The statistical inverse problem of scatterometry: Bayesian inference and the effect of different priors

Sebastian Heidenreich; Hermann Gross; Matthias Wurm; Bernd Bodermann; Markus Bär

doi:10.1117/12.2185707

21 June 2015 The statistical inverse problem of scatterometry: Bayesian inference and the effect of different priors

Sebastian Heidenreich, Hermann Gross, Matthias Wurm, Bernd Bodermann, Markus Bär

Author Affiliations +

Proceedings Volume 9526, Modeling Aspects in Optical Metrology V; 95260U (2015) https://doi.org/10.1117/12.2185707
Event: SPIE Optical Metrology, 2015, Munich, Germany

Abstract

Scatterometry is a fast indirect optical method for the determination of grating profile parameters of photomasks. Profile parameters are obtained from light diffracted intensities by solving an inverse problem. There are diverse methods to reconstruct profile parameters and to calculate associated uncertainties. To fit the upcoming need for improved accuracy and precision as well as for the reduction of uncertainties different measurements should be combined. Such a combination increases the knowledge about parameters and may yield smaller uncertainties. The Bayesian approach provides an appropriate method to evaluate combined measurements and to obtain the associated uncertainties. However, for computationally expensive problems like scatterometry, the direct application of Bayesian inference is very time consuming. Here, we use an approximation method based on a polynomial chaos expansion. To probe the quality of this approximation, we reconstructed geometry parameters, quantify uncertainties and study the effect of different prior informations onto the obtained grating profile parameters by using simulation data superimposed by noise.

Citation Download Citation

Sebastian Heidenreich, Hermann Gross, Matthias Wurm, Bernd Bodermann, and Markus Bär "The statistical inverse problem of scatterometry: Bayesian inference and the effect of different priors", Proc. SPIE 9526, Modeling Aspects in Optical Metrology V, 95260U (21 June 2015); https://doi.org/10.1117/12.2185707

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