Surface instability and pattern formation by ion-induced erosion and mass redistribution

The contribution of curvature dependent sputtering and mass redistribution to ion-induced self-organized formation of periodic surface nanopatterns is revisited. Ion incidence angle-dependent curvature coefficients and ripple wavelengths are calculated from 3-dimensional collision cascade data obtained from binary collision Monte Carlo simulations. Significant modifications concerning mass redistribution compared to the model of Carter and Vishnyakov and also models based on crater functions are introduced. Furthermore, I find that curvature-dependent erosion is the dominating contribution to pattern formation, except for very low-energy irradiation of a light matrix with heavy ions. The major modifications regarding mass redistribution and ion-induced viscous flow are related to the ion incidence angle-dependent thickness of the irradiated layer. A smaller modification concerns the relaxation of inward-directed mass redistribution. Ion-induced viscous flow in the surface layer also depends on the layer thickness and is thus strongly angle dependent. Simulation results are presented and compared to a variety of published experimental results. The simulations show that in most cases curvature-dependent erosion is the dominant contribution to surface instability and ripple pattern formation and also determines the pattern orientation transition. The simulations predict the occurrence of perpendicular ripple patterns at larger ion incidence angles, in agreement with experimental observations. Mass redistribution causes stabilization of the surface at near-normal ion incidence angles and dominates pattern formation only at very low ion energies.