Phase-field modeling for facet dendrite growth of silicon

Dendrite growth of silicon from its undercooled melt was investigated by using the phase-field model for a faceted crystal with anisotropic interfacial energy. The phase-field parameters at the thin interface limit were derived and used in the simulation. The accuracy of the model was estimated from the calculated equilibrium interface shape. The errors in anisotropy and Gibbs-Thomson coefficient were within 1% and 10%, respectively. The growth of a silicon crystal from its undercooled melt has been analyzed and it is shown that the shape of growing crystal changes from square-like to dendritic with increase of undercooling. In a facet dendrite growth the tip grows keeping its shape and the shape is the same regardless of undercooling or growth velocity. It is also shown that there exists the scaling law between the characteristic length of the tip and growth velocity similar to that of a non-facet dendrite.