Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

Computationally guided discovery of thermoelectric materials

Abstract

The potential for advances in thermoelectric materials, and thus solid-state refrigeration and power generation, is immense. Progress so far has been limited by both the breadth and diversity of the chemical space and the serial nature of experimental work. In this Review, we discuss how recent computational advances are revolutionizing our ability to predict electron and phonon transport and scattering, as well as materials dopability, and we examine efficient approaches to calculating critical transport properties across large chemical spaces. When coupled with experimental feedback, these high-throughput approaches can stimulate the discovery of new classes of thermoelectric materials. Within smaller materials subsets, computations can guide the optimal chemical and structural tailoring to enhance materials performance and provide insight into the underlying transport physics. Beyond perfect materials, computations can be used for the rational design of structural and chemical modifications (such as defects, interfaces, dopants and alloys) to provide additional control on transport properties to optimize performance. Through computational predictions for both materials searches and design, a new paradigm in thermoelectric materials discovery is emerging.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Relationships between real and reciprocal space, and diversity of the search space.
Figure 2: Dependence of the scattering rate on energy.
Figure 3: High-throughput searches to identify promising n-type Zintl thermoelectrics.
Figure 4: Predicting lattice thermal conductivity.

Similar content being viewed by others

References

  1. Baranowski, L. L. Snyder, G. J. & Toberer, E. S. Concentrated thermoelectric generators. Energy Environ. Sci. 5, 9055 (2012).

    Article  CAS  Google Scholar 

  2. Bell, L. E. Cooling, heating, generating power, and recovering waste heat with thermoelectric systems. Science 321, 1457 (2008).

    Article  CAS  Google Scholar 

  3. Snyder, G. J., Toberer, E. S., Khanna, R. & Seifert, W. Improved thermoelectric cooling based on the Thomson effect. Phys. Rev. B 86, 045202 (2012).

    Article  CAS  Google Scholar 

  4. Snyder, G. J. & Ursell, T. S. Thermoelectric efficiency and compatibility. Phys. Rev. Lett. 91, 148301 (2003).

    Article  CAS  Google Scholar 

  5. Snyder, G. J. & Toberer, E. S. Complex thermoelectric materials. Nat. Mater. 7, 105 (2008).

    Article  CAS  Google Scholar 

  6. Zhao, L. et al. Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals. Nature 508, 373 (2014).

    Article  CAS  Google Scholar 

  7. Wei P.-C. et al. The intrinsic thermal conductivity of SnSe. Nature 539, E1 (2016).

    Article  CAS  Google Scholar 

  8. Zevalkink, A. et al. Thermoelectric properties of Sr3GaSb3 — a chain-forming Zintl compound. Energy Environ. Sci. 5, 9121 (2012).

    Article  CAS  Google Scholar 

  9. Chung, D.-Y. et al. A new thermoelectric material: CsBi4Te6 . J. Am. Chem. Soc. 126, 6414 (2004).

    Article  CAS  Google Scholar 

  10. Lu, X. et al. High performance thermoelectricity in earth-abundant compounds based on natural mineral tetrahedrites. Adv. Energy Mat. 3, 342 (2013).

    Article  CAS  Google Scholar 

  11. Nolas, G. S., Cohn, J. L., Slack, G. A. & Schujman, S. B. Semiconducting Ge clathrates: promising candidates for thermoelectric applications. Appl. Phys. Lett. 73, 178 (1998).

    Article  CAS  Google Scholar 

  12. Zhang, J. et al. Discovery of high-performance low-cost n-type Mg3Sb2-based thermoelectric materials with multi-valley conduction bands. Nat. Commun. 8, 13901 (2017).

    Article  CAS  Google Scholar 

  13. Sales, B. C. et al. Filled skutterudite antimonides: electron crystals and phonon glasses. Phys. Rev. B. 56, 15081 (1997).

    Article  CAS  Google Scholar 

  14. Vining, C. B. et al. Thermoelectric properties of pressure-sintered Si0.8 Ge0.2 thermoelectric alloys. J. Appl. Phys. 69, 4333 (1991).

