Mathematical Modeling of Impurity Distribution in the Melt Meniscus in the Growth of Profiled Sapphire Crystals

摘要

The distribution of impurities in the growth of profiled sapphire crystals is simulated. The distribution of impurities was calculated with the use of the diffusion equation with convective terms. The melt flow was found by solving the Navier-Stokes equation. The distributions of impurities over the melt meniscus are obtained at different crystallization rates. The maximum concentration supersaturation in the meniscus is studied as a function of its geometric parameters.