A mathematical model for distribution of calcium in silicon by vacuum directional solidification
Calcium is one of the main impurity elements in silicon. The removal of calcium strongly affects the quality of the polycrystalline silicon ingot produced by a vacuum directional solidification method. Based on the considerations of the theory of segregation, mass transfer and evaporation during vacuum directional solidification process, a mathematical model for calcium distribution in silicon was proposed and it can be used to explain the removal mechanism. In order to confirm the mathematical model, an industrial scale experiment on UMG Si with an initial purity of 99.98 wt. was performed. Since the reaction temperature strongly influences both the evaporation and segregation of calcium, the dependences of effective segregation coefficient (keff) and the evaporation coefficient (kE) on temperature were carefully investigated. The results showed that the proposed mathematical model was highly consistent with the experimental data and the calcium removal efficiency mainly relied on the evaporation step.