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Numerical Simulations

Numerical Simulations

A software environment (Opens external link in new windowJCMsuite) developed at the Zuse Institute Berlin is used to model the electromagnetic waves and the interactions with the nanostructured surfaces.  It is a so-called finite element solver, which allows to model the electromagnetic fields of any 2D or 3D structure. These fields are also called the near field distribution. From these near fields the expected fluorescence intensities can be calculated directly. At the same time, the expected far fields can also be extrapolated from the near fields. This would correspond to the known diffraction intensities in a GISAXS experiment, provided that the structures on the surface are periodically ordered. For a fast modelling of the nanostructures different modern methods like Bayesian optimization or meta-heuristic approaches like differential evolution are often used. A validation of the dimensional uncertainties in the reconstructions is numerically much more complex and is realized with a Markov chain Monte Carlo (Opens external link in new windowMCMC) affine-invariant ensemble sampling method. This requires a strong parallelization of the simulations on several workstations or HPC. In order to keep up with the current developments in the semiconductor industry which generate ever more complex and smaller 3D structures, alternative simulation possibilities are actively researched in close cooperation with theory groups (Link to 8.41) within PTB and outside.
Different approaches are pursued in order to limit the metrological and numerical effort. One possibility, for example, is the approximation of the forward model by a surrogate model. The forward model simulates the photon-matter interaction for different nanostructures and generally requires the solution of a partial differential equation (Maxwell equations). The use of a surrogate model, which is based on a so-called polynomial chaos development, is particularly effective [Opens external link in current windowWorking group 8.41].
Alternatively to the surrogate model based on a rigorous solution, the solution itself can be approximated. For this purpose, new approaches are being pursued within PTB and by external cooperation partners. For example, the dynamic diffraction theory in many beam approximation (MB-DDT) also known as rigorous coupled wave analysis (RCWA).

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