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# Self-organised dynamics of nanodot patterns on a surface

03-12-2013

The evolution of nanodot patterns on a semiconductor surface was investigated during their formation through ion beam sputtering. These nanoscale patterns are known to evolve and reach a steady state in which the average morphology no longer changes. Scientists working at beamline ID01 have now determined that the local configuration of the nanodots is still changing in the steady state, but that the evolution of the surface morphology slows down with time and the patterns become more persistent.

Pattern formation is a fascinating aspect of nature: ordered patterns are found at all length scales, from the astronomic to the atomic length scale. Remarkable examples of patterns formed at very diverse length scales are the patterns induced by erosion. Due to the erosive action of the wind on a sand bed, ripples and dunes are formed on sandy soils. Structures resembling these morphologically, but about eight orders of magnitude smaller, can be formed at the nanoscale by eroding semiconductor surfaces with accelerated ions. Despite their diversity in size, similar models based on a hydrodynamic approach can often describe the properties of patterns induced by erosion at such disparate length-scales [1]. In the case of nanopatterned surfaces, the theoretical models to describe the evolution in time of the erosion process are still debated and little is known experimentally about the growth dynamics of the patterns once they have been formed. We have studied *in situ* the dynamics of a model system, namely the GaSb(001) surface sputtered at normal incidence with Ar^{+} ions.

Normal incidence sputtering of GaSb(001) induces the formation of nanodots on the surface and the appearance of a self-organised pattern [2,3]. The pattern wavelength (i.e. the mean distance between the nanodots) increases with sputtering time until it stabilises (**Figure 1**). After that, the average morphology and the lateral correlation length of the pattern do not change anymore but the pattern is still evolving due to erosion. Information about the pattern dynamics in this regime has been obtained using X-ray photon correlation spectroscopy (XPCS) at beamline **ID01**. Using numerical calculations, we have previously shown that XPCS can help to determine which theoretical model is more adequate to describe this process [4].

XPCS is a technique that exploits the coherence properties of the synchrotron radiation source. When a surface is illuminated with a coherent beam, the scattered intensity shows a characteristic grainy appearance called speckle. The speckle pattern depends on the exact arrangement of the scatterers; if the scatterers move, the intensities of the speckles will fluctuate in time. Therefore, information about the underlying dynamics can be obtained by studying the time correlations of the intensity fluctuations of the speckles.

**Figure 2** shows the results of such analysis, i.e. the correlation of speckle intensity fluctuations during the erosion process. The sputtering time is along the t_{1}=t_{2} diagonal. The growing width of the signal along the diagonal indicates that the correlation time increases with sputtering time, which shows that the system has non-equilibrium dynamics and slows down with sputtering time. Once the saturation regime of the pattern wavelength has been reached (at t_{sputt} ~ 5 min), the nanodot patterns are still evolving due to processes that tend to roughen or smoothen the surface. The patterns become more persistent with sputtering time and this persistence is ascribed to the increase in height of the nanostructures, which hinders the redistribution of sputtered material and may alter the sputtering-induced viscous flow. These results are relevant for the understanding of pattern formation dynamics and the improvement of fabrication processes that rely on self-organisation.

**Principal publication and authors **

Ageing dynamics of ion bombardment induced self-organization processes, O. Bikondoa (a,b), D. Carbone (c), V. Chamard (d) & T.H. Metzger (e); *Scientific Reports* **3**, 1850 (2013).

(a) XMaS, The UK-CRG Beamline, ESRF, Grenoble (France)

(b) Department of Physics, University of Warwick, Coventry (UK)

(c) ESRF

(d) Institut Fresnel, Aix-Marseille Université, CNRS, Ecole Centrale Marseille (France)

(e) Max Planck Institute of Colloids and Interfaces, Department of Biomaterials, Potsdam (Germany)

**References**

[1] T. Aste & U. Valbusa, *New J. Phys* **7**, 122 (2005).

[2] S. Facsko* et al.*, *Science* **285**, 1551 (1999).

[3] A. Keller *et al.*, *Appl. Phys. Lett.* **94**, 193103 (2009).

[4] O. Bikondoa *et al.*, *J. Phys: Cond. **Matter* **24**, 445006 (2012).