Effects of Fluorination and Molybdenum Codoping on Monoclinic BiVO4 Photocatalyst by HSE Calculations.

Monoclinic phase bismuth vanadate (BiVO4) is one of the most promising photoelectrochemical materials used in water-splitting photoelectrochemical cells. It could be even better if its band gap and charge transport characteristics were optimized. Although codoping of BiVO4 has proven to be an effective strategy, its effects are remarkably poorly understood. Using the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional, we estimate the formation energy, electronic properties, and photocatalytic activities of F and Mo codoped BiVO4. We find that Mo atoms prefer to replace V atoms, whereas F atoms prefer to replace O atoms (FOMoV-doped BiVO4) under oxygen-poor conditions according to calculated formation energies. BiVO4 doped with FOMoV is found to be shallow-level doped, occurring with some continuum states above the conduction band edge, which is advantageous for photochemical catalysis. Moreover, FOMoV-doped BiVO4 shows absorption stronger than that of pure BiVO4 in the visible spectrum. Based on the band-edge calculation, BiVO4 doped with FOMoV still retains a high oxidizing capacity. It has been shown that FOMoV-doped BiVO4 exhibits a very high photocatalytic activity under visible light.

Introduction

In 1999, Kudo et al.[1] reported monoclinic phase bismuth vanadate (BiVO4) as a photocatalyst to achieve water oxidation. They used Ag+ ions as an electron scavenger under visible light irradiation. Since then, BiVO4 has gradually been a hot research topic because of its great potential in energy conversion and the environmental field. However, the wide application of BiVO4 is still limited. This is due to its low electron transfer efficiency,[2] slow water oxidation kinetics,[3] poor charge carrier mobility,[4] and weak surface adsorption capacity.[5] Therefore, various modification strategies have enhanced photocatalytic performance in the past few years. These strategies included morphological modification,[6] crystal facet control,[7] semiconductor coupling,[8,9] deposition of cocatalysts,[10] element doping,[11] and defect formation.[12]

Among the above strategies, the doping of pure BiVO4 with either anions or cations remains one of the most common methods used to increase carrier density and reduce charge transfer resistance. For cation doping, notably, Mo doping could effectively modulate the electronic structure of BiVO4, leading to both increased carrier concentration and improved optical absorption.[13] For example, Yang et al. synthesized a high-quality Mo-doped BiVO4 photoanode using a simple drop-casting method.[14] The results revealed that Mo-doped BiVO4 produced a much higher photocurrent than undoped BiVO4 under AM 1.5G illumination for water oxidation. For anion doping, it has been widely adopted to improve the electrochemical properties of BiVO4. Experimentally, a F-doped BiVO4 photocatalyst is synthesized by a simple two-step hydrothermal process.[15] It is found that the substitution of O by F could result in the decrease of the BiVO4 lattice parameters, influence the chemical environment surrounding the Bi, V, and O elements, cause the red-shift of the adsorption edge, and modify the absorption abilities in the visible light region. More importantly, the anion–cation codoping has been an effective method to improve the photocatalytic effect. For instance, Rohloff et al. fabricated a F/Mo:BiVO4 thin film photoanode via soft fluorination.[16] They demonstrated that anion and cation codoping in BiVO4 allows combining the PEC-relevant benefits associated with each type of dopant, the increased conductivity and charge separation due to Mo doping, and the increased water oxidation catalysis efficiency introduced by fluorination. However, it is still unclear what exactly these promoting effects are. The F/Mo codoping effects on BiVO4’s photocatalytic activity are still not entirely understood.

Theoretically, F- or Mo-doped BiVO4 has been calculated with the generalized gradient approximation (GGA)[17] of the Perdew–Burke–Ernzerhof (PBE)[18] method (GGA-PBE) and GGA+U method. Ding et al.[19] calculated the band structure and density of states of F-doped BiVO4. It was discovered that the doped F would act as electron capture traps that would benefit the separation of the photoinduced carriers and improve the photocatalytic performance of BiVO4. Because of the difference in valence electrons between the F and O atoms, the F atom has one more. The substitution of an F atom for an O atom in BiVO4 will increase the Fermi level by one electron. Our previous GGA+U study[11] for Mo-doped BiVO4 indicated that the Mo 4d impurity states would be observed in the band gap when Mo is doped on the Bi lattice site. It is important to note that these impurities can easily trap carriers and lower carrier mobility, which can harm the application of Mo-doped BiVO4 in the photoelectrochemical conversion of solar energy. There is no impurity state in the band gap while Mo is doping on the V lattice site. The band gap is smaller in this case, resulting in higher optical absorption. These results are the same as the other GGA method.[20] However, it is known that the GGA-PBE usually suffers from band gap underestimation.[21] Furthermore, the GGA+U correction was only applied to the d electrons of V and Mo, while the other components were treated within GGA. Thus, quantitatively more accurate calculations are necessary.

