Application of the Monte Carlo Method for Simulation of Pattern Formation by Ion-Beam Sputtering of Amorphous Bodies

Abstract

The formation of ordered structures by ion-beam sputtering of a surface of an amorphous body in the case when a strong nonlinearity has a significant effect on the morphology of the irradiated surface is studied. Three modifications of the Monte Carlo method are used for the numerical simulation of the process, and the first of them is a kind of imitational simulation. It is shown that the direct (imitating) statistical simulation of the ion bombardment of the surface of the target, which best matches the considered physical process and is widely used in other papers, has a serious disadvantage. In the case of imitational simulation, random fluctuations of the depth of the sputtering roughen the target surface to such an extent that none of the modes provided by the continuous model can be observed. It especially concerns the modes set after the long ion bombardment of the surface of the target. However, solutions of the continuous model can be investigated numerically by means of other modifications of the Monte Carlo method with decreased dispersion. Two of these modifications are developed in this paper. Applying these methods, under certain conditions, an ordered structure composed of hexagonally symmetrical hollows is obtained on the surface of the target after the target’s long-term exposure to irradiation by a normal ion beam.