Self-organized Ripple and Dot Patterns Induced by Low Energy Ion Erosion


Basics of Pattern Formation with Ions
Theoretical Modeling of Pattern Formation
The Nonlinear Regime: Experiment vs. Theory
Applications: Thin films grown on rippled Si surfaces

Basics of Pattern Formation with Ions

Siliziumoberfläche nach 500 eV Ar+ Sputtern unter 67° GaSb-Oberfläche nach senkrechtem Sputtern mit 500 eV Ar+ Ionen

Figure 1 A silicon surface after 500 eV Ar+ sputtering under 67°. The ripples have a periodicity of 35 nm and a height of 2 nm.

Figure 2 A GaSb surface after normal 500 eV Ar+ sputtering. The periodicity and the height of the dots are both 30 nm.

Bombarding a surface with energetic ions leads to the removal of surface material. This process is called ion erosion or sputtering and is a common tool for surface modification. It is widely spread in industry as a simple technique to roughen, smoothen, or clean technical surfaces.

In 1962, Navez et al. showed that low energy ion erosion of glass surfaces can lead to the formation of self-organized periodic patterns. Since then, patterns have been found on a whole variety of materials, such as metals, semiconductors, and insulators, which shows the universality of the formation process. The periodicity of the patterns can be tuned by varying the energy of the ions and ranges from few 10 nm up to a few µm. Typical energies range from 0.1 to 100 keV. Two types of patterns are observed. In the case of off-normal ion incidence, regular ripple patterns form. Depending on the angle of incidence, these ripples can be oriented either parallel or perpendicular to the direction of the ion beam. Figure 1 shows an atomic force microscopy (AFM) image of a silicon surface after sputtering with Ar+ ions of an energy of 500 eV under an angle of incidence of 67°. The resulting ripples have a periodicity of 35 nm and a height of 2 nm. The direction of the ion beam is indicated by the black arrow. In the case of normal incidence, however, one can observe the formation of hexagonally ordered nanodots. In Figure 2, such nanodots on a GaSb surface induced by sputtering with 500 eV Ar+ ions are depicted. The periodicity as well as the height of the dots is 30 nm.

Theoretical Modeling of Pattern Formation

In 1988, Bradley and Harper developed a continuum model to describe the formation of the regular patterns. In this model, the surface is treated as a continuous height function h(x,t) without any crystalline structure. The initial modulation is given by the microscopic roughness of the surface and the stochastic nature of the sputtering process. When an ion now penetrates into the surface as indicated by the arrows, it deposits its kinetic energy at a certain depth d beneath the surface. The distribution of the deposited energy can be assumed to be Gaussian with the maximum at d. From simple geometrical considerations it becomes clear that the amount of energy deposited into a trough is higher than into a mound. The probability that an atom is removed from one point on the surface is proportional to the energy deposited in this point by all penetrating ions. This leads to an amplification of the initial surface modulation. Because this mechanism tends to increase the surface by keeping the volume constant, it is called »negative surface tension«. As a competing process surface diffusion tends to smoothen the surface. The interplay of these two processes leads to the formation of the patterns.

On the basis of this model, Bradley and Harper developed a linear continuum equation:


In this equation, v0 is the erosion velocity of the planar surface, γ is the lateral ripple motion in beam direction, νx,y are the »negative« surface tensions in x and y direction, respectively, and DT is the thermally activated surface diffusion

The Bradley-Harper (BH) equation is very successful in describing the formation and early evolution of the regular patterns. At later times, however, the surface enters a nonlinear regime which demands for additional nonlinear terms. One recent nonlinear extension of the BH equation is the so-called damped Kuramoto-Sivashinsky equation (dKSE):


Here,λx,y are nonlinear coefficients, DI is the ion induced surface diffusion, and η is a white noise term that accounts for the stochastic nature of the sputtering. α is a damping coefficient that is necessary for the stabilization of the pattern. Without damping, the equation would enter a chaotic regime with no order at all at late times.

The Nonlinear Regime: Experiment vs. Theory

Vergleich der experimentellen (oben) und simulierten (unten) Oberflächentopografien von Si zu verschiedenen Sputterzeiten
(click to enlarge)
Figure 4 Comparison of experiment (upper row) and simulations (lower row) at three different stages of the surface evolution.

One field of research in our group is the experimental and theoretical investigation of the evolution of the surface patterns in the nonlinear regime. To study this nonlinear regime experimentally one needs to apply very high ion fluences to the surface. For a series of silicon samples, this was done up to a fluence of 1020 ions/cm2. The samples were sputtered at different fluences and analyzed ex-situ by means of AFM. Figure 3 a) shows an AFM image with 1 µm scan size of a silicon surface sputtered with 300 eV Ar+ under an angle of incidence of 67°. The applied fluence was 1019 ions/cm2. Ripples oriented normal to the beam direction (indicated by the black arrow) with a periodicity of 35 nm can be seen. These ripples are overlayed by larger corrugations. An image with 5 µm scan size of the same surface region reveals that these corrugations actually form another quasi-periodic pattern oriented parallel to the ion beam (Figure 3 b)). This second pattern has a much larger periodicity of 800 nm. Both of the observed ripple modes show an increase of the ripple periodicity with time, i.e. fluence. This effect is called coarsening. Although it was reported several times, the origin of the coarsening is still absolutely unclear.

Simulations of the dKSE were able to reproduce the main features and the temporal evolution of the surface morphology qualitatively. This can be seen in Figure 4, where three different stages of the experimentally observed (upper row) and simulated (lower row) surface evolution are depicted. Although the simulations show ripple coarsening, they can not reproduce the quantitative increase of the periodicity. Therefore, the true nature of ripple coarsening remains unclear und will be subject of further research.

