Pattern Formation in Laser Induced Melting

A laser focussed onto a semiconductor film can create a disordered lamellae pattern of coexisting molten-solid regions. We present a continuum model based on the higher reflectivity of the molten regions. For large latent heat, this model becomes equivalent to a model of block copolymers. The characteristic wavenumber of the lamellae is that marginally stable to slow variations in the orientation (the zig-zag instability) and is obtained via systematic expansions from two limits. The lamellae can also be unstable to the zig-zag instability and Eckhaus instability simultaneously. This instability is a signal of dynamic steady states. We numerically study the behaviour after a quench. The lamellar size agrees with the analytic results and experiments. For shallow quenches, locally parallel stripes slowly straighten in time. For deep quenches, a disordered lamellae forms. We construct the director field and determine the orientational correlation length. Near onset the correlation is fixed by the system size. Far from onset the correlation length saturates at a finite value. We study the transition to the time-dependent asymptotic states with decreasing latent heat. postScript figures available on requestComment: 44 pages, revtex 3.