Dover, L. F. Mattheiss, W. A. Sunder, L. F. Schneemeyer, and J. V. Waszczak, "Large Electronic-Density Increase on Cooling a Layered Metal: Doped $Bi_2Te_3$," Phys. Rev. B., 46 [3] 1553 (1992). https://doi.org/10.1103/PhysRevB.46.1553
  34. T. Thonhauser, T. J. Scheidemantel, J. O. Sofo, J. V. Badding, and G. D. Mahan, "Thermoelectric Properties of $Sb_2Te_3$ Under Pressure and Uniaxial Stress," Phys. Rev. B, 68 [8] 085201 (2003). https://doi.org/10.1103/PhysRevB.68.085201
  35. H. Scherrer and S. Scherrer, "Bismuth Telluride, Antimony Telluride, and Their Solid Solutions, pp. 211-238 in CRC Handbook of Thermoelectrics. Ed. by D. M. Rowe, CRC Press, Boca Raton, 1995.
  36. H. J. Goldsmid, "The Electrical Conductivity and Thermoelectric Power of Bismuth Telluride," Proc. Phys. Soc., 71 [4] 633 (1958). https://doi.org/10.1088/0370-1328/71/4/312
  37. Y. Kang, S. H. Jeon, Y. W. Son, Y. S. Lee, M. Ryu, S. Lee, and S. Han, "Microscopic Origin of Universal Quasilinear Band Structures of Transparent Conducting Oxides," Phys. Rev. Lett., 108 196404 (2012). https://doi.org/10.1103/PhysRevLett.108.196404
  38. J. M. Ziman, Electrons and Phonons; pp. 288-333, Oxford University Press, Oxford, 1979.
  39. A. Bid, A. Bora, and A. K. Raychaudhuri, "Temperature Dependence of the Resistance of Metallic Nanowires of Diameter ${\geq}15nm$: Applicability of Bloch-Gruneisen Theorem," Phys. Rev. B, 74 [3] 035426 (2006). https://doi.org/10.1103/PhysRevB.74.035426
  40. J. Y. Kim, M. W. Oh, S. Lee, Y. C. Cho, J. H. Yoon, G. W. Lee, C. R. Cho, C. H. Park, and S. Y. Jeong, "Abnormal Drop in Electrical Resistivity with Impurity Doping of Single-Crystal Ag," Sci. Rep., 4 5450 (2014).
  41. P. B. Allen, W. E. Pickett, and H. Krakauer, "Band-Theory Analysis of Anisotropic Transport in $La_2CuO_4$-Based Superconductors," Phys. Rev. B, 36 [7] 3926-29 (1987).
  42. R. J. Mehta, Y. Zhang, H. Zhu, D. S. Parker, M. Belley, D. J. Singh, R. Ramprasad, T. Borca-Tasciuc, and G. Ramanath, "Seebeck and Figure of Merit Enhancement in Nanostructured Antimony Telluride by Antisite Defect Suppression through Sulfur Doping," Nano Lett., 12 [9] 4523-29 (2012). https://doi.org/10.1021/nl301639t
  43. P. B. Allen, "Empirical Electron-Phonon $\lambda$ Values from Resistivity of Cubic Metallic Elements," Phys. Rev. B, 36 [5] 2920-23 (1987). https://doi.org/10.1103/PhysRevB.36.2920
  44. P. B. Allen, T. P. Beaulac, F. S. Khan, W. H. Butler, F. J. Pinski, and J. C. Swihart, "DC Transport in Metals," Phys. Rev. B, 34 [6] 4331-33 (1986). https://doi.org/10.1103/PhysRevB.34.4331
  45. S. Y. Savrasov and D. Y. Savrasov, "Electron-Phonon Interactions and Related Physical Properties of Metals from Linear-Response Theory," Phys. Rev. B, 54 [23] 16487-501 (1996). https://doi.org/10.1103/PhysRevB.54.16487
