Two-dimensional facet crystal growth of silicon from undercooled melt of Si–Ni alloy

The two-dimensional facet crystal growth of silicon from the undercooled melt of silicon–nickel alloys has been investigated using a phase-field model. The phase-field parameters derived at the thin interface limit and the anisotropic interface energy model proposed by Eggleston et al. have been used in the simulation. The calculated dendrite growth velocity depends on the interface width and the correct values are obtained when the interfacial Péclet number is sufficiently small. The growth velocity follows a power law relation to undercooling and the exponents are approximately two for Si–10 wt.% Ni alloy and approximately three for Si–20 wt.% Ni alloy. A dendrite grows maintaining its tip shape and a scaling law between the tip size of a dendrite and the growth velocity is confirmed. The phase-field simulations have been compared with the experimental data on the facet dendrite growth velocity in a thin liquid film of Si–6 wt.% Ni alloy and both are acceptable in agreement.