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Self-diffusion parameters in carbon-subgroup crystals

  • Atomic Structure and Nonelectronic Propertties of Semiconductors
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Abstract

Self-diffusion parameters have been calculated for crystals of the carbon subgroup C (diamond), Si, Ge, α-Sn, Pb. It is shown that consideration of quantum effects in the delocalization of atoms leads to the following effect: at low temperatures (below the Debye temperature), the self-diffusion parameters depend strongly on temperature and the self-diffusion entropy is negative: s d < 0. With an increase in temperature, the function s d takes positive values. All thermodynamic parameters of self-diffusion in semiconductor crystals of carbon subgroup were calculated without any fitting parameters. The temperature dependences of self-diffusion parameters were studied for IVa-subgroup crystals upon isobaric heating from T = 0 K to the melting point. A good agreement with both experimental data and theoretical estimates obtained by other researchers is obtained. The correlation between the entropy and enthalpy of self-diffusion, as well as the correlation between the volume and entropy of self-diffusion for the entire temperature range under consideration, are discussed.

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References

  1. S. M. Stishov, Pis’ma Zh. Éksp. Teor. Fiz. 71, 25 (2000) [JETP Lett. 71, 15 (2000)].

    Google Scholar 

  2. M. N. Magomedov, Zh. Neorg. Khim. 49, 2057 (2004) [Russ. J. Inorg. Chem. 49, 1906 (2004)].

    Google Scholar 

  3. K. T. Koga and M. J. Walter, Eizo Nakamura, and Katsura Kobayashi, Phys. Rev. B 72, 024108 (2005).

    Google Scholar 

  4. Ch. Kittel, Introduction to Solid State Physics, 5th ed. (Wiley, New York, 1976; Moscow, Nauka, 1978)

    Google Scholar 

  5. S. D. Gertsriken and I. Ya. Dekhtyar, Diffusion in Metals and Alloys in the Solid Phase (GIFML, Moscow, 1960) [in Russian].

    Google Scholar 

  6. J. R. Manning, Diffusion Kinetics for Atoms in Crystals (Van Nostrand, Toronto, 1968).

    Google Scholar 

  7. B. S. Bokshtein, Diffusion in Metals (Metallurgiya, Moscow, 1978) [in Russian].

    Google Scholar 

  8. M. N. Magomedov, Fiz. Tekh. Poluprovodn. 42, 1153 (2008) [Semiconductors 42, 1133 (2008)].

    Google Scholar 

  9. Handbook of Mathematical Functions, Ed. by M. Abramovitz and I. Stegun (Nation. Bureau of Standards, New York, 1964; Nauka, Moscow, 1979).

    Google Scholar 

  10. M. N. Magomedov, Fiz. Met. Metalloved., No. 10, 13 (1992) [Phys. Met. Metallogr. 74, 319 (1992)].

  11. M. N. Magomedov, Metally, No. 6, 27 (2001) [Russian Metallurgy (Metally), No. 6, 582 (2001)].

  12. R. P. Feynman, Statistical Mechanics (Benjamin, Massachusetts, 1972; Nauka, Moscow, 1975).

    Google Scholar 

  13. L. A. Girifalco, Statistical Physics of Materials (Wiley, New York, 1973).

    Google Scholar 

  14. Problems in Thermodynamics and Statistical Physics, Ed. by P. T. Landsberg (Pion, London, 1971).

    Google Scholar 

  15. M. N. Magomedov, Fiz. Met. Metalloved. 80(4), 36 (1995) [Phys. Met. Metallogr. 80, 383 (1995)].

    Google Scholar 

  16. E. M. Sokolovskaya and L. S. Guzei, Metallochemistry (Mosc. Gos. Univ., Moscow, 1986) [in Russian].

    Google Scholar 

  17. M. N. Magomedov, Pis’ma Zh. Tekh. Fiz. 28(10), 64 (2002) [Tech. Phys. Lett. 28, 430 (2002)].

    Google Scholar 

  18. M. N. Magomedov, Fiz. Tverd. Tela 45, 33 (2003) [Phys. Solid State 45, 32 (2003)].

    Google Scholar 

  19. S. I. Novikova, Thermal Expansion in Solids (Nauka, Moscow, 1974) [in Russian].

    Google Scholar 

  20. A. F. Andreev and I. M. Lifshits, Zh. Éksp. Teor. Fiz. 56, 2057 (1969) [Sov. Phys. JETP 29, 1107 (1969)].

    Google Scholar 

  21. M. N. Magomedov, Pis’ma Zh. Tekh. Fiz. 34(10), 20 (2008) [Tech. Phys. Lett. 34, 414 (2008)].

    Google Scholar 

  22. L. A. Shul’man, Sverkhtverd. Mater., No. 4, 58 (1993).

  23. I. V. Aleksandrov, A. F. Goncharov, A. N. Zisman, and S. M. Stishov, Zh. Éksp. Teor. Fiz. 93, 680 (1987) [Sov. Phys. JETP 66, 384 (1987)].

    ADS  Google Scholar 

  24. B. F. Ormont, Introduction to Physical Chemistry and Crystal Chemistry of Semiconductors (Vyssh. Shkola, Moscow, 1968) [in Russian].

    Google Scholar 

  25. A. R. Regel’ and V. M. Glazov, Periodical Law and Physical Properties of Electronic Melts (Nauka, Moscow, 1978) [in Russian].

