Review Article

Computationally guided discovery of thermoelectric materials

  • Nature Reviews Materials 2, Article number: 17053 (2017)
  • doi:10.1038/natrevmats.2017.53
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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.

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References

  1. 1.

    & Concentrated thermoelectric generators. Energy Environ. Sci. 5, 9055 (2012).

  2. 2.

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

  3. 3.

    , , & Improved thermoelectric cooling based on the Thomson effect. Phys. Rev. B 86, 045202 (2012).

  4. 4.

    & Thermoelectric efficiency and compatibility. Phys. Rev. Lett. 91, 148301 (2003).

  5. 5.

    & Complex thermoelectric materials. Nat. Mater. 7, 105 (2008).

  6. 6.

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

  7. 7.

    et al. The intrinsic thermal conductivity of SnSe. Nature 539, E1 (2016).

  8. 8.

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

  9. 9.

    et al. A new thermoelectric material: CsBi4Te6. J. Am. Chem. Soc. 126, 6414 (2004).

  10. 10.

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

  11. 11.

    , , & Semiconducting Ge clathrates: promising candidates for thermoelectric applications. Appl. Phys. Lett. 73, 178 (1998).

  12. 12.

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

  13. 13.

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

  14. 14.

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

  15. 15.

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

  16. 16.

    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).

  17. 17.

    , , & Heavily doped p-type PbSe with high thermoelectric performance: an alternative for PbTe. Adv. Mater. 23, 1366 (2011).

  18. 18.

    , , & High thermoelectric efficiency of n-type PbSe. Adv. Energy Mater. 3, 488 (2013).

  19. 19.

    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).

  20. 20.

    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).

  21. 21.

    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).

  22. 22.

    , , & Nanostructure thermoelectrics: big efficiency gains from small features. Adv. Mater. 22, 3970 (2010).

  23. 23.

    , & Rationally designing high-performance bulk thermoelectric materials. Chem. Rev. 116, 12123 (2016).

  24. 24.

    , & Ab initio thermal transport in semiconductors. Phys. Rev. B 87, 165201 (2013).

  25. 25.

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

  26. 26.

    & Explicit, first-principles tight-binding theory. Phys. Rev. Lett. 53, 2571 (1984).

  27. 27.

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

  28. 28.

    , , , & Excellent p–n control in a high temperature thermoelectric boride. Appl. Phys. Lett. 101, 152101 (2012).

  29. 29.

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

  30. 30.

    & in High Thermal Conductivity Materials 37 (Springer, 2006).

  31. 31.

    , , & New developments in the Inorganic Crystal Structure Database (ICSD): accessibility in support of materials research and design. Acta Crystallogr. B 58, 364 (2002).

  32. 32.

    , , & Computational exploration of the binary A1B1 chemical space for thermoelectric performance. Chem. Mater. 27, 6213 (2015).

  33. 33.

    , , & Nanograined half-Heusler semiconductors as advanced thermoelectrics: an ab initio high-throughput statistical study. Adv. Funct. Mater. 24, 7427 (2014).

  34. 34.

    , & Computational identification of promising thermoelectric materials among known quasi-2D binary compounds. J. Mater. Chem. A 4, 11110 (2016).

  35. 35.

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

  36. 36.

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

  37. 37.

    , & USPEX — evolutionary crystal structure prediction. Comp. Phys. Commun. 175, 713 (2006).

  38. 38.

    , , & CALYPSO: a method for crystal structure prediction. Comp. Phys. Commun. 183, 2063 (2012).

  39. 39.

    & Crystal structure prediction from first principles. Nat. Mater. 7, 937 (2008).

  40. 40.

    & Prediction and Calculation of Crystal Structure (Springer, 2013).

  41. 41.

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

  42. 42.

    in Lectures on Gas Theory (Dover, 1995).

  43. 43.

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

  44. 44.

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

  45. 45.

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

  46. 46.

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

  47. 47.

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

  48. 48.

    Electron Transport Phenomena in Semiconductors (World Scientific, 1994).

