We have developed an algorithm to derive the IR-dispersion of the complex refractive index, n = η – i k, from the analysis of Reflectance and Transmittance optical spectra. Within the framework of the Drude model, this derivation allows the calculation of the plasma wavelength λ_p as well as the relaxation time τ. The mathematical approach to the problem is made by the use of the Newton-Raphson method [1]. The theoretical expressions for the Reflectance and the Transmittance, as well as their partial derivatives with respect to η and k which are necessary for the application of the method are introduced analytically improving speed and accuracy. The method has been applied to the analysis of optical spectra of Indium-Tin-oxide (ITO) as well as Indium-Tin-oxynitride (ITON) films produced by sputtering at different rf-power levels, these levels ranging from 150 to 550 W.

Within the wavelength range between 1.5 and 2.5 μm we notice the following. The detected  values of  τ range from  0.1×10^-14 to 1×10^-14sec while  those of  λ_p  from 2.0 to 5.0 μm, approximately. Thermal annealing at 600°C results in a decreased λ_p as well as an increased τ in the cases of ITO films, while for ITON films, the same trend is observed as regards λ_p , the opposite however as regards τ. This latter remark is consistent with an expected post annealing deterioration of the structure produced from the release of nitrogen. In the post annealing cases λ_p≈ 2.0 μm for either ITO or ITON films.

[1] W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetterling, Numrerical recipes in Fortran ( Cambridge University Press, Cambridge, U.K., 1986 ).

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