Skip to main content

Explaining the electronic band structure of half-Heusler thermoelectric semiconductors for engineering high valley degeneracy

Abstract

Half-Heusler compounds are attractive candidates for thermoelectric applications because they are inexpensive and have high thermal and mechanical stability. Band engineering to promote electronic structures with high valley degeneracy, \({N}_{V}\), is known to be an effective method for enhancing thermoelectric performance. In half-Heusler thermoelectrics, the valence band maximum can be found at the \(\Gamma\)-, L-, or W-point in the Brillouin zone, and there are two competing low-lying conduction bands at the X-point. Consequently, there are routes to increase the valley degeneracy of both the conduction band (CB) and valence band (VB) edges that involve converging the competing band extrema, and it has been found that the strategies for achieving VB and CB convergence are quite similar. Here, we review the chemical origins of these band extrema (using ZrNiSn and NbFeSb as particular examples) and the recommended strategies for achieving high band convergence, and hence, high \({N}_{V}\).

Graphical abstract

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

Figure 1
Figure 2
Figure 3

Adapted with permission from Reference 21. Copyright © 2020 Maxwell T. Dylla et al. Exclusive Licensee Science and Technology Review Publishing House. Distributed under a Creative Commons Attribution License (CC BY 4.0).

Figure 4
Figure 5
Figure 6

Reproduced with permission from Reference 49.

Figure 7
Figure 8
Figure 9
Figure 10

References

  1. L.E. Bell, Science 321, 1457 (2008)

    CAS  Article  Google Scholar 

  2. G.J. Snyder, E.S. Toberer, Nat. Mater. 7, 105 (2008)

    CAS  Article  Google Scholar 

  3. Y. Pei, X. Shi, A. Lalonde, H. Wang, L. Chen, G.J. Snyder, Nature 473, 66 (2011)

    CAS  Article  Google Scholar 

  4. A. Zevalkink, D.M. Smiadak, J.L. Blackburn, A.J. Ferguson, M.L. Chabinyc, O. Delaire, J. Wang, K. Kovnir, J. Martin, L.T. Schelhas, T.D. Sparks, S.D. Kang, M.T. Dylla, G.J. Snyder, B.R. Ortiz, E.S. Toberer, Appl. Phys. Rev. 5, 21303 (2018)

    Article  CAS  Google Scholar 

  5. H.J. Goldsmid, Introduction to Thermoelectricity (Springer, Berlin, 2009)

    Google Scholar 

  6. X. Zhang, Z. Bu, X. Shi, Z. Chen, S. Lin, B. Shan, M. Wood, A.H. Snyder, L. Chen, G.J. Snyder, Y. Pei, Sci. Adv. 6, 6 (2020)

