Large polaron formation and its effect on electron transport in hybrid perovskites

Abstract

Many experiments have indicated that a large polaron may be formed in hybrid perovskites, and its existence is proposed to screen the carrier–carrier and carrier–defect scattering, thus contributing to the long lifetime of the carriers.

Abstract

Many experiments have indicated that a large polaron may be formed in hybrid perovskites, and its existence is proposed to screen the carrier–carrier and carrier–defect scattering, thus contributing to the long lifetime of the carriers. However, a detailed theoretical study of the large polaron and its effect on carrier transport at the atomic level is still lacking. In particular, how strong is the large polaron binding energy? How does its effect compare with the effect of dynamic disorder caused by the A-site molecular rotation? And how does the inorganic sublattice vibration impact the motion of the large polaron? All of these questions are largely unanswered. In this work, using CH ₃NH ₃PbI ₃ as an example, we implement a tight-binding model fitted from density-functional theory to describe the electron large polaron ground state and to understand the large polaron formation and transport at its strong-coupling limit. We find that the formation energy of the large polaron is around −12 meV for the case without dynamic disorder, and −55 meV by including dynamic disorder. By performing the explicit time-dependent wavefunction evolution of the polaron state, together with the rotations of CH ₃NH ₃ ⁺ and vibrations of the PbI ₃ ⁻ sublattice, we studied the diffusion constant and mobility of the large polaron state driven by the dynamic disorder and the sublattice vibration. Two effects of the inorganic sublattice vibrations are found: on one hand, the vibration of the sublattice provides an additional driving force for carrier mobility; on the other hand, the large polaron polarization further localizes the electron, reducing its mobility. Overall, the effect of the large polaron is to slow down the electron mobility by roughly a factor of two. We believe that both dynamic disorder due to rotation of the organic molecule, and large polaron effects induced by the polarization and vibration of the inorganic sublattice, play important roles for the electronic structure and carrier dynamics of the system.