Finite Element Analysis of a Thermal‐Capillary Model for Liquid Encapsulated Czochralski Growth

Abstract

A two‐dimensional model for the coupled effects of heat transfer and capillarity in a liquid encapsulated Czochralski growth system is analyzed by solving the full free‐boundary problem describing the temperature field in each phase, the shapes of the melt/solid and fluid/fluid interfaces, and the radius of a steadily growing crystal. Solutions are based on a finite element analysis with Newton iteration for all the variables. Heat transfer in the melt is taken to be dominated by conduction, and radiation to a uniform ambient is included for a transparent encapsulant. Calculations for a model system give reasonable predictions of crystal size and axial temperature gradient. The results are most sensitive to radiation through the encapsulant.