Analysis of ellipsometric layer thickness measurements applying a novel optimization method for depolarizing Mueller matrices

We developed a novel optimization method to analyze depolarization containing Mueller ellipsometric measurements and show its application on measurements of layer thickness standards, which have been traced to traceable X-ray reflectometry (XRR) at PTB. Up to now a mathematically well-founded treatment of stochastic influencing parameters such as depolarization or measurement noise was missing, impeding complete uncertainty considerations. For the first time we recently treated these issues and developed a new optimization method for depolarizing Mueller matrices, which addresses depolarization as a weight by applying Cloude’s covariance matrix. The maximum likelihood method and Bayesian statistics are thereby enabled to use. Moreover, an extension to include measurement noise has been implemented. For the selection of the right model the Bayesian information criterion is used. We demonstrate the successful use analyzing measured data of SiO2 layer thickness standards measured by a SENTECH Mueller ellipsometer. The excellent matching significance of our mean values and expanded uncertainties to those traced to XRR is shown by the obtained normalized error values En.