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Numerical simulation of thermal-physical processes accompanying multisilicon crystal growing by the method of Bridgman — Stockbarger

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Abstract

Conjugate heat transfer was studied numerically at multisilicon production from flat-bottom crucible using a vertical version of the Bridgman — Stockbarger method. The equations of convective heat transfer in the area occupied by melt, and heat-conductivity equations for the solid silicon body and crucible walls were solved, considering the heat of phase transition.

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References

  1. V.A. Vanke, V.M. Lopukhin, and V.L. Savvin, Problems of solar space power stations, Sov. Phys.-Uspekhi, 1977, Vol. 123, No. 4, P. 633–655.

    ADS  Google Scholar 

  2. F. Farenbukh and R. Biyub, Solar Elements: Theory and Experiment, Energoatomizdat, Moscow, 1987.

    Google Scholar 

  3. D.S. Strebkov and N.L. Koshkin, The development of photo-voltaic power engineering in Russia, Thermal Engineering, 1996, Vol. 43, No. 5, P. 381–384.

    Google Scholar 

  4. I.E. Vasilieva, I.A. Eliseev, V.P. Eremin, A.V. Zolotaiko, B.A. Krasin, A.I. Nepomnyashchikh, S.I. Popov, and V.V. Sinitsky, Multicrystalline silicon for solar power engineering, Izv. VUZov, Materialy elektronnoy tekhniki, 2002, Vol. 4, No. 2, P. 16–24.

    Google Scholar 

  5. B.A. Krasin, A.I. Nepomnyashchikh, A.S. Tokarev, T.S. Shamirzaev, R.V. Presnyakov, and A.P. Maksikov, The structure and electric-physical properties of multicrystalline silicon, Ibid., 2005, Vol. 4, No. 1, P. 28–34.

    Google Scholar 

  6. V.I. Polezhaev, A.V. Bune, N.A. Verezub et al., Mathematic Modeling of Convective Heat Transfer Using the Navier — Stokes Equations, Nauka, Moscow, 1987.

    Google Scholar 

  7. V.S. Berdnikov, V.A. Vinokourov, V.V. Vinokourov, and V.A. Gaponov, Mixed convection flow of the melt and heat transfer during Czochralski crystal growth, Proc. of the 5th Intern. Conf. “Single Crystal Growth and heat & Mass Transfer”, Obninsk, 2003, September 22–26, Vol. 1, P. 43–67.

    Google Scholar 

  8. V.S. Berdnikov, M.V. Filippova, A.I. Nepomnyashchikh, and B.A. Krasin, Hydrodynamics of melt and heat transfer at multisilicon production by Bridgman method, Proc. of the 6th Intern. Conf. “Single Crystal growth and Heat & Mass Transfer”, Obninsk, 2005, September 25–30, Vol. 3, P. 556–569.

    Google Scholar 

  9. M.P. Marchenko and I.V. Fryazinov, The KARMA-1 program complex for solving time-dependent problems of crystal growth in ampoules, Computational Mathematics and Mathematical Physics, 1997, Vol. 37, No. 8, P. 956–966.

    MATH  Google Scholar 

  10. C.L. Yaws, L.L. Dickens, R. Lutwak, and G. Hsu, Semiconductor industry silicon: physical and thermodynamic properties, Solid State Technol., 1981, Vol. 24, No. 1, P. 87–92.

    Article  Google Scholar 

  11. Properties of Elements: Handbook in 2 Parts. Pt. 1, M.E. Dritz (Ed.), Metallurgia, GUP, J. Tsvetnye Metally, Moscow, 1997.

    Google Scholar 

  12. S.V. Stankus, R.A. Khairulin, and P.V. Tyagelsky, Thermal properties of germanium and silicon under the condensed state, High Temperatures, 1999, Vol. 37, No. 4, P. 559–564.

    Google Scholar 

  13. A. Mühlbauer, W. Erdmann, and W. Keller, Electrodynamic convection in silicon floating zones, J. Crystal Growth, 1983, Vol. 64, P. 529–545.

    Article  Google Scholar 

  14. V.M. Raskatov, V.S. Chuenkov, N.F. Bessonova, and D.A. Veis, Engineering Materials: Brief Handbook, Mashinostroenie, Moscow, 1980.

    Google Scholar 

  15. N.B. Vargaftik, Handbook on Thermal-Physical Properties of Gases and Liquids, Nauka, Moscow, 1972.

    Google Scholar 

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The work was financially supported by the Russian Foundation for Basic Research (Grants Nos. 02-01-00808, 05-01-00813, and 05-05-64752) and Integration projects of Siberian Branch of the Russian Academy of Sciences (Nos. 155-2003 and 156-2003).

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Berdnikov, V.S., Filippova, M.V., Krasin, B.A. et al. Numerical simulation of thermal-physical processes accompanying multisilicon crystal growing by the method of Bridgman — Stockbarger. Thermophys. Aeromech. 13, 257–274 (2006). https://doi.org/10.1134/S0869864306020089

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  • DOI: https://doi.org/10.1134/S0869864306020089

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