Modelling of mixed-phase MAPbI 3

Both x-ray diffraction (XRD) and photo-luminescence (PL) characterizations of methylammonium lead iodide perovskite (MAPbI 3 ) reveal signatures of a coexistence of the tetragonal and orthorhombic phases over a wide range of temperatures, suggesting that the phase transition does not happen sharply at a temperature of 164 K as reported in literature. To understand the causes of this discrepancy we investigated the evolution of the phase mixture from 300 K down to 80 K and its influence on electrical device characteristics. For this we developed a numerical approach to extract effective electrical parameters like resistivity for the mixed-phase MAPbI 3 as a function of temperature and volume ratio of the two phases. The spatial distribution of the tetragonal and orthorhombic phases and their evolution with temperature has been extracted from measured XRD maps, employing a Monte Carlo algorithm to interpolate between measured temperatures. The electrical simulations have been performed by means of the drift-diffusion model.