Analytic optical-constant model derived from Tauc-Lorentz and Urbach tail

Luis V. Rodríguez-de Marcos and Juan I. Larruquert

Abstract

Tauc-Lorentz model is commonly used to describe the dielectric constant of amorphous semiconductors as a function of few parameters. However, this model is not fully analytic and presents other mathematical shortcomings. A modified self-consistent model based on the integration of [E’-(E + ia)]-1 functions using Tauc-Lorentz’s ε2 expression as a weight function is presented. This new model is analytic and meets all other mathematical requirements of optical constants. The main difference with TL model stands at photon energies close to or smaller than the bandgap energy. The new model has been satisfactorily tested on SiC optical constants. Additionally, an analytic extension of the new model has been also developed to include the Urbach tail. The complete model has been tested with Si3N4 optical constants, and it enables to extend the optical-constant characterization of materials down to zero energy.