An Integrated Model for Czochralski Melt Growth of Optical Crystals

Abstract

This article presents the phenomena of melt flow, heat transfer, and solidification in Czochralski (CZ) melt growth processes of optical crystals, with emphasis on the effect of internal radiative heat transfer on the temperature distributions in oxide melt and crystal, melt convection, and melt-crystal interface shape. An integrated numerical model has been developed for simulating the physical phenomena in generic CZ furnaces, which includes the models for electromagnetic induction in crucible, surface exchange radiation in furnace, internal radiation in semi-transparent oxide melt and crystal, Marangoni convection in the melt, and solidification. Each developed model compares well with available analytical solutions. Numerical simulations were carried out for the prediction of fluid flow and heat transfer in furnaces. The simulation results show that the variation in optical properties of melt and crystal strongly impact their temperature distributions. It also affects the melt flow profile and intensity. The interface shape becomes more deeply convex toward the melt, as the optical thickness of the melt increases. However, the optical thickness of the crystal exhibits a minor impact on the interface shape. The results also show that the natural convection is dominated in the melt and the Marangoni flow enforces the natural convection.