A multilayer nucleation model for twinning during directional solidification of multi-crystalline silicon

Twin nucleation is an important phenomenon in the directional solidification of photovoltaic multi-crystalline silicon. Unfortunately, the models proposed so far were not sufficient to explain the small undercooling (<1 K) for twinning observed in the experiments. In this paper, we propose a multilayer nucleation mechanism for twinning during silicon directional solidification. When the nucleus contains more than one layer, the free energy of formation for the nucleus can be reduced. As a result, the critical radius decreases and the twinning probability increases. The required undercooling for twinning based on the present model could be reduced to around 0.4-0.6 K, which is much more consistent with the experimental observations.