Bridgman crystal growth with a strong, low-frequency, rotating magnetic field

Abstract

This paper treats the melt motion driven by a low-frequency, spatially uniform, rotating magnetic field that is perpendicular to the axis of a cylindrical Bridgman ampoule. The magnetic field is sufficiently strong that inertial effects are negligible and that viscous effects are confined to thin boundary layers that are adjacent to the ampoule surfaces and to the crystal–melt interface. Outside the boundary layers, the melt nearly rotates as a rigid body with the angular velocity of the rotating magnetic field. Each boundary layer provides a transition from this rigid-body rotation to the zero azimuthal velocity at each solid surface. In the boundary layer adjacent to the crystal–melt interface, which is parallel to the magnetic field, there are nonaxisymmetric radial and axial velocities associated with the azimuthal variations of the azimuthal velocity. Because of its nonzero electrical conductivity, the static crystal acts as a generator in the rotating magnetic field and drives electric currents through the crystal–melt interface boundary layer. These electric currents from the slightly conducting crystal interact with the magnetic field to accelerate the azimuthal velocity. Some of the melt in this layer may have an angular velocity that is more than twice the angular velocity of the magnetic field. For the actual small electrical conductivities of solid semiconductors, the radial and axial velocities inside the crystal–melt interface layer are very different from those for an electrically insulating crystal. The results indicate that a strong, low-frequency, rotating magnetic field would produce poor crystals with severe rotational striations.