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 I₀ as I₀^-1/3 in agreement with a model based on heat flow, interfacial surface tension, and the reflectivity difference of the solid and melt. When I₀ 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}.