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5 May 2020 Efficient Bayesian inversion for shape reconstruction of lithography masks
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Abstract

Background: Scatterometry is a fast, indirect, and nondestructive optical method for quality control in the production of lithography masks. To solve the inverse problem in compliance with the upcoming need for improved accuracy, a computationally expensive forward model that maps geometry parameters to diffracted light intensities has to be defined.

Aim: To quantify the uncertainties in the reconstruction of the geometry parameters, a fast-to-evaluate surrogate for the forward model has to be introduced.

Approach: We use a nonintrusive polynomial chaos-based approximation of the forward model, which increases speed and thus enables the exploration of the posterior through direct Bayesian inference. In addition, this surrogate allows for a global sensitivity analysis at no additional computational overhead.

Results: This approach yields information about the complete distribution of the geometry parameters of a silicon line grating, which in return allows for quantifying the reconstruction uncertainties in the form of means, variances, and higher order moments of the parameters.

Conclusions: The use of a polynomial chaos surrogate allows for quantifying both parameter influences and reconstruction uncertainties. This approach is easy to use since no adaptation of the expensive forward model is required.

© 2020 Society of Photo-Optical Instrumentation Engineers (SPIE) 1932-5150/2020/$28.00 © 2020 SPIE
Nando Farchmin, Martin Hammerschmidt, Philipp-Immanuel Schneider, Matthias Wurm, Bernd Bodermann, Markus Bär, and Sebastian Heidenreich "Efficient Bayesian inversion for shape reconstruction of lithography masks," Journal of Micro/Nanolithography, MEMS, and MOEMS 19(2), 024001 (5 May 2020). https://doi.org/10.1117/1.JMM.19.2.024001
Received: 31 October 2019; Accepted: 13 April 2020; Published: 5 May 2020
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