Multi-crystalline silicon (mc-Si) produced by the directional solidification (DS) method has been the main material for solar cells due to low manufacturing cost. However, solar cells made from mc-Si have disadvantages in photoelectric conversion efficiency. This is because a grown mc-Si ingot incorporates impurities, precipitates and structural defects, of which generation and distribution are determined mainly in the DS process. In order to improve ingot quality and therewith cell efficiency, it is vital to control and optimize the DS process. During the DS process, silicon melt convection, acting as an important carrier of heat and mass transfer, could significantly affect the temperature distribution, impurities transport and crystallization interface shape. Therefore, precise control of melt flow pattern is crucial to optimizing the DS process and improving ingot quality. In the conventional DS system, the melt flow is driven mainly by buoyant force resulting from horizontal temperature gradient. Control ability of this driving manner for melt flow pattern is limited. A more effective manner is the use of traveling magnetic fields (TMFs). Detailed understanding of heat transfer in the whole DS process under TMFs is the key to adopt TMFs to optimize the DS process. However, few studies have been conducted on the whole DS process under TMFs.

The DS process is a highly coupled nonlinear thermal process with complex thermal interaction among the melt convection, argon flow and different solid components. It is therefore necessary to employ global modeling, which takes into account thermal convection, conduction, radiation and phase change, to reproduce the whole DS process under TMFs. During the DS process, the crystallization interface is continuously moving and a steady-state position of the interface physically does not exist, i.e. the melt height is changing. This requires the incessant recalculation of the Lorentz force distribution during the DS process. The coupling effect between the melt height and the Lorentz force distribution makes the numerical modeling of the whole DS process under TMFs more complicated.

In this study, we developed a fully coupled transient global model for the whole DS process under TMFs. On the basis of this model, the evolutions of Lorentz force distribution, thermal field, melt flow and crystallization interface shape were predicted during the whole DS process. Special attention was paid to comparisons of the melt flow pattern and crystallization interface shape as well as their evolutions under different cases without TMFs, with downward directed TMFs and with upward directed TMFs. These results can provide essential knowledge for optimizing the DS process of mc-Si via TMFs.

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