## Jiří Vohánka, Daniel Franta, Martin Čermák, Vojtěch Homola, Vilma Buršíková, Ivan Ohlídal

# Ellipsometric characterization of highly non-uniform thin films with the shape of thickness non-uniformity modeled by polynomials

## Optics Express 28 (2020) 5492-5506

A common approach to non-uniformity is to assume that the local thicknesses inside the light spot are distributed according to a certain distribution, such as the uniform distribution or the Wigner semicircle distribution. A model considered in this work uses a different approach in which the local thicknesses are given by a polynomial in the coordinates x and y along the surface of the film. An approach using the Gaussian quadrature is very efficient for including the influence of the non-uniformity on the measured ellipsometric quantities. However, the nodes and weights for the Gaussian quadrature must be calculated numerically if the non-uniformity is parameterized by the second or higher degree polynomial. A method for calculating these nodes and weights which is both efficient and numerically stable is presented. The presented method with a model using a second-degree polynomial is demonstrated on the sample of highly non-uniform polymer-like thin film characterized using variable-angle spectroscopic ellipsometry. The results are compared with those obtained using a model assuming the Wigner semicircle distribution.

DOI: 10.1364/OE.380657

You can also contact one of the authors: vohanka@physics.muni.cz, franta@physics.muni.cz, 63855@mail.muni.cz, vilmab@physics.muni.cz, ohlidal@physics.muni.cz