Energy profile and hopping barriers for small electron polarons at ferroelectric domain walls in bismuth ferrite from first principles

Abstract

Evidence from first-principles calculations indicates that excess electrons in BiFeO$_3$ form small polarons with energy levels deep inside the electronic band gap. Hence, $n$-type electronic transport could occur by hopping of small electron polarons rather than by band-like transport. Here, by means of first-principles calculations, small electron polaron hopping in BiFeO$_3$ is investigated. Both bulk BiFeO$_3$ and a typical ferroelectric domain wall, the neutral 71{\deg} domain wall, are considered. The latter is included to account for experimental observations of electrical conductivity at domain walls in otherwise insulating ferroelectrics. The object of this study is to shed light on the intrinsic electron conduction in rhombohedral BiFeO$_3$ and the effect of pristine neutral ferroelectric domain walls. The computed energy barriers for small electron polaron hopping are near 0.2 eV, similar to other perovskite oxides, both in the bulk and within the neutral 71\deg\ domain wall. Trapping energies of small electron polarons at the three prevalent domain walls, the 71\deg, the 109\deg, and the 180\deg\ wall, were determined. The domain walls are found to act as two-dimensional traps for small electron polarons, with a trap depth of about two times the thermal energy at room temperature. Based on these findings, the intrinsic $n$-type mobility and the diffusion constant in BiFeO$_3$ at room temperature are estimated, and experimental conductivity data for BiFeO$_3$ are discussed.