In this paper, based on the Heyd–Scuseria–Ernzerhof (HSE) hybrid functional, we calculate the formation energy, electronic properties, and photocatalytic activity of F and Mo codoped BiVO4. According to calculated formation energies, Mo atoms prefer to replace V atoms, whereas F atoms prefer to replace O atoms (FOMoV-doped BiVO4) under oxygen-poor conditions. BiVO4 doped with FOMoV is found to be shallow-level doped, with some continuum states occurring above the conduction band edge. Moreover, FOMoV-doped BiVO4 shows absorption stronger than that of pure BiVO4 in the visible spectrum. Based on the band-edge calculation, BiVO4 doped with FOMoV still retains a high oxidizing capacity. Thus, FOMoV-doped BiVO4 is particularly suitable for visible light photocatalysis. Our results provide more general design guidelines for the preparation of codoped BiVO4 with the promise of further performance improvements.

Computational Details

A plane-wave projector-augmented wave (PAW) method[22] is used to perform all density functional theory calculations using the Vienna Ab initio Simulation Package (VASP).[23,24] A kinetic-energy cutoff of 500 eV is tested to be sufficient for plane-wave expansion to achieve good convergence. Electronic self-consistent interaction convergence is considered sufficient for a total energy difference of less than 10–5 eV, and the forces on each ion converged were less than 0.03 eV/Å. The positions of all atoms in the system are allowed to relax. The PAW potentials with the valence electrons 6s26p3 for Bi, 3d34s2 for V, 2s22p4 for O, 2s22p5 for F, and 4d55s1 for Mo have been employed. We used the PBE exchange-correlation functional within the GGA[18] for geometry optimizations. Doping defect calculations are performed in a 2 × 2 × 1 supercell. For these systems, we used 3 × 3 × 3 Monkhorst–Pack k-point meshes,[25] which are found to be sufficient to reach convergence for bulk calculations and used for geometry optimization and electronic property calculations. It is well-known that the PBE typically suffers from the underestimation of the band gap.[26,27] The HSE[28,29] functional can now provide more accurate band gap measurements than the GGA methods. Therefore, this paper obtains the electronic structures, the optical absorption coefficient, and electrostatic potential energy using the HSE functional. For the HSE hybrid functional, the screening parameter is set to 0.2 Å–1, the Hartree–Fock mixing parameter is α = 0.15. Using these HSE parameters, we calculated the band gap of pure BiVO4 to be 2.4 eV, which is consistent with experiment (2.5 eV[30]) and the previous theoretical study (2.45 eV[8] and 2.58 eV[12]).

The defect formation energy is an essential measure of the stability for the F and/or Mo defects in BiVO4, which is defined as

In the formula, Edef and Epure are the total energies of supercells with a defect and a perfect supercell, respectively. The μi is the chemical potential of chemical species i (i = Bi, V, O, F, Mo). For Bi, V, and O in BiVO4, chemical potentials are not arbitrary but are influenced by thermodynamic constraints that can represent actual experimental conditions. In our previous work, we calculated the phase diagram of BiVO4 as a two-dimensional panel with three independent variables ΔμBi, ΔμV, and ΔμO by the HSE functional.[12] Thus, as shown in Figure S3 of ref (12), in this paper, we use representative chemical potential point AHSE (ΔμBi, ΔμV, ΔμO) = (−3.69, −8.27, 0) for the O-rich growth condition and DHSE (ΔμBi, ΔμV, ΔμO) = (0, −2.12, −2.46) for the O-poor growth condition. Due to μBi = EBi + ΔμBi, μV = ΔμV – EV, μO = ΔμO + EO, the corresponding chemical potential (μ) limits for AHSE (μBi, μV, μO) = (−7.98, −18.0, −6.16) and DHSE (μBi, μV, μO) = (−4.29, −11.85, −8.62).

In order to avoid the formation of phases containing impurities, the chemical potential of the impurities must meet the constraints. For Mo and F doping, the chemical potential of Mo and F is constrained by

Table summarizes the calculated formation energy (given per formula unit) for MoO3, MoF6, BiF3, VF2, and VF5, together with available experimental data. It is found that the HSE calculations produce similar results, and the calculated values agree with the experimental values. HSE total energy calculations are performed using experimental lattice constants for MoO3, MoF6, BiF3, VF2, and VF5. Table lists these lattice constants. The following calculations use maximum Mo and F chemical potential that satisfies these inequations.[31,32] Under the O-rich growth condition, Mo and F chemical potentials are −18.86 and −4.71 eV, respectively, whereas under the O-poor growth condition, Mo and F chemical potentials are −11.48 and −5.94 eV, respectively. We use these chemical potentials to calculate formation energy for Mo- and F-related defects.

