Polarons in PbTiO3 ?
An Atomistic Investigation
2022/07/28 by K. Albe
The dissociation of short-lived excitons gives rise to free electrons and holes. If coupled with the motion of nuclei, these free charges get trapped at a lattice site and polarons form. Due to the involvement of lattice distortions in the formation of polarons, their lifetime exceeds that of excitons. In this study polaron formation and migration in PbTiO3 is addressed.
PbTiO3 is a prototypical ABO3 ferroelectric material, which is also the end member of several of the most important piezoelectric and ferroelectric solid solutions. Nevertheless, the formation and migration of small polarons on its technologically important tetragonal phase are missing in the literature. Using a Hubbard U parameter of 4.75 eV on a Ti d orbital, a 4 × 4 × 4 ?-centered k mesh, and the small-core PP of Ti, we identified the formation of a small STel with the trapping energy of 0.18 eV, which was in very good agreement with results obtained with the HSE06 functional (0.16 eV). Furthermore, we have investigated the migration of the STel using the nudged elastic band, resulting in a migration barrier of 0.21 eV, which is too high to have significant influence on the n-type conductivity of PbTiO3 .We also present the configuration coordinate diagram illustrating energy balance as a function of lattice distortions for delocalized and polaronic solutions and predict the energy required to absorb a photon for exciting an electron from a localized in-gap state to a delocalized band state to be 0.58 eV. Complementary insights on the optical transitions of the electron polaron were provided through calculating the schematic configuration coordinate diagram associated with the optical transitions of the STel using hybrid functional calculations. The results showed that recombination of the STel with a free hole in the valence band leads to an emission peak at 2.49 eV, giving rise to a green luminescence and in good agreement with the experimental optical emission peak at 2.4 eV. For the case of hole self-trapping on O 2p, we found that the localized holes are energetically less favorable than their delocalized counterparts.
