Model experiments and numerical simulations for directional solidification of multicrystalline silicon in a traveling magnetic field

Low-temperature model experiments and 3D, time-dependent flow simulations with relevance to the melt motion during directional solidification of multicrystalline silicon under a traveling magnetic field are presented. The influence of the inductor current, the relative inductormelt position, and the melt height on the flow pattern and velocity is studied in a square shaped GaInSn melt. Numerical simulations show a good agreement with measurements of the flow velocity by the ultrasonic Doppler velocimetry method. The toroidal flow structure already known from cylindrical melts is observed for a large parameter range. However, at small melt heights, the 3D melt geometry leads to a new flow pattern with a central horizontal vortex. The results obtained from the model experiments are transferred to silicon solidification processes using the proposed scaling laws.