An efficient approach to global sensitivity analysis and parameter estimation for line gratings

TL;DR

This paper presents a computationally efficient Bayesian approach using polynomial chaos expansion for global sensitivity analysis and parameter estimation in scatterometry of line gratings, improving accuracy and uncertainty quantification.

Contribution

It introduces a surrogate PDE model with polynomial chaos expansion for Bayesian inversion, enabling efficient global sensitivity analysis and uncertainty quantification in scatterometry.

Findings

Successful estimation of line grating parameters from scatterometry data.

Effective global sensitivity analysis using Sobol indices.

Reduced computational costs compared to traditional PDE-based Bayesian methods.

Abstract

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.