The role played by a glass substrate on the accurate determination of the optical constants and the thickness of a thin dielectric film deposited on it, when well-known envelope methods are used, is discussed. Analytical expressions for the two envelopes of the optical transmission spectra corresponding to film. with both uniform and nonuniform thicknesses are derived, assuming the substrate to be a weakly absorbing layer. It is shown that accurate determination of the refractive index and the film thickness is notably improved when the absorption of the substrate is considered. The analytical expressions for the upper and lower envelope, are used to characterize optically and geometrically both uniform and nonuniform amorphous chalcogenide films. The results obtained are compared with those derived by use of expressions for the envelopes that neglect the substrate absorption. The comparison shows that overestimated refractive indexes and underestimated thicknesses are obtained when the conventional approach, in which the substrate absorption is neglected, is used.
A method has been proposed for calculation of the optical constants of a thin layer upon a transparent substrate only from the reflection spectrum into the region of transmission of the layer. The envelopes of the maxima of the spectrum RM and of the minima Rm are used, taking into account the finite dimensions of the substrate. The algorithm of the calculations is similar to the one proposed by Swanepoel (1983) using the transmission spectrum. The method makes it possible to calculate the thickness of the layer and the refractive index n with an error of 0.2%. The correct description of the dispersive relationship of n is obtained for an amorphous layer Ge19As21S60.
A method has been proposed for exact calculation of the optical parameters n and k of a thin film on a transparent substrate by simultaneously solving the equations for two of the envelopes of the transmission and reflection spectra. The singularity of the solution and the convergency area are proved, and the influence of the inaccuracies in drawing the envelopes upon the errors made during the calculation of n and k is also investigated. The method is most accurate for the envelopes of the transmission minima and the reflection maxima in the region of strong and medium absorption. The accuracy of other methods which use data from the transmission or reflection envelopes has also been investigated. The present method describes correctly the change of n in the region of medium and strong absorption for an amorphous film with composition Ge28As12S60.
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