Locking of optical and thermodynamic length scales in laser-induced melt-solid patterns on silicon

We show that the time-independent disordered solid-melt patterns induced on silicon thin films by a continuous laser beam possess a characteristic length scale Λ which varies with irradiance ${\mathit{I}}_0$ as ${\mathit{I}}_0^{\mathrm{-}1/3}$ in agreement with a model based on heat flow, interfacial surface tension, and the reflectivity difference of the solid and melt. When ${\mathit{I}}_0$ is varied so that Λ decreases to a value comparable to λ, optical interference effects enhance (reduce) power deposition in molten (solid) regions, forcing a transition to a grating structure with orientation parallel to the polarization of the light beam and locking the length scale to Λ=λ.