Can Tauc plot extrapolation be used for direct-band-gap semiconductor nanocrystals?

Abstract

Despite that Tauc plot extrapolation has been widely adopted for extracting bandgap energies of semiconductors, there is a lack of theoretical support for applying it to nanocrystals. In this paper, direct-allowed optical transitions in semiconductor nanocrystals have been formulated based on a purely theoretical approach. This result reveals a size-dependant transition of the power factor used in Tauc plot, increasing from one half used in the 3D bulk case to one in the 0D case. This size-dependant intermediate value of power factor allows a better extrapolation of measured absorption data. Being a material characterization technique, the generalized Tauc extrapolation gives a more reasonable and accurate acquisition of the intrinsic bandgap, while the unjustified purpose of extrapolating any elevated bandgap caused by quantum confinement is shown to be incorrect.