Derivation of the complex refractive index in the infrared region of the spectrum from the analysis of optical measurements

Antonis Kondilis 1Elias Aperathitis 2Mircea Modreanu 3

1. Institute of Electronic Structure and Laser, FORTH,, P.O. Box 1527, Vassilika Vouton, Heraklion 71110, Greece
2. Microelectronics Research Group, Institute of Electronic Structure and Laser, Foundation for Research and Technology – Hellas, P.O. Box 1527, 71110 Heraklion, Crete, Greece, P.O. Box 1527, Heraklion 71110, Greece
3. University College Cork, Tyndall National Institute (TYNDALL), Lee Maltings, Prospect Row, Cork, Ireland

Abstract

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 [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  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.

[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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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
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