On continuum modeling of sputter erosion under normal incidence: interplay between nonlocality and nonlinearity

TL;DR

This paper investigates a nonlocal, damped Kuramoto-Sivashinsky equation as a continuum model for sputter erosion, revealing its derivation, equivalence to a local form, and implications for erosion dynamics.

Contribution

It formally derives a nonlocal model from basic principles and shows its equivalence to a local damped Kuramoto-Sivashinsky equation, advancing understanding of pattern formation in sputter erosion.

Findings

Derived the nonlocal equation from balance considerations.

Proved the nonlocal model is exactly equivalent to a local damped Kuramoto-Sivashinsky equation.

Analyzed the effects of non-stationary erosion dynamics.

Abstract

Under specific experimental circumstances, sputter erosion on semiconductor materials exhibits highly ordered hexagonal dot-like nanostructures. In a recent attempt to theoretically understand this pattern forming process, Facsko et al. [Phys. Rev. B 69, 153412 (2004)] suggested a nonlocal, damped Kuramoto-Sivashinsky equation as a potential candidate for an adequate continuum model of this self-organizing process. In this study we theoretically investigate this proposal by (i) formally deriving such a nonlocal equation as minimal model from balance considerations, (ii) showing that it can be exactly mapped to a local, damped Kuramoto-Sivashinsky equation, and (iii) inspecting the consequences of the resulting non-stationary erosion dynamics.