Numerical study on improved mixing in silicon melts by double-frequency TMF

During unidirectional solidification of multicrystalline (mc) silicon, the adjustment of controllable mixing patterns with high stirring efficiency can be obtained by application of a double-frequency travelling magnetic field (TMF). It is assumed that such Lorentz force mode is generated within KRISTMAG˜® heater magnet modules (HMM) positioned around a rectangular crystallization container with silicon melt. The induced flow distributions were studied numerically by 3D magnetic and transient flow calculations. The electromagnetic interference due to the presence of two frequencies and its effect on the resulting Lorentz force density have been estimated analytically. The results show that the flow can be intentionally intensified in the bulk volume without generation of hazardous high velocities in the peripheral region, i.e. near container walls. No considerable resonance effect has been found. As a result the TMF penetration and, hence, the melt mixing level within the central region is enhanced. Additionally, a general improvement of the process purity can be predicted.