Nanoscale model of surface erosion by ion bombardment

Abstract

The model of surface topography evolution during ion bombardment is developed. In contrast to the conventional approach, surface topography is considered a superposition of microscopic and submicron contours. The sputtering yield is treated as a function of the bombardment angle and surface deviation from the microscopic contour in points of primary ion implantation and secondary ion ejection. These improvements, subject to the surface inclination in the implantation point, result in two expressions, one of which is a known erosion equation of hyperbolic type. This equation describes the microscopic topography development whereas the other, relating to a class of delay equations, models the evolution of surface submicron topography. The proposed model, allowing piecewise continuous and smooth or periodic solutions simultaneously, explains a more wide class of experimentally observed phenomena than the conventional erosion equations of hyperbolic type. It is shown that the delay equation predicts wave solutions whose domain of existence coincides with the experimentally observed picture of nanowave generation during the silicon sputtering by ions.