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We find the spatially averaged sputter yield Y¯ analytically for non-planar surfaces that have slowly varying surface heights h=h(x,y). To begin, nonlocal effects like redeposition of sputtered material and secondary sputtering are neglected. We show that the leading order corrections to Y¯ are proportional to the spatial averages of (∂h/∂x)2 and (∂h/∂y)2. The constants of proportionality can be written in terms of the first and second derivatives of the sputter yield of a flat surface with respect to the ion incidence angle θ. For a range of θ values, Y¯ is a decreasing function of the amplitude of the surface texture. We also determine how the contribution of redeposition to Y¯ depends on the amplitude and characteristic lateral length scale of the surface morphology. As a test of our theory and to quantify the roles of redeposition and secondary sputtering, we performed Monte Carlo simulations of sputtering from Si targets with sinusoidal surfaces by 1 keV Ar+ ions. The theory agrees remarkably well with our Monte Carlo simulations. Our simulations also lead to the notable result that atoms that are sputtered and then strike the surface can themselves cause significant sputtering. 

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 H2 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.