A facile method for Tauc exponent and corresponding electronic transitions determination in semiconductors directly from UV–Vis spectroscopy data

In this work, a facile method allowing for estimation of the exponent in the Tauc equation directly from the UV–vis spectra is presented. It is based on the Taylor expansion of the logarithmic version of the Tauc equation. The Tauc exponent is calculated from the tangent slope of the absorption data. Knowledge of this coefficient provides information about the optical transition types and is used as an input for the calculations of the band gap. As an exemplar material, TiO2 in form of thin film and nanotubes as well as their nanocomposites with other metal oxides are chosen. For the transparent thin 15 nm film of TiO2, two linear ranges with n = 2.0 and 1.2 are found. The first is assigned to the well-established indirect (allowed) transition. In the case of the second one, the n does not correspond to typically used values. Therefore, it is speculated that more than one transition is probable. This consideration is supported with ab-initio DFT calculations of the band structure of TiO2 with Hubbard U correction. Similar results are found for TiO2 nanotubes using diffuse reflectance spectroscopy indicating that the presented method applies both to transmission and reflection.