Roughening of ion-eroded surfaces

TL;DR

This paper develops a stochastic growth equation to explain surface morphologies resulting from ion bombardment, revealing conditions for transitions between fractal and ripple structures, and provides analytical and numerical insights into surface roughening.

Contribution

It introduces a new stochastic growth model for ion-eroded surfaces, connecting physical parameters to surface morphology and transitions, with analytical and numerical analysis.

Findings

Morphological transitions depend on ion incidence angle and penetration depth.

Analytical calculation of ion-induced surface diffusion coefficient.

Numerical simulations illustrate ripple formation and surface roughening.

Abstract

Recent experimental studies focusing on the morphological properties of surfaces eroded by ion-bombardment report the observation of self-affine fractal surfaces, while others provide evidence about the development of a periodic ripple structure. To explain these discrepancies we derive a stochastic growth equation that describes the evolution of surfaces eroded by ion bombardment. The coefficients appearing in the equation can be calculated explicitly in terms of the physical parameters characterizing the sputtering process. Exploring the connection between the ion-sputtering problem and the Kardar-Parisi-Zhang and Kuramoto-Sivashinsky equations, we find that morphological transitions may take place when experimental parameters, such as the angle of incidence of the incoming ions or their average penetration depth, are varied. Furthermore, the discussed methods allow us to calculate analytically the ion-induced surface diffusion coefficient, that can be compared with experiments. Finally, we use numerical simulations of a one dimensional sputtering model to investigate certain aspects of the ripple formation and roughening.