  49. 49.

    & Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964).

  50. 50.

    & Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133 (1965).

  51. 51.

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

  52. 52.

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

  53. 53.

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

  54. 54.

    & 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).

  55. 55.

    & Electronic structure of the Co4Sn6Te6 ternary skutterudite phase. Phys. Stat. Sol. 1, 244 (2007).

  56. 56.

    & 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.

  57. 57.

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

  58. 58.

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

  59. 59.

    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.

  60. 60.

    , , , & Transport coefficients from first-principles calculations. Phys. Rev. B 68, 125210 (2003).

  61. 61.

    , & Calculating the thermal conductivity of the Si clathrates using quasi-harmonic approximation. Physica Status Solidi A 213, 802 (2015).

  62. 62.

    , & High throughput density functional investigations of the stability, electronic structure and thermoelectric properties of binary silicides. Phys. Chem. Chem. Phys. 14, 16197 (2012).

  63. 63.

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

  64. 64.

    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).

  65. 65.

    & High-throughput exploration of alloying as design strategy for thermoelectrics. Phys. Rev. B 92, 085205 (2015).

  66. 66.

    , , , & 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).

  67. 67.

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

  68. 68.

    , , , & First-principles mode-by-mode analysis for electron–phonon scattering channels and mean free path spectra in GaAs. Phys. Rev. B. 95, 075206 (2017).

  69. 69.

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

  70. 70.

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

  71. 71.

    , , & Bulk nanostructured thermoelectric materials.: current research and future prospects. Energy Environ. Sci. 2, 466 (2009).

  72. 72.

    , , & High-throughput zT predictions of nanoporous bulk materials as next-generation in thermoelectric materials: a materials genome approach. Phys. Rev. B 93, 205206 (2016).

  73. 73.

    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

  74. 74.

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

  75. 75.

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

  76. 76.

    & Combinatorial solid-state chemistry of inorganic materials. Nat. Mater. 3, 429 (2004).

  77. 77.

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

  78. 78.

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

  79. 79.

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

  80. 80.

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

  81. 81.

    , , , & Band engineering and rational design of high-performance thermoelectric materials by first-principles. J. Materiomics 2, 114 (2016).

  82. 82.

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

  83. 83.

    , , , & Thermoelectric properties of p-type LiZnSb: assessment of ab initio calculations. J. Appl. Phys. 105, 063701 (2009).

  84. 84.

    , , , & High-throughput study of the structural stability and thermoelectric properties of transition metal silicides. New J.Phys. 15, 105010 (2013).

  85. 85.

    , & Lower limit to the thermal conductivity of disordered crystals. Phys. Rev. B 46, 6131 (1992).

  86. 86.

    , & Distributions of phonon lifetimes in Brillouin zones. Phys. Rev. B 91, 094306 (2015).

  87. 87.

    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).

  88. 88.

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

  89. 89.

    , , & Thermoelectric performance and defect chemistry of n-type Zintl KGaSb4. Chem. Mater. 29, 4523 (2017).

  90. 90.

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

  91. 91.

    , & Estimation of the isotope effect on the lattice thermal conductivity of group IV and group III–V semiconductors. Phys. Rev. B 66, 195304 (2002).

  92. 92.

    , & Phonon engineering through crystal chemistry. J. Mater. Chem. 21, 15843 (2011).

  93. 93.

    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).

  94. 94.

    et al. Predicting the lattice thermal conductivity of solids by solving the Boltzmann transport equation: AFLOW-AAPL an automated, accurate and efficient framework. arXiV (2016).

  95. 95.

    , , & ShenBTE: a solver of the Boltzmann transport equation for phonons. Comp. Phys. Commun. 185, 1747 (2014).

  96. 96.

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

  97. 97.

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

  98. 98.

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

  99. 99.

    , & General gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).

  100. 100.

    & A simple effective potential for exchange. J. Chem. Phys. 124, 221101 (2006).

  101. 101.

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

  102. 102.

    , & Chemical accuracy for the van der Waals density functional. J. Phys. Condens. Matter 22, 022201 (2010).

