Front propagation in self-sustained and laser-driven explosive crystal growth: Stability analysis and morphological aspects

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Abstract
We study a simple nonlinear-heat-conduction model for the dynamics of rapid crystallization of amorphous films, and provide a linear stability analysis of the steady-state solutions which describe the propagation with a constant velocity of a straight interface separating the crystalline and amorphous phases. Results are given for the case of self-sustained "explosive" crystallization as well as for the case of cw-laser-driven crystallization. The steady states of the model can have oscillatory instabilities, which result in periodic variations in the amorphous-crystalline interface velocity. For some ranges of the parameters the instability is morphological, so that the interface acquires a wavy shape, while for others it leaves the interface straight. We argue that these two types of instabilities will produce qualitatively different patterns of surface undulations on the crystallized films, similar to those seen in recent experiments on (In,Ga)Sb. Similarities and differences with the Mullins-Sekerka instability are discussed and the importance of interface kinetics for this instability is pointed out. The onset of the instability is predominantly determined by a parameter related to the activation energy for the amorphous-crystalline transition. Values of this stability parameter are given for Si, Ge, and Sb. The latter material appears to be close to the threshold for the instability and hence is best suited for an experimental test of our theory.