Sigmund's model of spatially resolved sputtering is the underpinning of many models of nanoscale pattern formation induced by ion bombardment. It is based on three assumptions: (i) the number of sputtered atoms is proportional to the nuclear energy deposition (NED) near the surface, (ii) the NED distribution is independent of the orientation and shape of the solid surface and is identical to the one in an infinite medium, and (iii) the NED distribution in an infinite medium can be approximated by a Gaussian. We test the validity of these assumptions using Monte Carlo simulations of He, Ar, and Xe impacts on Si at energies of 2, 20, and 200 keV with incidence angles from perpendicular to grazing. We find that for the more commonly-employed beam parameters (Ar and Xe ions at 2 and 20 keV and nongrazing incidence), the Sigmund model's predictions are within a factor of 2 of the Monte Carlo results for the total sputter yield and the first two moments of the spatially resolved sputter yield. This is partly due to a compensation of errors introduced by assumptions (i) and (ii). The Sigmund model, however, does not describe the skewness of the spatially resolved sputter yield, which is almost always significant. The approximation is much poorer for He ions and/or high energies (200 keV). All three of Sigmund's assumptions break down at grazing incidence angles. In all cases, we discuss the origin of the deviations from Sigmund's model.

• Received 9 November 2015
• Revised 9 March 2016

DOI:https://doi.org/10.1103/PhysRevB.93.205443