Second Order Corrections To The Sputter Yield Of A Curved Surface

We study the sputter yield Y of a curved surface that is struck by a normally incident ion for radii of curvature that are large compared to the size of the collision cascade. The leading order correction to Y is proportional to the mean curvature H at the point of impact. We demonstrate analytically that there are two second order corrections to Y. One of these is proportional to H-2 and the other is proportional to the Gaussian curvature at the point of impact. The predictions of the theory are compared to the results of Monte Carlo simulations of the sputtering of a variety of silicon surface morphologies for three different noble gas ion species and three ion energies. We find that including the second order correction terms considerably extends the range of radii of curvature for which the approximate formula for Y is applicable. Finally, we highlight our theory's implications for nanoscale pattern formation on an initially flat solid surface that is bombarded with a broad ion beam.