Origin of the Temperature-Induced Gap Bowing of Formamidinium-Methylammonium Lead Iodide Perovskites: Role of Cationic Rattlers

Abstract

A thorough understanding of the temperature dependence of semiconductor band gaps is essential for optimizing optoelectronic devices. In this respect, the origin of the pronounced temperature-induced gap bowing observed in low-temperature phases of formamidinium-methylammonium (FA-MA) lead iodide perovskites has remained elusive until now. By combining temperature and pressure-dependent photoluminescence measurements on a series of FA$_x$MA$_{1-x}$PbI$_3$ mixed-cation single crystals with $x\in[0,1]$, we unravel the origin of this bowing. Both thermal expansion as well as electron-phonon interaction effects are responsible. However, the latter is the leading term, driven by the activation of an anomalous electron-phonon coupling mechanism linked to mixed vibrational modes, which combine inorganic-cage phonons involving octahedral tilting with low-frequency FA librations, i.e., FA rattler modes. This occurs in the orthorhombic and (pseudo)tetragonal low-temperature phases, presumably featuring stripe domains with alternating octahedral tilt-axis patterns for FA concentrations between 20\% and 90\%. In this way, we have shed light on an intriguing behavior of lead halide perovskites that directly affects their optoelectronic properties.