    Article  CAS  Google Scholar 

  15. Sharp, J. W. et al. Thermoelectric properties of CoSb3 and related alloys. J. Appl. Phys. 78, 1013 (1995).

    Article  CAS  Google Scholar 

  16. Yan, X. et al. Stronger phonon scattering by larger differences in atomic mass and size in p-type half-Heuslers Hf1 − xTixCoSb0.8Sn0.2 . Energy Environ. Sci. 5, 7543 (2012).

    Article  CAS  Google Scholar 

  17. Wang, H., Pei, Y., LaLonde, A. D. & Snyder, G. J. Heavily doped p-type PbSe with high thermoelectric performance: an alternative for PbTe. Adv. Mater. 23, 1366 (2011).

    Article  CAS  Google Scholar 

  18. Wang, H., Schechtel, E., Pei, Y. & Snyder, G. J. High thermoelectric efficiency of n-type PbSe. Adv. Energy Mater. 3, 488 (2013).

    Article  CAS  Google Scholar 

  19. Toberer, E. S. et al. Traversing the metal–insulator transition in a Zintl phase: rational enhancement of thermoelectric efficiency in Yb14Mn1 − xAlxSb11 . Adv. Funct. Mater. 18, 2795 (2008).

    Article  CAS  Google Scholar 

  20. Lei, W. et al. Convergence of conduction bands as a means of enhancing thermoelectric performance of n-type Mg2Si1 − xSnx solid solutions. Phys. Rev. Lett. 108, 166601 (2012).

    Article  CAS  Google Scholar 

  21. Zhao, L. D. et al. All-scale hierarchical thermoelectrics: MgTe in PbTe facilitates valence band convergence and suppresses bipolar thermal transport for high performance. Energy Environ. Sci. 6, 3346 (2013).

    Article  CAS  Google Scholar 

  22. Vineis, C. J., Shakouri, A., Majumdar, A. & Kanatzidis, M. G. Nanostructure thermoelectrics: big efficiency gains from small features. Adv. Mater. 22, 3970 (2010).

    Article  CAS  Google Scholar 

  23. Tan, G., Zhao, L. & Kanatzidis, M. G. Rationally designing high-performance bulk thermoelectric materials. Chem. Rev. 116, 12123 (2016).

    Article  CAS  Google Scholar 

  24. Lindsay, L., Broido, D. A. & Reinecke, T. L. Ab initio thermal transport in semiconductors. Phys. Rev. B 87, 165201 (2013).

    Article  CAS  Google Scholar 

  25. Ohta, S. & Nomura, T. High-temperature carrier transport and thermoelectric properties of heavily La- and Nb-doped SrTiO3 single crystals. J. Appl. Phys. 97, 034106 (2005).

    Article  CAS  Google Scholar 

  26. Andersen, O. K. & Jepsen, O. Explicit, first-principles tight-binding theory. Phys. Rev. Lett. 53, 2571 (1984).

    Article  CAS  Google Scholar 

  27. Mori, T. High temperature thermoelectric properties of B12 icosahedral cluster-containing rare earth boride crystals. J. Appl. Phys. 97, 093703 (2005).

    Article  CAS  Google Scholar 

  28. Maruyama, S., Miyazaki, Y., Hayashi, K., Kajitani, T. & Mori, T. Excellent p–n control in a high temperature thermoelectric boride. Appl. Phys. Lett. 101, 152101 (2012).

    Article  CAS  Google Scholar 

  29. Heremans, J. P. et al. Enhancement of thermoelectric efficiency in PbTe by distortion of the electronic density of states. Science 321, 554 (2008).

    Article  CAS  Google Scholar 

  30. Morelli, D. T. & Slack, G. A. in High Thermal Conductivity Materials 37 (Springer, 2006).

    Book  Google Scholar 

  31. Belsky, A., Hellenbrandt, M., Karen, V. L. & Luksch, P. New developments in the Inorganic Crystal Structure Database (ICSD): accessibility in support of materials research and design. Acta Crystallogr. B 58, 364 (2002).

    Article  CAS  Google Scholar 

  32. Gorai, P., Parilla, P., Toberer, E. S. & Stevanovic, V. Computational exploration of the binary A1B1 chemical space for thermoelectric performance. Chem. Mater. 27, 6213 (2015).