    CAS  Google Scholar 

  7. S. Dongmin Kang, G. Jeffrey Snyder, Nat. Mater. 16, 252 (2017)

    CAS  Article  Google Scholar 

  8. J. Park, M. Dylla, Y. Xia, M. Wood, G.J. Snyder, A. Jain, Nat. Commun. 12, 3425 (2021)

    CAS  Article  Google Scholar 

  9. K. Imasato, S.D. Kang, S. Ohno, G.J. Snyder, Mater. Horiz. 5, 59 (2018)

    CAS  Article  Google Scholar 

  10. S. Guo, S. Anand, M.K. Brod, Y. Zhang, G.J. Snyder, J. Mater. Chem. A 10(6), 3051 (2022)

    CAS  Article  Google Scholar 

  11. W.G. Zeier, J. Schmitt, G. Hautier, U. Aydemir, Z.M. Gibbs, C. Felser, G.J. Snyder, Nat. Rev. Mater. 1, 16032 (2016)

    CAS  Article  Google Scholar 

  12. T. Graf, C. Felser, S.S.P. Parkin, Prog. Solid State Chem. 39, 1 (2011)

    CAS  Article  Google Scholar 

  13. M.M. Al Malki, Q. Qiu, T. Zhu, G.J. Snyder, D.C. Dunand, Mater. Today 9, 100134 (2019)

    Article  Google Scholar 

  14. L. Huang, Q. Zhang, B. Yuan, X. Lai, X. Yan, Z. Ren, Mater. Res. Bull. 76, 107 (2016)

    CAS  Article  Google Scholar 

  15. S. Anand, K. Xia, T. Zhu, C. Wolverton, G.J. Snyder, Adv. Energy Mater. 8, 1801409 (2018)

    Article  CAS  Google Scholar 

  16. S. Anand, M. Wood, Y. Xia, C. Wolverton, G.J. Snyder, Joule 3, 1226 (2019)

    CAS  Article  Google Scholar 

  17. S. Anand, K. Xia, V.I. Hegde, U. Aydemir, V. Kocevski, T. Zhu, C. Wolverton, G.J. Snyder, Energy Environ. Sci. 11, 1480 (2018)

    CAS  Article  Google Scholar 

  18. J.R. Sootsman, D.Y. Chung, M.G. Kanatzidis, Angew. Chem. Int. Ed. 48, 8616 (2009)

    CAS  Article  Google Scholar 

  19. S.J. Poon, D. Wu, S. Zhu, W. Xie, T.M. Tritt, P. Thomas, R. Venkatasubramanian, J. Mater. Res. 26, 2795 (2011)

    CAS  Article  Google Scholar 

  20. H. Zhu, J. Mao, Y. Li, J. Sun, Y. Wang, Q. Zhu, G. Li, Q. Song, J. Zhou, Y. Fu, R. He, T. Tong, Z. Liu, W. Ren, L. You, Z. Wang, J. Luo, A. Sotnikov, J. Bao, K. Nielsch, G. Chen, D.J. Singh, Z. Ren, Nat. Commun. 10, 270 (2019)

    Article  CAS  Google Scholar 

  21. M.T. Dylla, A. Dunn, S. Anand, A. Jain, G.J. Snyder, Research 2020, 6375171 (2020)

    CAS  Article  Google Scholar 

  22. J.W.G. Bos, R.A. Downie, J. Phys. Condens. Matter 26, 433201 (2014)

    Article  CAS  Google Scholar 

  23. A. Page, P.F.P. Poudeu, C. Uher, J. Materiomics 2, 104 (2016)

    Article  Google Scholar 

  24. P. Larson, S.D. Mahanti, M.G. Kanatzidis, Phys. Rev. B 62, 12754 (2000)

    CAS  Article  Google Scholar 

  25. S.R. Culp, S.J. Poon, N. Hickman, T.M. Tritt, J. Blumm, Appl. Phys. Lett. 88, 042106 (2006)

    Article  CAS  Google Scholar 

  26. S.R. Culp, J.W. Simonson, S.J. Poon, V. Ponnambalam, J. Edwards, T.M. Tritt, Appl. Phys. Lett. 93, 22105 (2008)

    Article  CAS  Google Scholar 

  27. S. Chen, K.C. Lukas, W. Liu, C.P. Opeil, G. Chen, Z. Ren, Adv. Energy Mater. 3, 1210 (2013)

    CAS  Article  Google Scholar 

  28. B. Yuan, B. Wang, L. Huang, X. Lei, L. Zhao, C. Wang, Q. Zhang, J. Electron. Mater. 46, 3076 (2017)

    CAS  Article  Google Scholar 

  29. K. Kawano, K. Kurosaki, T. Sekimoto, H. Muta, S. Yamanaka, Appl. Phys. Lett. 91, 62115 (2007)

    Article  CAS  Google Scholar 

  30. N.J. Takas, P. Sahoo, D. Misra, H. Zhao, N.L. Henderson, K. Stokes, P.F.P. Poudeu, J. Electron. Mater. 40, 662 (2011)

