Dynamics of ripple formation in sputter erosion: nonlinear phenomena

Many morphological features of sputter eroded surfaces are determined by the balance between ion induced linear instability and surface diffusion. However, the impact of the nonlinear terms on the morphology is less understood. We demonstrate that while at short times ripple formation is described by the linear theory, after a characteristic time the nonlinear terms determine the surface morphology by either destroying the ripples, or generating a new rotated ripple structure. We show that the morphological transitions induced by the nonlinear effects can be detected by monitoring the surface width and the erosion velocity.