Explosive crystallization in the presence of melting

Received 18 January 2006; published 24 May 2006 An experimental investigation of explosive crystallization EC of thin amorphous Ge films deposited on a solid substrate is performed, and a theory of EC front propagation accompanied by melting in a class of films that includes Ge films is developed. The experiments show that the propagation of a planar EC front is possible for a certain range of substrate temperatures and film thicknesses. It is found that for substrate temperatures larger than a certain threshold, the macroscopically planar front leaves behind a columnar microstructure in the crystal. The theory of EC front propagation is based on the experimental observation that the propagating front exhibits a thin layer of Ge melt between the amorphous and crystalline phases. A uniformly propagating planar front solution is determined, whose propagation speed is found as a function of the substrate temperature and the heat loss parameter that, in turn, depends on the film thickness. A linear stability analysis of the uniformly propagating EC front with a melting layer is performed. It is found that in a certain interval of substrate temperatures the EC front undergoes a monotonic morphological instability with a preferred wave number that explains the formation of the columnar structures observed in experiments. We also perform a nonlinear analysis describing the evolution of the morphological instability. The interval of substrate temperatures for which the instability is observed, as well as the wavelength of the columnar structure, are found to be in good agreement with experimental observations.