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

Abstract

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^'A_<i>n</i>-1M_<i>n</i>X_3<i>n</i>+1, where <i>n</i> 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 <i>n</i>-dependent properties. A transition of the electronic and optical properties from quasi-two-dimensional behavior to three-dimensional behavior is shown for increasing <i>n</i>, and the nonhydrogenic character of the excitonic Rydberg series is analyzed. For methylammonium lead iodide perovskites with butylammonium spacers, our <i>n</i>-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 <i>n</i> = 1, 97 meV for <i>n</i> = 5, and 37 meV for <i>n</i> = ∞ (bulk MAPbI₃). A calculation for an exfoliated <i>n</i> = 1 bilayer predicts a very large 1s exciton binding energy of 444 meV.