Nonlinear stabilization mechanisms in amplitude saturation during sputter ripple formation on silicon

Sputter rippling refers to the formation of regular surface patterns during glancing incidence energetic ion beam etching of surfaces, usually as a result of a competition between etching (from the ion beam) and capillary action (driving smoothening via surface diffusion). Many different kinds of morphologies are often observed, including ripples oriented parallel and perpendicular to the projected ion beam direction and "quantum dots" arranged in hexagonal or rectangular arrays. Theoretical analyses of ripple evolution have concentrated on the initial stages of the surface instability leading to pattern formation, and the details associated with the nonlinear mechanisms leading to amplitude saturation and pattern stabilization remain a subject of active interest. The Si(I 11) surface is a single component surface with isotropic surface diffusion kinetics; for these reasons, this system provides a useful probe of surface evolution without complicating effects of compositional inhomogeneities and anisotropic terrace diffusion. Our examination of the Si(111) surface indicates that step-step interactions may play an important role in the evolution of sputter ripples in this system. To argue for this conclusion, a comparison with sputter ripple evolution on Si(001) is made.