New optical dispersion models for the accurate description of the electrical permittivity in direct and indirect semiconductors

We propose new optical dispersion 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 semi-empirical Tauc-Lorentz dispersion model and the band-fluctuations approach to derive a five-parameter formula that describes the Urbach, Tauc and high-absorption regions of direct and indirect semiconductors. Main features of the dispersion models are the self-consistent generation of the exponential Urbach tail below the bandgap and the incorporation of the Lorentz oscillator behavior due to electronic transitions above the fundamental region. We apply and test these models on optical data of direct (MAPbI₃, gallium arsenide and indium phosphide), indirect (gallium phosphide and crystalline silicon), and amorphous hydrogenated silicon semiconductors, accurately describing the spectra of the imaginary part of the electrical permittivity. Lastly, we compare our results with other similarly inspired dispersion models to assess the optical bandgap, Urbach tail and oscillator central resonance energy.