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In the crater function approach to the erosion of a solid surface by a broadion beam, the average crater produced by the impact of an ion is used tocompute the constant coefficients in the continuum equation of motion for thesurface. We extend the crater function formalism so that it includes thedependence of the crater on the curvature of the surface at the point ofimpact. We then demonstrate that our formalism yields the correct coefficientsfor the Sigmund model of ion sputtering if terms up to second order in thespatial derivatives are retained. In contrast, if the curvature dependence ofthe crater is neglected, the coefficients can deviate substantially from theirexact values. Our results show that accurately estimating the coefficientsusing craters obtained from molecular dynamics simulations will requiresignificantly more computational power than was previously thought.

The crater function approach to ion-induced nanoscale pattern formation: Craters for flat surfaces are insufficient