Applications: Thin films grown on rippled Si surfaces

In collaboration with other groups of our institute we investigate potential applications of nanopatterned surfaces. Rippled silicon substrates are very attractive as templates for thin film deposition, because the morphological anisotropy of the substrate can influence the properties of the films significantly. As one application, thin magnetic films were deposited by molecular beam epitaxy (MBE) on rippled silicon samples. The magnetic properties of the deposited films are much different from similar films on flat substrates (for further information see Morphology induced magnetic correlation effects in mesoscopic wire and island structures).

Not only magnetic but also optical properties can be influenced by the use of rippled templates. Silver nanoparticles deposited by magnetron sputtering on a surface are known to exhibit a plasmon resonance in the region of visible light. When deposited on a rippled silicon substrate, these nanoparticles align with respect to the ripple direction. Figure 5 shows a scanning electron microscopy (SEM) image of silver islands on rippled silicon. The direction of the ion beam is indicated by the arrow. It can be seen that the particles form chains parallel to the ripples (normal to the direction of the ion beam). In the transmission electron microscopy (TEM) image depicted in Figure 6 one can see that the nanoparticles sit preferentially in the ripple valleys. Because of the different distances between the particles in the direction parallel and perpendicular to the ripples, the value of the plasmon resonance is decreased by 0.21 eV for incident light with polarisation parallel to the ripples. In this example, a morphological anisotropy of the substrate induces an optical anisotropy of the deposited film.

REM Aufnahme von gerichteten Ag Cluster auf ionenstrahlgewelltem Si Substrat TEM Aufnahme von Ag Cluster auf Si Wellenstrukturen
Figure 5 SEM image of aligned silver nanoparticles on rippled silicon substrate. Figure 6 TEM image of nanoparticles on silicon ripples.

Recent Publications

  • M. Buljan, S. Facsko, I.D. Marion, V.M. Trontl, M. Kralj, M. Jerčinović, C. Baehtz, A. Muecklich, V. Holy, N. Radic, and J. Grenzer, Self-assembly of Ge quantum dots on periodically corrugated Si surfaces, Appl. Phys. Lett. 107, 203101 (2015) [doi:10.1063/1.4935859].
  • X. Ou, K.-H. Heinig, R. Hübner, J. Grenzer, X. Wang, M. Helm, J. Fassbender, and S. Facsko, Faceted nanostructure arrays with extreme regularity by self-assembly of vacancies, Nanoscale 7, 18928 (2015) [doi:10.1039/C5NR04297F].
  • M. Engler, F. Frost, S. Müller, S. Macko, M. Will, R. Feder, D. Spemann, R. Hübner, S. Facsko, and T. Michely, Silicide induced ion beam patterning of Si(001), Nanotechnology 25, 115303 (2014) [doi:10.1088/0957-4484/25/11/115303].
  • B. Teshome, S. Facsko, A. Keller, Topography-controlled alignment of DNA origami nanotubes on nanopatterned surfaces, Nanoscale (2014) [doi:10.1039/c3nr04627c].
  • M. Krause, M. Buljan, A. Mucklich, W. Möller, M. Fritzsche, S. Facsko, R. Heller, M. Zschornak, S. Wintz, et al., Compositionally modulated ripples during composite film growth: Three-dimensional pattern formation at the nanoscale, Phys. Rev. B 89 085418 (2014) [doi:10.1103/PhysRevB.89.085418].
  • M. Engler, F. Frost, S. Müller, S. Macko, M. Will, R. Feder, D. Spemann, R. Hübner, S. Facsko, et al., Silicide induced ion beam patterning of Si(001), Nanotechnology25(11), 115303 (2014) [doi:10.1088/0957-4484/25/11/115303].
  • D. K. Ball, K. Lenz, M. Fritzsche, G. Varvaro, S. Günther, P. Krone, D. Makarov, A. Mucklich, S. Facsko, et al., “Magnetic properties of granular CoCrPt:SiO 2thin films deposited on GaSb nanocones,” Nanotechnology 25(8), 085703, (2014) [doi:10.1088/0957-4484/25/8/085703].

  • M. Korner, K. Lenz, R. A. Gallardo, M. Fritzsche, A. Mucklich, S. Facsko, J. Lindner, P. Landeros, and J. Fassbender, Two-magnon scattering in permalloy thin films due to rippled substrates, Phys. Rev. B 88, 054405 (2013) [doi:10.1103/PhysRevB.88.054405].

  • X. Ou, A. Keller, M. Helm, J. Fassbender, and S. Facsko, Reverse Epitaxy of Ge: Ordered and Faceted Surface PatternsPhys. Rev. Lett. 111, 016101 (2013) [doi:10.1103/PhysRevLett.111.016101].

  • B. Khanbabaee, A. Biermanns, S. Facsko, J. Grenzer, and U. Pietsch, Depth profiling of Fe-implanted Si(100) by means of X-ray reflectivity and extremely asymmetric X-ray diffraction, Journal of Applied Crystallography 46, 505 (2013) [doi:10.1107/S0021889813004597].

  • M. O. Liedke, M. Korner, K. Lenz, M. Fritzsche, M. Ranjan, A. Keller, E. Čižmár, S. A. Zvyagin, S. Facsko, et al., Crossover in the surface anisotropy contributions of ferromagnetic films on rippled Si surfaces, Phys. Rev. B 87, 024424 (2013) [doi:10.1103/PhysRevB.87.024424].

  • R. Boettger, A. Keller, L. Bischoff, and S. Facsko, Mapping the local elastic properties of nanostructured germanium surfaces: from nanoporous sponges to self-organized nanodots, Nanotechnology 24, 115702 (2013) [doi:10.1088/0957-4484/24/11/115702].


Dr. Stefan Facsko

Head of Ion Beam Center
Phone: +49 351 260 2987