Efficient global sensitivity analysis for silicon line gratings using polynomial chaos

Nando Farchmin; Martin Hammerschmidt; Philipp-Immanuel Schneider; Matthias Wurm; Bernd Bodermann; Markus Bär; Sebastian Heidenreich

doi:10.1117/12.2525978

21 June 2019 Efficient global sensitivity analysis for silicon line gratings using polynomial chaos

Nando Farchmin, Martin Hammerschmidt, Philipp-Immanuel Schneider, Matthias Wurm, Bernd Bodermann, Markus Bär, Sebastian Heidenreich

Author Affiliations +

Proceedings Volume 11057, Modeling Aspects in Optical Metrology VII; 110570J (2019) https://doi.org/10.1117/12.2525978
Event: SPIE Optical Metrology, 2019, Munich, Germany

Abstract

Scatterometry is a fast, indirect and nondestructive optical method for the quality control in the production of lithography masks. Geometry parameters of line gratings are obtained from diffracted light intensities by solving an inverse problem. To comply with the upcoming need for improved accuracy and precision and thus for the reduction of uncertainties, typically computationally expansive forward models have been used. In this paper we use Bayesian inversion to estimate parameters from scatterometry measurements of a silicon line grating and determine the associated uncertainties. Since the direct application of Bayesian inference using MarkovChain Monte Carlo methods to physics-based partial differential equation (PDE) model is not feasible due to high computational costs, we use an approximation of the PDE forward model based on a polynomial chaos expansion. The expansion provides not only a surrogate for the PDE forward model, but also Sobol indices for a global sensitivity analysis. Finally, we compare our results for the global sensitivity analysis with the uncertainties of estimated parameters.

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Citation Download Citation

Nando Farchmin, Martin Hammerschmidt, Philipp-Immanuel Schneider, Matthias Wurm, Bernd Bodermann, Markus Bär, and Sebastian Heidenreich "Efficient global sensitivity analysis for silicon line gratings using polynomial chaos", Proc. SPIE 11057, Modeling Aspects in Optical Metrology VII, 110570J (21 June 2019); https://doi.org/10.1117/12.2525978

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