Computer simulation of liquid encapsulated vertical bridgman crystal growth: pseudo steady‐state calculations

A pseudo steady‐state model is developed to study heat transfer, fluid flow, and the interface shape in the liquid encapsulated vertical Bridgman crystal growth. The model, which is governed by momentum, heat, and overall mass balances in the system, is solved by a finite‐volume/Newton method. Flow and temperature fields, as well as unknown melt/crystal and melt/encapsulant interfaces, are calculated simultaneously. Sample calculations are mainly conducted for the GaAs/B₂O₃/PBN system. Calculated results for the Germanium/graphite system are compared with finite element calculations by Adornato and Brown, and they are in good agreement. The effects of some process parameters, including the growth speed, ambient temperature profile and heat transfer conditions, on flow patterns,temperature fields and the interface shape are illustrated through calculated results. Interface inversion from concave to convex, by modifying the ambient temperature profile, is also demonstrated through computer simulation. Particularly, through an inverse problem approach, a flat interface can be easily obtained for various operation conditions.