Measurement of layer thicknesses with an improved optimization method for depolarizing Mueller matrices

For the analysis of measured data in spectroscopic Mueller matrix ellipsometry (MME) there exist some commonly used optimization techniques to calculate for example layer thicknesses of samples under test. Concentrating on metrological aspects of MME we identified a non-optimal treatment of depolarization in all these techniques. Therefore, we recently developed an improved optimization method to take depolarization in MME adequately into account. In a further step we also included statistical measurement noise and derived a likelihood function, which enabled us to apply both the maximum likelihood method and Bayesian statistics as well as the Bayesian information criterion for the data evaluation. In this paper we concentrate on the application of this new method for measurements of SiO2-layer thicknesses on silicon. With a state-of-the-art SENTECH SENresearch 4.0 Mueller ellipsometer we measured different SiO2-layer thickness standard samples with calibrated thicknesses between about 6 nm and 1000 nm. The MME results are compared to the calibration data. For all samples an SiO2-SiO double-layer-model turned out to be optimal. The measured total oxid layer thicknesses match excellently with the calibration values within the estimated uncertainties. All results are presented here. It is a first comparison with traceable reference measurements demonstrating the validity of our novel MME analysis method.


Further information:

Tobias Grunewald, Matthias Wurm, Sven Teichert, Bernd Bodermann, Johanna Reck, Uwe Richter: Measurement of layer thicknesses with an improved optimization method for depolarizing Mueller matrices, Meas. Sci. Technol. 31 (2020), 105010 (9pp), https://doi.org/10.1088/1361-6501/ab95da