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