Extended Tauc-Lorentz Model for Amorphous Materials With Non-Exponential Band Tails

Abstract

Dielectric function models are essential for determining the optical constants of a substance as a function of photon energy using optical transmission, reflection or spectroscopic ellipsometry measurements. In this letter, we present an extended Tauc–Lorentz model tailored for amorphous materials with non-exponential band tails. Our method employs an exponential function with a polynomial argument to define the imaginary part of the dielectric function in the sub-gap region, with the polynomial order varying based on the complexity of sub-gap absorption features and the precision of the fitted experimental data. The real part of the dielectric function is obtained through the Kramers–Kronig relations as a sum of two components associated with interband and sub-gap transitions, allowing for the comparison of their contributions. These components are calculated analytically and numerically, simplifying the model’s implementation. We illustrate the model’s application by extracting the optical constants from the transmission spectrum of a hydrogenated silicon nitride thin film.