Efficacy of the DFT +  U formalism for modeling hole polarons in perovskite oxides

Abstract

We investigate the formation of self-trapped holes (STH) in three prototypical perovskites (SrTiO3, BaTiO3, PbTiO3) using a combination of density functional theory (DFT) calculations with local potentials and hybrid functionals. First we construct a local correction potential for polaronic configurations in SrTiO3 that is applied via the DFT+U method and matches the forces from hybrid calculations. We then use the DFT+U potential to search the configuration space and locate the lowest energy STH configuration. It is demonstrated that both the DFT+U potential and the hybrid functional yield a piece-wise linear dependence of the total energy on the occupation of the STH level suggesting that self-interaction effects have been properly removed. The DFT+U model is found to be transferable to BaTiO3 and PbTiO3, and STH formation energies from DFT+U and hybrid calculations are in close agreement for all three materials. STH formation is found to be energetically favorable in SrTiO3 and BaTiO3 but not in PbTiO3, which can be rationalized by considering the alignment of the valence band edges on an absolute energy scale. In the case of PbTiO3 the strong coupling between Pb 6s and O 2p states lifts the valence band minimum (VBM) compared to SrTiO3 and BaTiO3. This reduces the separation between VBM and STH level and renders the STH configuration metastable with respect to delocalization (band hole state). We expect that the present approach can be adapted to study STH formation also oxides with different crystal structures and chemical composition.

DFT+ U study of self-trapping, trapping, and mobility of oxygen-type hole polarons in barium stannate

“…(i) In titanates ATiO 3 (A = Pb, Ba, Sr), Erhart et al [13] have shown that LDA+U , with U = 8 eV, can be used to simulate oxygen-type self-trapped small hole polarons, reproducing in a satisfactory manner the results obtained on these entities by the hybrid HSE06 functional.…”

“…This is related to the band-gap problem, more precisely to the incorrect position of the valence band maximum, formed by oxygen-2p states, obtained with GGA. Moreover, density functional theory (DFT) at its local and semilocal level of approximation (LDA, GGA) is unable to capture the localized oxygen-type hole polarons, while hybrid functionals such as PBE0 or HSE06 are able to [13,14]. This is mainly due to the self-interaction error that local and semilocal functionals exhibit.…”

“…Alternatively, the so-called DFT+U with an onsite correction Hubbard term U applied on the p orbitals of oxygen, may successfully remove part of this self-interaction [15]. Indeed, it has been used in the past years to describe oxygen-type hole polarons in various charge-transfer insulating oxides, including titanate/zirconate perovskite oxides [4,13] or TiO 2 [16,17]. It is interesting to note that very large values of U (typically ∼5−10 eV) are needed, typical of the ones used in strongly correlated systems.…”

“…As a consequence, it exhibits self-interaction effects [42] when calculated in GGA-PBE, which destabilize the polaron and favor the delocalized state. Following Erhart et al [13] and Lindman et al [4], we compute, in the STHP geometry, the energy as a function of a fractional excess electronic charge in PBE + U . We plot this energy on Fig.…”

Density functional theory + U modeling of polarons in organohalide lead perovskites

“…In this letter, we employ the DFT+U Hubbard correction formalism developed by P. Erhart et al 24 performed using the Vienna Ab initio Simulation package (VASP), together with the projector augmented wave method (VASP-PAW) [25][26][27][28] and GGA-PBE for exchange and correlation. 29 First, we present the results of calculations for the perovskite CH 3 NH 3 PbI 3 , which is a benchmark absorber for solar cell devices.…”