  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 Markov-Chain 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.
