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Background:  Scatterometry is a fast, indirect and non-destructive optical method forquality control in the production of lithography masks. To solve the inverseproblem in compliance with the upcoming need for improved accuracy, acomputationally expensive forward model has to be defined which maps geometryparameters to diffracted light intensities.  Aim:  To quantify the uncertainties in the reconstruction of the geometryparameters, a fast to evaluate surrogate for the forward model has to beintroduced.  Approach:  We use a non-intrusive polynomial chaos based approximation of the forwardmodel which increases speed and thus enables the exploration of the posteriorthrough direct Bayesian inference. Additionally, this surrogate allows for aglobal sensitivity analysis at no additional computational overhead.  Results:  This approach yields information about the complete distribution of thegeometry parameters of a silicon line grating, which in return allows toquantify the reconstruction uncertainties in the form of means, variances andhigher order moments of the parameters.  Conclusion:  The use of a polynomial chaos surrogate allows to quantify both parameterinfluences and reconstruction uncertainties. This approach is easy to use sinceno adaptation of the expensive forward model is required.

Efficient Bayesian inversion for shape reconstruction of lithography masks