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

摘要

Under specific experimental circumstances, sputter erosion on semiconductormaterials exhibits highly ordered hexagonal dot-like nanostructures. In arecent attempt to theoretically understand this pattern forming process, Facskoet al. [Phys. Rev. B 69, 153412 (2004)] suggested a nonlocal, dampedKuramoto-Sivashinsky equation as a potential candidate for an adequatecontinuum model of this self-organizing process. In this study we theoreticallyinvestigate this proposal by (i) formally deriving such a nonlocal equation asminimal model from balance considerations, (ii) showing that it can be exactlymapped to a local, damped Kuramoto-Sivashinsky equation, and (iii) inspectingthe consequences of the resulting non-stationary erosion dynamics.