Genetic algorithm using independent component analysis in x-ray reflectivity curve fitting of periodic layer structures

Abstract

A novel genetic algorithm (GA) utilizing independent component analysis (ICA) was developed for x-ray reflectivity (XRR) curve fitting. EFICA was used to reduce mutual information, or interparameter dependences, during the combinatorial phase. The performance of the new algorithm was studied by fitting trial XRR curves to target curves which were computed using realistic multilayer models. The median convergence properties of conventional GA, GA using principal component analysis and the novel GA were compared. GA using ICA was found to outperform the other methods with problems having 41 parameters or more to be fitted without additional XRR curve calculations. The computational complexity of the conventional methods was linear but the novel method had a quadratic computational complexity due to the applied ICA method which sets a practical limit for the dimensionality of the problem to be solved. However, the novel algorithm had the best capability to extend the fitting analysis based on Parratt's formalism to multiperiodic layer structures.

Nanometer‐Scale Depth‐Resolved Atomic Layer Deposited SiO2 Thin Films Analyzed by Glow Discharge Optical Emission Spectroscopy

“…A SENTECH SE400adv ellipsometer was used at 632.8 nm wavelength and 70° angle of incidence, and a Phillips X́Pert Pro X‐ray diffractometer was used with Cu‐K α1 radiation. The measured XRR data were then simulated applying a software of Parratt's formalism in order to obtain thickness and density of the thin films. Moreover, the thin films sputtering rate by GDOES was calculated as the ratio of film thickness measured by ellipsometry over film sputtering time.…”

Combined evaluation of grazing incidence X-ray fluorescence and X-ray reflectivity data for improved profiling of ultra-shallow depth distributions

“…Thus global optimization algorithms like direct search, simulated annealing or evolutionary algorithms are required to find the global minimum. Good fitting results have been obtained using genetic algorithms [21–23] and Wormington et al [24] reported excellent results for XRR and diffraction data fitting utilizing differential evolution [25] , which is used in our optimization procedure.…”

An Efficient Method for the Experimental Characterization of Periodic Multilayer Mirrors: A Global Optimization Approach

“…In every iteration, the parameters of the model are updated. The iterative process is considered complete when the discrepancy between the theoretical reconstructions of the electromagnetic model and the experimental data become minimal [16]. The fitting of the XRR curves of the PMMs can be simplified because the curves are periodic; therefore, the number of optimization parameters in the iterative process can be reduced.…”