Magnetic stabilization of the buoyant convection in the liquid-encapsulated Czochralski process

Abstract

This paper presents a linear stability analysis for the buoyant convection during the liquid-encapsulated Czochralski growth of compound semiconductor crystals with a steady, uniform, vertical magnetic field. Results are presented for two values of the Prandtl number, corresponding to indium-phosphide (InP) and gallium-arsenide (GaAs). Most of the results are for a melt depth equal to the crucible diameter, but some results are also presented for a smaller depth. For the cases considered here, the instability involves a transition from a steady axisymmetric flow to a steady nonaxisymmetric flow corresponding to the first Fourier mode in the azimuthal direction. For the weaker magnetic fields, the critical Rayleigh number is close to that for the Rayleigh–Bénard instability in a vertical cylinder. For the stronger magnetic fields, the critical Rayleigh number for GaAs is higher than that for InP because convective heat transfer in the GaAs base flow reduces the vertical temperature gradient.