Stochastic Model for Surface Erosion Via Ion-Sputtering: Dynamical Evolution from Ripple Morphology to Rough Morphology

TL;DR

This paper introduces a stochastic model for ion-sputtering surface erosion that explains the transition from ripple to rough morphologies, linking experimental observations to a noisy Kuramoto-Sivashinsky equation.

Contribution

The paper presents a unified stochastic framework that captures the morphological evolution of eroded surfaces from ripples to roughness, connecting discrete models to continuum equations.

Findings

Initial ripple morphology transitions to self-affine roughness over time

Surface evolution can be described by a noisy Kuramoto-Sivashinsky equation

The model unifies experimental observations within a single theoretical framework

Abstract

Surfaces eroded by ion-sputtering are sometimes observed to develop morphologies which are either ripple (periodic), or rough (non-periodic). 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.