The influence of the surface slope on ion induced mass drift

The irradiation of solids with energetic ions can lead to the formation of periodic ripples on the surface. Furthermore, the wavevector of the ripples turns from parallel to perpendicular to the projected ion beam direction as the incidence angle increases beyond a critical angle. Here, we want to investigate this phenonemon theoretically by examination of the so called crater function.

The crater function is the average surface height change per single ion impact averaged over a stochastically representative number of ion impacts, each hitting an undisturbed target. It describes a mean mass drift that is induced by the impingment. Obviously, the crater function is symmetric to the projected ion beam direction when it is incident on a horizontal plane. But, if the beam is incident on a tilted plane the crater function is rotated and becomes asymmetric resulting in a mass drift up or down the slope.

By mathematical treatment, we give a condition on that mass can drift up the slope leading to an instability. It is shown with the help of atomistic simulations that this condition is fulfilled for gracing incidence. This explains the change in ripple orientation for increasing incidence angle as the flank of longitudinal ripples can be seen as tilted planes in a first order approximation.