Open AccessMeasurement of layer thicknesses with an improved optimization method for depolarizing Mueller matrices
Author(s) -
Tobias Grunewald,
Matthias Wurm,
Sven Teichert,
Bernd Bodermann,
Johanna Reck,
Uwe Richter
Publication year - 2020
Publication title -
measurement science and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.48
H-Index - 136
eISSN - 1361-6501
pISSN - 0957-0233
DOI - 10.1088/1361-6501/ab95da
Subject(s) - calibration , mueller calculus , ellipsometry , bayesian optimization , materials science , layer (electronics) , metrology , depolarization , range (aeronautics) , optics , algorithm , computer science , statistics , mathematics , physics , nanotechnology , thin film , polarimetry , composite material , artificial intelligence , medicine , endocrinology , scattering
There are some commonly-used optimization techniques for the analysis of measured data in spectroscopic Mueller matrix ellipsometry (MME) used, for example, to calculate the layer thicknesses of samples under test. Concentrating on the metrological aspects of MME, we identified a non-optimal treatment of depolarization in all these techniques. We therefore recently developed an improved optimization method to adequately take depolarization in MME 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 data evaluation. In this paper we concentrate on the application of this new method to measurements of SiO 2 -layer thicknesses on silicon. With a state-of-the-art SENTECH SENresearch 4.0 Mueller ellipsometer, we measured standard samples of different SiO 2 -layer thicknesses, whose calibrated thicknesses were between about 6 nm and 1000 nm. The MME results were compared to the calibration data. For all samples, an SiO 2 -SiO double-layer model turned out to be optimal. The measured total oxide layer thicknesses matched excellently with the calibration values, within the estimated range of uncertainties. All the results are presented here. This is the first comparison with traceable reference measurements demonstrating the validity of our novel MME analysis method.