  The existence of strongly bound excitons is one of the hallmarks of the newly
discovered atomically thin semi-conductors. While it is understood that the
large binding energy is mainly due to the weak dielectric screening in two
dimensions (2D), a systematic investigation of the role of screening on 2D
excitons is still lacking. Here we provide a critical assessment of a widely
used 2D hydrogenic exciton model which assumes a dielectric function of the
form {\epsilon}(q) = 1 + 2{\pi}{\alpha}q, and we develop a quasi-2D model with
a much broader applicability. Within the quasi-2D picture, electrons and holes
are described as in-plane point charges with a finite extension in the
perpendicular direction and their interaction is screened by a dielectric
function with a non-linear q-dependence which is computed ab-initio. The
screened interaction is used in a generalized Mott-Wannier model to calculate
exciton binding energies in both isolated and supported 2D materials. For
isolated 2D materials, the quasi-2D treatment yields results almost identical
to those of the strict 2D model and both are in good agreement with ab-initio
many-body calculations. On the other hand, for more complex structures such as
supported layers or layers embedded in a van der Waals heterostructure, the
size of the exciton in reciprocal space extends well beyond the linear regime
of the dielectric function and a quasi-2D description has to replace the 2D
one. Our methodology has the merit of providing a seamless connection between
the strict 2D limit of isolated monolayer materials and the more bulk-like
screening characteristics of supported 2D materials or van der Waals
heterostructures.
