|
Applied Math Seminar
Surface Diffusion vs. the Ehrlich-Schwoebel Effect in Thin-film Growth
|
|
The surface of an epitaxially growing thin film often exhibits a mound-like structure with its characteristic lateral size increasing in time. In this talk, we consider two competing mechanisms for such a coarsening process: (1) surface diffusion described by high-order gradients of the surface profile; and (2) the Ehrlich-Schwoebel (ES) effect which is the asymmetry in the adatom (adsorbed atoms) attachment and detachment to and from atomic steps. We present a theory based on a class of continuum models that are mathematically gradient-flows of some effective free-energy functionals describing these mechanisms. This theory consists of two parts: (1) variational properties of the free energies, in particular, their large-system-size asymptotics, showing the unboundedness of surface slope and revealing the relation between some of the models; (2) rigorous bounds for the scaling law of the roughness, the rate of increase of surface slope, and the rate of energy dissipation, all of which characterize the coarsening process. |