Application of the Monte Carlo method for simulation of pattern formation by ion-beam sputtering the amorphous bodies

Formation of ordered structures at ion-beam sputtering a surface of amorphous bodies in case the strong nonlinearity has significant effect on morphology of the irradiated surface is studied. For numerical simulation of process three modifications of a Monte-Carlo method are used, first of which represents a kind of an imitating modeling. It is shown that direct (imitating) statistical simulation of ion-bombing of a surface of a target which best of all answers the considered physical process and is widely used in other works has an essential shortcoming. This shortcoming is that the casual fluctuations of the target sputtering depth in an imitating modeling lead to roughening of a surface which extent does not allow to observe those modes which follow from the continuous model. Especially it refers to the modes which are set after the long ion-radiation of a surface of a target. However, solutions of the continuous model can be investigated numerically by means of other modifications of a Monte-Carlo method with the under dispersion. Two such modifications are developed in this work. With their help the ordered structure from hollows with a hexagonal symmetry after the long radiation of a surface of a target by a normal stream of ions is under certain conditions received.