An Accurate Description of Excitonic Absorption in GaAs and Tri-Halide Perovskites (MAPbX3) by Combining the Sommerfeld Enhancement Factor and Bands Fluctuations

One of the biggest challenges of excitonic materials is the determination of the band gap and binding energy of excitons. Many researches have based the behaviour of the absorption edge of these materials on the Elliot model and its several modifications such as non-parabolic bands, magnetic potentials and electro-hole-polaron interactions [1][2]. However, there is a lack of agreement in the obtained binding energies for the same tri-halide perovskite material, whose range of binding energy values has been reported from 9 meV up to 98 meV [1][2]. Here, we propose an alternative and rather simple approach, which has previously been successful in the determination of the optical bandgap of amorphous, direct and indirect semiconductors, based on bands-fluctuations (BF) model [3] and a pseudo-Voigt profile for accounting the thermal and uncertainty principle widening contributions. In the BF model, the fluctuations arise from disorder, temperature or lattice vibrations, giving rise to the well known Urbach tails [3]. We follow the same approach but for the Elliot's dielectric constant yielding to an analytic equation. By combining this with a Lorentz function in a pseudo-Voigt profile, we get an analytic description of the discrete and continuous part of the absorption edge of excitonic materials. To test the capability of this model to accurately determine the binding energies and optical bandgap of excitonic materials, we focus our analysis on GaAs and the family of tri-halide perovskites (MAPbX3), X=Br,I,Cl. The results for the bandgap, FWHM and 1st binding energy are in good agreement with the values obtained for GaAs and Pervoskites in previous reports involving photoluminescence, magnetic fields or polaronic effects. [1][2].<br/>Acknowledgments: Exciton, Pervoskites, Elliot model, bands fluctuations, polaron.<br/>References:<br/>[1] M. Baranowski and P. Plochocka. Advanced Energy Materials. 10, 26 (2020).<br/>[2] K. Galkowski et al. Energy Environ. Sci. 9, 3 (2016).<br/>[3] J A Guerra et al. J. Phys. D: Appl. Phys.52 (2019)