On the stabilization of ion sputtered surfaces

Abstract

The classical theory of ion beam sputtering predicts the instability of a flat surface to uniform ion irradiation at any incidence angle. We relax the assumption of the classical theory that the average surface erosion rate is determined by a Gaussian response function representing the effect of the collision cascade, and consider the surface dynamics for other physically motivated response functions. We show that although instability of flat surfaces at any beam angle results from all Gaussian and a wide class of non-Gaussian erosive response functions, there exist classes of modifications to the response that can have a dramatic effect. In contrast to the classical theory, these types of response render the flat surface linearly stable, while imperceptibly modifying the predicted sputter yield vs incidence angle. We discuss the possibility that such corrections underlie recent reports of a "window of stability" of ion-bombarded surfaces at a range of beam angles for certain ion and surface types, and describe some characteristic aspects of pattern evolution near the transition from unstable to stable dynamics. We point out that careful analysis of the transition regime may provide valuable tests for the consistency of any theory of pattern formation on ion sputtered surfaces.

Molecular dynamics of single-particle impacts predicts phase diagrams for large scale pattern formation

“…Whereas these effects have traditionally been treated separately by unrelated phenomenological models, viewing the crater function as fundamental integrates erosion and redistribution into a unified description, allowing both processes to be treated identically and readily separated and compared. Indeed, this approach has permitted us to confirm for the first time conjectures 11,19,22 that the stability of irradiated surfaces could be dominated by redistributive effects. The most striking aspect of this result is the logical conclusion that erosion is essentially irrelevant for determining the patterns: according to Figure 2 the contributions of redistribution to the S coefficients, which determine stability and patterns, are about an order of magnitude greater and opposite in sign.…”

“…Hence, it is important to be able to predict the expected behaviour within a given environment. Unfortunately, precisely which physical effects cause observed transitions between different regimes 9,10 has remained a matter of speculation 11 .…”

“…Displaced atoms that reach the surface with enough kinetic energy to leave are permanently sputtered away; all other displaced atoms come to rest within the solid or on the surface after phonon emission times of ~10 − 12 s. These processes contribute prompt erosive 14,15 and prompt redistributive 11,16,17 components of morphology evolution and are collectively denoted P [x].…”

“…21; here we provide a brief summary of the important points for the linear case. Given the crater function ∆h and the flux distribution I(x), we write the prompt contribution to surface evolution as a fluxweighted integral of the crater function 11,22 :…”

Surface instability and pattern formation by ion-induced erosion and mass redistribution

“…In the BH and CV theory, a gradient and curvaturedependent stochastic differential equation describes the stability (or instability) of a surface exposed to an oblique incident ion beam. According to recent publications by Madi et al [19], Davidovitch et al [20,21] and Norris et al [22], directed mass redistribution seems to be the dominating contribution to ripple pattern formation with ripple wave vectors parallel to the projected ion beam direction.…”