    Article  CAS  Google Scholar 

  33. Carrete, J., Mingo, N., Wang, S. & Curtarolo, S. Nanograined half-Heusler semiconductors as advanced thermoelectrics: an ab initio high-throughput statistical study. Adv. Funct. Mater. 24, 7427 (2014).

    Article  CAS  Google Scholar 

  34. Gorai, P., Toberer, E. S. & Stevanovic, V. Computational identification of promising thermoelectric materials among known quasi-2D binary compounds. J. Mater. Chem. A 4, 11110 (2016).

    Article  CAS  Google Scholar 

  35. Carrete, J. et al. Finding unprecedentedly low-thermal conductivity half-Heusler semiconductors via high-throughput materials modeling. Phys. Rev. X 4, 011019 (2014).

    Google Scholar 

  36. He, J. et al. Ultralow thermal conductivity in full Heusler semiconductors. Phys. Rev. Lett. 117, 046602 (2016).

    Article  CAS  Google Scholar 

  37. Glass, C. W., Oganov, A. R. & Hansen, N. USPEX — evolutionary crystal structure prediction. Comp. Phys. Commun. 175, 713 (2006).

    Article  CAS  Google Scholar 

  38. Wang, Y., Lv, J., Zhu, L. & Ma, Y. CALYPSO: a method for crystal structure prediction. Comp. Phys. Commun. 183, 2063 (2012).

    Article  CAS  Google Scholar 

  39. Woodley, S. M. & Catlow, R. Crystal structure prediction from first principles. Nat. Mater. 7, 937 (2008).

    Article  CAS  Google Scholar 

  40. Atahan-Evrenk, S. & Aspuru-Guzik, A. Prediction and Calculation of Crystal Structure (Springer, 2013).

    Google Scholar 

  41. Stevanovic, V. Sampling polymorphs of ionic solids using random superlattices. 116, 075503 (2016).

  42. Boltzmann, L. in Lectures on Gas Theory (Dover, 1995).

    Google Scholar 

  43. Drude, P. Zur Elektronentheorie der Metalle [German]. Annalen Physik 306, 566 (1900).

    Article  Google Scholar 

  44. Drude, P. Zur Elektronentheorie der Metalle II: Galvanomagnetische und thermomagnetische Effecte [German]. Ann. Phys. 308, 369 (1900).

    Article  Google Scholar 

  45. Kubo, R. Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn 12, 570 (1957).

    Article  Google Scholar 

  46. Landauer, R. Spatial variation of currents and fields due to localized scatterers in metallic conduction. IBM J. Res. Dev. 1, 223 (1957).

    Article  Google Scholar 

  47. Datta, S. Lessons from Nanoelectronics: A New Perspective on Transport (World Scientific, 2012).

    Book  Google Scholar 

  48. Askerov, B. M. Electron Transport Phenomena in Semiconductors (World Scientific, 1994).

    Book  Google Scholar 

  49. Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964).

    Article  Google Scholar 

  50. Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133 (1965).

    Article  Google Scholar 

  51. Blake, N. P. et al. Band structures and thermoelectric properties of the clathrates Ba8Ga16Ge30, Sr8Ga16Ge30, Ba8Ga16Si30, and Ba8In16Sn30 . J. Chem. Phys. 115, 8060 (2001).

    Article  CAS  Google Scholar 

  52. Demkov, A. A. et al. Theoretical investigation of alkali-metal doping in Si clathrates. Phys. Rev. B 50, 17001 (1994).

    Article  CAS  Google Scholar 

  53. Stiewe, C. et al. Nanostructured Co1 − xNix(Sb1 − yTey)3 skutterudites: theoretical modeling, synthesis, and thermoelectric properties. J. Appl. Phys. 97, 044317 (2005).

    Article  CAS  Google Scholar 

  54. Bertini, L. & Gatti, C. The impact of the actual geometrical structure of a thermoelectric material on its electronic transport properties: the case of doped skutterudite systems. J. Chem. Phys. 121, 8983 (2004).

    Article  CAS  Google Scholar 

  55. Bertini, L. & Cenedese, C. Electronic structure of the Co4Sn6Te6 ternary skutterudite phase. Phys. Stat. Sol. 1, 244 (2007).

