Dynamic scaling of ion-sputtered rotating surfaces

Surfaces eroded by off-normal incidence ion bombardment often have a rippled topography, and this is undesirable in a number of applications. Sample rotation during sputtering inhibits or prevents surface roughening and is widely used in precision depth profiling. In this paper, I study the surface roughening of a sample that is simultaneously rotated and sputtered in the limit in which viscous flow can be neglected. I find that the structure of the surface depends on the sign of a parameter characterizing the curvature dependence of the sputter yield, μₐᵥ. For μₐᵥ>0, the asymptotic scaling behavior of the surface is in the same universality class as the Kardar-Parisi-Zhang equation in 2+1 dimensions. At long times the surface is composed of a patchwork of paraboloids of revolution whose mean lateral dimension grows algebraically in time, a topography quite reminiscent of those observed experimentally. In contrast, the interface has a chaotic cellular structure described by the isotropic Kuramoto-Sivashinsky equation if μₐᵥ<0. The mean cell width is constant in time in this case.