Optical Properties of Layered Hybrid Organic–Inorganic Halide Perovskites: A Tight-Binding GW-BSE Study

We
present a many-body calculation of the band structure and optical
spectrum of the layered hybrid organic–inorganic halide perovskites
in the Ruddlesden–Popper phase with the general formula A2′An–1MnX3n+1, where n controls the thickness
of the primarily inorganic perovskite layers. We calculate the mean-field
band structure with spin–orbit coupling, quasi-particle corrections
within the GW approximation, and optical spectra using the Bethe–Salpeter
equation. The model is parametrized by first-principles calculations
and classical electrostatic screening, enabling an accurate but cost-effective
study of large unit cells and corresponding n-dependent
properties. A transition of the electronic and optical properties
from quasi-two-dimensional behavior to three-dimensional behavior
is shown for increasing n, and the nonhydrogenic
character of the excitonic Rydberg series is analyzed. For methylammonium
lead iodide perovskites with butylammonium spacers, our n-dependent 1s and 2s exciton energy levels are in good agreement
with those from recently reported experiments, and the 1s exciton
binding energy is calculated to be 302 meV for n =
1, 97 meV for n = 5, and 37 meV for n = ∞ (bulk MAPbI3). A calculation for an exfoliated n = 1 bilayer predicts a very large 1s exciton binding energy
of 444 meV.