Analysis of particle engulfment during the growth of crystalline silicon

To better understand the physical mechanisms responsible for foreign inclusions during the growth of crystalline silicon, steady-state and dynamic models are developed to simulate the engulfment of solid particles by solidification fronts. A Galerkin finite element method is developed to accurately represent forces and interfacial phenomena previously inaccessible by approaches using analytical approximations. The steady-state model is able to evaluate critical engulfment velocities, which are further validated using the dynamic model. When compared with experimental results for the SiC-Si system, our model predicts a more realistic scaling of critical velocity with particle size than that predicted by prior theories. Discrepancies between model predictions and experimental results for larger particles are posited to arise from dynamic effects, a topic worthy of future attention.