Hole Polaron Transport in Bismuth Vanadate BiVO₄from Hybrid Density Functional Theory

Abstract

We address here the chemical character and the mobility of hole polarons in BiVO 4 (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 (BiO 8 ) dodecahedroncentered 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 + (BiO 8 ) hole structure and the h + (O) hole structure. For the smaller values of α, the h + (BiO 8 ) 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 + (BiO 8 ) holes from the Marcus/Holstein two-state model. The activation barrier for Bi-to-Bi hops (ΔG # ∼ 76 meV) and mobility (μ ∼ 0.029 cm 2 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 cm 2 V −1 s −1 , respectively). In h + (BiO 8 ) 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.

Boosting Charge Transport in BiVO4 Photoanode for Solar Water Oxidation

“…[9,10] In recent years, theoretical and experimental investigations have demonstrated that the charge polaron formation during the charge migration in the lattice of metal oxide photoanodes is an essential factor to impede charge transport in bulk as the polaron formed by charge carrier interacted with surrounding atoms moves slowly enough. [11][12][13][14] To inhibit the polaron formation, researchers have made many attempts, such as heteroatom doping, oxygen vacancy control, etc. [15][16][17][18] However, the electron and hole polarons of the BiVO 4 are localized in VO 4 units and BiO 8 units, respectively, [15][16][17][18][19] these previous attempts by heteroatom doping (substituting V atom), oxygen vacancies control, etc., that are suggested to be efficient for alleviating bulk recombination might only promote the electron migration, while the hole transport is scarcely tackled.…”

Charge Carrier Transport Mechanism in Ta2O5, TaON, and Ta3N5 Studied by Applying Polaron Hopping and Bandlike Models

“…[32] Usually, the parameters of hybrid functional can be selected by fitting it to match the band gap of a material in the experiment. From the study of doing polarons calculations in TiO 2 [33] and BiVO 4 [34] etc., we find in some cases, the commonly used hybrid functional, like PBE0 and HSE06 (α = 0.25), have already given a band gap in good consistent with the experimental velue, but the polaronic states cannot be achieved using these hybrid functionals. Here in cases of the Ta 2 O 5 , TaON, and Ta 3 N 5 , the band gap in experiment [35] is 3.9, 2.4, and 2.1 eV, respectively.…”

Detection and correction of delocalization errors for electron- and hole-polarons using density-corrected DFT

“…[16][17][18][19][20][21][22][23] Of particular interest in the present work are polaron defects in transition metal and maingroup oxides, where the extent of defect delocalization is sensitive to the fraction of exact exchange. [18][19][20][21][22][23][24][25][26][27][28][29][30] We demonstrate that density-corrected (DC-)DFT can be used both to detect and to correct over-delocalization of polaron defects. DC-DFT is a simple procedure whereby a selfconsistent Hartree-Fock (HF) density (ρ HF ) is used to evaluate the XC energy via a single Roothaan step: E xc [ρ HF ].…”