Efficient Bayesian inversion for shape reconstruction of lithography masks

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.