Use and misuse of the Kubelka-Munk function to obtain the band gap energy from diffuse reflectance measurements

The determination of the optical band gap energy (Eg) is important for optimization of the generation of electron/hole pairs in semiconductor materials under illumination. For this purpose, the classical theory proposed by Kubelka and Munk (K-M) has been largely employed for the study of amorphous and polycrystalline materials. In this paper, the authors demonstrate, step by step, how to use the K-M function and apply it thoroughly to the determination of the Eg of TiO2 semiconductor powder (pressed at different thicknesses) from diffuse reflectance spectroscopy (DRS) measurements. For the sample thicknesses 1–4 mm, Eg values of 3.12–3.14 eV were obtained. With this work it is envisaged a clarification to the procedure of determination of the Eg from the K-M theory and DRS data, since some drawbacks, and misconceptions have been identified in the recent literature. In particular, the widely used practice of determining the Eg of a material directly from the K-M function is found to be inadequate.