Lizárraga, K.; Serquen, E.; Llontop, P.; Enrique, L.A.; Piñeiro, M.; Perez, E.; Tejada, A.; Ruske, F.; Korte, L.; Guerra, J.A.: Description of excitonic absorption using the Sommerfeld enhancement factor and band-fluctuations. Journal of Physics D 58 (2025), p. 065102/1-21
10.1088/1361-6463/ad91c1
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Abstract:
One of the challenges of excitonic materials is the accurate determination of the exciton bindingenergy and bandgap from optical measurements. The difficulty arises from the overlap of thediscrete and continuous excitonic absorption at the band edge. Many researches have modeledthe shape of the absorption edge of such materials on the seminal formulation proposed byElliott in 1957 (Phys. Rev.1081384-9) and its several modifications such as non-parabolicbands, magnetic potentials and electron-hole-polaron interactions. However, exciton bindingenergies obtained from optical absorption often vary strongly depending on the chosen 'Elliottformula'. Here, we propose an alternative and rather simple approach, which has previouslybeen successful in the determination of the optical bandgap of amorphous, direct and indirectsemiconductors, based on the band-fluctuations (BFs) model. In this model, the fluctuations dueto disorder, temperature or lattice vibrations give rise to the well known exponential shape ofband tail states. The formulation results in an analytic equation for the fundamental absorptionwith 6 parameters only. To test it, the binding energy and optical bandgap of GaAs and thefamily of tri-halide perovskites (MAPbX3), X=Br,I,Cl, over a wide range of temperatures, areobtained by fitting the modified Elliott model. The results for the bandgap, linewidth andexciton binding energy are in good agreement with reports based on non-optical measurements.Moreover, due to the polar nature of perovskites, the retrieved binding energies can becompared with those computed with a model proposed by Kane (1978Phys. Rev.B186849). Inthe latter model, the exciton is surrounded by a cloud of virtual phonons interacting via theFr & ouml;lich interaction. As a consequence, the upper bound for the binding energy of theexciton-polaron system can be estimated. These results are in good agreement with the opticalparameters obtained with the proposed Elliott equation including BFs.