Propagation of ripples in Monte Carlo models of sputter-induced surface morphology

Abstract

Periodic ripples generated from the off-normal-incidence ion-beam bombardment of solid surfaces have been observed to propagate with a dispersion in the velocity. We investigate this ripple behavior by means of a Monte Carlo model of the erosion process, in conjuction with one of two different surface-diffusion mechanisms, representative of two different classes of materials; one is a Arrhenius-type Monte Carlo method including a term ͑possibly zero͒ that accounts for the Schwoebel effect, while the other is a thermodynamic mechanism without the Schwoebel effect. We find that the behavior of the ripple velocity and wavelength depends on the sputtering time scale, which is qualitatively consistent with experiments. Futhermore, we observe a strong temperature dependance of the ripple velocity, calling for experiments at different temperatures. Also, we observe that the ripple velocity vanishes ahead of the periodic ripple pattern.

Protein Adsorption on Nano-scaled, Rippled TiO2 and Si Surfaces

“…We calculated a value for the exponent m of 0.65 ± 0.15 for TiO 2 , which is above the value of m = 0.3 expected from the theory for ion-induced surface self-diffusion. However, the discrepancy can be explained by considering redeposition processes during the sputter process, which lead to a coarsening of the ripple wavelength over irradiation time [24,25]. For our Si reference sample set we obtained an exponent m of 0.5 ± 0.05 (see supplementary information), which is well in agreement with experimental data already published [26], obtained from irradiation with argon ions.…”

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

“…From the figure we can also conclude that qualitative behaviors of distributions (18) and (20) are similar, the advantage of the first one being its greater analytical simplicity. Parameters employed in Fig.…”

“…In this case, the prediction for the local velocity of erosion has a shape that is similar to (18), albeit with more complex coefficients, whose detailed analytical expressions are again left to Appendix A 2:…”

“…In particular the long-time behavior, which is governed in the continuum theory by non-linear terms, depends even qualitatively on the surface diffusion mechanism. Given that the surface topographies resulting from different mechanisms of surface diffusion have been studied by simulations elsewhere, 18 in the present work we will focus on specificities due to the energy deposition process.…”

Surfactant Sputtering: Theory of a new method of surface nanostructuring by ion beams

“…[5,6,7,8]. It uses a a discrete height profile h(x, y) of a solid-on-solid surface over a L × L (x, y)-lattice.…”