Ion beam induced surface pattern formation and stable travelling wave solutions

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.