High-Order Surface Relaxation vs. the Ehrlich-Schwoebel Effect in Thin-film Growth
UCSD Department of Mathematics
The surface of an epitaxially growing thin film often exhibits amound-like structure with its characteristic lateral size increasingin time. In this talk, we consider two competing mechanisms forsuch a coarsening process: (1) surface relaxation described byhigh-order gradients of the surface profile; and (2) the Ehrlich-Schwoebel(ES) effect which is the upper-lower terrace asymmetry in the adatomattachment and detachment to and from atomic steps. We present atheory based on a class of continuum models that are mathematicallygradient-flows of some effective free-energy functionals describingthese mechanisms. This theory consists of two parts: (1) variationalproperties of the energies, such as ``ground states' and theirlarge-system-size asymptotics, showing the unboundedness of surfaceslope and revealing the relation between some of the models;(2) rigorous bounds for the scaling law of the roughness, the rate ofincrease of surface slope, and the rate of energy dissipation, all ofwhich characterize the coarsening process. Predictions on scalinglaws made by our theory agree well with experiments.
Tuesday, September 26, 2006
11:00AM AP&M 2402
Center for Computational Mathematics9500 Gilman Dr. #0112La Jolla, CA 92093-0112Tel: (858)534-9056