  One of the challenges of excitonic materials is the accurate determination of
the exciton binding energy and bandgap. 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 Elliott model and its several modifications such as non-parabolic bands,
magnetic potentials and electro-hole-polaron interactions. However, exciton
binding energies obtained from measured data often vary strongly depending on
the chosen model. 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
bands-fluctuations (BF) model. In this model, the fluctuations due to disorder,
temperature or lattice vibrations give rise to the well known exponential
distribution of band tail states (Urbach tails). This analysis results in an
analytic equation with 5 parameters only. The binding energies and optical
bandgaps of GaAs and the family of tri-halide perovskites
($\textrm{MAPbX}_{3}$), $\textrm{X=Br,I,Cl}$, over a wide range of
temperatures, are obtained with this model. The results for the bandgap,
linewidth and exciton binding energy are in good agreement with previous
reports. Moreover, due to the polar nature of perovskites, the obtained binding
energies can be compared with the ones computed with a theoretical model for
polar materials via a model proposed by Kane et al. In this model, the exciton
is surrounded by a cloud of virtual phonons interacting via the
Fr$\ddot{\textrm{o}}$lich interaction. As a consequence, the upper bound for
the binding energy of the exciton-polaron system is calculated. Coincidentally,
these results are in good agreement with the optical constants obtained with
the EBF model.
