Phase boundaries of nanodots and nanoripples over a range of collision cascades

Abstract

One of the open problems of the formation and evolution of the nanostructures on solid surfaces that are driven by particle irradiation is whether all the nano-patterns can be accounted for by the continuum theory, since the Cuerno-Barabasi continuum theory explanations have thus far focused mainly on ripple patterns and rough self-affine scaling. In this article, we extend continuum theoretical calculations based on the nonlinear Cuerno-Barabasi theory to regions yet unexplored in the continuum theory literature but recently shown, in Monte Carlo simulations, to be devoid of ripple patterns. We obtained results of weighted ion penetrations and for different impingement angles. Our results show that the balance of sputtering coefficients required for ripple patterns was never attained in this region, which confirmed that ripple patterns are indeed absent and that the continuum theory does not fail as previous studies indicated. In particular our results show a remarkable agreement between the continuum and the discrete (solid-on-solid) models; by calculations based on the continuum theory cascade parameters alone, we obtained the same topographic phase diagram predicted in the recent Monte Carlo simulation studies.