Skip to main content
SpringerLink
Log in

Planar Defects as a Way to Account for Explicit Anharmonicity in High Temperature Thermodynamic Properties of Silicon

  • SOLIDS AND LIQUIDS
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

Silicon is indispensable in semiconductor industry. Understanding its high-temperature thermodynamic properties is essential both for theory and applications. However, first-principle description of high-temperature thermodynamic properties of silicon (thermal expansion coefficient and specific heat) is still incomplete. Strong deviation of its specific heat at high temperatures from the Dulong–Petit law suggests substantial contribution of anharmonicity effects. We demonstrate, that anharmonicity is mostly due to two transverse phonon modes, propagating in (111) and (100) directions, and can be quantitatively described with formation of the certain type of nanostructured planar defects of the crystal structure. Calculation of these defects' formation energy enabled us to determine their input into the specific heat and thermal expansion coefficient. This contribution turns out to be significantly greater than the one calculated in quasi-harmonic approximation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

REFERENCES

  1. L. Landau, L. Pitaevskii, and E. Lifshitz, Course of Theoretical Physics, Vol. 5: Statistical Physics (Pergamon, Oxford, 1980).

  2. C. A. Swenson, J. Phys. Chem. Ref. Data 12, 179 (1983).

    Article  ADS  Google Scholar 

  3. M. Born and E. Brody, Z. Phys. 6, 132 (1921).

    Article  ADS  Google Scholar 

  4. D. C. Wallace, Phys. Rev. A 139, 877 (1965).

    Article  ADS  Google Scholar 

  5. R. A. Cowley, Rep. Progr. Phys. 31, 123 (1968).

    Article  ADS  Google Scholar 

  6. D. Gerlich, B. Abeles, and R. E. Miller, J. Appl. Phys. 36, 76 (1965).

    Article  ADS  Google Scholar 

  7. P. D. Desai, J. Phys. Chem. Ref. Data 15, 967 (1986).

    Article  ADS  Google Scholar 

  8. K. Yamaguchi and K. Itagaki, J. Therm. Anal. Calorim. 69, 1059 (2002).

    Article  Google Scholar 

  9. L. Maissel, J. Appl. Phys. 31, 211 (1960).

    Article  ADS  Google Scholar 

  10. H. Watanabe, N. Yamada, and M. Okaji, Int. J. Thermophys. 25, 221 (2004).

    Article  ADS  Google Scholar 

  11. B. N. Dutta, Phys. Status Solidi B 2, 984 (1962).

    Article  ADS  Google Scholar 

  12. Y. Okada and Y. Tokumaru, J. Appl. Phys. 56, 314 (1984).

    Article  ADS  Google Scholar 

  13. R. B. Roberts, J. Phys. D: Appl. Phys. 14, L163 (1981).

    Article  ADS  Google Scholar 

  14. B. Grabowski, L. Ismer, T. Hickel, et al., Phys. Rev. B 79, 134106 (2009).

  15. D. S. Kim, O. Hellman, J. Herriman, et al., Proc. Natl. Acad. Sci. U. S. A. 115, 1992 (2018).

    Article  ADS  Google Scholar 

  16. M. Kondrin, Y. Lebed, and V. Brazhkin, Diamond Relat. Mater. 110, 108114 (2020).

  17. M. V. Kondrin, Y. B. Lebed, and V. V. Brazhkin, Phys. Rev. Lett. 126, 165501 (2021).

  18. M. Kondrin, Y. Lebed, and V. Brazhkin, Phys. Status Solidi B 259, 2100463 (2022).

  19. A. I. Savvatimskii and S. V. Onufriev, Phys. Usp. 63, 1015 (2020).

    Article  ADS  Google Scholar 

  20. A. Savvatimskiy, S. Onufriev, and A. Kondratyev, Carbon 98, 534 (2016).

