Using a theoretical analysis of the ion beam sputtering dynamics, we demonstrate how ion bombardment on an initially sloped surface can create knife-edge-like ridges on the surface. These ridges arise as nonclassical shock-like solutions that are undercompressive on both sides, and appear to control the dynamics over a large range of initial conditions. The slope of the ridges is selected uniquely by the dynamics, and can be up to 30 or more depending on the orientation dependence of the

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... ing yield. For 1keV Ar + on Si(001), the scale of the ridge is ≈ 2nm. This is much smaller than the most unstable lengthscale and suggests a method for creating very steep, very sharp features on a surface spontaneously, by pre-patterning the surface to contain relatively modest slopes on the macroscale.