Energetic ion bombardment of solid targets can lead to the production of atomic recoils and defects within the solid and the ejection or sputtering of atoms from the surface with the consequent erosion of the solid. The yield of sputtered atoms per ion depends on a number of ion and target parameters but, particularly, on the gradient of the surface with respect to the incident ion flux, the surface curvature and higher spatial derivatives of the height. As a result of these dependences of the local erosion rate, the morphology of a surface can be modified. But, in addition, surface atomic relaxation effects which may be mediated by the irradiation can occur and so the evolution of the surface may be complex. If the nature of these, often competing, processes is understood and can be suitably controlled by selection of experimental conditions, ion beam erosion can be employed to generate useful surface geometries. This review briefly summarizes current understanding of the sputtering process and the origin of the above dependences and describes how, if only a surface gradient related mechanism dominates, the evolution of surface geometry can be accurately predicted. The higher-order and surface relaxation processes are then considered in both a deterministic approach and in a stochastic approach and these are shown to lead to fine spatial scale modifications to evolving surfaces. In both these areas, the physical models are supported by experimental observations. It is then shown how the lowest and higher orders and competing mechanisms can be selected in order to produce the desired surface morphologies in several application areas, including depth profiling of impurities in solids, ion milling and polishing, and the creation of repetitive surface structures.

The morphology of surfaces, depending on the nature of their environment, may be altered by erosional and/or accretional processes. Analytic description of the changing topography is possible through a knowledge of a locally variable parameter, which is the surface motion velocity in an arbitrarily specified direction. For sputter-related processes in which this parameter is spatially and temporally invariant over specific regions of a surface (e.g. ion milling, reactive-ion etching), the evolution of those regions may be forecast by geometric methods. Inhomogeneity of this parameter, which would generally result from the secondary and tertiary effects of ion irradiation, tenders evolution predictable only by iterative computer techniques. This paper summarises the status of analytic, geometric and computer methods of macroscopic surface simulation and notes the suitability of computer methods for simulation at the atomic scale.