Facet formation and coarsening modeled by a geometric evolution law for epitaxial growth

We consider surface modulations in epitaxial growth and study the formation of facets. Thereby the dynamics is assumed to be essentially interface-controlled and driven by a strongly anisotropic surface energy together with the incoming flux and modeled by a geometric evolution equation, which leads to facets and corners in the corresponding Wulff-shape. This interface evolution law, which is derived from a curvature dependent interfacial energy, is solved numerically using parametric finite elements. The numerical results indicate two basic stages for the formation of facets and corners. First, a rather periodic structure of hills and valleys is formed, being in agreement with the most unstable wavelength of the linearized dynamics. At the second stage, three distinct morphologies emerge, depending on the growth rate of the surface: faceting and coarsening occurs, periodic patterns emerge, or the surface becomes rough. Moreover, in the first case, the only coarsening event is a kink ternary, i.e. a coalescence of two kinks and one antikink resulting in a kink.