The statistical inverse problem of scatterometry: Bayesian inference and the effect of different priors

摘要

Scatterometry is a fast indirect optical method for the determination of grating profile parameters of photomasks. Profile parameters are obtained from light diffracted intensities by solving an inverse problem. There are diverse methods to reconstruct profile parameters and to calculate associated uncertainties. To fit the upcoming need for improved accuracy and precision as well as for the reduction of uncertainties different measurements should be combined. Such a combination increases the knowledge about parameters and may yield smaller uncertainties. The Bayesian approach provides an appropriate method to evaluate combined measurements and to obtain the associated uncertainties. However, for computationally expensive problems like scatterometry, the direct application of Bayesian inference is very time consuming. Here, we use an approximation method based on a polynomial chaos expansion. To probe the quality of this approximation, we reconstructed geometry parameters, quantify uncertainties and study the effect of different prior informations onto the obtained grating profile parameters by using simulation data superimposed by noise.