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

TL;DR

This study extends continuum theory to explain nanostructure formation on surfaces under particle irradiation, confirming the absence of ripple patterns in certain regions and aligning with recent Monte Carlo simulations.

Contribution

It demonstrates that the nonlinear Cuerno-Barabasi continuum theory accurately predicts phase boundaries of nanodots and nanoripples, even where ripple patterns are absent, aligning with discrete models.

Findings

Ripple patterns are absent in certain regions, as predicted by the extended continuum theory.

Continuum and discrete models show remarkable agreement in phase diagram predictions.

The continuum theory successfully explains nanostructure formation beyond previous limitations.

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.