Impact of electron-phonon scattering on optical properties of CH$_3$NH$_3$PbI$_3$ hybrid perovskite material

Abstract: We investigate numerically the impact of the electron-phonon scattering on the optical properties of a perovskite material (CH3NH3PbI3). Using non-equilibrium Green functions formalism, we calculate the local density-of-states for several values of the electron-phonon scattering strength as well as in the case of ballistic transport. We report an Urbach-like penetration of the density-of-states in the bandgap due to scattering. The density-of-states expands deeper in the bandgap with the scattering strength. We determine the electronic current contributions relative to photon absorption and photon emission. This allows to estimate the Urbach energy from the absorption coefficient below the bandgap. Values of Urbach energy up to 9.5 meV are obtained, meaning that scattering contribution to the total experimental Urbach energy of 15meV is quite important. The Urbach tail is generally attributed to the disorder of the system, leaving hope for further improvement. Yet, we show in this work that a significant contribution to the Urbach tail comes from carriers-phonon interactions, an intrinsic properties of the material which thus set a lower bound on the improvement margin. Finally, we estimate the open-circuit voltage Voc for a solar cell assuming such a material as an absorber. Voc losses increase with the scattering strength, up to 41 mV. This study then confirms that scattering of electrons in perovskite material modifies the optical behaviour.