Prediction of ion-induced nanopattern formation using Monte Carlo simulations and comparison to experiments

Abstract

Ion induced nanopattern formation has been experimentally investigated for many different ion-target combinations and different ion irradiation conditions. Several theories and models have been developed throughout the past few years to explain the observed boundary conditions for pattern formation as well as features of the patterns like wavelengths, growth rates, shapes, and amplitudes. To compare specific experiments with the predictions of analytical theories, it is necessary to calculate the linear and non-linear coefficients of the respective equation of motion of a surface profile. Monte Carlo simulations of ion–solid interactions based on the binary collision approximation provide a very fast, rather universal, and accurate way to calculate these coefficients. The universality expresses the broad range of ion species, ion energies, and target compositions accessible by the simulations. The coefficients are obtained from the moments of calculated crater functions, describing ion erosion, mass redistribution, and ion implantation. In this contribution, we describe how most linear, non-linear, and higher order coefficients can be determined from crater function moments. We use the obtained data to compare the results of selected experimental studies with the predictions of theoretical models. We find good quantitative agreement, e.g., for irradiation of Si with Ar and Kr ions, Al2O3 with Ar and Xe ions, and amorphous carbon with Ne ions.