  46. G. P. Srivastava, Physics of Phonons; pp. 122-174, CRC Press, Boca Raton, 1990.
  47. P. Giannozzi, S. De Gironcoli, P. Pavone, and S. Baroni, "Ab initio Calculation of Phonon Dispersions in Semiconductors," Phys. Rev. B, 43 [9] 7231 (1991). https://doi.org/10.1103/PhysRevB.43.7231
  48. G. Deinzer, G. Birner, and D. Strauch, "Ab initio Calculation of the Linewidth of Various Phonon Modes in Germanium and Silicon," Phys. Rev. B, 67 [14] 144304 (2003). https://doi.org/10.1103/PhysRevB.67.144304
  49. D. A. Broido, M. Malorny, G. Birner, N. Mingo, and D.A. Stewart, "Intrinsic Lattice Thermal Conductivity of Semiconductors from First Principles," Appl. Phys. Lett., 91 [23] 231922 (2007). https://doi.org/10.1063/1.2822891
  50. K. Esfarjani, H. T. Stokes, "Method to Extract Anharmonic Force Constants from First Principles Calculations," Phys. Rev. B, 77 [14] 144112 (2008). https://doi.org/10.1103/PhysRevB.77.144112
  51. X. Tang and J. Dong, "Pressure Dependence of Harmonic and Anharmonic Lattice Dynamics in MgO: a First-Principles Calculation and Implications for Lattice Thermal Conductivity," Phys. Earth Planet. Inter., 174 [1] 33 (2009). https://doi.org/10.1016/j.pepi.2008.10.003
  52. X. Tang and J. Dong, "Lattice Thermal Conductivity of MgO at Conditions of Earth's Interior," Proc. Natl. Acad. Sci. USA, 107 [10] 4539-43 (2010). https://doi.org/10.1073/pnas.0907194107
  53. L. Chaput, A. Togo, I. Tanaka, and G. Hug, "Phonon-Phonon Interactions in Transition Metals," Phys. Rev. B, 84 [9] 094302 (2011). https://doi.org/10.1103/PhysRevB.84.094302
  54. A. Togo, L. Chaput, and I. Tanaka, "Distributions of Phonon Lifetimes in Brillouin Zones," Phys. Rev. B, 91 [9] 094306 (2015). https://doi.org/10.1103/PhysRevB.91.094306
  55. A. Katre, A. Togo, I. Tanaka, and G. K. H. Madsen, "First-Principles Study of Thermal Conductivity Cross-over in Nanostructured Zinc-Chalcogenides," J. Appl. Phys., 117 [4] 045102 (2015). https://doi.org/10.1063/1.4906461
  56. A. Togo and I. Tanaka, "First Principles Phonon Calculations in Materials Science," Scr. Mater., 108 1-5 (2015). https://doi.org/10.1016/j.scriptamat.2015.07.021
  57. Webpage of phono3py, http://atztogo.github.io/phono3py. Accessed on 11/04/2016.
  58. W. Li, J. Carrete, N. A. Katcho, and N. Mingo, "ShengBTE: A Solver for the Boltzmann Transport Equation for Phonons," Comput. Phys. Commun., 185 [6] 1747 (2014). https://doi.org/10.1016/j.cpc.2014.02.015
  59. O. Hellman and D. A. Borido, "Phonon Thermal Transport in $Bi_2Te_3$ from First Principles," Phys. Rev. B, 90 [13] 134309 (2014). https://doi.org/10.1103/PhysRevB.90.134309
  60. K. Esfarjani, G. Chen, and H. T. Stokes, "Heat Transport in Silicon from First-Principles Calculations," Phys. Rev. B, 84 [8] 085204 (2011). https://doi.org/10.1103/PhysRevB.84.085204
  61. Z. Tian, K. Esfarjani, J. Shiomi, A. S. Henry, and G. Chen, "On the Importance of Optical Phonons to Thermal Conductivity in Nanostructures," Appl. Phys. Lett., 99 [5] 053122 (2011). https://doi.org/10.1063/1.3615709
  62. B. Qiu, Z. Tian, A. Vallabhaneni, B. Liao, J. M. Mendoza, O. D. Restrepo, X. Ruan, and G. Chen, "First-Principles Simulation of Electron Mean-Free-Path Spectra and Thermoelectric Properties in Silicon," EPL(Europhysics Letters), 109 [5] 57006 (2015). https://doi.org/10.1209/0295-5075/109/57006
  63. Z. Tian, J. Garg, K. Esfarjani, T. Shiga, J. Shiomi, and G. Chen, "Phonon Conduction in PbSe, PbTe, $PbSe_{1-x}Te_x$ from First-Principles Calculations," Phys. Rev. B, 85 [18] 184303 (2012). https://doi.org/10.1103/PhysRevB.85.184303
  64. J. M. Seklton, S. C. Parker, A. Togo, I. Tanaka, and A. Walsh, "Thermal Physics of the Lead Chalcogenides PbS, PbSe, and PbTe from First Principles," Phys. Rev. B, 89 [20] 205203 (2014). https://doi.org/10.1103/PhysRevB.89.205203
  65. G. K. H. Madsen, "Automated Search for New Thermoelectric Materials: The case of LiZnSb," J. Amer. Chem. Soc., 128 [37] 12140-46 (2006). https://doi.org/10.1021/ja062526a
  66. P. Gorai, P. Parilla, E. S. Toberer, and Vladan Stevanovic, "Computational Exploration of the Binary $A_1B_1$ Chemical Space for Thermoelectric Performance," Chem. Mater., 27 [18] 6213-21 (2015). https://doi.org/10.1021/acs.chemmater.5b01179

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