Influence of Collision Cascade Statistics on Pattern Formation of Ion-Sputtered Surfaces

TL;DR

This paper investigates how deviations from Sigmund's energy distribution in ion sputtering affect surface pattern formation, revealing a non-monotonous sputtering yield dependence on incidence angle through simulations and a modified theoretical model.

Contribution

It introduces a modified continuum theory accounting for non-Gaussian energy distributions observed in Cu crystal sputtering simulations.

Findings

Energy deposition has a minimum at ion penetration point.

Decay of energy deposition is exponential, not Gaussian.

Sputtering yield peaks at non-grazing angles.

Abstract

Theoretical continuum models that describe the formation of patterns on surfaces of targets undergoing ion-beam sputtering, are based on Sigmund's formula, which describes the spatial distribution of the energy deposited by the ion. For small angles of incidence and amorphous or polycrystalline materials, this description seems to be suitable, and leads to the classic BH morphological theory [R.M. Bradley and J.M.E. Harper, J. Vac. Sci. Technol. A 6, 2390 (1988)]. Here we study the sputtering of Cu crystals by means of numerical simulations under the binary-collision approximation. We observe significant deviations from Sigmund's energy distribution. In particular, the distribution that best fits our simulations has a minimum near the position where the ion penetrates the surface, and the decay of energy deposition with distance to ion trajectory is exponential rather than Gaussian. We provide a modified continuum theory which takes these effects into account and explores the implications of the modified energy distribution for the surface morphology. In marked contrast with BH's theory, the dependence of the sputtering yield with the angle of incidence is non-monotonous, with a maximum for non-grazing incidence angles.