Effect of cooling rate on solidification of electron beam melted silicon ingots

Solidification rate has a significant influence on purification of silicon due to segregation of impurities at a liquid solid interface of a solidifying silicon ingot. A mathematical model is developed to evaluate time-dependent position of the liquid solid interface and solidification rate of electron beam melted ingots. A series of solidification experiments with different cooling rates are conducted to measure position of a line which separates directionally grown columnar crystals visible in cross-sections of the solidified ingots. Results show that not the whole ingot solidifies directionally when the reduction rate of the beam current is larger than 1.67 mA/s. The position of the dividing line depends on cooling rate and the experimental trend is consistent with that resulted from theoretical simulations. Modeling shows that the solidification rate changes fast when the beam current reduces linearly that is detrimental for segregation of impurities. It also predicts that an exponential reduction of the beam current leads to a uniform solidification rate which is beneficial to segregation of impurities, though not all exponential current reductions lead to this kind of solidification behavior. (C) 2012 Elsevier Ltd. All rights reserved.