Mesoscale computational study of the nanocrystallization of amorphous Ge via a self-consistent atomistic phase-field model

Germanium is the base element in many phase-change materials, i.e. systems that can undergo reversible transformations between their crystalline and amorphous phases. These materials are widely used in current digital electronics and hold great promise for the next generation of non-volatile memory devices. However, the ultra-fast phase transformations required for these applications can be exceedingly complex even for single-component systems, and a full physical understanding of these phenomena is still lacking. In this paper we study the growth of crystalline Ge from amorphous thin films at high temperature using phase-field models informed by atomistic calculations of fundamental material properties. The atomistic calculations capture the full anisotropy of the Ge crystal lattice, which results in orientation dependences for interfacial energies and mobilities. These orientation relations are then exactly recovered by the phase-field model at finite thickness via a novel parametrization strategy based on invariance solutions of the Allen-Cahn equations. By means of this multiscale approach, we study the interplay between nucleation and growth and find that the relation between the mean radius of the crystallized Ge grains and the nucleation rate follows simple Avrami-type scaling laws. We argue that these can be used to cover a wide region of the nucleation rate space, hence facilitating comparison with experiments.