Statistical simulation of pattern formation by ion-beam sputtering

Purpose - The purpose of this paper is to investigate the influence of ion-flow parameters on surface topography and making numerical simulation at the times when the process of surface erosion becomes strongly nonlinear. Design/methodology/approach - The base of the mathematical model of target ion-sputtering is nonlinear evolutionary equation in which the erosion velocity dependence on ion flux is evaluated by means of a Monte Carlo method. The difference between this equation and the one of continuum theory is that the ion flux is not smooth function. Instead, it is a set of separate incident ions. Findings - Some simulations with using independent random points of arrival for the incident ions leads to results uncorrelated with the continuum model at early times. The ripples are not quite developed or observed. This phenomenon is explained by random fluctuations of the target sputtering depth. Sufficiently big values of the random fluctuations destroy the ripple structure on target surface. The simulation with using equally distributed sequence (Holton sequence) of points of arrival for the incident ions leads to results well correlated with the continuum model. Originality/value - The discrete model which goes into the equation of continuum theory within the appropriate asymptotic limit has been proposed. The discretization parameters influence on surface morphology formation has been studied. This paper may be interesting to researchers making the theoretical and numerical analysis of pattern formation on plane target surfaces undergoing ion-beam sputtering.