Sputter yields of surfaces with nanoscale textures: Analytical results and Monte Carlo simulations

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.