Nano-patterning of surfaces by ion sputtering: Numerical study of the anisotropic damped Kuramoto-Sivashinsky equation

TL;DR

This study numerically investigates surface pattern evolution under ion sputtering using an anisotropic damped Kuramoto-Sivashinsky equation, revealing pattern formation, chaos, and anisotropic effects influenced by physical parameters.

Contribution

It introduces a finite-difference semi-implicit scheme for simulating the anisotropic damped Kuramoto-Sivashinsky equation with realistic physical parameters.

Findings

Ripples and hexagonal patterns form under certain damping conditions.

Spatiotemporal chaos occurs at lower damping coefficients.

Anisotropy influences pattern orientation and evolution.

Abstract

Nonlinear models for pattern evolution by ion beam sputtering on a material surface present an ongoing opportunity for new numerical simulations. A numerical analysis of the evolution of preexisting patterns is proposed to investigate surface dynamics, based on a 2D anisotropic damped Kuramoto-Sivashinsky equation, with periodic boundary conditions. A finite-difference semi-implicit time 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 analyzed with time step and grid spacing tests for the pattern evolution, and the Method of Manufactured Solutions has been used to verify the proposed scheme. Ripples and hexagonal patterns were obtained from a monomodal initial condition for certain values of the damping coefficient, while spatiotemporal chaos appeared for lower values. The anisotropy effects on pattern formation were studied, varying the angle of incidence of the ion beam with respect to the irradiated surface. Analytical discussions are based on linear and weakly nonlinear analysis.