A modified Chang–Brown model for the determination of the dopant distribution in a Bridgman–Stockbarger semiconductor crystal growth system

Abstract

In this paper, we start from the Chang–Brown model which allows computation of flow, temperature and dopant concentration in a vertical Bridgman–Stockbarger semiconductor growth system. The modifications made by us concern the melt/solid interface. Namely, we assume that the phase transition does not take place on a flat mathematical surface, but in a thin region (the so-called precrystallization-zone), masking the crystal, where both phases, liquid and solid, co-exist. We deduce for this zone new effective equations which govern flow, heat and dopant transport and make the coupling of these equations with those governing the same phenomena in the pure melt. We compute flow, temperature and dopant concentration for crystal and melt with thermophysical properties similar to gallium-doped germanium using the modified Chang–Brown model and compare the results to those obtained using the Chang–Brown model.