Tow different regimes of nano-pattern formation by sputtering of single crystalline surfaces have been observed in experiments. Valbusa et al. have named these two regimes, erosive and diffusive according to the topological features of emerging patterns [1].

The key-parameters of the crossover between these two regimes are substrate temperature and ion flux. In the erosive regime (low temperature and high flux) , one dimensional structures, aligned in a direction determined by the ion-beam trajectory form, whereas in the diffusive regime (high temperature and low flux), pyramidal structure, following crystallographic orientation are mainly observed.

Here, for the first time, using a simple cubic, discrete, Kinetic Monte Carlo model [2], we demonstrate this transition, which occurs by changing a single kinetic parameter in the model. The characteristics of patterns in both regimes and corresponding pattern formation scenarios are discussed. We also show that by gradually increasing the kinetic parameter (corresponding to higher temperature and lower flux) a non-roughening regime emerges, in which the surface roughness remains extremely small and no pattern formation happens during surface erosion.

[1] U. Valbusa, C. Boragno, and F.B. de Mongeot, J. Phys. 14 (2002) 8153-8175.
[2] A.K. Hartmann, R. Kree, and T. Yasseri, J. Phys. 21 (2009) 224015.