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.

  • Article
  • Published:

Convergence of multi-valley bands as the electronic origin of high thermoelectric performance in CoSb3 skutterudites

Nature Materials volume 14, pages 1223–1228 (2015)Cite this article

Subjects

Abstract

Filled skutterudites RxCo4Sb12 are excellent n-type thermoelectric materials owing to their high electronic mobility and high effective mass, combined with low thermal conductivity associated with the addition of filler atoms into the void site. The favourable electronic band structure in n-type CoSb3 is typically attributed to threefold degeneracy at the conduction band minimum accompanied by linear band behaviour at higher carrier concentrations, which is thought to be related to the increase in effective mass as the doping level increases. Using combined experimental and computational studies, we show instead that a secondary conduction band with 12 conducting carrier pockets (which converges with the primary band at high temperatures) is responsible for the extraordinary thermoelectric performance of n-type CoSb3 skutterudites. A theoretical explanation is also provided as to why the linear (or Kane-type) band feature is not beneficial for thermoelectrics.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Figure 1: Experimental and theoretical evidence showing multiple conduction bands in n-type CoSb3.
Figure 2: Band non-parabolicity and its effect on the Seebeck coefficient and energy-dependent Seebeck effective mass, mS∗(E).
Figure 3: High-temperature band convergence in CoSb3 as shown from optical absorption and thermoelectric figure of merit.

Similar content being viewed by others

References

  1. Caillat, T., Borshchevsky, A. & Fleurial, J. P. Properties of single crystalline semiconducting CoSb3 . J. Appl. Phys. 80, 4442–4449 (1996).

    Article  CAS  Google Scholar 

  2. Tang, Y., Chen, S. W. & Snyder, G. J. Temperature dependent solubility of Yb in Yb–CoSb3 skutterudite and its effect on preparation, optimization and lifetime of thermoelectrics. J. Materiom. 1, 75–84 (2015).

    Article  Google Scholar 

  3. Pei, Y. Z. et al. Improving thermoelectric performance of caged compounds through light-element filling. Appl. Phys. Lett. 95, 042101 (2009).

    Article  Google Scholar 

  4. Chen, L. D. et al. Anomalous barium filling fraction and n-type thermoelectric performance of BayCo4Sb12 . J. Appl. Phys. 90, 1864–1868 (2001).

    Article  CAS  Google Scholar 

  5. Tang, Y. et al. Phase diagram of In–Co–Sb system and thermoelectric properties of In-containing skutterudites. Energy Environ. Sci. 7, 812–819 (2014).

    Article  CAS  Google Scholar 

  6. Tang, Y., Hanus, R., Chen, S. W. & Snyder, G. J. Solubility design leading to high figure of merit in low-cost Ce–CoSb3 skutterudites. Nature Commun. 6, 7584 (2015).

    Article  CAS  Google Scholar 

  7. Li, H., Tang, X., Zhang, Q. & Uher, C. High performance InxCeyCo4Sb12 thermoelectric materials with in situ forming nanostructured InSb phase. Appl. Phys. Lett. 94, 102114 (2009).

    Article  Google Scholar 

  8. Rogl, G. et al. n-type skutterudites (R, Ba, Yb)yCo4Sb12 (R = Sr, La, Mm, DD, SrMm, SrDD) approaching ZT ≍ 2.0. Acta Mater. 63, 30–43 (2014).

    Article  CAS  Google Scholar 

  9. Shi, X. et al. Multiple-filled skutterudites: High thermoelectric figure of merit through separately optimizing electrical and thermal transports. J. Am. Chem. Soc. 133, 7837–7846 (2011).

    Article  CAS  Google Scholar 

  10. Meisner, G., Morelli, D., Hu, S., Yang, J. & Uher, C. Structure and lattice thermal conductivity of fractionally filled skutterudites: Solid solutions of fully filled and unfilled end members. Phys. Rev. Lett. 80, 3551–3554 (1998).

    Article  CAS  Google Scholar 

  11. Koza, M. M. et al. Breakdown of phonon glass paradigm in La- and Ce-filled Fe4Sb12 skutterudites. Nature Mater. 7, 805–810 (2008).

