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The existence of strongly bound excitons is one of the hallmarks of the newlydiscovered atomically thin semi-conductors. While it is understood that thelarge binding energy is mainly due to the weak dielectric screening in twodimensions (2D), a systematic investigation of the role of screening on 2Dexcitons is still lacking. Here we provide a critical assessment of a widelyused 2D hydrogenic exciton model which assumes a dielectric function of theform {\epsilon}(q) = 1 + 2{\pi}{\alpha}q, and we develop a quasi-2D model witha much broader applicability. Within the quasi-2D picture, electrons and holesare described as in-plane point charges with a finite extension in theperpendicular direction and their interaction is screened by a dielectricfunction with a non-linear q-dependence which is computed ab-initio. Thescreened interaction is used in a generalized Mott-Wannier model to calculateexciton binding energies in both isolated and supported 2D materials. Forisolated 2D materials, the quasi-2D treatment yields results almost identicalto those of the strict 2D model and both are in good agreement with ab-initiomany-body calculations. On the other hand, for more complex structures such assupported layers or layers embedded in a van der Waals heterostructure, thesize of the exciton in reciprocal space extends well beyond the linear regimeof the dielectric function and a quasi-2D description has to replace the 2Done. Our methodology has the merit of providing a seamless connection betweenthe strict 2D limit of isolated monolayer materials and the more bulk-likescreening characteristics of supported 2D materials or van der Waalsheterostructures.

Excitons in van der Waals heterostructures: The important role of dielectric screening