A New Method of Evaluating Multi-Color Ellipsometric Mapping on Big-Area Samples

Kálvin, Sándor Csaba and Zereay, Berhane Nugusse and Juhász, György and Major, Csaba and Petrik, Péter and Horváth, György Zoltán and Fried, Miklós (2026) A New Method of Evaluating Multi-Color Ellipsometric Mapping on Big-Area Samples. SCI, 8 (1). No. 17. ISSN 2413-4155

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Abstract

Ellipsometric mapping measurements and Bayesian evaluation were performed with a non-collimated, imaging ellipsometer using an LCD monitor as a light source. In such a configuration, the polarization state of the illumination and the local angle of incidence vary spatially and spectrally, rendering conventional spectroscopic ellipsometry inversion methods hardly applicable. To address these limitations, a multilayer optical forward model is augmented with instrument-specific correction parameters describing the polarization state of the monitor and the angle-of-incidence map. These parameters are determined through a Bayesian calibration procedure using well-characterized Si-SiO2 reference wafers. The resulting posterior distribution is explored by global optimization based on simulated annealing, yielding a maximum a posteriori estimate, followed by marginalization to quantify uncertainties and parameter correlations. The calibrated correction parameters are subsequently incorporated as informative priors in the Bayesian analysis of unknown samples, including polycrystalline–silicon layers deposited on Si-SiO2 substrates and additional Si-SiO2 wafers outside the calibration set. The approach allows consistent propagation of calibration uncertainties into the inferred layer parameters and provides credible intervals and correlation information that cannot be obtained from conventional least-squares methods. The results demonstrate that, despite the broadband nature of the RGB measurement and the limited number of analyzer orientations, reliable layer thicknesses can be obtained with quantified uncertainties for a wide range of technologically relevant samples. The proposed Bayesian framework enables a transparent interpretation of the measurement accuracy and limitations, providing a robust basis for large-area ellipsometric mapping of multilayer structures.

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