Description of excitonic absorption using the Sommerfeld enhancement factor and band-fluctuations

Abstract One of the challenges of excitonic materials is the accurate determination of the exciton binding energy and bandgap from optical measurements. The difficulty arises from the overlap of the discrete and continuous excitonic absorption at the band edge. Many researches have modeled the shape of the absorption edge of such materials on the seminal formulation proposed by Elliott in 1957 ( Phys. Rev. 108 1384–9) and its several modifications such as non-parabolic bands, magnetic potentials and electron–hole-polaron interactions. However, exciton binding energies obtained from optical absorption often vary strongly depending on the chosen ‘Elliott formula’. 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 the band-fluctuations (BFs) model. In this model, the fluctuations due to disorder, temperature or lattice vibrations give rise to the well known exponential shape of band tail states. The formulation results in an analytic equation for the fundamental absorption with 6 parameters only. To test it, the binding energy and optical bandgap of GaAs and the family of tri-halide perovskites ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mtext>MAPbX</mml:mtext> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ), <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">X</mml:mi> <mml:mo>=</mml:mo> <mml:mi>Br</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">I</mml:mi> <mml:mo>,</mml:mo> <mml:mi>Cl</mml:mi> </mml:mrow> </mml:mrow> </mml:math> , over a wide range of temperatures, are obtained by fitting the modified Elliott model. The results for the bandgap, linewidth and exciton 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 be compared with those computed with a model proposed by Kane (1978 Phys. Rev. B 18 6849). In the latter model, the exciton is surrounded by a cloud of virtual phonons interacting via the Frölich interaction. As a consequence, the upper bound for the binding energy of the exciton-polaron system can be estimated. These results are in good agreement with the optical parameters obtained with the proposed Elliott equation including BFs.