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- ItemSite-controlled formation of single Si nanocrystals in a buried SiO2 matrix using ion beam mixing(Frankfurt am Main : Beilstein-Institut zur Förderung der Chemischen Wissenschaften, 2018) Xu, X.; Prüfer, T.; Wolf, D.; Engelmann, H.-J.; Bischoff, L.; Hübner, R.; Heinig, K.-H.; Möller, W.; Facsko, S.; von Borany, J.; Hlawacek, G.For future nanoelectronic devices - such as room-temperature single electron transistors - the site-controlled formation of single Si nanocrystals (NCs) is a crucial prerequisite. Here, we report an approach to fabricate single Si NCs via medium-energy Si+ or Ne+ ion beam mixing of Si into a buried SiO2 layer followed by thermally activated phase separation. Binary collision approximation and kinetic Monte Carlo methods are conducted to gain atomistic insight into the influence of relevant experimental parameters on the Si NC formation process. Energy-filtered transmission electron microscopy is performed to obtain quantitative values on the Si NC size and distribution in dependence of the layer stack geometry, ion fluence and thermal budget. Employing a focused Ne+ beam from a helium ion microscope, we demonstrate site-controlled self-assembly of single Si NCs. Line irradiation with a fluence of 3000 Ne+/nm2 and a line width of 4 nm leads to the formation of a chain of Si NCs, and a single NC with 2.2 nm diameter is subsequently isolated and visualized in a few nanometer thin lamella prepared by a focused ion beam (FIB). The Si NC is centered between the SiO2 layers and perpendicular to the incident Ne+ beam.
- ItemComputer modeling of single-layer nanocluster formation in a thin SiO2 layer buried in Si by ion mixing and thermal phase decomposition(College Park, MD : American Institute of Physics, 2019) Prüfer, T.; Möller, W.; Heinig, K.-H.; Wolf, D.; Engelmann, H.-J.; Xu, X.; Von Borany, J.A single sheet of Si nanoclusters with an average diameter of about 2 nm has been formed in a 30 nm Si/7 nm SiO2/Si layer stack by 50 and 60 keV Si+ ion-beam mixing at room temperature and fluences between 8.5 ⋯ 1015 and 2.6 ⋯ 1016 ions/cm2 and by subsequent thermal annealing at a temperature above 1000 °C. Computer modeling of the process is accomplished by TRIDYN dynamic ballistic simulation of ion mixing and subsequent lattice kinetic Monte Carlo simulation of the phase decomposition of substoichiometric silicon oxide into Si nanoclusters in a SiO2 matrix. The simulation algorithms are briefly described with special emphasis on the choice of governing parameters for the present system. In comparison to the experimental results, it is concluded that the predicted ion mixing profiles overestimate the interface broadening. This discrepancy is attributed to the neglect of chemical driving forces in connection with thermal-spike induced diffusion, which tends to reconstitute the Si/SiO2 interfaces. With a corresponding correction and a suitable number of Monte Carlo steps, the experimentally obtained areal densities and average diameters of the nanoclusters are successfully reproduced.
- ItemStatic Disorder in Excitation Energies of the Fenna-Matthews-Olson Protein: Structure-Based Theory Meets Experiment(Washington, DC : ACS, 2020) Chaillet, Martin L.; Lengauer, Florian; Adolphs, Julian; Müh, Frank; Fokas, Alexander S.; Cole, Daniel J.; Chin, Alex W.; Renger, ThomasInhomogeneous broadening of optical lines of the Fenna-Matthews-Olson (FMO) light-harvesting protein is investigated by combining a Monte Carlo sampling of low-energy conformational substates of the protein with a quantum chemical/electrostatic calculation of local transition energies (site energies) of the pigments. The good agreement between the optical spectra calculated for the inhomogeneous ensemble and the experimental data demonstrates that electrostatics is the dominant contributor to static disorder in site energies. Rotamers of polar amino acid side chains are found to cause bimodal distribution functions of site energy shifts, which can be probed by hole burning and single-molecule spectroscopy. When summing over the large number of contributions, the resulting distribution functions of the site energies become Gaussians, and the correlations in site energy fluctuations at different sites practically average to zero. These results demonstrate that static disorder in the FMO protein is in the realm of the central limit theorem of statistics. © 2020 American Chemical Society.
- ItemPotentials and limits to basin stability estimation(Bristol : Institute of Physics Publishing, 2017) Schultz, P.; Menck, P.J.; Heitzig, J.; Kurths, J.Stability assessment methods for dynamical systems have recently been complemented by basin stability and derived measures, i.e. probabilistic statements whether systems remain in a basin of attraction given a distribution of perturbations. Their application requires numerical estimation via Monte Carlo sampling and integration of differential equations. Here, we analyse the applicability of basin stability to systems with basin geometries that are challenging for this numerical method, having fractal basin boundaries and riddled or intermingled basins of attraction. We find that numerical basin stability estimation is still meaningful for fractal boundaries but reaches its limits for riddled basins with holes.
- ItemPercolation of rigid fractal carbon black aggregates(Melville, NY : American Institute of Physics, 2021) Coupette, Fabian; Zhang, Long; Kuttich, Björn; Chumakov, Andrei; Roth, Stephan V.; González-García, Lola; Kraus, Tobias; Schilling, TanjaWe examine network formation and percolation of carbon black by means of Monte Carlo simulations and experiments. In the simulation, we model carbon black by rigid aggregates of impenetrable spheres, which we obtain by diffusion-limited aggregation. To determine the input parameters for the simulation, we experimentally characterize the micro-structure and size distribution of carbon black aggregates. We then simulate suspensions of aggregates and determine the percolation threshold as a function of the aggregate size distribution. We observe a quasi-universal relation between the percolation threshold and a weighted average radius of gyration of the aggregate ensemble. Higher order moments of the size distribution do not have an effect on the percolation threshold. We conclude further that the concentration of large carbon black aggregates has a stronger influence on the percolation threshold than the concentration of small aggregates. In the experiment, we disperse the carbon black in a polymer matrix and measure the conductivity of the composite. We successfully test the hypotheses drawn from simulation by comparing composites prepared with the same type of carbon black before and after ball milling, i.e., on changing only the distribution of aggregate sizes in the composites.
- ItemSimple Monte Carlo and the metropolis algorithm(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Mathé, Peter; Novak, ErichWe study the integration of functions with respect to an unknown density. Information is available as oracle calls to the integrand and to the non-normalized density function. We are interested in analyzing the integration error of optimal algorithms (or the complexity of the problem) with emphasis on the variability of the weight function. For a corresponding large class of problem instances we show that the complexity grows linearly in the variability, and the simple Monte Carlo method provides an almost optimal algorithm. Under additional geometric restrictions (mainly log-concavity) for the density functions, we establish that a suitable adaptive local Metropolis algorithm is almost optimal and outperforms any non-adaptive algorithm.
- ItemOn non-asymptotic optimal stopping criteria in Monte Carlo simulations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Bayer, Christian; Hoel, Hakon; von Schwerin, Erik; Tempone, RaúlWe consider the setting of estimating the mean of a random variable by a sequential stopping rule Monte Carlo (MC) method. The performance of a typical second moment based sequential stopping rule MC method is shown to be unreliable in such settings both by numerical examples and through analysis. By analysis and approximations, we construct a higher moment based stopping rule which is shown in numerical examples to perform more reliably and only slightly less efficiently than the second moment based stopping rule.