Evolution of ion induced ripple patterns on silicon surfaces

It is well known that oblique low and medium energy (typically 0.1 – 100 keV) ion erosion of solid surfaces can lead to the formation of periodic ripple patterns with wavelengths ranging from 10 to 1000 nm. The ripples produced in this way are oriented either parallel or normal to the projection of the ion beam and their wavelength scales with ion energy. These structures were found on a large variety of materials, such as semiconductors, metals, and insulating surfaces [1]. The formation and early evolution of the ripple patterns can be qualitatively reproduced by a linear continuum equation derived by Bradley and Harper [2]. However, at longer times nonlinear terms have to be taken into account, leading to nonlinear models based on the Kuramoto-Sivashinsky equation [3].
In this work, we studied the evolution of ion induced ripple patterns on Si(100) during sputtering at sub-keV energies by means of ex-situ AFM. At a certain stage of the evolution, larger corrugations appear and superpose the ripple pattern. With increasing time, these corrugations get more pronounced until they become the dominating feature of the surface. The morphology of the surface was characterized by determining the dynamic scaling exponents in direction normal and parallel to the ripples. Different scaling behavior is found for the ripples and the corrugations, respectively.
In order to gain better understanding of the evolution of the surface morphology, simulations of the damped Kuramoto-Sivshinsky equation [4] were performed, finding good qualitative agreement. Quantitatively, however, the simulations fail to reproduce the experimentally observed scaling behavior.

[1] U. Valbusa et al., J. Phys.: Condens. Matter 14 (2002), 8153
[2] R. Bradley and J. Harper, J. Vac. Sci. Technol. A 6 (1988), 2390
[3] M. A. Makeev et al., Nucl. Inst. Meth. Phys. Res. B 197 (2002), 185
[4] S. Facsko et al., Phys. Rev. B 69 (2004), 153412