Formulation of error propagation and estimation in grating reconstruction by a dual-rotating compensator Mueller matrix polarimeter

Recently, the Mueller matrix polarimeter (MMP) has been introduced for critical dimension and overlay metrology. In practice, the measurement process invariably has errors. These errors, which can be generally categorized into random and systematic errors, have great influences on the final precision and accuracy of the extracted structural parameters. In this paper, we present detailed formulations for the propagation and estimation of random and systematic errors in grating reconstruction using a dual-rotating compensator MMP (DRC-MMP). We derive a generalized first-order error propagating formula, which reveals the mechanism of error propagation in grating reconstruction using the DRC-MMP. According to this first-order error propagating formula and the measurement principle of the DRC-MMP, we then derive detailed formulations for the estimation of random and systematic errors that are propagated into the final extracted structural parameters. Simulations performed on silicon grating samples have demonstrated the validity of the present theoretical derivations.