Robust characterization of small grating boxes using rotating stage Mueller matrix polarimeter

In this paper we demonstrate the robustness of the Mueller matrix polarimetry used in multiple-azimuth configuration. We first demonstrate the efficiency of the method for the characterization of small pitch gratings filling 250 mu m wide square boxes. We used a Mueller matrix polarimeter directly installed in the clean room has motorized rotating stage allowing the access to arbitrary conical grating configurations. The projected beam spot size could be reduced to 60x25 mu m, but for the measurements reported here this size was 100x100 mu m. The optimal values of parameters of a trapezoidal profile model, acquired for each azimuthal angle separately using a non-linear least-square minimization algorithm, are shown for a typical grating. Further statistical analysis of the azimuth-dependent dimensional parameters provided realistic estimates of the confidence interval giving direct information about the accuracy of the results. The mean values and the standard deviations were calculated for 21 different grating boxes featuring in total 399 measured spectra and fits. The results for all boxes are summarized in a table which compares the optical method to the 3D-AFM. The essential conclusion of our work is that the 3D-AFM values always fall into the confidence intervals provided by the optical method, which means that we have successfully estimated the accuracy of our results without using direct comparison with another, non-optical, method. Moreover, this approach may provide a way to improve the accuracy of grating profile modeling by minimizing the standard deviations evaluated from multiple-azimuths results.