Ion-induced surface evolution in the linear instability regime: Continuum theory and kinetic Monte Carlo simulations

Low energy ion sputtering produces spontaneous pattern formation on many surfaces. A continuum theory that balances the processes of roughening by sputter removal of atoms and smoothing by surface diffusion of defects explains many features of the early stages of pattern formation. The sputtering is based on a mechanism proposed by Sigmund (1969, 1973) which couples the rate of atom removal to the local surface morphology. Results of kinetic Monte Carlo simulations of surface evolution using the Sigmund mechanism for sputtering are found to agree quantitatively with the predictions of the continuum theory in the linear regime. This suggests that the continuum theory correctly accounts for many of the essential physical mechanisms that lead to the initial formation of the ion-induced pattern.