Stability and symmetry of ion-induced surface patterning

Christopher S R Matthes,Daniel Walgraef,Nasr M Ghoniem

doi:10.1186/s41313-017-0005-1

Abstract

We present a continuum model of ion-induced surface patterning. The model incorporates the atomic processes of sputtering, re-deposition and surface diffusion, and is shown to display the generic features of the damped Kuramoto-Sivashinsky (KS) equation of non-linear dynamics. Linear and non-linear stability analyses of the evolution equation give estimates of the emerging pattern wavelength and spatial symmetry. The analytical theory is confirmed by numerical simulations of the evolution equation with the Fast Fourier Transform method, where we show the influence of the incident ion angle, flux, and substrate surface temperature. It is shown that large local geometry variations resulting in quadratic non-linearities in the evolution equation dominate pattern selection and stability at long time scales.

Highlights

The erosion of surface material by ion sputtering is a fundamental process, which leads to the formation of surface roughness and patterns at the nanoscale
We develop a numerical method to describe the evolution of surface patterns, where the competition between erosion, redeposition, and surface diffusion is considered
When an obliquely-incident ion bombards the surface, it initiates a collision cascade downstream, leading to the removal of surface atoms that are energized by the Primary Knock-on Atom (PKA)

Summary

Introduction

The erosion of surface material by ion sputtering is a fundamental process, which leads to the formation of surface roughness and patterns at the nanoscale. While a fraction of the ejected atoms may find their way back to be deposited on the surface, the majority travel farther away as the surface is eroded The result of such atomistic events is a complex process of roughening, pattern formation, erosion and re-deposition; all of which have the ingredients of producing pattern-forming instabilities (Makeev et al 2002). If the surface location where the cascade initiates is concave (a local trough), more surface atoms will be closer to the PKA position than a convex surface, and more material will be removed This fundamental idea was introduced by Bradley and Harper (1988), and it obviously leads to surface instabilities, since troughs will continue to be deeper as disproportionately more atoms are removed. The presented study, is constrained to the primary known mechanisms for modeling ion sputtering, including curvature-induced erosion, temperature-induced surface diffusion, and the effect of nonlinearities and linear damping

Objectives

Methods

Conclusion