Publication
Formamidinium-lead-iodide (FAPbI3) has established itself as the state of the art for high solar-energy conversion efficiency in perovskite-based solar cells. FAPbI3 has a rich phase diagram, and it has been noted that long-range correlation between organic and lattice dipoles can influence phase transitions and, consequently, optoelectronic properties. In this regard, system size effects can play a crucial role for an appropriate theoretical description of FAPbI3. In this context, we perform a systematic study on the structural and electronic properties of the photoactive phase of FAPbI3 (α-FAPbI3) as a function of system size. By means of large-scale first-principles calculations and ab initio molecular dynamics simulations at 300 K, we demonstrated that in order to get an accurate description of the structural and electronic properties of the α-phase of FAPbI3 the size of the simulated system needs to approach the nanoscale. In particular, we showed that three conditions have to be met simultaneously, namely a proper description of the band gap, minimization of structural distortions, and the zeroing out of the total dipole moment. For first-principles calculations, it is essential to start from an initial configuration where the FAs are pseudo-randomly oriented by preserving the 3-fold symmetry and minimizing the dipole moment. At 300 K, because of the finite temperature dynamics, the initial configuration of the FAs is not stringent and, from a 2592-atoms cell upwards the PBE approximation is already able to describe the electronic band gap of α-FAPbI3. For the 6144-atoms cell, we have computed a band gap of 1.47 ± 0.08 eV which is in excellent agreement with the experimental values of 1.45-1.51 eV reported in literature (highlighting that PBE0 and SOC corrections only cancel out for this system size range). The same cell minimizes structural distortions with respect to the perfect α-FAPbI3 structure and has the lowest dipole moment among all the systems studied. A significant correlation was discovered between PbI6 octahedral tilting, band gap oscillations, and dipole moment. In particular, the dipole moment goes to zero only if the system size is large enough to properly relax the tilting pattern of the octahedra. Overall, an adequate size of the system (at least 6144-atoms cell) is needed to correctly describe its physics, as we have demonstrated with the identification of band gap domains related to a correct description of the octahedral tilting. Our work provides a detailed insight into the connection between structural and electronic properties of α-FAPbI3 - and MHPs in general - making an important contribution to the field of ab initio simulations dedicated to understanding fundamental physical principles, such as hole-electron transport, which is of paramount importance in the development of increasingly high-performance PSC devices.