Thermoelectric magnetohydrodynamic effects during Bridgman semiconductor crystal growth with a uniform axial magnetic field

Abstract

During semiconductor crystal growth with an externally applied magnetic field, thermoelectric currents may drive a significant melt circulation. This paper treats a model problem for a cylindrical Bridgman ampoule with a uniform axial magnetic field, a planar crystal—melt interface, a parabolic temperature variation along the interface and two different uniform values of the absolute thermoelectric power for the melt and crystal. For an axisymmetric motion, there are different characteristic velocities for the azimuthal velocity and the meridional (radial and axial) velocities. The meridional circulation involves radially outward flow in the melt near the crystal—melt interface. As the magnetic- field strength is increased from zero, the magnitude of the meridional circulation first increases from zero to a maximum at a Hartmann number of approximately ten and then decreases toward zero as the magnetic damping increases faster than thermoelectric effects.