Measurement configuration optimization for accurate grating reconstruction by Mueller matrix polarimetry

Abstract

Abstract. Due to the rich information provided by the Mueller matrices when the most general conical diffraction configuration is considered, the Mueller matrix polarimetry has demonstrated a great potential in semiconductor manufacturing. As the configurations of the incidence and azimuthal angles have different influences on the measurement accuracy, it is necessary to select an optimal one among the multitude of possible options. We introduce the norm of a configuration error propagating matrix to assess the measurement accuracy for different measurement configurations. The optimal configuration for a Si grating sample was achieved by minimizing the norm of the configuration error propagating matrix. Experimental results show the agreement between the theoretically predicted optimal configuration and the experimental exhibited one obtained by using a dual-rotating compensator Mueller matrix polarimeter and thus demonstrated the validity of the proposed optimization method. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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

“…e J a and e J þ x represent the maximum gain factors in the propagation of different error sources, which can be used as objective functions to optimize the measurement configuration of the MMP for more accurate grating reconstruction [30]. In order to make the above description much clearer, the important symbols adopted in the theoretical derivations are listed in Appendix C.…”

Enhancing one dimensional sensitivity with plasmonic coupling

“…Most commonly, the resulting precision will be on the order of angstroms such as in [15]. For a fully optimized system measuring silicon fins, this precision is reduced to about 20 picometers as seen in [16]. The structure we propose achieves precision below 10 picometers without optimization.…”

Development of a broadband Mueller matrix ellipsometer as a powerful tool for nanostructure metrology

“…(22), the systematic error μ Δx inx will be mainly induced by the configuration error Δa if we assume the measurement system is well calibrated and the systematic error μ Δy in y is small. In this case, we can optimize the measurement configuration by [21,25] …”

“…It was shown that the Mueller matrices measured in proper conical diffraction configurations may help decouple some of the fitting parameters. We further proposed a measurement configuration optimization method for MME to find an optimal combination of the incidence and azimuthal angles, with which more accurate measurement can be achieved [21]. Kim and Li et al investigated the possibility of measuring overlay and grating asymmetry with MME [22,23].…”

“…Several researchers have investigated the MME-based nanostructure metrology over the past years [19][20][21][22][23][24][25]. Novikova et al implemented MME in different azimuthal angles to characterize one-dimensional diffraction gratings [19,20].…”