Ripples and ripples: from sandy deserts to ion-sputtered surfaces

We study the morphological evolution of surfaces during ion sputtering and we compare their dynamical corrugation with aeolian ripple formation in sandy deserts. We show that, although the two phenomena are physically different, they must obey similar geometrical constraints and therefore they can be described within the same theoretical framework. The present theory distinguishes between atoms that stay bounded in the bulk and others that are mobile on the surface. We describe the excavation mechanisms, the adsorption and the surface mobility by means of a continuous equation derived from the study of dune formation on sand. We explore the spontaneous development of ordered nanostructures and explain the different dynamical behaviours experimentally observed in metals or in semiconductors or in amorphous systems. We also show that this novel approach can describe the occurrence of rotation in the ripple direction and the formation of other kinds of self-organized patterns induced by changes in the sputtering incidence angle.