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

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VOHÁNKA Jiří FRANTA Daniel ČERMÁK Martin HOMOLA Vojtěch BURŠÍKOVÁ Vilma OHLÍDAL Ivan

Rok publikování 2020
Druh Článek v odborném periodiku
Časopis / Zdroj Optics Express
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
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Doi http://dx.doi.org/10.1364/OE.380657
Klíčová slova optical characterization;thickness non-uniform films;ellipsometry
Popis 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.
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