    Article  CAS  Google Scholar 

  12. Nolas, G. S., Fowler, G. & Yang, J. Assessing the role of filler atoms on the thermal conductivity of filled skutterudites. J. Appl. Phys. 100, 043705 (2006).

    Article  Google Scholar 

  13. Pei, Y. et al. Convergence of electronic bands for high performance bulk thermoelectrics. Nature 473, 66–69 (2011).

    Article  CAS  Google Scholar 

  14. 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, 3346–3355 (2013).

    Article  CAS  Google Scholar 

  15. Wang, H., Gibbs, Z. M., Takagiwa, Y. & Snyder, G. J. Tuning bands of PbSe for better thermoelectric efficiency. Energy Environ. Sci. 7, 804–811 (2014).

    Article  CAS  Google Scholar 

  16. Liu, 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  Google Scholar 

  17. Parker, D., Chen, X. & Singh, D. J. High three-dimensional thermoelectric performance from low-dimensional bands. Phys. Rev. Lett. 110, 146601 (2013).

    Article  Google Scholar 

  18. Pei, Y., Wang, H. & Snyder, G. J. Band engineering of thermoelectric materials. Adv. Mater. 24, 6125–6135 (2012).

    Article  CAS  Google Scholar 

  19. Singh, D. J. & Pickett, W. E. Skutterudite antimonides: Quasilinear bands and unusual transport. Phys. Rev. B 50, 11235–11238 (1994).

    Article  CAS  Google Scholar 

  20. Sofo, J. O. & Mahan, G. D. Electronic structure of CoSb3: A narrow-band-gap semiconductor. Phys. Rev. B 58, 15620–15623 (1998).

    Article  CAS  Google Scholar 

  21. Pei, Y., LaLonde, A. D., Wang, H. & Snyder, G. J. Low effective mass leading to high thermoelectric performance. Energy Environ. Sci. 5, 7963–7969 (2012).

    Article  CAS  Google Scholar 

  22. Kuznetsov, V. L., Kuznetsova, L. A. & Rowe, D. M. Effect of partial void filling on the transport properties of NdxCo4Sb12 skutterudites. J. Phys. Condens. Matter 15, 5035–5048 (2003).

    Article  CAS  Google Scholar 

  23. Salvador, J. R., Yang, J., Wang, H. & Shi, X. Double-filled skutterudites of the type YbxCayCo4Sb12: Synthesis and properties. J. Appl. Phys. 107, 043705 (2010).

    Article  Google Scholar 

  24. Anno, H., Matsubara, K., Notohara, Y., Sakakibara, T. & Tashiro, H. Effects of doping on the transport properties of CoSb3 . J. Appl. Phys. 86, 3780–3786 (1999).

    Article  CAS  Google Scholar 

  25. Dyck, J. S. et al. Thermoelectric properties of the n-type filled skutterudite Ba0.3Co4Sb12 doped with Ni. J. Appl. Phys. 91, 3698–3705 (2002).

    Article  CAS  Google Scholar 

  26. Zhou, A., Liu, L.-S., Zhai, P.-C., Zhao, W.-Y. & Zhang, Q.-J. Electronic structures and transport properties of single-filled CoSb3 . J. Electron. Mater. 39, 1832–1836 (2010).

    Article  CAS  Google Scholar 

  27. Yang, J., Xi, L., Zhang, W., Chen, L. D. & Yang, J. Electrical transport properties of filled CoSb3 skutterudites: A theoretical study. J. Electron. Mater. 38, 1397–1401 (2009).

    Article  CAS  Google Scholar 

  28. Takagiwa, Y., Pei, Y. Z., Pomrehn, G. & Snyder, G. J. Validity of rigid band approximation of PbTe thermoelectric materials. Appl. Phys. Lett. Mater. 1, 011101 (2013).

    Google Scholar 

  29. Liu, W-S., Zhao, L-D., Zhang, B-P., Zhang, H.-L. & Li, J.-F. Enhanced thermoelectric property originating from additional carrier pocket in skutterudite compounds. Appl. Phys. Lett. 93, 042109 (2008).

