Publication details

Approximations of reflection and transmission coefficients of inhomogeneous thin films based on multiple-beam interference model

Authors

OHLÍDAL Ivan VOHÁNKA Jiří MISTRÍK Jan ČERMÁK Martin VIŽĎA František FRANTA Daniel

Year of publication 2019
Type Article in Periodical
Magazine / Source Thin Solid Films
MU Faculty or unit

Faculty of Science

Citation
Web odkaz na stránku nakladatele
Doi http://dx.doi.org/10.1016/j.tsf.2019.03.001
Keywords Reflectance;Transmittance;Ellipsometric parameters;Inhomogeneous thin films
Description A multiple-beam interference model is used to derive approximate formulae for the reflection and transmission coefficients of inhomogeneous thin films exhibiting large gradients of refractive index profiles. It is shown that these formulae are constituted by series containing the Wentzel-Kramers-Brillouin-Jeffreys term and correction terms with increasing order corresponding to number of considered internal reflections inside the films. A numerical analysis enabling us to show the influence of a degree of inhomogeneity on spectral dependencies of reflectance and ellipsometric parameters of inhomogeneous films is performed. Advantages and disadvantages of our approach compared with other approximate approaches are discussed. The optical characterization of a selected non-stoichiometric silicon nitride film prepared by reactive magnetron sputtering onto silicon single crystal substrate is performed for illustration of using our formulae in practice.
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