3D cellular automaton modelling of silicon crystallization including grains in twin relationship

Abstract

Abstract Production of silicon for solar cells in photovoltaic systems is mainly based on directional casting processes. Twin nucleation is favoured during silicon growth due to the low-level twin energy of formation. As a consequence, in all solidification process, a large amount of grain boundaries (GB) are in twin relationship. A 3D cellular automaton (CA) model has been recently developed for the growth of multi-crystalline silicon including facet formation and nucleation of new grains in twin relationship. Activation of facets is based on an undercooling parameter assigned to each grain and for each of the <111> crystal directions. The model also considers nucleation and growth of grains on <111> facets corresponding to Σ3 twin relationships between twin grains. This model is first applied to comparison with experimental observations. It is found that impingement of growing grains that nucleated in Σ3 twin relationships meet during growth and form Σ3, Σ9 and Σ27 GB, in good agreement with experimental observations. Finally, the model is applied at a larger scale to generate grain structures representative of industrial practice. While quantitative experimental data is missing for comparison at such scale, the model is promising and its implementation in heat and mass transfer models should be considered for assistance to production of silicon for solar cells dedicated to photovoltaic systems.