Model for roughening and ripple instability due to ion-induced mass redistribution [Addendum to H. Hofsäss, Appl. Phys. A 114 (2014) 401, “Surface instability and pattern formation by ion-induced erosion and mass redistribution”]

Carter and Vishnyakov introduced a model (CV model) to describe roughening and ripple instability due to ion-induced mass redistribution. This model is based on the assumption that the irradiated surface layer on a static solid substrate is described by a viscous incompressible thin film bound to the substrate by a “no slip” and “no transport” kinematic boundary condition, i.e. similar to a thin film of viscous paint. However, this boundary condition is incomplete for a layer under ion irradiation. The boundary condition must allow exchange of atoms between the substrate and the irradiated film, so that the thickness of the film is always determined by the size of the collision cascade, independent of the evolution of the surface height profile. In addition, the film thickness depends on the local ion incidence angle, which leads to a time dependence of the film thickness at a given position. The equation of motion of the surface and interface profiles for these boundary conditions is introduced, and a new curvature-dependent coefficient is found which is absent in the CV model. This curvature coefficient depends on the angular derivative of the layer thickness and the atomic drift velocity at the film surface induced by recoil events. Such a stabilizing curvature coefficient was introduced in Appl. Phys. A 114 (2014) 401 and is most pronounced at intermediate angles.