Validation of a 3D multi-physics model for unidirectional silicon solidification

Abstract

A model for transient movements of solidification fronts has been added to X-stream, an existing multi-physics simulation program for high temperature processes with flow and chemical reactions. The implementation uses an enthalpy formulation and works on fixed grids. First we show the results of a 2D tin solidification benchmark case, which allows a comparison of X-stream to two other codes and to measurements. Second, a complete 3D solar silicon Heat Exchange Method (HEM) furnace, as built by PVA TePla is modeled. Here, it was necessary to model the complete geometry including the quartz crucible, radiative heaters, bottom cooling, inert flushing gas, etc. For one specific recipe of the transient heater power steering, PVA TePla conducted dip-rod measurements of the silicon solidification front position as function of time. This yields a validation of the model when applied to a real life industrial crystallization process. The results indicate that melt convection does influence the energy distribution up to the start of crystallization at the crucible bottom. But from that point on, the release of latent heat seems to dominate the solidification process, and convection in the melt does not significantly influence the transient front shape.