Sapphire fibers grown from the melt by the EFG technique: dependence of the impurity distribution on temperature and surface tension gradients

Abstract

A stationary 2D axis-symmetric model able to evaluate the impurity distribution is developed by the finite element method for single-crystal sapphire fibers grown from the melt by the edge-defined film-fed growth (EFG) technique. The computations are carried out for two cases – one where the buoyancy is taken into account and the other where the buoyancy is neglected – using different vertical temperature gradients kg in the furnace. The dependence of the impurity distribution on kg and the Marangoni numbers Ma corresponding to the different surface tension gradients dγ/dT is analyzed. Computations reveal critical Marangoni numbers Mac determined by the fluid flow behavior, and that a smaller kg assures the best homogeneity of the crystal over a wide range of dγ/dT.