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Derivation of the complex refractive index in the infrared region of the spectrum from the analysis of optical measurements
|Antonis Kondilis 1, Elias Aperathitis 2, Mircea Modreanu 3|
1. Institute of Electronic Structure and Laser, FORTH,, P.O. Box 1527, Vassilika Vouton, Heraklion 71110, Greece
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 λp as well as the relaxation time τ. The mathematical approach to the problem is made by the use of the Newton-Raphson method . 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 λp from 2.0 to 5.0 μm, approximately. Thermal annealing at 600°C results in a decreased λp as well as an increased τ in the cases of ITO films, while for ITON films, the same trend is observed as regards λp , 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 λp≈ 2.0 μm for either ITO or ITON films.
 W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetterling, Numrerical recipes in Fortran ( Cambridge University Press, Cambridge, U.K., 1986 ).
Presentation: Oral at E-MRS Fall Meeting 2007, Symposium H, by Antonis Kondilis
See On-line Journal of E-MRS Fall Meeting 2007
Submitted: 2007-05-23 11:05 Revised: 2009-06-07 00:44