COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics
(click here for colloquia)

Colloquium: Nonlinear Stability Analyses of Pattern Formation on Solid Surfaces during Ion-Sputterred Erosion at Normal


4:10 p.m. Neill Hall 5W

David Wollkind

Abstract The development of stationary equilibrium patterns on metallic or semiconductor solid surfaces during ion-sputtered erosion at normal incidence is investigated by means of various weakly nonlinear stability analyses applied to the appropriate governing equation for this phenomenon. In particular, that process can be represented by a damped Kuramoto-Sivashinsky nonlinear partial differential time-evolution equation describing the interfacial deviation from a planar surface. This governing evolution equation is defined on an unbounded two-dimensional spatial domain and includes a deterministic ion-bombardment arrival term. The etching of coherent ripples, rhombic arrays of rectangular mounds or pits, and hexagonal lattices of nanoscale quantum dots or holes during this erosion process is based upon the interplay of roughening caused by ion sputtering and smoothing due to surface diffusion. Then the theoretical predictions from these analyses are compared with both relevant experimental evidence and numerical simulations as well as placed in the context of some recent pattern formation studies.