    CAS  Article  Google Scholar 

  31. Y. Liu, P.F.P. Poudeu, J. Mater. Chem. A 3, 12507 (2015)

    CAS  Article  Google Scholar 

  32. T.J. Slade, S. Anand, M. Wood, J.P. Male, K. Imasato, D. Cheikh, M.M. Al Malki, M.T. Agne, K.J. Griffith, S.K. Bux, C. Wolverton, M.G. Kanatzidis, G.J. Snyder, Joule 5, 1168 (2021)

    CAS  Article  Google Scholar 

  33. R. Gurunathan, R. Hanus, M. Dylla, A. Katre, G.J. Snyder, Phys. Rev. Appl. 13, 034011 (2020)

    CAS  Article  Google Scholar 

  34. R. Gurunathan, R. Hanus, G.J. Snyder, Mater. Horiz. 7, 1452 (2020)

    CAS  Article  Google Scholar 

  35. E.S. Toberer, A.F. May, G.J. Snyder, Chem. Mater. 22, 624 (2010)

    CAS  Article  Google Scholar 

  36. S.M. Kauzlarich, Chemistry, Structure, and Bonding of Zintl Phases and Ions (VCH Publishers, New York, 1996)

    Google Scholar 

  37. A. Zevalkink, W.G. Zeier, E. Cheng, J. Snyder, J.-P. Fleurial, S. Bux, Chem. Mater. 26, 5710 (2014)

    CAS  Article  Google Scholar 

  38. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)

    CAS  Article  Google Scholar 

  39. T. Jia, J. Carrete, Z. Feng, S. Guo, Y. Zhang, G.K.H. Madsen, Phys. Rev. B 102, 125204 (2020)

    CAS  Article  Google Scholar 

  40. B. Ryu, S. Park, E.-A. Choi, J. de Boor, P. Ziolkowski, J. Chung, S.D. Park, J. Korean Phys. Soc. 75, 144 (2019)

    CAS  Article  Google Scholar 

  41. C.W. Wang, Y.Y.Y. Xia, Z. Tian, J. Jiang, B.H. Li, S.T. Cui, H.F. Yang, A.J. Liang, X.Y. Zhan, G.H. Hong, S. Liu, C. Chen, M.X. Wang, L.X. Yang, Z. Liu, Q.X. Mi, G. Li, J.M. Xue, Z.K. Liu, Y.L. Chen, Phys. Rev. B 96, 165118 (2017)

    Article  Google Scholar 

  42. K. Berland, C. Persson, J. Appl. Phys. 123, 205703 (2018)

    Article  CAS  Google Scholar 

  43. C. Fu, T. Zhu, Y. Pei, H. Xie, H. Wang, G.J. Snyder, Y. Liu, Y. Liu, X. Zhao, Adv. Energy Mater. 4, 1400600 (2014)

    Article  CAS  Google Scholar 

  44. C. Fu, T. Zhu, Y. Liu, H. Xie, X. Zhao, Energy Environ. Sci. 8, 216 (2015)

    CAS  Article  Google Scholar 

  45. C. Fu, S. Bai, Y. Liu, Y. Tang, L. Chen, X. Zhao, T. Zhu, Nat. Commun. 6, 8144 (2015)

    Article  Google Scholar 

  46. K. Kutorasinski, J. Tobola, S. Kaprzyk, Phys. Status Solidi A 211, 1229 (2014)

    CAS  Article  Google Scholar 

  47. H. Zhu, R. He, J. Mao, Q. Zhu, C. Li, J. Sun, W. Ren, Y. Wang, Z. Liu, Z. Tang, A. Sotnikov, Z. Wang, D. Broido, D.J. Singh, G. Chen, K. Nielsch, Z. Ren, Nat. Commun. 9, 2497 (2018)

    Article  CAS  Google Scholar 

  48. W. Xie, A. Weidenkaff, X. Tang, Q. Zhang, J. Poon, T.M. Tritt, Nanomaterials 2, 379 (2012)

    CAS  Article  Google Scholar 

  49. M.K. Brod, S. Anand, G.J. Snyder, Adv. Electron. Mater. 8, 2101367 (2022)

    CAS  Article  Google Scholar 

  50. J. Zhou, H. Zhu, T.-H. Liu, Q. Song, R. He, J. Mao, Z. Liu, W. Ren, B. Liao, D.J. Singh, Z. Ren, G. Chen, Nat. Commun. 9, 1721 (2018)

