Computational Study of Contact Solidification for Silicon Film Growth in the Ribbon Growth on Substrate System

Ribbon growth on substrate (RGS) has emerged as a new method for growing silicon films at low cost for photovoltaic applications by contact solidification. Thermal conditions play an important role in determining the thickness and quality of the as-grown films. In this study, we have developed a mathematical model for heat transfer, fluid flow, and solidification in the RGS process. In particular, a semi-analytical approach is used in this model to predict solidification with a sharp solid–liquid interface without using a moving grid system. A more realistic analytical relationship that considers the varying rate of heat removal at the interface has been developed to evaluate the effective heat transfer rate, solidification rate, and solidification front. These models were used to predict the flow patterns in the crucible, the temperature distributions in the system, the velocity fields in the crucible, the solidification rates, and the film thicknesses. The effects of important operational parameters, such as pulling speed, preheat temperature, and thermal properties of the substrate material, have been examined. In addition, an order of magnitude analysis has been performed to understand heat transfer in the growing film and substrate. This analysis leads to a simplified mathematical model for heat transfer and solidification, which can be resolved analytically to derive theoretical solutions for the effective heat transfer coefficient, the rate of solidification, and the film thickness. The results show that the solidification rate varies largely on the substrate. The non-uniformity can be mitigated by altering the temperature distribution in the silicon melt through manipulating heat generation in the top heater. The rates of solidification and film thickness are very sensitive to both the thermal conductivity and preheat temperature of the substrate. Increasing pulling velocity will increase the rate of solidification at the leading edge but reduce the film thickness. The numerical model and the theoretical solution provide an important tool for thermal design and optimization of the RGS system.