Stochastic model for surface erosion via ion sputtering: Dynamical evolution from ripple morphology to rough morphology.

Surfaces eroded by ion sputtering are sometimes observed to develop morphologies which are either ripple (periodic) or rough (nonperiodic). We introduce a discrete stochastic model that allows us to interpret these experimental observations within a unified framework. We find that a periodic ripple morphology characterizes the initial stages of the evolution, whereas the surface displays self-affine scaling in the later time regime. Further, we argue that the stochastic continuum equation describing the surface height is a noisy version of the Kuramoto-Sivashinsky equation.