Determination of optical constants of thin films on substrates by reflectance and transmittance measurements

摘要

We describe a method for determination of the optical constants the refractive index n and the extinction coefficient k of thin films on relatively thick transparent substrate from measurements, at normal incidence, of reflectance R and trasmittance T. The derivation is complicated by the existence of multiple solutions of the equations relating the above measurements to n and k. Another complication comes from the effects of multiple reflection in the substrate leading to the channelled spectra. The thicker the substrate the smaller the distance in spectra is between the interference maxima (minima). A frequently occurring situation is that the measurements of R and T do not exhibit a channelled spectra appearance because the measuring instruments do not have sufficient spectral resolution and/or because the interfaces and surfaces of substrate are not ideal, parallel. We present the formulae for the reflectance and transmittance for the system thin-film on substrate which reflect these experimental conditions. This allows to simplify the algorithm of calculation of the optical constants. The method is applied to the semiconducting thin film of β-FeSi_2 on silicon substrate.