A Comprehensive Model for the Optical Transmission for Determining the Optimal Thickness and Figure of Merit of Al-Doped ZnO Films as Transparent Conducting Coatings

In this work a comprehensive model for the optical transmission as a function of wavelength and thickness of ZnO :Al films deposited on glass substrates by ultrasonic spray pyrolysis, is developed. The mathematical expression developed for the transmission of the transparent conducting film on a transparent substrate, considers: 1) the interference effects of multiple specular reflections of coherent light from the front and the back of the flat-parallel-sided interfaces film-air and filmglass substrate, 2) the contribution of free carrier concentration (electrons in the conduction band due to Al doping) to the weak absorption in the visible and nearinfrared range, 3) the Urbach tail absorption edge at the low wavelength region ( < 400 nm ), 4) the effect of surface diffuse scattering of light originated by the roughness of these interfaces on the specular reflection and transmission coefficients. The wavelength dependence of the coefficients of reflection and transmission, and the absorption coefficient of the ZnO :Al film in the low absorptionvisible region (400-800 nm), were calculated from the formulas derived for the refractive index and extinction coefficient by using a LorentzDrude expression to separate the contribution of the bound-electrons and free-electrons, respectively, to the complex dielectric function. The carrier concentration and dc-electrical conductivity of the ZnO : Al films were measured using Hall effect and currentvoltage measurements in the van der Pauw configuration. The optical transmission of the films, in the range of wavelengths from 190 to 1100 nm, was measured using an Uv-Vis spectrometer. The fitting of the semi-empirical formula for the optical transmission with the experimental transmission spectrum for each film was good and the effects of the different parameters involved in the model was evidenced. The formulas derived here for the optical transmission can be used for a more precise determination of previously defined figures of merit for these type of films for their use as transparent conductive electrodes as a function of thickness of ZnO : Al. The correctness of the figures of merits considered and the usefulness of the model for selecting the optimal thickness for a transparent conductive contact was discussed.