Hole Polaron Transport in Bismuth Vanadate BiVO₄from Hybrid Density Functional Theory

Abstract

In this paper, we address the chemical character and the mobility of hole polarons in BiVO₄ (BVO). Two distinct structures for hole polarons in BVO have been reported in the literature to date. “Standard” hybrid density functional theory (DFT) calculations have predicted hole polarons to be (BiO₈) dodecahedron-centered polarons, while Hubbard U-DFT (DFT + U) calculations have predicted single oxygen atom-centered polarons. Resolving these contrasting findings is critical to validate theory in materials research. We investigated the structure of hole polarons in BVO using hybrid DFT with varying fractions (α) of the exact exchange interaction that enters hybrid functionals. For values of the fraction α, from α = 0.25 to α = 0.45, we obtained both structures, the h⁺(BiO₈) hole structure and the h⁺(O) hole structure. For the smaller values of α, the h⁺(BiO₈) structure is lower in energy, while for the larger values of α, the h+(O) structure is more stable. The piece-wise linearity of DFT energies E(q) with respect to a point defect charge q is maintained satisfactorily in all cases, although the deviation is the smallest for hybrid DFT with a small exact exchange fraction. For α = 0.25, we determined the diffusivity of h⁺(BiO₈) holes from the Marcus/Holstein two-state model. The activation barrier for Bi-to-Bi hops (ΔG^# ~76 meV) and mobility (μ ~0.029 cm2 V^–1 s^–1) are found to be in close agreement with the published THz experimental data (ΔG^# ~90 meV and μ_exp ~0.02 cm2 V^–1 s^–1, respectively). In h⁺(BiO₈) structures, nearly 25% of the hole charge and unpaired spin reside on the Bi atom and the rest is divided among the eight O atoms. The hole is best described as a Bi-centered hole, rather than a Bi 6s hole. In contrast, in h⁺(O) structures, about 75% of the unpaired spin population resides on the O atom. These findings suggest that if one wishes to resolve this theoretical dichotomy, there remains a need for further experimental characterization of hole polarons in BVO with techniques that could identify the oxidation state of Bi and O atoms in operando conditions and help validate theoretical results of structure and transport.