The effect of crystalline anisotropy on pattern formation in laser-melted thin silicon films

Abstract

When heated radiatively, thin silicon films on a cooled substrate can develop partially melted regions consisting of alternating parallel bands of liquid and solid phases separated by planar solid-liquid interfaces. As the power of the heat source increases, the lamellar array can break down, giving rise to a corrugated set of interface patterns. In this work we investigate the effect of surface tension anisotropy on nonlinear, finite amplitude pattern formation, extending previous results that have only included the effect of isotropic surface tension. Using weakly nonlinear pertubation theory, we show that parallel lamellar interfaces may become unstable with respect to the development of a finite amplitude traveling wave, due to the anisotropy in surface tension. However, for lamella aligned in special crystallographic orientations (corresponding to extrema in the surface tension) instability is time-independent. In the latter case, using a simple model for anisotropic surface tension, we show that if the alignment of the lamellar interfaces is an orientation having less than the average value of the interfacial energy, then a pertubation of the most dangerous wavenumber will bifurcate subcritically from the planar state, provided that the surface tension anisotropy is above a critical value. Furthermore, for larger anisotropy, the subcritical behavior becomes increasingly more severe. For those lamellar arrays having interfaces initially of higher than average interfacial energy, bifurcation of the most dangerous wavenumber is supercritical. By using a boundary integral method to obtain steady-state numerical solutions for nonplanar solid-liquid interfaces and by using eigenvalue calculations to determine the linear stability of the nonplanar interface shapes, we show the manner in which anisotropic surface tension alters the stability of shapes and influences the interaction between unstable modes.