  We propose new models to describe the imaginary part of the electrical
permittivity of dielectric and semiconductor materials in the fundamental
absorption region. We work out our procedure based on the well-known structure
of the Tauc-Lorentz model and the band-fluctuations approach to derive a
5-parameter formula that describes the Urbach, Tauc and high-absorption regions
of direct and indirect semiconductors. Main features of the models are the
self-consistent generation of the exponential Urbach tail below the bandgap and
the incorporation of the Lorentz oscillator behaviour due to electronic
transitions above the fundamental region. We apply and test our models on
optical data of direct (MAPbI$_{3}$, GaAs and InP), indirect (GaP and c-Si),
and amorphous (a-Si) semiconductors, accurately describing the spectra of the
imaginary part of the electrical permittivity. Lastly, we compare our models
with other similarly inspired models to assess the optical bandgap, Urbach tail
and oscillator central resonance energy.
