Phase-field modeling of the morphological evolution of ringlike structures during growth: Thermodynamics, kinetics, and template effects

Understanding and controlling the morphology of crystals growing from prepatterned shapes, as in selective-area epitaxy, is fundamental for the development of novel device architectures. Here, an in-depth analysis of the faceted growth of ring-shaped crystal structures is presented. This is a prototypical case for assessing the role of thermodynamic and kinetic driving forces, as they induce different faceting between the outer convex region and the inner concave one. The well-established concepts of equilibrium crystal shape, set by surface energy minimization, and its kinetic counterpart, determined by orientation-dependent growth rates, provide a qualitative indication of the outcome of growth experiments. However, they are insufficient to capture the whole evolution pathway. A phase-field growth model including deposition, incorporation, and surface diffusion dynamics is considered, and extensive two- and three-dimensional simulations are performed. A continuum transition in the crystal morphology is recognized by varying the magnitude of the anisotropic surface energy vs the incorporation times. The in-depth analysis of a realistic case, mimicking experiments in the literature, highlights the prominent role of kinetics and of material redistribution from the outer to the inner perimeter of the ring. Finally, the templating effect of the initial pattern is investigated by considering polygonal profiles with different orientations, showing their effect on the facet formation and evolution.