    CAS  Google Scholar 

  56. Madsen, G. K. H. & Singh, D. BoltzTraP: a code for calculating band-structure dependent quantities. J. Comput. Phys. Commun. 175, 67 (2006). This paper describes the most widely used software code, BoltzTraP, for the calculation of transport coefficients within the Boltzmann transport formalism.

    Article  CAS  Google Scholar 

  57. Yang, J. et al. Evaluation of half-Heusler compounds as thermoelectric materials based on the calculated electrical transport properties. Adv. Func. Mater. 18, 2880 (2008).

    Article  CAS  Google Scholar 

  58. Hao, S. et al. Computational prediction of high thermoelectric performance in hole doped layered GeSe. Chem. Mater. 28, 3218 (2016).

    Article  CAS  Google Scholar 

  59. Madsen, G. K. H. Automated search for new thermoelectric materials: the case of LiZnSb. J. Am. Chem. Soc. 128, 12140 (2006). This paper reports one of the earliest computationally guided high-throughput searches for new thermoelectric materials.

    Article  CAS  Google Scholar 

  60. Scheidemantel, T. J., Ambrosch-Draxl, C., Thonhauser, T., Badding, J. V. & Sofo, J. O. Transport coefficients from first-principles calculations. Phys. Rev. B 68, 125210 (2003).

    Article  CAS  Google Scholar 

  61. Madsen, G. K. H., Katre, A. & Bera, C. Calculating the thermal conductivity of the Si clathrates using quasi-harmonic approximation. Physica Status Solidi A 213, 802 (2015).

    Article  CAS  Google Scholar 

  62. Opahle, I., Madsen, G. K. H. & Drautz, R. High throughput density functional investigations of the stability, electronic structure and thermoelectric properties of binary silicides. Phys. Chem. Chem. Phys. 14, 16197 (2012).

    Article  CAS  Google Scholar 

  63. Bera, C. et al. Integrated computational materials discovery of silver doped tin sulfide as a thermoelectric material. Phys. Chem. Chem. Phys. 16, 19894 (2014).

    Article  CAS  Google Scholar 

  64. Zhu, H. et al. Computational and experimental investigation of TmAgTe2 and XYZ2 compounds, a new group of thermoelectric materials identified by first-principles high-throughput screening. J. Mater. Chem. C 3, 10554 (2015).

    Article  CAS  Google Scholar 

  65. Bhattacharya, S. K. & Madsen, G. H. High-throughput exploration of alloying as design strategy for thermoelectrics. Phys. Rev. B 92, 085205 (2015).

    Article  CAS  Google Scholar 

  66. Pizzi, G., Volja, D., Kozinsky, B., Fornari, M. & Marzari, N. BoltzWann: a code for the evaluation of thermoelectric and electronic transport properties with a maximally-localized Wannier function basis. Comp. Phys. Commun. 185, 422 (2014).

    Article  CAS  Google Scholar 

  67. Lundstrom, M. Fundamentals of Carrier Transport (Cambridge Univ. Press, 2009). This is a classic book on carrier transport in materials.

    Google Scholar 

  68. Liu, T.-H., Zhou, J., Liao, B., Singh, D. J. & Chen, G. First-principles mode-by-mode analysis for electron–phonon scattering channels and mean free path spectra in GaAs. Phys. Rev. B. 95, 075206 (2017).

    Article  Google Scholar 

  69. Bernardi, M. et al. Ab initio study of hot electrons in GaAs. Proc. Natl Acad. Sci. 112, 5291 (2015).

    Article  CAS  Google Scholar 

  70. Wang, S. et al. Assessing the thermoelectric properties of sintered compounds via high-throughput ab-initio calculations. Phys. Rev. X 1, 021012 (2011).

    Google Scholar 

  71. Minnich, A. J., Dresselhaus, M. S., Ren, Z. F. & Chen, G. Bulk nanostructured thermoelectric materials.: current research and future prospects. Energy Environ. Sci. 2, 466 (2009).

    Article  CAS  Google Scholar 

  72. Hao, Q., Xu, D., Lu, N. & Zhao, H. High-throughput zT predictions of nanoporous bulk materials as next-generation in thermoelectric materials: a materials genome approach. Phys. Rev. B 93, 205206 (2016).

