Non-isothermal model experiments and numerical simulations for directional solidification of multicrystalline silicon in a traveling magnetic field

Abstract

A new experimental setup containing a GaInSn melt with a square horizontal cross section of 10×10cm2 and a variable melt height up to 10cm has been developed. The melt is positioned in the center of a coil system generating a traveling magnetic field (TMF). Using a cooling system at the bottom and a heating system at the top of the melt, a vertical temperature difference up to approximately 50K can be applied to the melt, imitating the thermal conditions during the directional solidification of multicrystalline silicon. Direct measurements of the time-dependent velocity and the temperature profiles were performed using ultrasonic Doppler velocimetry and thermocouples, respectively. Complementary three-dimensional (3D) numerical simulations of the model experiments were used to validate the numerical tools and to gain a deeper insight into the characteristics of TMF flows in square melts. The classical toroidal flow structure known from isothermal cylindrical melts is shown to obtain a large horizontal central vortex at a small height of the square melt, whereas a distinct 3D asymmetry appears at a large height. A vertical temperature gradient tends to suppress the vertical melt motion and leads to new complex horizontal flow structures.