    Google Scholar 

  26. S. V. Stankus, R. A. Khairulin, and P. V. Tyagel’skii, Teplofiz. Vysok. Temp. 37(4), 559 (1999).

    Google Scholar 

  27. V. E. Zinov’ev, Thermophysical Properties of Metals and High Temperatures, The Handbook (Metallurgiya, Moscow, 1989) [in Russian].

    Google Scholar 

  28. G. M. de’Munari, L. Gabba, F. Giusiano, and G. Mambriani, Phys. Stat. Solidi A 34(2), 455 (1976).

    Article  ADS  Google Scholar 

  29. M. I. Heggie, J. Phys.: Condens. Matter 3, 3065 (1991).

    Article  ADS  Google Scholar 

  30. U. Krause, J. P. Kuska, and R. Wedell, Phys. Stat. Solidi B 151, 479 (1989).

    Article  ADS  Google Scholar 

  31. Y. Taji, J. Phys. Soc. Jpn. 48, 1237 (1980).

    Article  ADS  Google Scholar 

  32. N. F. Uvarov, E. F. Hairetdinov, and W. Bollmann, Cryst. Res. Technol. 24, 413 (1989); Cryst Res. Technol. 24, 543 (1989).

    Article  Google Scholar 

  33. A. N. Orlov and Yu. V. Trushin, Energy of Point Defects in Metals (Énergoatomizdat, Moscow, 1983) [in Russian].

    Google Scholar 

  34. D. Sh. Tsagareishvilli, Methods for Calculating the Thermal and Elastic Properties of Crystalline Inorganic Substances (Tbilisi, Metsniereba, 1977) [in Russian].

    Google Scholar 

  35. V. K. Grigorovich, Mendeleev’ Periodical Law and Electronic Structure of Metals (Moscow, Nauka, 1966) [in Russian].

    Google Scholar 

  36. S. V. Stankus and R. A. Khairulin, Teplofiz. Vysok. Temp. 44(3), 393 (2006).

    Google Scholar 

  37. Physical Acoustics, Ed. by W. P. Mason (Academic Press, London, 1965) v. 3, pt B.

    Google Scholar 

  38. R. Svolin, in Atomic Diffusion in Semiconductors, Ed. by D. Shaw (Plenum, London, 1973; Mir, Moscow, 1975).

    Google Scholar 

  39. Metals Reference Book, Ed. by Colin I. Smithells (Butterworth, London, 1976; Metallurgiya, Moscow, 1980).

    Google Scholar 

  40. CRC Handbook of Chemistry and Physics, 74th ed., Ed. by David R. Lide (CRC Press, London, 1993–1994).

    Google Scholar 

  41. P. M. Fahey, P. B. Griffin, and J. D. Plummer, Rev. Mod. Phys. 61, 289 (1989).

    Article  ADS  Google Scholar 

  42. S. Hu, in Atomic Diffusion in Semiconductors, Ed. by D. Shaw (Plenum, London, 1973; Mir, Moscow, 1975).

    Google Scholar 

  43. T. Soma and A. Morita, J. Phys. Soc. Jpn. 32, 357 (1972).

    Article  ADS  Google Scholar 

  44. Y. Shimizu, M. Uematsu, and K. M. Itoh, Phys. Rev. Lett. 98, 095901 (2007).

    Article  ADS  Google Scholar 

  45. H. Bracht, E. E. Haller, and R. Clark-Phelps, Phys. Rev. Lett. 81, 393 (1998).

    Article  ADS  Google Scholar 

  46. H. M. Pinto, J. Coutinho, V. J. B. Torres, G. Oberg, and P. R. Briddon, Mater. Sci. Semicond. Proc. 9(4–5), 498 (2006).

    Article  Google Scholar 

  47. D. Lazarus and N. Nakhtrib, Solids under Pressure, Ed. by W. Paul and D. M. Warschauer (McGraw-Hill, New York, 1963; Mir, Moscow, 1966).

    Google Scholar 

  48. R. Keyes, in Solids under Pressure, Ed. by W. Paul and D. M. Warschauer (McGraw-Hill, New York, 1963; Mir, Moscow, 1966).

    Google Scholar 

  49. V. A. Kisilishin, Dokl. Akad. Nauk SSSR 295, 127 (1987).

    Google Scholar 

  50. A. Yelon and B. Movaghar, Phys. Rev. Lett. 65, 618 (1990).

    Article  ADS  Google Scholar 

  51. M. R. Magomedov. Teplofiz. Vysok. Temp. 40, 152 (2002) [High Temp. 40, 142 (2002)].

    Google Scholar 

  52. P. A. Varotsos, Phys. Rev. B 75, 172107 (2007).

    Article  ADS  Google Scholar 

  53. P. Varotsos and K. Alexopoulos, Phys. Stat. Solidi B 110(9), 9 (1982).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Institute for Geothermal Research, Dagestan Scientific Center, Russian Academy of Sciences, Makhachkala, Dagestan, 367003, Russia

    M. N. Magomedov

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Correspondence to M. N. Magomedov.

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Original Russian Text © M.N. Magomedov, 2010, published in Fizika i Tekhnika Poluprovodnikov, 2010, Vol. 44, No. 3, pp. 289–301.

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Magomedov, M.N. Self-diffusion parameters in carbon-subgroup crystals. Semiconductors 44, 271–284 (2010). https://doi.org/10.1134/S1063782610030012

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