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- ItemPhenomenology of iron-assisted ion beam pattern formation on Si(001)(Bristol : IOP, 2011) MacKo, S.; Frost, F.; Engler, M.; Hirsch, D.; Höche, T.; Grenzer, J.; Michely, T.Pattern formation on Si(001) through 2 keV Kr+ ion beam erosion of Si(001) at an incident angle of # = 30° and in the presence of sputter codeposition or co-evaporation of Fe is investigated by using in situ scanning tunneling microscopy, ex situ atomic force microscopy and electron microscopy. The phenomenology of pattern formation is presented, and experiments are conducted to rule out or determine the processes of relevance in ion beam pattern formation on Si(001) with impurities. Special attention is given to the determination of morphological phase boundaries and their origin. Height fluctuations, local flux variations, induced chemical inhomogeneities, silicide formation and ensuing composition-dependent sputtering are found to be of relevance for pattern formation.
- ItemIron-assisted ion beam patterning of Si(001) in the crystalline regime(Bristol : IOP, 2012) Macko, S.; Grenzer, J.; Frost, F.; Engler, M.; Hirsch, D.; Fritzsche, M.; Mücklich, A.; Michely, T.We present ion beam erosion experiments on Si(001) with simultaneous sputter co-deposition of steel at 660 K. At this temperature, the sample remains within the crystalline regime during ion exposure and pattern formation takes place by phase separation of Si and iron-silicide. After an ion fluence of F ≈ 5.9×10 21 ions m -2, investigations by atomic force microscopy and scanning electron microscopy identify sponge, segmented wall and pillar patterns with high aspect ratios and heights of up to 200 nm. Grazing incidence x-ray diffraction and transmission electron microscopy reveal the structures to be composed of polycrystalline iron-silicide. The observed pattern formation is compared to that in the range of 140-440K under otherwise identical conditions, where a thin amorphous layer forms due to ion bombardment.
- ItemPattern formation on Ge by low energy ion beam erosion(Bristol : IOP, 2013) Teichmann, M.; Lorbeer, J.; Ziberi, B.; Frost, F.; Rauschenbach, B.Modification of nanoscale surface topography is inherent to low-energy ion beam erosion processes and is one of the most important fields of nanotechnology. In this report a comprehensive study of surface smoothing and self-organized pattern formation on Ge(100) by using different noble gases ion beam erosion is presented. The investigations focus on low ion energies ( 2000 eV) and include the entire range of ion incidence angles. It is found that for ions (Ne, Ar) with masses lower than the mass of the Ge target atoms, no pattern formation occurs and surface smoothing is observed for all angles of ion incidence. In contrast, for erosion with higher mass ions (Kr, Xe), ripple formation starts at incidence angles of about 65° depending on ion energy. At smaller incident angles surface smoothing occurs again. Investigations of the surface dynamics for specific ion incidence angles by changing the ion fluence over two orders of magnitude gives a clear evidence for coarsening and faceting of the surface pattern. Both observations indicate that gradient-dependent sputtering and reflection of primary ions play crucial role in the pattern evolution, just at the lowest accessible fluences. The results are discussed in relation to recently proposed redistributive or stress-induced models for pattern formation. In addition, it is argued that a large angular variation of the sputter yield and reflected primary ions can significantly contribute to pattern formation and evolution as nonlinear and non-local processes as supported by simulation of sputtering and ion reflection.
- ItemDelay-induced patterns in a two-dimensional lattice of coupled oscillators(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Kantner, Markus; Schöll, Eckehard; Yanchuk, SerhiyWe show how a variety of stable spatio-temporal periodic patterns can be created in 2D-lattices of coupled oscillators with non-homogeneous coupling delays. The results are illustrated using the FitzHugh-Nagumo coupled neurons as well as coupled limit cycle (Stuart-Landau) oscillators. A "hybrid dispersion relation" is introduced, which describes the stability of the patterns in spatially extended systems with large time-delay.
- ItemBumps, chimera states, and Turing patterns in systems of coupled active rotators(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Franović, Igor; Omel'chenko, Oleh E.; Wolfrum, MatthiasSelf-organized coherence-incoherence patterns, called chimera states, have first been reported in systems of Kuramoto oscillators. For coupled excitable units, similar patterns where coherent units are at rest, are called bump states. Here, we study bumps in an array of active rotators coupled by non-local attraction and global repulsion. We demonstrate how they can emerge in a supercritical scenario from completely coherent Turing patterns: a single incoherent unit appears in a homoclinic bifurcation, undergoing subsequent transitions to quasiperiodic and chaotic behavior, which eventually transforms into extensive chaos with many incoherent units. We present different types of transitions and explain the formation of coherence-incoherence patterns according to the classical paradigm of short-range activation and long-range inhibition.
- ItemLocal control of globally competing patterns in coupled Swift-Hohenberg equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Becker, Maximilian; Frenzel, Thomas; Niedermayer, Thomas; Reichelt, Sina; Mielke, Alexander; Bär, MarkusWe present analytical and numerical investigations of two anti-symmetrically coupled 1D Swift-Hohenberg equations (SHEs) with cubic nonlinearities. The SHE provides a generic formulation for pattern formation at a characteristic length scale. A linear stability analysis of the homogeneous state reveals a wave instability in addition to the usual Turing instability of uncoupled SHEs. We performed weakly nonlinear analysis in the vicinity of the codimension-two point of the Turingwave instability, resulting in a set of coupled amplitude equations for the Turing pattern as well as left and right traveling waves. In particular, these complex Ginzburg-Landau-type equations predict two major things: there exists a parameter regime where multiple different patterns are stable with respect to each other; and that the amplitudes of different patterns interact by local mutual suppression. In consequence, different patterns can coexist in distinct spatial regions, separated by localized interfaces. We identified specific mechanisms for controlling the position of these interfaces, which distinguish what kinds of patterns the interface connects and thus allow for global pattern selection. Extensive simulations of the original SHEs confirm our results.