Hydrodynamic thermal-capillary model for Czochralski crystal growth: effects of crystal rotation

A Hydrodynamic Thermal-Capillary Model (HTCM) for heat transfer in Czochralski crystal growth systems is used to calculate steady-state, axisymmetric solutions for heat transfer and fluid mechanics while incorporating a self-consistent description of the free-boundaries of the melt/crystal interface, the melt meniscus, and the crystal diameter. The model employs a Galerkin finite-element method to discretize the model equations, and solutions are obtained using a Newton-Raphson iterative scheme. Sample results are presented for the growth of a large-dimension oxide crystal with thermophysical properties similar to those of gadolinium gallium garnet (GGG). Calculations with the HTCM show the effects of crystal rotation on heat transfer, flow in the melt, and melt/crystal interface shape. Sever deflections of the melt/crystal interface are calculated for moderate rotation rates, and limit points in the steady-state-solutions are found with respect to crystal rotation.