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 roughening with aeolian ripple formation in sandy deserts. We show that the two phenomena can be described within the same theoretical framework. This approach explains the different dynamical behaviors experimentally observed in metals or in semiconductors and amorphous systems. In the case of ion erosion, we find exponential growth at constant wavelength up to a critical roughness $W_c$. Whereas, in metals, by introducing the contribution of the Erlich-Schwoebel barrier, we find a transition from an exponential growth to a power law evolution.