Propagation of Ripples in Monte Carlo Models of Sputter Induced Surface   Morphology
  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 behaviour 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 an Arrhenius-type Monte Carlo method including a term (possibly zero) that accounts for the Schwoebel effect, the other a thermodynamic mechanism without the Schwoebel effect. We find that the behavior of the ripple velocity and wavelength depends on the sputtering timescale, 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. 
Emmanuel O. Yewande, Alexander K. Hartmann, and Reiner Kree