Effect of a traveling magnetic field on heat and mass transfer during submerged heater crystal growth

Abstract

The effect of traveling magnetic field (TMF) on heat and mass transfer during the 4" Ga:Ge semiconductor single crystal growth by the Axial Heat Processing technique has been studied numerically. The heat and mass transfer processes in the composite multiphase system consisting of crystal, melt, crucible, and submerged heater were analyzed in an axisymmetric unsteady formulation, with the instantaneous position and shape of the crystallization front being unknown and determined during the simulation. The influence of the TMF is accounted for through an analytically defined Lorentz force applied for the case of electrically insulating boundaries. The flow patterns and dopant distribution in the melt and crystal were determined for various temperature profiles applied to the submerged heater, axial temperature gradients, and at different directions and induction values of the applied TMF. It was found that the temperature boundary conditions applied to the submerged heater significantly affect mass transfer in the melt and, consequently, dopant segregation in the grown crystal. The downward TMF improves the axial and radial dopant homogeneity in the grown crystal. Within a certain range of intensities, the TMF reduced the intensity of flow driven by the radial temperature gradient at the submerged heater and the curvature of the crystallization front. Moreover, the positive effect of the TMF increased with higher growth rates. In the investigated configuration, a fourfold reduction in radial dopant segregation was achieved under stringent growth conditions by expanding the convective dopant transfer zone toward the symmetry axis through the TMF, thereby eliminating the accumulation of dopant concentration in this region.