    Article  CAS  Google Scholar 

  73. Yan, J. et al. Materials descriptors for predicting thermoelectric performance. Energy Environ. Sci. 8, 983 (2015). This paper introduces semi-empirical models for calculating transport properties and the quality factor without making constant scattering approximations

    Article  Google Scholar 

  74. Chasmar, R. P. & Stratton, R. The thermoelectric figure of merit and its relation to thermoelectric generators. J. Electron. Control 7, 52 (1959).

    Article  CAS  Google Scholar 

  75. Miller, S. et al. Capturing anharmonicity in a lattice thermal conductivity model for high-throughput predictions. Chem. Mater. 29, 2494 (2017).

    Article  CAS  Google Scholar 

  76. Koinuma, H. & Takeuchi, I. Combinatorial solid-state chemistry of inorganic materials. Nat. Mater. 3, 429 (2004).

    Article  CAS  Google Scholar 

  77. Otani, M. et al. A high-throughput thermoelectric power-factor screening tool for rapid construction of thermoelectric property diagrams. Appl. Phys. Lett. 91, 132102 (2007).

    Article  CAS  Google Scholar 

  78. Yang, J. et al. On tuning of electrical and thermal transport in thermoelectrics: an integrated theory–experiment perspective. NPJ Compt. Mater. 2, 15015 (2016).

    Article  CAS  Google Scholar 

  79. Zhang, J. et al. Designing high-performance layered thermoelectric materials through orbital engineering. Nat. Commun. 7, 10892 (2016).

    Article  CAS  Google Scholar 

  80. Xing, G. et al. Perspective: n-type oxide thermoelectrics via visual search strategies. Appl. Phys. Lett. Mater. 4, 053201 (2016).

    Google Scholar 

  81. Xi, L., Yang, J., Wu, L., Yang, J. & Zhang, W. Band engineering and rational design of high-performance thermoelectric materials by first-principles. J. Materiomics 2, 114 (2016).

    Article  Google Scholar 

  82. Chen, W. et al. Understanding thermoelectric properties from high-throughput calculations: trends, insights, and comparisons with experiments. J. Mater. Chem. C 4, 4414 (2016).

    Article  CAS  Google Scholar 

  83. Toberer, E. S., May, A. F., Scanlon, C. J., & Snyder, G. J. Thermoelectric properties of p-type LiZnSb: assessment of ab initio calculations. J. Appl. Phys. 105, 063701 (2009).

    Article  CAS  Google Scholar 

  84. Opahle, I., Parma, A., McEniry, E. J., Drautz, R. & Madsen, G. J. H. High-throughput study of the structural stability and thermoelectric properties of transition metal silicides. New J.Phys. 15, 105010 (2013).

    Article  CAS  Google Scholar 

  85. Cahill, D. G., Watson, S. K. & Pohl, R. O. Lower limit to the thermal conductivity of disordered crystals. Phys. Rev. B 46, 6131 (1992).

    Article  CAS  Google Scholar 

  86. Togo, A., Chaput, L. & Tanaka, I. Distributions of phonon lifetimes in Brillouin zones. Phys. Rev. B 91, 094306 (2015).

    Article  CAS  Google Scholar 

  87. Ortiz, B. et al. Potential for high thermoelectric performance in n-type Zintl compounds: a case study of Ba doped KAlSb4 . J. Mater. Chem. A 5, 4036 (2017).

    Article  CAS  Google Scholar 

  88. Duong, A. T. et al. Achieving zT = 2.2 with Bi-doped n-type SnSe single crystals. Nat. Commun. 7, 13713 (2016).

    Article  CAS  Google Scholar 

  89. Ortiz, B., Gorai, P., Stevanovic, V. & Toberer, E. S. Thermoelectric performance and defect chemistry of n-type Zintl KGaSb4 . Chem. Mater. 29, 4523 (2017).

    Article  CAS  Google Scholar 

  90. Seko, A. et al. Prediction of low thermal conductivity compounds with first-principles anharmonic lattice-dynamics calculations and Bayesian optimization. Phys. Rev. Lett. 115, 205901 (2015).

