A developed model for the determination of the dielectric function for some absorbing thin films using pseudo-Urbach tail

The proposed model is presented to manipulate the dielectric functions of Tauc–Lorentz–Urbach (TLU) model for determining optical constants in some absorbing thin films within the energy range 1.5–3 eV. This approach is applicable for strong absorbing thin films that their transmittance decreases with increasing energy in the visible region. In the proposed approach, the exponential function (similar to Urbach tail) is added to the Tauc–Lorentz dielectric function for the energy ranges above energy gap. The presented model provided more accurate estimates of the optical constants in the above band gap region compared to Tauc–Lorentz–Urbach (TLU) or Tauc–Lorentz (TL) model for the investigated strong absorbing thin films. The accuracy of the proposed parametric dielectric function model is verified by the use of some literature data. Also, the validity and applicability of this model is confirmed by the results of the optimization process for retrieving of the optical constants and thickness of thin film by a single transmission spectrum. The results of this approach are in good agreement with the optical constants and thickness of literature data and our experimental data.