    Article  CAS  Google Scholar 

  51. F. Serrano-Sánchez, T. Luo, J. Yu, W. Xie, C. Le, G. Auffermann, A. Weidenkaff, T. Zhu, X. Zhao, J.A. Alonso, B. Gault, C. Felser, C. Fu, J. Mater. Chem. A 8, 14822 (2020)

    Article  Google Scholar 

  52. R. Yan, R. Xie, W. Xie, C. Shen, W. Li, B. Balke, S. Yoon, H. Zhang, A. Weidenkaff, ACS Appl. Mater. Interfaces 13, 34533 (2021)

    CAS  Article  Google Scholar 

  53. Q. Wang, J. Huang, C. Wang, P. Luo, Z. Li, R. Liu, Q. Ma, J. Luo, ACS Appl. Energy Mater. 4, 12458 (2021)

    CAS  Article  Google Scholar 

  54. K.K. Johari, R. Bhardwaj, N.S. Chauhan, S. Bathula, S. Auluck, S.R. Dhakate, B. Gahtori, ACS Appl. Energy Mater. 4, 3393 (2021)

    CAS  Article  Google Scholar 

  55. N.S. Chauhan, S. Bathula, A. Vishwakarma, R. Bhardwaj, K.K. Johari, B. Gahtori, M. Saravanan, A. Dhar, J. Phys. Chem. Solids 123, 105 (2018)

    CAS  Article  Google Scholar 

  56. J.J. Pulikkotil, D.J. Singh, S. Auluck, M. Saravanan, D.K. Misra, A. Dhar, R.C. Budhani, Phys. Rev. B 86, 155204 (2012)

    Article  CAS  Google Scholar 

  57. V.K. Zaitsev, M.I. Fedorov, E.A. Gurieva, I.S. Eremin, P.P. Konstantinov, A.Yu. Samunin, M.V. Vedernikov, Phys. Rev. B 74, 045207 (2006)

    Article  CAS  Google Scholar 

  58. W. Liu, X. Tan, K. Yin, H. Liu, X. Tang, J. Shi, Q. Zhang, C. Uher, Phys. Rev. Lett. 108, 166601 (2012)

    Article  CAS  Google Scholar 

  59. G. Shi, E. Kioupakis, J. Appl. Phys. 123, 085114 (2018)

    Article  CAS  Google Scholar 

  60. C.-E. Kim, A. Soon, C. Stampfl, Phys. Chem. Chem. Phys. 18, 939 (2016)

    CAS  Article  Google Scholar 

  61. W. Liu, H. Chi, H. Sun, Q. Zhang, K. Yin, X. Tang, Q. Zhang, C. Uher, Phys. Chem. Chem. Phys. 16, 6893 (2014)

    CAS  Article  Google Scholar 

  62. C. Yu, T.-J. Zhu, R.-Z. Shi, Y. Zhang, X.-B. Zhao, J. He, Acta Mater. 57, 2757 (2009)

    CAS  Article  Google Scholar 

  63. S. Populoh, M.H. Aguirre, O.C. Brunko, K. Galazka, Y. Lu, A. Weidenkaff, Scr. Mater. 66, 1073 (2012)

    CAS  Article  Google Scholar 

  64. A.N. Gandi, U. Schwingenschlögl, Phys. Chem. Chem. Phys. 18, 14017 (2016)

    CAS  Article  Google Scholar 

  65. Y. Stadnyk, A. Horyn, V. Sechovsky, L. Romaka, Y. Mudryk, J. Tobola, T. Stopa, S. Kaprzyk, A. Kolomiets, J. Alloys Compd. 402, 30 (2005)

