Ion beam induced surface pattern formation and stable travelling wave solutions

Abstract

The formation of ripple structures on ion bombarded semiconductor surfaces is examined theoretically. Previous models are discussed and a new nonlinear model is formulated, based on the infinitesimal local atomic relocation induced by elastic nuclear collisions in the early stages of collision cascades and an associated density change in the near surface region. Within this framework ripple structures are shown to form without the necessity to invoke surface diffusion or large sputtering as important mechanisms. The model can also be extended to the case where sputtering is important, and it is shown that in this case certain 'magic' angles can occur at which the ripple patterns are most clearly defined. The results are in very good agreement with experimental observations.

Ripple structures on ion bombarded surfaces arising from the sputter yield dependence on incidence angle

“…The theory cannot explain how initial undulations in the surface height occur on a flat uniform surface since it is based on the idea that surface orientations are preserved under ion erosion but what it shows is that when certain preferred angles of orientation are formed they remain stable under erosion and in some circumstances initial undulations can be magnified. These stable structures are in some sense similar to the travelling wave solutions previously found [18] but without the need to invoke mass redistribution as a mechanism. We conclude that non-linear effects are highly significant to explain the stability of ripple patterns on ion bombarded surfaces.…”

“…In the case of [18] a travelling wave solution was found for a specific incidence angle for the non-linear equations of motion, in the form of a cycloid which matched experimental observations very well.…”

“…The stepped structures predicted in Fig. 5 are thus equivalent in some sense to the stable travelling wave solutions described in [18] but without the need to invoke mass redistribution as a mechanism for their formation. The theory cannot explain how initial undulations in the surface height occur on a flat uniform surface since it is based on the idea that surface orientations are preserved under ion erosion but what it shows is that when certain preferred angles of orientation are formed they remain stable under erosion and in some circumstances initial undulations can be magnified.…”

“…Carter and Vishnyakov [3] first proposed that instead of the micro-roughening proposal, mass redistribution could be the mechanism by which surface features may be formed and this argument has also been used by Madi et al [17] and by Numazawa and Smith [18] to show that ripple features can arise purely as a result of mass redistribution alone without even the necessity to use erosion in the argument. In the case of [18] a travelling wave solution was found for a specific incidence angle for the non-linear equations of motion, in the form of a cycloid which matched experimental observations very well.…”