Driving forces of ion-beam-induced nanopatterning

The driving forces of ion-beam-induced nanopatterning will be reconsidered. The original model proposed by Bradley and Harper [1] is a continuum theory for the change of the surface height due to sputtering, based on a linear expansion of the Sigmund model of ion erosion [2], and surface diffusion in the form proposed by Herring and Mullins [3]. Another model, which might be relevant for amorphous surface layers and relatively high ion energies, assumes a smoothing mechanism by viscous relaxation [4]. Taking into consideration the “ion hammering effect” [5], viscous flow could be even responsible for ripple formation. For monocrystalline metallic systems, the step edge barrier for surface vacancy and adatom diffusion results in typical surface pattern under ion irradiation [6].
Besides these driving forces discussed in the literature so far, at least two additional mechanisms have to be considered. (i) After first indications seen by Bellon [7], we found by systematic studies that under ion irradiation the steady-state stability of crystal facets depends on ion flux and temperature [8]. We investigated this instability of crystal facets under ion irradiation by kinetic Monte-Carlo simulations and explained consistently the temperature dependent ripple rotation of Ag(110) surfaces under normal Ar ion impact [9]. (ii) Finally, a mechanism related to ion-irradiation-induced “inverse Oswald ripening” [10] can cause ripple formation: The Gibbs-Thomson relation, which describes the radius-dependent solute concentration around a precipitate, determines the curvature-dependent vacancy/adatom concentration on surfaces too (this is the driving force for ripple smoothing used by by Herring and Mullins [3]). Under high ion fluxes the capillary radius in the Gibbs-Thomson relation can become negative [10], i.e. vacancy/adatom diffusion leads no longer to smoothing but to growth of surface ripples.
Atomistic computer simulation studies of the mechanisms listed above will be presented and discussed in relation with experiments.

[ 1] R. M. Bradley and J. M. E. Harper, J. Vac. Sci. Technol. A 6, 2390 (1988).
[ 2] P. Sigmund, Phys. Rev. 184, 383 (1969).
[ 3] C. Herring, J. Appl. Phys. 21, 301 (1950); W. W. Mullins, J. Appl. Phys. 30, 77 (1959).
[ 4] C. C. Umbach, R. L. Headrick, and K. C. Chang, Phys. Rev. Lett. 87, 246104 (2001).
[ 5] see, e.g., T. van Dillen, A. Polman, P.R. Onck, and E. van der Giessen, Phys. Rev. B 71, 024103 (2005).
[ 6] see, e.g., T. Michely, M. Kalff, G. Comsa, M. Strobel, and K.-H. Heinig, Phys. Rev. Lett. 86, 2589 (2001).
[ 7] P. Bellon, Phys. Rev. Lett. 81, 4176 (1998).
[ 8] Lars Roentzsch, PhD Thesis 2007, K.-H. Heinig and L. Roentzsch, to be published.
[ 9] U. Valbusa, C. Boragno, and F. Buatier de Mongeot, J. Phys.: Condens. Matter 14, 8153 (2002).
[10] K.-H. Heinig, T. Mueller, B. Schmidt, M. Strobel, and W. Moeller, Appl. Phys. A 77, 17 (2003).