Amorphous-crystalline boundary dynamics in cw laser crystallization

Two theoretical descriptions have been developed for the phase-boundary dynamics during crystallization of amorphous films by scanning with the slit image of a cw energy beam. The first reduces the problem to the solution of a one-dimensional integral equation, which allows a choice of initial conditions. Depending on the background temperature, numerical solutions yield either periodic or runaway motion of the amorphouscrystalline ($a-c$) boundary, as observed in experiments on scanned laser crystallization of thin films of $a$-Ge on fused-silica substrates. The calculations give a semiquantitative fit to the experimental results for the spatial periodicity observed in the crystallized films as a function of background temperature. Profiles of film temperature as a function of distance from the laser image at successive times have been computed for both the periodic and runaway cases. The model qualitatively explains many of the effects observed during scanned cw laser crystallization, including periodic fluctuations in light emission. The second theoretical description is a more exact two-dimensional treatment applicable only to cases of steady-state motion of the $a-c$ boundary, which can rigorously handle heat flow into the substrate. This treatment has been used to calculate the boundary velocity during steady-state runaway. The dependence of this velocity on background temperature and on film and substrate thermal properties and thickness has been determined from the theory. At the minimum background temperature required for runaway the calculated value of the steady-state velocity $v_{\mathrm{ac}}$ is $\sim 140$ cm/sec for the case of a Ge film 0.3-μm thick on a fused-silica substrate 1-mm thick. Experimental values for $v_{\mathrm{ac}}$ lie in the range 100-300 cm/sec. However, comparison of the theory with experiment suggests the presence of a thermal barrier between substrate and film, which would modify the theoretical results for $v_{\mathrm{ac}}$. A class of laser-guided steady-state solutions has been obtained for which the boundary velocity is equal to the laser scanning velocity but lower than the boundary velocity for uncontrolled runaway.