Influence of collision cascade statistics on pattern formation of ion-sputtered surfaces

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.

Self-organized nanopatterning of silicon surfaces by ion beam sputtering

“…In summary, higher-order linear and non-linear refinements of the original BH equation not only may be of a limited physical applicability, but are also affected by issues on mathematical consistency. Note that probably this is not necessarily due to the approximations involved in Sigmund's Gaussian description of energy deposition: As seen for exponential [226] as well as for more general [203] energy deposition functions, the main qualitative pattern-forming properties are essentially unchanged as compared with those induced by Gaussian decay. Actually, as has been recently discussed, [212,211], formula (4) relating the local surface velocity with collisional energy deposition is morphologically unstable at all length scales.…”

Coupling of morphology to surface transport in ion-beam-irradiated surfaces: normal incidence and rotating targets

“…As mentioned above, for typical distributions of energy deposition, α 2 is a positive number [2,12,23] and therefore ν < 0. Thus, just as in the KS system, equation (6) features a band of linearly unstable Fourier modes h k (t) exp(ω k t), associated with k values that make the dispersion relation ω k = −νk 2 − Kk 4 a positive number.…”

On the stabilization of ion sputtered surfaces

“…Indeed, the recent simulations of Cu crystals bombarded by 5 keV Cu + ions 17 by Feix et al have demonstrated energy distributions with a maximum along an annulus surrounding the ion trajectory. Such a response is, thus, characterized by a g͑r͒ with a minimum at r min = r 0 Ͼ 0.…”