Analysis of Island Dynamics in Epitaxial Growth of Thin Films

This work is concerned with analysis and refinement for a class of island dynamics models for epitaxial growth of crystalline thin films. An island dynamics model consists of evolution equations for step edges (or island boundaries), coupled to a diffusion equation for the adatom density, on an epitaxial surface. The island dynamics model with irreversible aggregation is confirmed to be mathematically ill-posed, with a growth rate that is approximately linear for large wavenumbers. By including a kinetic model for the structure and evolution of step edges, the island dynamics model is made mathematically well-posed. In the limit of small edge Péclet number, the edge kinetics model reduces to a set of boundary conditions, involving line tension and one-dimensional surface diffusion, for the adatom density. Finally, in the infinitely fast terrace diffusion limit, a simplified model of one-dimensional surface diffusion and kink convection is derived and found to be linearly stable.