  103. 103.

    Electrons and Phonons (Oxford Univ. Press, 2001).

  104. 104.

    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).

  105. 105.

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

  106. 106.

    , & Electron–phonon interaction using Wannier functions. Phys. Rev. B 76, 165108 (2007).

  107. 107.

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

  108. 108.

    , & First-principles calculations of electron mobilities in Si: phonon and Coulomb scattering. Appl. Phys. Lett. 94, 212103 (2009).

  109. 109.

    , , & Phonon anharmonicities in graphite and grapheme. Phys. Rev. Lett. 99, 176802 (2007).

  110. 110.

    & First principles calculation of electron–phonon and alloy scattering strained SiGe. J. Appl. Phys. 110, 123706 (2011).

  111. 111.

    , & Electron–phonon coupling and electron heat capacity of metals under conditions of strong electron–phonon nonequilbrium. Phys. Rev. B 77, 075133 (2008).

  112. 112.

    , & Small phonon contribution to the photoemission kink in the copper oxide superconductors. Nature 452, 975 (2008).

  113. 113.

    , , & EPW: electron–phonon coupling, transport, and superconducting properties using maximally localized Wannier functions. Comp. Phys. Commun. 209, 116 (2016).

  114. 114.

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

  115. 115.

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

  116. 116.

    , & Ab initio calculations of intrinsic point defects in ZnSb. Chem. Mater. 24, 2111 (2012).

  117. 117.

    , , & Effect of tellurium doping on the thermoelectric properties of ZnSb. Mater. Trans. 50, 2473 (2009).

  118. 118.

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

  119. 119.

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

  120. 120.

    & Fundamentals of zinc oxide as a semiconductor. Rep. Prog. Phys. 72, 126501 (2009).

  121. 121.

    , & Energetic and electronic structure analysis of intrinsic defects in SnO2. J. Phys. Chem. C. 113, 439 (2008).

  122. 122.

    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).

  123. 123.

    , , , & A computational framework for automation of point defect calculations. Comp. Mater. Sci. 130, 1 (2017).

  124. 124.

    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).

  125. 125.

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

  126. 126.

    & Validity of rigid band approximation in the study of the thermopower of narrow band gap semiconductors. Phys. Rev. B 85, 165149 (2012).

  127. 127.

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

  128. 128.

    , , & New perspective on formation energies and energy levels of point defects in nonmetals. Phys. Rev. Lett. 108, 066404 (2012).

  129. 129.

    , , , & Intrinsic material properties dictating oxygen vacancy formation energetics in metal oxides. J. Phys. Chem. Lett. 6, 1948 (2015).

  130. 130.

    , , , & Oxide enthalpy of formation and band gap energy as accurate descriptors of oxygen vacancy formation energetics. Energy Environ. Sci. 7, 1996 (2014).

  131. 131.

    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).

  132. 132.

    & Limits to doping in oxides. Phys. Rev. B. 83, 075205 (2011).

  133. 133.

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

  134. 134.

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

  135. 135.

    , , , & Materials design and discovery with high-throughput density functional theory: the open quantum materials database (OQMD). JOM 65, 1501 (2013).

  136. 136.

    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.

  137. 137.

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

  138. 138.

    , , , & Data mining our way to the next generation of thermoelectrics. Scr. Mater. 111, 10 (2016).

  139. 139.

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

  140. 140.

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

  141. 141.

    & 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.

  142. 142.

    , & in Materials Aspect of Thermoelectricity Ch. 1 (ed. Uher, C.) 1–38 (CRC Press, 2016).

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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

Affiliations

  1. Colorado School of Mines, Golden, Colorado 80401, USA.

    • Prashun Gorai
    • , Vladan Stevanović
    •  & Eric S. Toberer
  2. National Renewable Energy Laboratory, Golden, Colorado 80401, USA.

    • Prashun Gorai
    • , Vladan Stevanović
    •  & Eric S. Toberer

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The authors declare no competing interests.

Corresponding authors

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