Transient global simulations were carried out to investigate the effect of argon flow on oxygen and carbon coupled transport in an industrial directional solidification furnace for quasi-single crystalline silicon ingots. Global calculation of impurity transport in the argon gas and silicon melt was based on a fully coupled calculation of the thermal and flow fields. Numerical results show that the argon flow rate affects the flow intensity along the melt–gas surface, but has no significant effect on the flow patterns of silicon melt and argon gas above the melt–gas surface. It was found that the evaporation flux of SiO along the melt–gas surface decreases with the increasing argon flow rate during the solidification process. However, the net flux of oxygen atoms (SiO evaporation flux minus CO dissolution flux) away from the melt–gas surface increases with the increasing argon flow rate, leading to a decrease in the oxygen concentration in the grown ingot. The carbon concentration in the grown ingot shows an exponential decrease with the increase of the argon flow rate, owing to the fact that the dissolution flux of CO significantly decreases with the increasing argon flow rate. The numerical results agree well with the experimental measurements.
Mathematical modeling of vacuum refining of silicon melt under the conditions of electromagnetic stirring
