Skip to main content

Phenomenological model of the diffusion of impurity atoms in ultrathin silicon layers with a nonuniform distribution of temperatures

Abstract

The influence of fluxes of intrinsic nonequilibrium semiconductor defects on impurity diffusion in a nonuniform temperature field is considered in the framework of the phenomenological theory of irreversible processes. The mass transfer coefficient defined as the ratio of the concentrations of nonequilibrium and equilibrium defects is introduced to take the excessive concentration of nonequilibrium defects into account. The introduction of this coefficient into equations for matter and heat fluxes makes it possible to express the parameters of the process of thermal diffusion (the diffusion coefficient and the heat of transport) as a time-dependent function of the excessive concentration of intrinsic nonequilibrium semiconductor defects.

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

References

  1. 1.

    A. T. Fiory, J. Mater. 57, 21 (2005).

    CAS  Google Scholar 

  2. 2.

    R. Singh, J. Appl. Phys. 63(8), R59 (1988).

    Article  ADS  CAS  Google Scholar 

  3. 3.

    O. W. Holland, Appl. Phys. Lett. 54(9), 798 (1989).

    Article  ADS  CAS  Google Scholar 

  4. 4.

    F. F. Komarov, A. P. Novikov, V. S. Solov’ev, and S. Yu. Shiryaev, Structural Defects in Ion-Implanted Silicon (Minsk. Gos. Univ., Minsk, 1990) [in Russian].

    Google Scholar 

  5. 5.

    A. R. Chelyadinskii and F. F. Komarov, Usp. Fiz. Nauk 173(8), 813 (2003) [Phys.—Usp. 46, 789 (2003)].

    Article  Google Scholar 

  6. 6.

    V. A. Shklovskii, Zh. Eksp. Teor. Fiz. 82, 536 (1982) [Sov. Phys. JETP 55, 311 (1982)].

    Google Scholar 

  7. 7.

    R. B. Fair, J. J. Wortman, and J. Liu, J. Electrochem. Soc. 131(10), 2387 (1984).

    Article  CAS  Google Scholar 

  8. 8.

    R. B. Fair and S. Li, J. Appl. Phys. 83(8), 4081 (1998).

    Article  ADS  CAS  Google Scholar 

  9. 9.

    H. U. Jager, T. Feudel, and S. Ulbricht, Phys. Stat. Solidi 116, 571 (1989).

    Article  Google Scholar 

  10. 10.

    H. U. Jager, J. Appl. Phys. 78(1), 176 (1995).

    Article  ADS  CAS  MathSciNet  Google Scholar 

  11. 11.

    R. A. Oriani, J. Phys. Chem. Solids 30, 339 (1969).

    Article  ADS  CAS  Google Scholar 

  12. 12.

    J. P. Stark, Solid State Diffusion (Wiley, New York, 1976; Energiya, Moscow, 1980).

    Google Scholar 

  13. 13.

    S. De Groot, Thermodynamics of Irreversible Processes (Intersci. Publ., New York, 1951; Inostr. Liter., Moscow, 1956).

    MATH  Google Scholar 

  14. 14.

    Ad. Agarwal, D. H. Eagleasham, H. J. Gassmann, et al., Lecture Tu-1430, “Modeling Enhanced Diffusion of Implanted Dopants,” http://www.ihp-microelectronics.com/chipps/Djpg/Agarwal.html.

  15. 15.

    L. Manu and A. G. R. Evans, Semicond. Sci. Technol. 4, 711 (1989).

    Article  ADS  Google Scholar 

  16. 16.

    Y. Ishikava, K. Yamauchi, and I. Nakamichi, Jpn. J. Appl. Phys. 28(8), L1319 (1989).

    Article  ADS  Google Scholar 

  17. 17.

    Y. M. Kim, G. Q. Lo, and D. L. Kwong, Appl. Phys. Lett. 55(22), 2316 (1989).

    Article  ADS  CAS  Google Scholar 

  18. 18.

    Y. M. Kim, G. Q. Lo, H. Kinoshita, et al., J. Electrochem. Soc. 138(4), 1122 (1991).

    Article  CAS  Google Scholar 

  19. 19.

    I. Prigozhin and D. Kondespudi, Modern Thermodynamics: From Heat Engines to Dissipative Structures (Wiley, New York, 1998; Mir, Moscow, 2002).

    Google Scholar 

  20. 20.

    G. Manning, Diffusion Kinetics for Atoms in Crystals (Van Nostrand, New York, 1968; Mir, Moscow, 1971).

    Google Scholar 

  21. 21.

    V. I. Rudakov and V. V. Ovcharov, Int. J. Heat Mass Transfer 45, 743 (2001).

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to V. V. Ovcharov.

Additional information

Original Russian Text © V.V. Ovcharov, V.I. Rudakov, 2009, published in Poverkhnost’. Rentgenovskie, Sinkhrotronnye i Neitronnye Issledovaniya, No. 8, pp. 76–80.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ovcharov, V.V., Rudakov, V.I. Phenomenological model of the diffusion of impurity atoms in ultrathin silicon layers with a nonuniform distribution of temperatures. J. Synch. Investig. 3, 639–643 (2009). https://doi.org/10.1134/S1027451009040260

Download citation

Keywords

  • Surface Investigation
  • Effective Diffusion
  • Neutron Technique
  • Impurity Atom
  • Intrinsic Defect