Three-dimensional cellular automaton modeling of silicon crystallization with grains in twin relationships. (1st June 2020) - Pineau, A.; Guillemot, G.; Reinhart, G.; Regula, G.; Mangelinck-Noël, N.; Gandin, Ch.-A.
Abstract: A three-dimensional model is proposed to simulate the grain structure in directionally solidified silicon. This includes the nucleation and growth of grains in twin relationship whose formation is very frequent during silicon solidification. Based on analyses of in-situ and real-time observations of the crystallization front, a three-dimensional cellular automaton method is developed to model the dynamic of 111 facets, groove formation at grain boundaries, nucleation and growth of grains in twin relationship. The model is applied to well-characterized experiments assuming the frozen temperature approximation. A comparison of solidification sequences, crystallographic orientation maps, and coincidence site lattice maps in both experiment and simulation results is achieved. Results demonstrate that the model could be applied to optimize crystallization processes for both polycrystalline and cast-mono silicon fabrication processes. Graphical Abstract: Comparison of the grain structure map deduced from (left) post-mortem electron back-scattered diffraction analyses of a directionally solidified silicon sample with in-situ real-time x-ray radiography and (right) three-dimensional cellular automaton simulation. Nucleation on (111) solid-liquid growing facets of the bottom A-type grain are at the origin of the first B- and C-type grains, both in Σ3-twin relationship with the A-type grain. Boundaries between B- and C-grains are Σ9 twins. Nucleation of the D-type grain took place on a (111) solid-liquid growing facets of a C-type grain at a faceted/faceted groove formed with a B-type grain. The B-D grain boundary forms a Σ27 twin. Image, graphical abstract