A multiscale crater function model for ion-induced pattern formation in silicon

The ion-induced formation of nanometer-scale ripples on semiconductors, long known as the sputter erosion surface instability, is explained using a coupled atomistic-continuum framework. Molecular dynamics simulations of individual medium energy ion impacts on an amorphous silicon target show that the average effect of an incident ion is to leave an ångström-scale crater-like impression on the surface, complete with a crater rim. The summation of many such impacts on a micron-scale surface, combined with the smoothing effect of surface diffusion, leads to the formation of surface ripples aligned perpendicular to the projected ion beam direction. The same numerical approach can be used to evaluate the standard analytical model for this process, known as the Bradley-Harper model. Both Bradley-Harper surface evolution and the atomistically determined crater function surface evolution are computed over time under conditions similar to those for known experimental data. The results show that the surface mass rearrangement associated with the finite atomistic crater rims explains a key experimental observation, ripple amplitude saturation, which cannot be accurately explained using the Bradley-Harper model or any other known numerical or analytical model for the sputter erosion surface instability.