    Article  Google Scholar 

  30. Nagamoto, Y., Tanaka, K. & Koyanagi, T. Thermoelectrics, 1998. Proceedings ICT 98. XVII International Conference on 302–305 (IEEE, 1998).

    Google Scholar 

  31. Kajikawa, Y. Refined analysis of the transport properties of Co1−xNixSb3 according to a model including a deep donor level and the second lowest valleys of the conduction band. J. Alloys Compd. 621, 170–178 (2015).

    Article  CAS  Google Scholar 

  32. Yang, J. et al. Solubility study of Yb in n-type skutterudites YbxCo4Sb12 and their enhanced thermoelectric properties. Phys. Rev. B 80, 115329 (2009).

    Article  Google Scholar 

  33. Chaput, L., Pécheur, P., Tobola, J. & Scherrer, H. Transport in doped skutterudites: Ab initio electronic structure calculations. Phys. Rev. B 72, 085126 (2005).

    Article  Google Scholar 

  34. Gnutzman, U. & Clauseck, K. Theory of direct optical-transitions in an optical indirect semiconductor with a superlattice structure. Appl. Phys. 3, 9–14 (1974).

    Article  Google Scholar 

  35. Ackermann, J. & Wold, A. The preparation and characterization of the cobalt skutterudites CoP3, CoAs3 and CoSb3 . J. Phys. Chem. Solids 38, 1013–1016 (1977).

    Article  CAS  Google Scholar 

  36. Kliche, G. & Lutz, H. D. Temperature dependence of the FIR reflection spectra of the skutterudites CoAs3 and CoSb3 . Infrared Phys. 24, 171–177 (1984).

    Article  CAS  Google Scholar 

  37. Kane, E. O. Band structure of indium antimonide. J. Phys. Chem. Solids 1, 249–261 (1957).

    Article  Google Scholar 

  38. Smith, S. D., Moss, T. S. & Taylor, K. W. The energy-dependence of electron mass in indium antimonide determined from measurements of the infrared Faraday effect. J. Phys. Chem. Solids 11, 131–139 (1959).

    Article  CAS  Google Scholar 

  39. Cardona, M. Electron effective masses of InAs and GaAs as a function of temperature and doping. Phys. Rev. 121, 752–758 (1961).

    Article  Google Scholar 

  40. Dixon, J. R. & Riedl, H. R. Electric-susceptibility hole mass of lead telluride. Phys. Rev. 138, A873–A881 (1965).

    Article  Google Scholar 

  41. Dionne, G. & Woolley, J. C. Optical properties of some Pb1−xSnxTe alloys determined from infrared plasma reflectivity measurements. Phys. Rev. B 6, 3898–3913 (1972).

    Article  CAS  Google Scholar 

  42. Arushanov, E., Respaud, M., Rakoto, H., Broto, J. M. & Caillat, T. Shubnikov–de Haas oscillations in CoSb3 single crystals. Phys. Rev. B 61, 4672–4676 (2000).

    Article  CAS  Google Scholar 

  43. Harman, T. C. Galvano-thermomagnetic effects in semiconductors and semimetals—IV. mercury selenide. J. Phys. Chem. Solids 25, 931–940 (1964).

    Article  CAS  Google Scholar 

  44. Young, D. L., Coutts, T. J., Kaydanov, V. I., Gilmore, A. S. & Mulligan, W. P. Direct measurement of density-of-states effective mass and scattering parameter in transparent conducting oxides using second-order transport phenomena. J. Vac. Sci. Technol. A 18, 2978–2985 (2000).

    Article  CAS  Google Scholar 

  45. Pshenaı̆-Severin, D. A. & Fedorov, M. I. Effect of the band structure on the thermoelectric properties of a semiconductor. Phys. Solid State 49, 1633–1637 (2007).

