Analysis of a solid-on-solid type block model for particle redeposition in ion-beam erosion processes under normal incidence

In this paper we present and investigate a simple yet physically plausible solid-on-solid type block model for the redeposition of eroded particles during ion-beam erosion processes under normal ion incidence. This model, which is based on a more general version presented in an earlier study, focuses on the very essential aspects of what one will commonly associate with the redeposition of sputtered particles. Other potential surface effects such as the Bradley-Harper mechanism are thus not taken account of. Additionally, the model is kept one-dimensional for reasons of simplicity. We introduce that model in detail, and then discuss its properties thoroughly. In particular, we show how to decouple the erosion and redeposition component in the formal description of the evolution process of the sputtered surfaces in order to derive a semi-analytical continuum approximation for both the erosion and the redeposition subprocess. The latter is investigated at length, and eventually a connection is drawn to the non-locally stabilized Kuramoto-Sivashinsky equation to discuss the potential role of particle redeposition as the physical origin of the damping term in that equation.