Application of the Holomorphic Tauc-Lorentz-Urbach Function to Extract the Constants of Amorphous Semiconductor Thin Films

Abstract

The Tauc–Lorentz–Urbach (TLU) dispersion model allows us to build a dielectric function

from only a few parameters. However, this dielectric function is non-analytic and presents some mathematical

drawbacks. As a consequence of this issue, the model becomes inaccurate. In the present

work, we will adopt a procedure to conveniently transform the TLU model into a self-consistent dispersion

model. The transformation involves the integration of the original TLU imaginary dielectric

function e2 by using a Lorentzian-type function of semi-width, G. This novel model is analytic and

obeys the other necessary mathematical requirements of the optical constants of solid-state materials.

The main difference with the non-analytic TLU model occurs at values of the photon energy near or

lower than that of the bandgap energy (within the Urbach absorption region). In particular, this new

model allows us to reliably extend the optical characterization of amorphous-semiconductor thin

films within the limit to zero photon energy. To the best of our knowledge, this is the first time that

the analytic TLU model has been successfully used to accurately determine the optical constants of

unhydrogenated a-Si films using only their normal-incidence transmission spectra.