Theory of nanodot and sputter cone arrays produced by ion sputtering with concurrent deposition of impurities

We advance a theory governing the early-time dynamics of an initially flat solid surface that is seeded with impurities during ion bombardment. The surface is destabilized if the impurity flux exceeds a critical value, leading to the formation of a disordered array of nanoscale mounds. The predicted dependence of the intermound spacing on the impurity flux and the sample temperature compares favorably with experimental studies of both sputter cones and impurity-seeded nanodots. Contrary to previous ideas about the genesis of sputter cones, we find that the impurities need not diffuse and agglomerate for cones to form---in fact, they can develop even if the impurities on the surface are completely immobile.