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A theoretical model for excitons confined in layered metal halide perovskitesis presented. The model accounts for polaronic effects, dielectric and quantumconfinement by means of effective mass theory, image charges and Hakenpotentials. We use it to describe the band edge exciton of MAPbI$_3$ structuressurrounded by organic ligands. It is shown that the quasi-2D quantum anddielectric confinement of layered perovskites squeezes the exciton radius, andthis in turn enhances polaronic effects as compared to 3D structures. Thestrong polaronic effects boost the binding energies and radiative recombinationprobabilities, which allows one to match experimental data in related systems.The thickness dependence of Coulomb polarization and self-energy potentials isin fair agreement with sophisticated atomistic models.

Excitons in layered metal halide perovskites: an effective mass description of polaronic, dielectric and quantum confinement effects