Bootstrap Method for Uncertainty Evaluation in Critical Dimension Small-Angle X-Ray Scattering

Uncertainty evaluation is essential in critical dimension small-angle X-ray scattering (CD-SAXS) as it reflects the reliability of the measurement results. In this work, we introduce a new version of the bootstrap method for uncertainty evaluation in CD-SAXS to obtain both mean values and their associated uncertainties of nanostructure parameters. We further incorporate a more suitable centered bootstrap percentile method and a bias correction procedure for skewed bootstrap distributions in CD-SAXS. Subsequently, we conduct simulations and measurements on CD-SAXS using both 1-D and 2-D gratings. The accuracy of the proposed method is verified by comparison with the optical critical dimension (OCD), and the precision of the proposed method is verified by comparison with the Markov chain Monte Carlo (MCMC) method. The results indicate that the proposed bootstrap method is an effective candidate for uncertainty evaluation in CD-SAXS and other model-based measurement techniques.