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 CHNHPbI 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 CHNHPbI 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 CsPbI. Our results unambiguously confirm for the first time the importance of high-order terms in the electron-phonon coupling by direct comparison with experiment.