Ripple rotation in the anisotropic Kuramoto-Sivashinsky equation

Ripple rotation in the anisotropic Kuramoto-Sivashinsky equation

Keller, A.; Nicoli, M.; Cuerno, R.; Facsko, S.; Möller, W.

The formation of regular nanopatterns during low energy ion sputtering of solid surfaces has become a topic of intense research. This research is mainly motivated by promising applications of nanopatterned surfaces e.g. in thin film growth. On the other hand, these surfaces represent an interesting example of spontaneous pattern formation in non-equilibrium systems exhibiting different features like wavelength coarsening or a transition to spatiotemporal chaos. Different pattern types are observed for different experimental conditions, i.e. wavelike ripple patterns and hexagonally ordered dot arrays under oblique and normal ion incidence, respectively [1].
According to the model of Bradley and Harper (BH) [2], the regular patterns result from the competition between curvature dependent roughening and diffusional smoothing of the surface. Since the local erosion rate is higher in troughs than on crests, the eroded surface is unstable against any periodic perturbances. In the presence of a smoothing mechanism, however, wave vector selection occurs and a periodic pattern with a characteristic spatial frequency is observed. During recent years, several nonlinear extensions of the linear BH model have been proposed with the stochastic Kuramoto-Sivashinsky (KS) equation having played a prominent role [3]. However, although most experimental investigations on ion-induced pattern formation were performed under oblique ion incidence, only few theoretical studies focused on the corresponding anisotropic KS (aKS) equation.
In this work, we have investigated the influence of anisotropy on the morphology evolution in numerical integrations of the aKS equation. For a strong nonlinear anisotropy, a rotation by 90° of the initially formed ripple pattern was observed for intermediate and long integration times. Comparison with analytical predictions indicates that the observed rotated ripple pattern arises from anisotropic renormalization properties of the aKS equation. This result may also offer an explanation for the recent observation of transient structures in high-temperature experiments on Si(111) [4].

[1] W. L. Chan and E. Chason, J. Appl. Phys. 101, 121301 (2007)
[2] R. Bradley and J. Harper, J. Vac. Sci. Technol. A 6, 2390 (1988)
[3] R. Cuerno and A.-L. Barabási, Phys. Rev. Lett. 74 4746 (1995)
[4] A.-D. Brown, J. Erlebacher, W.-L. Chan, and E. Chason, Phys. Rev. Lett. 95 056101 (2005)

  • Lecture (Conference)
    MRS Spring Meeting, 13.-17.04.2009, San Francisco, USA

Publ.-Id: 12691