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Determination of Optical Constants of an Absorbing Film upon a Finite Absorbing Substrate

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Abstract

A majority of the commonly used methods of determining index of refraction n1 and extinction coefficient k1 (n1 ≫ k1) of a layer deposited upon a substrate with n2 ≫ k2 is based on combination of the transmission and reflectance measurements. In case of strong absorbance of the film or substrate transmission measurements are hampered. Then the reflection measurements of themselves are not sufficient or cannot guarantee the acceptable sensitivity. Fortunately, further we shall show that by adopting both front and back reflectivities of the overlayered thick substrate at the specific angles it is possible determine the optical constants of an absorbing layer upon a substrate of an arbitrary absorbance. Here the concept of a “thick” (when the interference fringes are fully suppressed) layer, first introduced in [1] and extensively used by Swanepoel [2,3] in application to inhomogeneous films, was adopted. Since this concept is independent of the particular mechanism of fringe suppression it may be applied not only to “films with not perfectly parallel planes” [3] but to many other situations for real films with the surface roughness, refractive index inhomogeneity or, in other circumstances, for a finite spectral width of the incident light. In a special model of a thick film with linear variation in film thickness or constant spectral frequency distribution in sufficiently broad interval ∆ω (“blurred” film model [4,5]) the analytical expressions for reflectivity and transmittivity may be obtained and utilized for calculation of such quantities for any layered stack which includes the “blurred” film. On the other hand, any layer for which the interference effects remain uninhibited will be referred as a “thin” layer.

© 2001 Optical Society of America

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