    CAS  Article  Google Scholar 

  66. D.P. Young, P. Khalifah, R.J. Cava, A.P. Ramirez, J. Appl. Phys. 87, 317 (2000)

    CAS  Article  Google Scholar 

  67. L. Jodin, J. Tobola, P. Pecheur, H. Scherrer, S. Kaprzyk, Phys. Rev. B 70, 184207 (2004)

    Article  CAS  Google Scholar 

  68. R.A. de Groot, F.M. Mueller, P.G. van Engen, K.H.J. Buschow, Phys. Rev. Lett. 50, 2024 (1983)

    Article  Google Scholar 

  69. H.C. Kandpal, C. Felser, R. Seshadri, J. Phys. D 39, 776 (2006)

    CAS  Article  Google Scholar 

  70. S. Ogut, K.M. Rabe, Phys. Rev. B 51, 10443 (1995)

    CAS  Article  Google Scholar 

  71. M.S. Dresselhaus, G. Dresselhaus, A. Jorio, Group Theory: Application to the Physics of Condensed Matter (Springer, Berlin, 2007)

    Google Scholar 

  72. R. Nelson, C. Ertural, J. George, R. Dronskowski, J. Comput. Chem. 41, 1931 (2020)

    CAS  Article  Google Scholar 

  73. S. Maintz, V.L. Deringer, A.L. Tchougréeff, R. Dronskowski, J. Comput. Chem. 34, 2557 (2013)

    CAS  Article  Google Scholar 

  74. R. Dronskowski, P.E. Blöchl, J. Phys. Chem. 97, 8617 (1993)

    CAS  Article  Google Scholar 

  75. W.A. Harrison, Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond (Dover Publications, New York, 1989)

    Google Scholar 

  76. W.A. Harrison, Pure Appl. Chem. 61, 2161 (1989)

    CAS  Article  Google Scholar 

  77. J.C. Slater, G.F. Koster, Phys. Rev. 94, 1498 (1954)

    CAS  Article  Google Scholar 

  78. M. Wood, U. Aydemir, S. Ohno, G.J. Snyder, J. Mater. Chem. A 6, 9437 (2018)

    CAS  Article  Google Scholar 

  79. H.-S. Kim, N.A. Heinz, Z.M. Gibbs, Y. Tang, S.D. Kang, G.J. Snyder, Mater. Today 20, 452 (2017)

    CAS  Article  Google Scholar 

  80. A.L. Allred, J. Inorg. Nucl. Chem. 17, 215 (1961)

    CAS  Article  Google Scholar 

  81. G.S. Rohrer, Structure and Bonding in Crystalline Materials (Cambridge University Press, New York, 2001)

    Book  Google Scholar 

  82. A. Zunger, S.-H. Wei, L.G. Ferreira, J.E. Bernard, Phys. Rev. Lett. 65, 353 (1990)

    CAS  Article  Google Scholar 

  83. R. Yan, W. Xie, B. Balke, G. Chen, A. Weidenkaff, Sci. Technol. Adv. Mater. 21, 122 (2020)

    Article  CAS  Google Scholar 

  84. D.A. Ferluccio, R.I. Smith, J. Buckman, J.W.G. Bos, Phys. Chem. Chem. Phys. 20, 3979 (2018)

    CAS  Article  Google Scholar 

Download references

Acknowledgments

M.K.B. and G.J.S. acknowledge support from “Accelerated Discovery of Compositionally Complex Alloys for Direct Thermal Energy Conversion” DOE Award No. DE-AC02-76SF00515. Y.Z. acknowledges support from National Natural Science Foundation of China Grant No. 11774347.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. Jeffrey Snyder.

Ethics declarations

Conflict of interest

There are no conflict to declare.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Brod, M.K., Guo, S., Zhang, Y. et al. Explaining the electronic band structure of half-Heusler thermoelectric semiconductors for engineering high valley degeneracy. MRS Bulletin 47, 573–583 (2022). https://doi.org/10.1557/s43577-022-00360-z

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/s43577-022-00360-z