    Article  CAS  Google Scholar 

  91. Morelli, D. T., Heremans, J. P. & Slack, G. A. Estimation of the isotope effect on the lattice thermal conductivity of group IV and group III–V semiconductors. Phys. Rev. B 66, 195304 (2002).

    Article  CAS  Google Scholar 

  92. Toberer, E. S., Zevalkink, A. & Snyder, G. J. Phonon engineering through crystal chemistry. J. Mater. Chem. 21, 15843 (2011).

    Article  CAS  Google Scholar 

  93. Toher, C. et al. High-throughput computational screening of thermal conductivity, Debye temperature, Gruneisen parameter using a quasi-harmonic Debye model. Phys. Rev. B 90, 174107 (2014).

    Article  CAS  Google Scholar 

  94. Plata, J. J. et al. Predicting the lattice thermal conductivity of solids by solving the Boltzmann transport equation: AFLOW-AAPL an automated, accurate and efficient framework. arXiVhttps://arxiv.org/abs/1611.05481 (2016).

  95. Li, W., Carrete, G. A., Katcho, N. A. & Mingo, N. ShenBTE: a solver of the Boltzmann transport equation for phonons. Comp. Phys. Commun. 185, 1747 (2014).

    Article  CAS  Google Scholar 

  96. Tadone, T., Gohda, Y. & Tsuneyuki, S. Anharmonic force constants extracted from first-principles molecular dynamics: applications to heat transfer simulations. J. Phys. Condens. Matter. 26, 225402 (2014).

    Article  CAS  Google Scholar 

  97. Curtarolo, S. et al. AFLOWLIB.ORG: a distributed materials properties repository from high-throughput ab initio calculations. Comp. Mater. Sci. 58, 227 (2012).

    Article  CAS  Google Scholar 

  98. Becke, A. D. Density-functional thermochemistry III: the role of exact exchange. J. Chem. Phys. 98, 5648 (1993).

    Article  CAS  Google Scholar 

  99. Perdew, J. P., Burke, K. & Ernzerhof, M. General gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).

    Article  CAS  Google Scholar 

  100. Becke, A. D. & Johnson, E. R. A simple effective potential for exchange. J. Chem. Phys. 124, 221101 (2006).

    Article  CAS  Google Scholar 

  101. Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comp. Chem. 27, 1787 (2006).

    Article  CAS  Google Scholar 

  102. Klimes, J., Bowler, D. R. & Michaelides, A. Chemical accuracy for the van der Waals density functional. J. Phys. Condens. Matter 22, 022201 (2010).

    Article  CAS  Google Scholar 

  103. Ziman, J. M. Electrons and Phonons (Oxford Univ. Press, 2001).

    Book  Google Scholar 

  104. Allen, P. B. Electron Transport in Conceptual Foundations of Materials Properties: A Standard Model for Calculation of Ground- and Excited-State Properties (eds Cohen, M. L. & Louie, S. G. ) (Elsevier, 2006).

    Google Scholar 

  105. Dirac, P. A. M. The quantum theory of the emission and absorption of radiation. Proc. R. Soc. A 114, 243 (1927).

    Article  CAS  Google Scholar 

  106. Giustino, F., Cohen, M. L. & Louie, S. G. Electron–phonon interaction using Wannier functions. Phys. Rev. B 76, 165108 (2007).

    Article  CAS  Google Scholar 

  107. Sjakste, J., Vast, N. & Tyuterev, V. Ab initio method for calculation electron–phonon scattering times in semiconductors: application to GaAs and GaP. Phys. Rev. Lett. 99, 236405 (2007).

    Article  CAS  Google Scholar 

  108. Restrepo, O. D., Varga, K. & Pantelides, S. T. First-principles calculations of electron mobilities in Si: phonon and Coulomb scattering. Appl. Phys. Lett. 94, 212103 (2009).

    Article  CAS  Google Scholar 

  109. Bonini, N., Lazzeri, M., Marzari, N. & Mauri, F. Phonon anharmonicities in graphite and grapheme. Phys. Rev. Lett. 99, 176802 (2007).

    Article  CAS  Google Scholar 

  110. Murphy-Armando, F. & Fahy, S. First principles calculation of electron–phonon and alloy scattering strained SiGe. J. Appl. Phys. 110, 123706 (2011).

