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Optical modeling of free electron behavior in highly doped ZnO films
Transparent conductive oxides (TCOs) with tailor-made electrical and optical properties are essential for a variety of applications. The linkage of optical and electrical properties in these films is usually described by the Drude theory despite the fact, that earlier investigations have already shown that the Drude theory fails to accurately describe optical properties. In this work we use an extension to the Drude theory to model optical spectra of reactively sputtered ZnO:Al thin films. The model uses a simple analytic expression, which can describe the general course of the dielectric function as calculated by others with more elaborate models. Using this approach optical spectra can be accurately modeled with low computational effort and reliable values for plasma frequency and damping can be obtained. By comparing these results with Hall measurements we derived the effective mass of free carriers m* in the conduction band as a function of carrier concentration. The resultsclearly showed the non-parabolicity of the conduction band for high doping levels. Using the band structure proposed by Pisarkiewicz and assuming an effective mass of 0.24 electron masses at the conduction band minimum we derived a non-parabolicity parameter of ~ 0.27 (2) eV- 1. Finally we used the values for the effective mass to determine carrier mobility from optical measurements. Contradictions to Hall measurements can be explained by the effect of grain boundary scattering.