Numerical Model for Bridgman-Stockbarger Crystal Growth with a Magnetic Field

Abstract

This paper presents a model for the unsteady species transport for the growth of doped semiconductor crystals during the vertical Bridgman‐Stockbarger process with a steady axial magnetic field. This dilute species transport depends on the convective and diffusive species transport of the dopant. This convective species transport is driven by buoyant convection in the melt, which produces compositional nonuniformities in both the melt and the crystal. This transient model predicts the distribution of species in the entire crystal grown in a steady axial magnetic field. The present study presents results of concentration in the crystal and in the melt at several different stages during crystal growth. I. Introduction D URING crystal growth without a magnetic field or with a weak magnetic field, turbulent or oscillatory melt motions can produce undesirable spatial oscillations of the concentration, or microsegregation, in the crystal. 1 Turbulent or oscillatory melt motions lead to fluctuations in the heat transfer across the growth interface from the melt to the crystal. Because the local rate of crystallization depends on the balance between the local heat fluxes in the melt and the crystal, fluctuations in the heat flux from the melt create fluctuations in the local growth rate, which create microsegregation. A moderate magnetic field can be used to create a body force that provides an electromagnetic (EM) damping of the melt motion can to eliminate oscillations in the melt motion and thus in the concentration of the crystal. Unfortunately, the elimination of mixing and a moderate or strong EM damping of the residual melt motion can lead to a large variation of the crystal’s composition in the direction perpendicular to the growth direction (radial macrosegregation). On the other hand, if the magnetic field strength is so strong that the melt motion is reduced sufficiently so that it has no effect on the composition in the crystal, then this diffusion-controlled species transport can produce a radially and axially uniform composition in the crystal grown. 2 To achieve diffusion-controlled species trans