Modeling Multi-Crystalline Silicon Growth in Directional Solidification Systems

Abstract

The key to achieving high solar cell efficiency is to increase average grain size in silicon multicrystals and reduce dislocation density. The grain size and dislocation distributions in a silicon multicrystal are strongly influenced by the design of the solidification furnace and the operating conditions during solidification. This paper discusses a reported mathematical model that quantifies the temperature field in the furnace, silicon melt flow distribution, and the shape of the melt/solid interface, which influences the grain size and dislocations distributions. The global model described here takes into account all modes of heat transfer coupled with turbulent melt and inert gas flows, and can be used to manipulate the growth conditions to produce silicon multicrystals of higher qualities. The numerical approach discussed in this paper can be used to evaluate changes in equipment design and process conditions to increase the solidification rate with acceptable compromise in the multicrystal quality.