Abstract
A mathematical model and numerical method are developed and used to investigate nonstationary flow and heat and mass transfer regimes in a melt appropriate to the conditions of Czochralski crystal growth. A study is made of the separate and combined influence of rotation and thermal, concentration, and thermocapillary convection on the distribution of the temperature and the dopant in the range of regime parameters corresponding to large charging masses of the melt with small value of the kinematic viscosity. Large-scale fluctuations are found to occur when rotation and thermal convection interact. Thermocapillary convection is shown to have an important influence on the resulting motion when it interacts with the thermal and concentration forms of convection. A comparison is made with the results of experimental and theoretical investigations of other authors.
Similar content being viewed by others
Literature cited
R. A. Landise, The Growth of Single Crystals, Prentice-Hall (1970),
M. G. Mil'vidskii and B. M. Turovskii, “Simulation of mixing of the melt when crystals are grown by the Czochralski method,” Kristallografiya,6, 759 (1961).
Yu. P. Konakov and G. A. Tret'yakov, “Experimental investigation of the velocity field of the melt in the case of pulling of single crystals,” Tr. Mosk. Inst. Inzh. Zheleznodorozhn. Transp., No. 254, 18 (1967).
K. Shiroki, “Simulations of Czochralski growth on crystal rotation rate influence in fixed crucibles,” J. Cryst. Growth,40, 129 (1977).
V. P. Grishin, O. A. Remizov, N. I. Kazimirov, and Yu. P. Fedulov, “Some hydrodynamic features of the growth of silicon crystals by Czochralski's method,” Nauch. Tr. Gos. Inst. Redkometallicheskoi Prom., 65, 11 (1975).
W. R. Wilcox and L. D. Fullmer, “Turbulent free convection in Czochralski crystal growth,” J. Appl. Phys.,36, 2201 (1963).
M. A. Filippov, T. A. Cherepanova, V. A. Smirnov, and L. N. Tityunik, “On inhomogeneity of the dopant distribution when germanium and gallium arsenide single crystals are grown from the melt,” in: Problems in the Theory of Crystallization, No. 2 [in Russian], Riga (1975), p. 25.
N. Kobayashi, “Computational analysis of the flow in a crucible,” J. Cryst. Growth,30, 177 (1975).
N. Kobayashi, “Computational simulation of the melt flow during Czochralski growth,” J. Cryst, Growth,43, 357 (1978).
W. E. Langlois, “Digital simulation of Czochralski bulk flow in a parameter range appropriate for liquid semiconductors,” J. Cryst. Growth,42, 386 (1977).
W. E. Langlois, “Effect of the buoyancy parameter on Czochralski bulk flow in garnet growth,” J. Cryst. Growth,46, 743 (1979).
W. E. Langlois, “Digital simulation of Czochralski bulk flow in microgravity,” J. Cryst. Growth,48, 25 (1980).
D. Schwabe, A. Scharmann, R. Preisser, and R. Oeder, “Experiments on surface tension driven flow in floating zone melting,” J. Cryst. Growth,43, 305 (1978).
L. O. Wilson, “The effect of fluctuating growth rates on segregation in crystals grown from the melt,” J. Cryst. Growth, 48, 435 (1980).
V. L. Gryaznov and V. I. Polezhaev, “Numerical simulation of a turbulent convection regime in a vertical layer,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 8 (1977).
A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1977), p. 656.
V. L. Gryaznov and V. I. Polezhaev, “Investigation of some difference schemes and approximations of boundary conditions for the numerical solution of the equations of thermal convection,” Preprint No. 40 [in Russian], Institute of Problems of Mechanics, USSR Academy of Sciences, Moscow (1974), p. 71.
E. D. Lyumkis, B. Ya. Martuzan, and É. N. Martuzane, “Numerical investigation of nonstationary hydrodynamic and thermal processes in the Czochralski method,” Izv. Akad. Nauk SSSR, Ser. Fiz.,44, 373 (1980).
K. Morison et al., “The distribution of impurities in single crystals,” in: Crystal Growth Symposium, Boston, 1966 (ed by H. Steffen Peiser), Pergamon Press, Oxford (1967).
G. Z. Gershuni and E. M. Zhukhovitskii, Convective Stability of Incompressible Fluids [in Russian], Nauka, Moscow (1972), p. 392.
V. I. Polezhaev, “Thermocapillary convection of a fluid in a cylindrical vessel for given heat supply,” in: Some Applications of the Mesh Method in Gas Dynamics, No. 3 [in Russian], Izd. MGU, Moscow (1971), p. 175.
Author information
Authors and Affiliations
Additional information
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 55–65, January–February, 1981.
Rights and permissions
About this article
Cite this article
Polezhaev, V.I., Prostomolotov, A.I. Investigation of hydrodynamic and heat and mass transfer processes for crystal growing by the Czochralski method. Fluid Dyn 16, 42–50 (1981). https://doi.org/10.1007/BF01094811
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01094811