Thermoelectric Magnetohydrodynamic Effects During Bridgman Semiconductor Crystal Growth with a Uniform Axial Magnetic Field: Large Hartmann-Number Asymptotic Solution
Abstract
This paper treats the thermoelectric magnetohydrodynamic (TEMHD) effects during Bridgman semiconductor crystal growth in a cylindrical ampoule with a strong uniform axial magnetic field. The melt is bounded by a planar crystal-melt interface, the cylindrical ampoule surface and a planar free surface. Inertial effects are negligible everywhere with a sufficiently strong magnetic field, while viscous effects are important only in thin boundary layers. A parabolic temperature variation is assumed at the crystal-melt interface. The thermoelectric current circulates through the crystal and the Hartmann layer adjacent to the crystal-melt interface. There is no current in the core and in the free surface Hartmann layer. The axially uniform azimuthal velocity in the inviscid core region is zero at the centerline and at the ampoule wall, with a maximum at some radial position. The meridional melt motion involves radially inward flow near the crystal-melt interface. The differences between the numerical and asymptotic Bridgman models are discussed.
Keywords
Azimuthal Velocity Axial Magnetic Field Buoyant Convection Meridional Motion Hartmann LayerPreview
Unable to display preview. Download preview PDF.
References
- 1.Garandet, J.P.: Microsegregarion in crystal growth from the melt: an analytical approach, J. Crystal Growth 131 (1993), 431–438.CrossRefGoogle Scholar
- 2.Ravishankar, P.S., Braggins, T.T., and Thomas, R.N.: Impurities in commercial-scale magnetic Czochralski silicon: axial versus transverse magnetic fields, J. Crystal Growth 104 (1990), 617–628.CrossRefGoogle Scholar
- 3.Shercliff, J.A.: Thermoelectric magnetohydrodynamics, J. Fluid Mechanics 91 (1979), 231–251.CrossRefGoogle Scholar
- 4.Gorbunov, L.A.: Effect of thermoelectromagnetic convection on the production of bulk single-crystals consisting of semiconductor melts in a constant magnetic field, Magnetohydrodynamics 23 (1987), 404–408.Google Scholar
- 5.Gel’fgat, Y.M. and Gorbunov, L.A.: An additional source of forced convection in semiconductor melts during single-crystal growth in magnetic fields, Sov. Phys. Dokl. 34 (1989), 470–473.Google Scholar
- 6.Moreau, R., Laskar, O., Tanaka, M., and Camel, D.: Thermoelectric magnetohydrodynamic effects on solidification of metallic alloys in the dendritic regime, Materials Science and Engineering A173 (1993), 93–100.Google Scholar
- 7.Khine, Y.Y. and Walker, J.S.: Thermoelectric magnetohydrodynamic effects during Bridgman semiconductor crystal growth with a uniform axial magnetic field, J. Crystal Growth 183 (1998), 150–158.CrossRefGoogle Scholar
- 8.Khine, Y.Y., Ma, N. and Walker, J.S.: Thermoelectrically driven melt motion during floating zone crystal growth with a strong axial magnetic field, Proceedings of the Seventh AIAA/ASME Joint Thermophysics and Heat Transfer Conference, June 1998.Google Scholar
- 9.Khine, Y.Y. and Walker, J.S.: Thermoelectrically driven melt motion during floating zone crystal growth with an axial magnetic field, submitted to J. Fluids Engineering.Google Scholar
- 10.Hjellming, L.N. and Walker, J.S.: Melt motion in a Czochralski crystal puller with an axial magnetic field: isothermal motion, J. Fluid Mechanics 164 (1986), 237–273.CrossRefGoogle Scholar
- 11.Hjellming, L.N. and Walker, J.S.: Melt motion in a Czochralski crystal puller with an axial magnetic field: motion due to buoyancy and thermocapillarity, J. Fluid Mechanics 182 (1987), 335–368.CrossRefGoogle Scholar