    Article  Google Scholar 

  21. A. M. Kondratyev and A. D. Rakhel, Phys. Rev. Lett. 122, 175702 (2019).

  22. J. Vanhellemont, A. K. Swarnakar, and O. V. der Biest, ECS Trans. 64, 283 (2014).

    Article  Google Scholar 

  23. V. A. Goncharova, E. V. Chernysheva, and F. F. Voronov, Sov. Phys. Solid State 25, 2118 (1983).

    Google Scholar 

  24. D. S. Kim, H. L. Smith, J. L. Niedziela, et al., Phys. Rev. B 91, 014307 (2015).

  25. S. Wei, C. Li, and M. Y. Chou, Phys. Rev. B 50, 14587 (1994).

    Article  ADS  Google Scholar 

  26. C. Wang, J. Gu, X. Kuang, et al., Z. Naturforsch. A 70 (2015). https://doi.org/10.1515/zna-2015-0027

  27. A. R. Oganov and C. W. Glass, J. Chem. Phys. 124, 244704 (2006).

  28. Q. Li, Y. Ma, A. R. Oganov, et al., Phys. Rev. Lett. 102, 175506 (2009).

  29. C. He, L. Sun, C. Zhang, et al., Solid State Commun. 152, 1560 (2012).

    Article  ADS  Google Scholar 

  30. J. P. Goss, P. R. Briddon, R. Jones, et al., Phys. Rev. B 73, 115204 (2006).

  31. V. L. Deringer, G. Csanyi, and D. M. Proserpio, Chem. Phys. Chem. 18, 873 (2017).

    Article  Google Scholar 

  32. P. Giannozzi, O. Andreussi, T. Brumme, et al., J. Phys.: Condens. Matter 29, 465901 (2017).

  33. T. Björkman, Comp. Phys. Commun. 182, 1183 (2011).

    Article  ADS  Google Scholar 

  34. L. Balogh, G. Ribárik, and T. Ungár, J. Appl. Phys. 100, 023512 (2006).

  35. T. R. Hart, R. L. Aggarwal, and B. Lax, Phys. Rev. B 1, 638 (1970).

    Article  ADS  Google Scholar 

  36. P. C. Trivedi, H. O. Sharma, and L. S. Kothari, J. Phys. C: Solid State Phys. 10, 3487 (1977).

    Article  ADS  Google Scholar 

  37. V. A. Greshnyakov, JETP Lett. 117, 306 (2023).

    Article  ADS  Google Scholar 

  38. J. Menéndez and M. Cardona, Phys. Rev. B 29, 2051 (1984).

    Article  ADS  Google Scholar 

  39. A. Debernardi, S. Baroni, and E. Molinari, Phys. Rev. Lett. 75, 1819 (1995).

    Article  ADS  Google Scholar 

  40. S. Klotz, J. M. Besson, M. Braden, et al., Phys. Rev. Lett. 79, 1313 (1997).

    Article  ADS  Google Scholar 

  41. V. V. Brazhkin, S. G. Lyapin, I. A. Trojan, et al., JETP Lett. 72, 195 (2000).

    Article  ADS  Google Scholar 

Download references

ACKNOWLEDGMENTS

This work is supported by the Russian Science Foundation (grant no. 19-12-00111).

Author information

Authors and Affiliations

  1. Institute for High Pressure Physics, Russian Academy of Sciences, 108840, Troitsk, Moscow, Russia

    M. V. Kondrin & V. V. Brazhkin

  2. Institute for Nuclear Research, Russian Academy of Sciences, 117312, Moscow, Russia

    Y. B. Lebed

Authors
  1. M. V. Kondrin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. B. Lebed
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. V. Brazhkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. V. Kondrin.

Ethics declarations

The authors declare that they have no conflicts of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kondrin, M.V., Lebed, Y.B. & Brazhkin, V.V. Planar Defects as a Way to Account for Explicit Anharmonicity in High Temperature Thermodynamic Properties of Silicon. J. Exp. Theor. Phys. 137, 342–349 (2023). https://doi.org/10.1134/S1063776123090091

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776123090091

Search

Navigation