Forced Convection During Liquid Encapsulated Crystal Growth With an Axial Magnetic Field

Abstract

This paper treats the forced convection, which is produced by the rotation of the crystal about its vertical centerline during the liquid-encapsulated Czochralski or Kyropoulos growth of compound semiconductor crystals, with a uniform vertical magnetic field. The model assumes that the magnetic field strength is sufficiently large that convective heat transfer and all inertial effects except the centripetal acceleration are negligible. With the liquid encapsulant in the radial gap between the outside surface of the crystal and the vertical wall of the crucible, the forced convection is fundamentally different from that with a free surface between the crystal and crucible for the Czochralski growth of silicon crystals. Again unlike the case for silicon growth, the forced convection for the actual nonzero electrical conductivity of an indium-phosphide crystal is virtually identical to that for an electrically insulating crystal. The electromagnetic damping of the forced convection is stronger than that of the buoyant convection. In order to maintain a given balance between the forced and buoyant convections, the angular velocity of the crystal must be increased as the magnetic field strength is increased.