Nano-patterning of Surfaces by Ion Sputtering: Numerical Study of the Damping Effect on the Anisotropic Kuramoto-Sivashinsky Equation

Abstract

This paper presents a numerical approach to a model describing the pattern formation by ion beam sputtering on a material surface. This process is responsible for the appearance of unexpectedly organized patterns, such as ripples, nanodots and hexagonal arrays of nanoholes. A numerical analysis of preexisting patterns is proposed to investigate surface dynamics, based on a model derived from a anisotropic damped Kuramoto-Sivashinsky equation, in a two dimen- sional surface with periodic boundary conditions. While deterministic, its highly nonlinear character gives a rich range of results, making it possible to describe accurately different patterns. A finite-difference semi-implicit splitting scheme is employed on the discretization of the governing equation. Simulations were conducted with realistic coefficients related to physical parameters (anisotropies, beam orientation, diffusion). The stability of the numerical scheme is verified with time step and grid spacing tests for the pattern evolution. Hexagonal patterns were obtained from a monomodal initial condition for a higher value of the damping coefficient a, while spatiotemporal chaos appeared for lower values. The hexagonal ordered character of the structure was shown to be directly proportional to a.