Temperature Dependence of the Energy Levels of Methylammonium Lead Iodide Perovskite from First-Principles

Environmental effects and intrinsic energy-loss processes lead to fluctuations in the operational temperature of solar cells, which can profoundly influence their power conversion efficiency. Here we determine from first principles the effects of temperature on the band gap and band edges of the hybrid pervoskite CH3NH3PbI3 by accounting for electron-phonon coupling and thermal expansion. From 290 to 380 K, the computed band gap change of 40 meV coincides with the experimental change of 30-40 meV. The calculation of electron-phonon coupling in CH3NH3PbI3 is particularly intricate as the commonly used Allen-Heine-Cardona theory overestimates the band gap change with temperature, and excellent agreement with experiment is only obtained when including high-order terms in the electron-phonon interaction. We also find that spin orbit coupling enhances the electron-phonon coupling strength but that the inclusion of nonlocal correlations using hybrid functionals has little effect. We reach similar conclusions in the metal-halide perovskite CsPbI3. Our results unambiguously confirm for the first time the importance of high-order terms in the the electron-phonon coupling by direct comparison with experiment.