Nonlinear stability analyses of pattern formation on solid surfaces during ion-sputtered erosion

The development of spontaneous 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 for the interfacial deviation from a planar surface which includes a deterministic ion-bombardment arrival term and is defined on an unbounded spatial domain. 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 between 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.