Fig. 4: Roles of doping and impurities in phase transition kinetics and thermodynamics of FAPbI₃.

Kinetic α-δ phase transition barrier \({E}_{b}\) and thermodynamic phase energy difference \({\triangle E}_{\delta -\alpha }\) of pristine FAPbI₃ and those with dopants and impurity interstitials. B-site cation engineering predominantly impacts the kinetics of the FAPbI₃ phase transition that dedicates the device longevity, as depicted by the green dashed circle (ellipse), whereas A-site doping more effectively alters the phase transition thermodynamics that can impact the perovskite crystallization, as depicted by the red dashed circle (ellipse). Moreover, the yellow region highlights various lanthanide doping and the purple stars stand for A-B mixed doping. The evolution of the bandgap and potential energy as a function of the reaction coordinate of the α-δ phase transition in the representative Cs−, Br−, Cl−, La−, and Ce-doped systems are shown in Supplementary Fig. 7.