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.