    Article  CAS  Google Scholar 

  111. Lin, Z., Zhigilei, L. V. & Celli, V. Electron–phonon coupling and electron heat capacity of metals under conditions of strong electron–phonon nonequilbrium. Phys. Rev. B 77, 075133 (2008).

    Article  CAS  Google Scholar 

  112. Giustino, F., Cohen, M. L. & Louie, S. G. Small phonon contribution to the photoemission kink in the copper oxide superconductors. Nature 452, 975 (2008).

    Article  CAS  Google Scholar 

  113. Ponc, S., Margine, E., Verdi, C. & Giustino, F. EPW: electron–phonon coupling, transport, and superconducting properties using maximally localized Wannier functions. Comp. Phys. Commun. 209, 116 (2016).

    Article  CAS  Google Scholar 

  114. Mounet, N. & Marzari, N. First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives. Phys. Rev. B 71, 205214 (2005).

    Article  CAS  Google Scholar 

  115. Wang, Z. et al. Thermoelectric transport properties of silicon: toward an ab initio approach. Phys. Rev. B 83, 205208 (2011).

    Article  CAS  Google Scholar 

  116. Bjerg, L., Madsen, G. K. H. & Iversen, B. B. Ab initio calculations of intrinsic point defects in ZnSb. Chem. Mater. 24, 2111 (2012).

    Article  CAS  Google Scholar 

  117. Ueda, T., Okamura, C., Noda, Y. & Hasezaki, K. Effect of tellurium doping on the thermoelectric properties of ZnSb. Mater. Trans. 50, 2473 (2009).

    Article  CAS  Google Scholar 

  118. Parker, D. & Singh, D. J. High-temperature thermoelectric performance of heavily doped PbSe. Phys. Rev. B. 82, 035204 (2010).

    Article  CAS  Google Scholar 

  119. Niedziolka, K. et al. Theoretical and experimental search for ZnSb-based thermoelectric materials. J. Phys. Condens. Matter 26, 365401 (2014).

    Article  CAS  Google Scholar 

  120. Janotti, A. & Van de Walle, C. G. Fundamentals of zinc oxide as a semiconductor. Rep. Prog. Phys. 72, 126501 (2009).

    Article  CAS  Google Scholar 

  121. Godinho, K. G., Walsh, A. & Watson, G. W. Energetic and electronic structure analysis of intrinsic defects in SnO2 . J. Phys. Chem. C. 113, 439 (2008).

    Article  CAS  Google Scholar 

  122. Ding, H. et al. PyDII: a python framework for computing equilibrium intrinsic point defect concentrations and extrinsic solute site preferences in intermetallic compounds. Comp. Phys. Commun. 193, 118 (2015).

    Article  CAS  Google Scholar 

  123. Goyal, A., Gorai, P., Peng, H., Lany, S. & Stevanovic, V. S. A computational framework for automation of point defect calculations. Comp. Mater. Sci. 130, 1 (2017).

    Article  Google Scholar 

  124. Zhao, L. et al. Superior intrinsic thermoelectric performance with zT of 1.8 in single-crystal and melt-quenched highly dense Cu2 − xSe bulks. Sci. Rep. 5, 1 (2015).

    Google Scholar 

  125. Snyder, G. J. et al. Disordered zinc in Zn4Sb3 with phonon-glass and electron-crystal thermoelectric properties. Nat. Mater. 3, 458 (2004).

    Article  CAS  Google Scholar 

  126. Lee, M.-S. & Mahanti, S. D. Validity of rigid band approximation in the study of the thermopower of narrow band gap semiconductors. Phys. Rev. B 85, 165149 (2012).

    Article  CAS  Google Scholar 

  127. Tani, J. & Kido, H. Thermoelectric properties of Bi-doped Mg2Si semiconductors. Phys. B Condens. Matter 364, 218 (2005).

    Article  CAS  Google Scholar 

  128. Ramprasad, R., Zhu, H., Rinke, P. & Scheffler, M. New perspective on formation energies and energy levels of point defects in nonmetals. Phys. Rev. Lett. 108, 066404 (2012).

