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Melt motion in a Czochralski crystal puller with an axial magnetic field: motion due to buoyancy and thermocapillarity

Published online by Cambridge University Press:  21 April 2006

L. N. Hjellming  and
J. S. Walker
L. N. Hjellming
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, IL 61801, USA
J. S. Walker
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, IL 61801, USA
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Abstract

In the Czochralski process a single crystal is grown from liquid in a crucible. An axial magnetic field suppresses turbulence in the melt and thus reduces the density of microdefects in the crystal. This paper treats the melt motion due to buoyancy and thermocapillarity. The magnitude of this motion decreases roughly like B−2, as the magnetic field strength B is increased. The separate circulations due to buoyancy and thermocapillarity are roughly equal at an early stage of growing a crystal. However the circulation due to thermocapillarity is nearly independent of the melt depth, while that due to buoyancy is proportional to the square of the depth. Therefore as the crystal grows and the melt depth decreases, thermocapillarity becomes progressively more dominant. When the heat flux into the melt is used to define the characteristic temperature difference and velocity, the stream functions are rather insensitive to changes in the thermal boundary conditions at the free surface and at the crucible bottom, provided the overall heat balance of the system is correctly estimated. This is fortunate because there is considerable uncertainty about these boundary conditions. The exception to this insensitivity is that the melt motion due to thermocapillarity is sensitive to changes in the amount of heat lost through the part of the free surface adjacent to the crystal.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 182 , September 1987 , pp. 335 - 368
Copyright
© 1987 Cambridge University Press

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References

Hjellming, L. N. & Walker, J. S. 1986 Melt motion in a Czochralski crystal puller with an axial magnetic field: isothermal motion. J. Fluid Mech. 164, 237–273.Google Scholar
Hjellming, L. N. & Walker, J. S. 1987 Melt motion in a Czochralski crystal puller with an axial magnetic field: uncertainty in the thermal constants. Submitted to J. Cryst Growth.Google Scholar
Kim, K. M. & Langlois, W. E. 1986 Computer simulation of boron transport in magnetic Czochralski growth of silicon. J. Electrochem. Soc. 133, 2586–2590.Google Scholar
Kuroda, E., Kozuka, H. & Takano, Y. 1984 The effect of temperature oscillations at the growth interface on crystal perfection. J. Cryst. Growth 68, 613–623.Google Scholar
Langlois, W. E. 1981 Convection in Czochralski growth melts. Physico chem. Hydrodyn. 2, 245–261.Google Scholar
Langlois, W. E., Hjellming, L. N. & Walker, J. S. 1987 Effects of the finite electrical conductivity of the crystal on hydromagnetic Czochralski flow. Submitted to J. Cryst Growth.Google Scholar
Langlois, W. E. & Kim, K. M. 1987 The effect of incorporating radiation enclosure theory into the simulation of melt flow in magnetic Czochralski growth of silicon. In Proc. 2nd ASME/JSME Thermal Engng Joint Conf., Honolulu, March, 1987.
Langlois, W. E. & Lee, K. J. 1983a Czochralski crystal growth in an axial magnetic field: effects of Joule heating. J. Cryst. Growth 62, 481–486.Google Scholar
Langlois, W. E. & Lee, K. J. 1983b Digital simulation of magnetic Czochralski flow under various laboratory conditions for silicon growth. IBM J. Res. Develop. 27, 281–284.Google Scholar
Langlois, W. E. & Walker, J. S. 1982 Czochralski crystal growth in an axial magnetic field. In Computational and Asymptotic Methods for Boundary and Interior Layers, Proc. BAIL II Conf., pp. 299–304.
Lee, K. J., Langlois, W. E. & Kim, K. M. 1984 Digital simulation of oxygen transfer and oxygen segregation in magnetic Czochralski growth of silicon. Physico Chem. Hydrodyn. 5, 135–141.Google Scholar
Ramachandran, P. A. & Dudukovic, M. P. 1985 Simulation of temperature distribution in crystals grown by Czochralski method. J. Cryst. Growth 71, 399–408.Google Scholar
Srivastava, R. K., Ramachandran, P. A. & Dudukovic, M. P. 1985 Interface shape in Czochralski grown crystals: effect of conduction and radiation. J. Cryst. Growth 73, 487–504.Google Scholar
Srivastava, R. K., Ramachandran, P. A. & Dudukovic, M. P. 1986 Radiation view factors in Czochralski crystal growth apparatus for short crystals. J. Cryst. Growth 74, 281–291.Google Scholar
Stern, E. J. 1985 Mathematical modelling of radiative heat exchanges in Czochralski crystal pulling. IMA J. Appl. Maths 35, 205–222.Google Scholar
Walker, J. S., Ludford, G. S. S. & Hunt, J. C. R. 1971 Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 2. Variable-area rectangular ducts with conducting sides. J. Fluid Mech. 46, 657–684.Google Scholar