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Jiří Vohánka, Ivan Ohlídal, Jaroslav Ženíšek, Petr Vasina, Martin Čermák, Daniel Franta

Use of the Richardson extrapolation in optics of inhomogeneous layers: application to optical characterization

Surface and Interface Analysis 50 (2018) 757-765

A new approach to calculation of optical quantities of inhomogeneous layers is presented. In this approach the Richardson extrapolation is used to improve the accuracy of the method in which the inhomogeneous layer is approximated by a stack of thin homogeneous layers. The results presented in this paper are based on the assumption that the media are isotropic and the inhomogeneity is along the axis normal to the boundary. The results obtained by the new method are compared with those obtained without the Richardson extrapolation. The Richardson extrapolation brings significant improvement in accuracy, especially if the number of approximating layers is large. Moreover, the method utilizing the Richardson extrapolation proceeds in steps with an error estimate available in each step, thus, the calculation can be stopped when the desired accuracy is reached. The use of the method is illustrated by means of the optical characterization of strongly inhomogeneous film of non-stoichiometric silicon nitride.

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