Analysis of a geometric evolution equation for modeling the morphology of anisotropic thin films

The morphology of the solid-vapor interface of a nano-scale thin crystalline film is influenced by many factors. We consider an interface whose evolution is governed by surface diffusion, attachment-detachment, deposition and kinetic effects, and we present and analyze a geometric evolution equation to model the interface morphology under these effects. Previous studies have only considered some of these effects individually. Our study includes results for a closed interface in the shape of a perturbed circle and an open interface in the shape of a perturbed horizontal line. We perform a detailed linear stability analysis of the closed curve which reveals the need for a regularizing term in the presence of strong anisotropy.;We also derive a general convective Cahn-Hilliard-type equation which represents the long-wave approximation for the geometric evolution equation used in our analysis. We present a number of simulations for both the closed curve and the open curve using a numerical method in which the tangent angle theta and the curve length L are the dynamical variables. The simulations for the open curve show that the inclusion of an attachment-detachment term leads to additional coarsening compared to the dynamics that result from driven surface diffusion without attachment-detachment. It is known that the amount of deposition taking place leads to different coarsening regimes: fast-coarsening, periodic structures or chaotic behavior. It is also known that kinetic effects in the absence of deposition slow down the dynamics of the evolving interface. We show numerically that when deposition and kinetics are both considered, the kinetic effects necessitate a decrease in the deposition rate in order to produce a desired coarsening regime. Our numerical results also demonstrate kink-ternary behavior, wherein two kinks always annihilate an anti-kink. We perform a matched asymptotic analysis for the open curve and show analytically that the kink-ternary is the only possible coarsening event for our model when deposition is present.