Analysis of faceted solidification in the horizontal ribbon growth crystallization process

Horizontal ribbon growth (HRG), in which a thin sheet of solidified material is pulled horizontally from the surface of a molten pool, is proposed as an efficient technique for growth of single-crystal silicon sheets. Despite recent results, some details of the process are still not understood, in particular the solidification mechanism at the triple junction point (TJP) where the solid, the liquid, and the surrounding gas meet. The solidification mechanism in the HRG process is investigated in this paper both analytically and numerically, incorporating the solidification kinetics that lead to faceted growth. The conventional solid-liquid problem in the HRG process is formulated analytically in the vicinity of the triple junction point (TJP). The temperature distribution is obtained for the liquid and solid regions as a function of the underlying parameters of the HRG process, such as the material properties, the ribbon pull speed, and the cooling heat fluxes. Using the analytical results, the TJP temperature, the facet length, interfacial temperature gradients, and liquid supercooling can be predicted. The analytical formulation is validated against accurate numerical simulations of the same problem, showing a good agreement in predicting the temperature gradients and the facet growth. The findings of this study suggest that using the analytical model, the behavior of the solid ribbon and the existence of a supercooled region in the liquid in the HRG process can be predicted without the need for numerical simulations. The model also gives criteria for optimal performance of the HRG process.