    Article  Google Scholar 

  46. Yu, P. Y. & Cardona, M. Fundamentals of Semiconductors 259–264 (Springer, 1996).

    Book  Google Scholar 

  47. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  CAS  Google Scholar 

  48. Giannozzi, P. et al. QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).

    Article  Google Scholar 

  49. Agapito, L. A., Ferretti, A., Calzolari, A., Curtarolo, S. & Buongiorno, N. M. Effective and accurate representation of extended Bloch states on finite Hilbert spaces. Phys. Rev. B 88, 165127 (2013).

    Article  Google Scholar 

  50. Kokalj, A. Computer graphics and graphical user interfaces as tools in simulations of matter at the atomic scale. Comput. Mater. Sci. 28, 155–168 (2003).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We acknowledge the funding support of the Materials Project by Department of Energy Basic Energy Sciences Program under Grant No. EDCBEE, DOE Contract DE-AC02-05CH11231 (DFT band structure calculation, Fermi surface plot, optical measurements, modelling); DOE-Gentherm (sample synthesis, structural characterization and thermoelectric property measurements); Solid-State Solar-Thermal Energy Conversion Center (S3TEC), an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences under Award #DE-SC0001299 (modelling, preparation of the manuscript). L.A., M.B.N. and S.C. acknowledge the support of the DOD (ONR-MURI under Contract N00014-13-1-0635). The band structure analysis for this project was mainly performed at Texas Advanced Computing Center (TACC) at the University of Texas Austin. The authors thank the Molecular Materials Research Center (MMRC) at the Beckman Institute at Caltech for use of their optical equipment for measurements performed in this work. We thank Y. Li, X. Shi and L. Chen of the Shanghai Institute of Ceramics, Chinese Academy of Sciences for ZEM-3 measurements as part of the International S&T Cooperation Program of China (2015DFA51050). We also thank H. Xiao and T. Chapasis for helpful discussions regarding this paper.

Author information

Author notes

  1. Yinglu Tang and Zachary M. Gibbs: These authors contributed equally to this work.

Authors and Affiliations

  1. Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA

    Yinglu Tang, Guodong Li, Hyun-Sik Kim & G. Jeffrey Snyder

  2. Materials Science, California Institute of Technology, Pasadena, California 91125, USA

    Yinglu Tang, Guodong Li, Hyun-Sik Kim & G. Jeffrey Snyder

  3. Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA

    Zachary M. Gibbs

  4. Department of Physics, University of North Texas, Denton, Texas 76203, USA

    Luis A. Agapito & Marco Buongiorno Nardelli

  5. Department of Mechanical Engineering and Materials Science, Physics and Chemistry, Duke University, Durham, North Carolina 27708, USA

    Luis A. Agapito & Stefano Curtarolo

  6. State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan, Hubei 430070, China

    Guodong Li

  7. Materials Research Center, Samsung Advanced Institute of Technology, Samsung Electronics, Suwon 443-803, South Korea

    Hyun-Sik Kim

Authors
  1. Yinglu Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zachary M. Gibbs
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luis A. Agapito
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guodong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hyun-Sik Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Marco Buongiorno Nardelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Stefano Curtarolo
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. G. Jeffrey Snyder
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

This paper was written collaboratively by Y.T., Z.M.G. and G.J.S. with input from all other authors. Sample synthesis, structural characterization and thermoelectric transport property measurements were performed by Y.T. Optical measurements were performed by Z.M.G. Development of the Kane band model effective mass relation was performed by Z.M.G. and confirmed by Y.T. Band modelling was done collaboratively by Y.T. and Z.M.G. with assistance from H.-S.K. Electronic band structure calculations and Fermi surface plotting were performed by L.A.A. G.L. validated L.A.A.’s DFT calculations and provided additional results and insight. M.B.N. and S.C. contributed to helpful discussions.

Corresponding author

Correspondence to G. Jeffrey Snyder.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 2675 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tang, Y., Gibbs, Z., Agapito, L. et al. Convergence of multi-valley bands as the electronic origin of high thermoelectric performance in CoSb3 skutterudites. Nature Mater 14, 1223–1228 (2015). https://doi.org/10.1038/nmat4430

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat4430

This article is cited by

Search

Advanced 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