Theory of nanoscale pattern formation induced by normal-incidence ion bombardment of binary compounds

A theory is developed that explains the genesis of the strikingly regular hexagonal arrays of nanodots that can form when the flat surface of a binary compound is subjected to normal-incidence ion bombardment. We demonstrate analytically that nanodot arrays with short-range hexagonal order emerge spontaneously for a certain range of the parameters. In our theory, the coupling between the topography of the surface and a thin surface layer of altered composition is the key to the observed pattern formation. We find that the species with the higher sputter yield is concentrated at the peaks of the nanodots, and that an unforeseen smoothing mechanism suppresses the instability that would otherwise occur for small wave numbers. In a second range of the parameters, our simulations reveal that the nanodot arrays coarsen with the passage of time, as they sometimes do in experiments. Surface ripples are formed in yet another range of the parameters, even though the sample is subject to normal-incidence ion bombardment. Finally, if a transition is observed between the flat and the hexagonally ordered states as the sample temperature is varied, our theory predicts that the transition will be hysteretic.