    Article  CAS  Google Scholar 

  129. Deml, A. M., Holder, A. M., O'Hayre, R. P., Musgrave, C. B. & Stevanovic, V. Intrinsic material properties dictating oxygen vacancy formation energetics in metal oxides. J. Phys. Chem. Lett. 6, 1948 (2015).

    Article  CAS  Google Scholar 

  130. Deml, A. M., Stevanovic, V., Muhich, C. L., Musgrave, C. B. & O'Hayre, R. Oxide enthalpy of formation and band gap energy as accurate descriptors of oxygen vacancy formation energetics. Energy Environ. Sci. 7, 1996 (2014).

    Article  CAS  Google Scholar 

  131. Schleife, A. et al. Branch-point energies and band discontinuities of III-nitrides and III-/II-oxides from quasiparticle band-structure calculations. Appl. Phys. Lett. 94, 012104 (2009).

    Article  CAS  Google Scholar 

  132. Roberston, J. & Clark, S. J. Limits to doping in oxides. Phys. Rev. B. 83, 075205 (2011).

    Article  CAS  Google Scholar 

  133. Pomrehn, G. S. et al. Defect-controlled electronic properties in AZn2Sb2 Zintl phases. Angew. Chem. Int. Ed. 53, 3422 (2014).

    Article  CAS  Google Scholar 

  134. Jain, A. et al. The materials project: a materials genome approach to accelerating materials innovation. APL Mater. 1, 011002 (2013).

    Article  CAS  Google Scholar 

  135. Saal, J., Kirklin, S., Aykol, M., Meredig, B. & Wolverton, C. Materials design and discovery with high-throughput density functional theory: the open quantum materials database (OQMD). JOM 65, 1501 (2013).

    Article  CAS  Google Scholar 

  136. Gorai, P. et al. TEDesignLab: a virtual laboratory for thermoelectric material design. Comp. Mater. Sci. 112, 368 (2016). This paper introduces TEDesignLab, a thermoelectrics-focused database and design platform for the computationally guided discovery of new thermoelectric materials.

    Article  Google Scholar 

  137. Gaultois, M. W. et al. Data-driven review of thermoelectric materials: performance and resource considerations. Chem. Mater. 25, 2911 (2013).

    Article  CAS  Google Scholar 

  138. Sparks, T. D., Gaultois, M. W., Oliynyk, A., Brgoch, J. & Meredig, B. Data mining our way to the next generation of thermoelectrics. Scr. Mater. 111, 10 (2016).

    Article  CAS  Google Scholar 

  139. Gaultois, M. W. et al. Web-based machine learning models for real-time screening of thermoelectric materials properties. APL Mater. 4, 053213 (2016).

    Article  CAS  Google Scholar 

  140. Oliynyk, A. O. et al. High-throughput machine-learning driven synthesis of full-Heusler compounds. Chem. Mater. 28, 7324 (2016).

    Article  CAS  Google Scholar 

  141. Mahan, G. D. & Sofo, J. O. The best thermoelectric. Proc. Natl Acad. Sci. USA 93, 7436 (1996). This seminal work formulates the transport distribution function and its desired characteristics for high-performance thermoelectrics.

    Article  CAS  Google Scholar 

  142. Toberer, E. S., Gorai, P. & Stevanović, V. in Materials Aspect of Thermoelectricity Ch. 1 (ed. Uher, C. ) 1–38 (CRC Press, 2016).

    Book  Google Scholar 

Download references

Acknowledgements

The authors acknowledge support from the US National Science Foundation DMR programme (Grant No. 1334713), the US Department of Energy (Contract No. DE-AC36-08GO28308), the National Renewable Energy Laboratory (NREL) and through NREL's LDRD programme (Grant No. 06591403).

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Prashun Gorai, Vladan Stevanović or Eric S. Toberer.

Ethics declarations

Competing interests

The authors declare no competing interests.

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gorai, P., Stevanović, V. & Toberer, E. Computationally guided discovery of thermoelectric materials. Nat Rev Mater 2, 17053 (2017). https://doi.org/10.1038/natrevmats.2017.53

Download citation

  • Published:

  • DOI: https://doi.org/10.1038/natrevmats.2017.53

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing