Relaxation of a Coupling Energy of Electrons with Phonons in Metals

M. I. Grygorchuk

Bogolyubov Institute for Theoretical Physics, NAS of Ukraine, 14-b Metrologichna Str., UA-03143 Kyiv, Ukraine

Received: 20.10.2017. Download: PDF

The relaxation of electron energy by means of the lattice vibrations in a metal is investigated. The energy distribution between the states is considered as equilibrium one that can be described by the Fermi and Bose functions. An analytical formula is obtained for the electron-energy loss per unit time that is necessary to trigger the lattice acoustic vibrations. As shown, the value of power absorbed by lattice is defined by both relations of the Debye temperature to the lattice temperature and the lattice temperature to the electrons’ temperature.

Key words: metals, electron–phonon coupling, electrons’ temperature.

URL: http://mfint.imp.kiev.ua/en/abstract/v39/i11/1445.html

DOI: https://doi.org/10.15407/mfint.39.11.1445

PACS: 03.50.De, 63.20.kd, 71.10.Ca, 71.45.Gm, 72.15.Lh, 73.20.Mf, 78.20.Bh, 78.67.Bf

Citation: M. I. Grygorchuk, Relaxation of a Coupling Energy of Electrons with Phonons in Metals, Metallofiz. Noveishie Tekhnol., 39, No. 11: 1445—1454 (2017) (in Ukrainian)


REFERENCES
  1. J. M. Ziman, Electrons and Phonons (Oxford: Clarendon Press: 1960).
  2. V. L. Ginzburg and V. P. Shabanski, Sov. Doklady AN SSSR, 100: 445 (1955).
  3. J. Bardin, L. N. Cooper, and J. R. Schriffer, Phys. Rev., 106: 162 (1957); ibidem, 108: 1175 (1957). Crossref
  4. T. Holstein, Annals of Physics, 29: 410 (1964). Crossref
  5. P. E. Hopkins, J. L. Kassebaum, and P. M. Norris, J. Appl. Phys., 105: 023710 (2009). Crossref
  6. A. N. Smith and J. P. Calame, Int. J. Thermophys., 25: 409 (2004). Crossref
  7. J. K. Chen, W. P. Latham, and J. E. Beraun, J. Laser. Appl., 17: 63 (2005). Crossref
  8. M. I. Kaganov, I. M. Lifshitz, and L. V. Tanatarov, Sov. Phys. JETP, 4: 173 (1957).
  9. S. I. Anisimov, B. L. Kapeliovich, and T. L. Perelman, Sov. Phys. JETP, 39: 375 (1974).
  10. T. Q. Qui and C. L. Tien, Trans. ASME J. Heat Transf., 115: 835 (1993). Crossref
  11. R. D. Fedorovich, A. G. Naumovets, and P. M. Tomchuk, Phys. Rep., 328: 73 (2000). Crossref
  12. Y. Bilitsky, N. I. Grigorchuk, and P. M. Tomchuk, Surf. Sci., 603: 3267 (2009). Crossref
  13. N. I. Grigorchuk, Condens. Matter Phys., 16: 33706 (2013). Crossref
  14. A. Crut, P. Maioli, N. Del Fatti, and F. Vallèe, Chem. Soc. Rev., 43: 3921 (2014). Crossref
  15. P. M. Tomchuk and M. I. Grigorchuk, Metallofiz. Noveishie Tekhnol., 29, No. 5: 623 (2007) (in Ukrainian).
  16. V. G. Karpov, M. Nardone, and N. I. Grigorchuk, Phys. Rev. B, 86: 075463 (2012). Crossref
  17. D. Gall, J. Appl. Phys., 119: 085101 (2016). Crossref
  18. Ch. Kittel, Introduction to Solid State Physics (New York: Wiley: 1995).
  19. F. Zeitz, The Modern Theory of Solids (New York: McGraw-Hill Book: 1940).
  20. E. A. Coronado and G. C. Schatz, J. Chem. Phys., 119: 3926 (2003). Crossref
  21. N. I. Grigorchuk, J. Phys. Chem. C, 116: 23704 (2012). Crossref
  22. S. L. Koroljuk, Osnovy Statystychnoi Fizyky ta Termodynamiky (Chernivtsi: Knygy-XXI: 2004) (in Ukrainian).
  23. W. A. Harrison, Solid State Theory (New York–London–Toronto: McGraw-Hill: 1970).
  24. Handbook of Mathematical Functions (New York: Dover Publ.: 1972).