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International Journal of Optics
Volume 2010, Article ID 137572, 18 pages
Research Article

Substrate Effect on the Optical Reflectance and Transmittance of Thin-Film Structures

Electronics Department, Saint Petersburg State Electrotechnical University, Saint Petersburg 197376, Russia

Received 8 September 2010; Accepted 3 November 2010

Academic Editor: Robert G. Elliman

Copyright © 2010 Anatoly Barybin and Victor Shapovalov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A rigorous and consistent approach is demonstrated to develop a model of the 4M structure (the four-media structure of a film on a substrate of finite thickness). The general equations obtained for the reflectance and transmittance spectra of the 4M structure are simplified by employing a procedure of the so-called device averaging to reduce them to a succinct form convenient for processing of experimental spectra for the structures with a thick substrate. The newly derived equations are applied to two special cases: (i) an arbitrary film on highly absorbing substrates and (ii) a slightly absorbing film on transparent substrates. The reflectance and transmittance spectra represented in the simplified (with the device averaging) form have a practical application for determining the film thickness and optical constants from experimental spectra by using the known techniques.