Table 1

Formation Enthalpy (eV/formula unit) Calculated by HSE Functional Compared to Experimental Values[33]

	HSE	experiment
ΔHf(MoO3)	–6.80	–7.76
ΔHf(MoF6)	–16.58	–17.65
ΔHf(BiF3)	–9.90	–9.41
ΔHf(VF2)	–6.95	–8.72
ΔHf(VF5)	–16.23	–14.60

Table 2

Experimental Lattice Constants of MoO3, MoF6, BiF3, VF2, and VF5 Used for the HSE Functional Total Energy Calculationsa

	k-points	space group	experiment
MoO3	8 × 3 × 10	Pbmn	a = 3.964, b = 13.863, c = 3.699; α = 90, β = 90, γ = 90[34]
MoF6	3 × 4 × 6	Pnma	a = 9.480, b = 8.600, c = 4.993; α = 90, β = 90, γ = 90[35]
BiF3	5 × 5 × 5	Pm3m	a = 5.861, b = 5.861, c = 5.861; α = 90, β = 90, γ = 90[36]
VF2	6 × 6 × 9	P42/mnm	a = 4.804, b = 4.804, c = 3.236; α = 90, β = 90, γ = 90[37]
VF5	6 × 2 × 4	Pmcn	a = 5.4, b = 16.72, c = 7.53; α = 90, β = 90, γ = 90[38]

Values a, b, and c are in angstroms, and the values α, β, and γ are in degrees.

Results and Discussion

Doped Configuration and Formation Energies

Because the I2/b space group is easily related to the tetragonal scheelite structure for pure BiVO4, we chose to use it.[39] We used two BiVO4 units (primitive units) to determine the structure through careful optimization of volume and relaxation of atomic positions. The optimization parameters are as follows: a = 5.1556 Å, b = 5.0958 Å, c = 11.6067 Å, and γ = 90.2416°. There is good agreement between these lattice parameters and experimental values.[40] The results indicate that our calculation methods are accurate, while the calculated results are legitimate. In order to dope the structures, we used the 2 × 2 × 1 supercell of monoclinic BiVO4 (Figure a), which contains 64 oxygen atoms and 16 bismuth atoms. The doping concentration is about 1–2 atom %, consistent with the experimental results.[16] In order to introduce impurity atoms into the supercell, we use the modes FO (F atoms substituting for O atoms in the lattice, Figure b), MoBi (Mo atoms substituting for the Bi atoms in the lattice, Figure c), and MoV (Mo atoms substituting for V atoms in the lattice, Figure d), resulting in two different modes of F/Mo codoped monoclinic BiVO4 models FOMoBi-BiVO4 (Figure e) and FOMoV-BiVO4 (Figure f).

Figure 1

Doping structures of BiVO4 after geometry optimization. (a) Pure BiVO4, (b) FO, (c) MoBi, (d) MoV, (e) FOMoBi, and (f) FOMoV-doped BiVO4. The purple, green, red, black and blue spheres represent Bi, V, O, Mo and F atoms, respectively.

Table lists the formation energies for F and Mo monodoped and F/Mo codoped BiVO4 under O-poor and O-rich growth conditions. It can be seen from Table that the formation energies under the oxygen-poor condition are smaller than those of the oxygen-rich condition, which is consistent with the previous theoretical calculation.[31] This result implies that the oxygen-poor condition should always be used, whether cation site doping or anion site doping. Under the O-poor growth condition, the formation energy of FO is 0.75 eV, which is close to 0 eV. This result suggests that the F doping on the O site in BiVO4 is realized experimentally.[15,41,42] Under the O-poor and O-rich growth conditions, the formation energies of MoV are smaller than those of MoBi. This means the Mo atom prefers to substitute the V atom, consistent with the experimental[43] and theoretical[11,31] results. This has resulted in the formation energies of FOMoV being smaller than those of FOMoBi. This result suggests that the F/Mo codoped BiVO4 is much easier to form FOMoV-BiVO4,[16] and FOMoBi-BiVO4 is generally hard to obtain experimentally.

Table 3

Formation Energies (eV) for F and Mo Monodoped and F/Mo Codoped BiVO4

doped BiVO4	O-poor	O-rich
FO	0.75	1.98
MoBi	1.77	5.46
MoV	0.22	1.45
FOMoBi	2.19	7.11
FOMoV	0.75	3.21

Electronic Structures

Figure shows the total density of states (TDOS) and partial density of states (PDOS) of FO, MoBi, MoV, FOMoBi, and FOMoV-doped BiVO4 between −5 and 2 eV based on the HSE function. Additionally, the electronic properties of pure BiVO4 are also calculated in order to compare the F- and Mo-doped BiVO4. As shown in Figure a, the band gap of pure BiVO4 is 2.40 eV, consistent with the experimental data (2.50 eV)[30] and theoretical results.[8,12]

Figure 2

Total density of states and partial density of states for (a) bulk BiVO4 and (b) FO, (c)MoBi, (d)MoV, (e) FOMoBi, and (f) FOMoV-doped BiVO4. The red dot-dash lines denote the Fermi level.

For FO-doped BiVO4, the Fermi level is located at the top of the conduction band, as shown in Figure b. It is a typical n-type doping as the F atom has one more p electron than does the O atom. The band gap is 2.3 eV, similar to that of pure BiVO4, which is in excellent agreement with the experimental results.[15,41] The partial charge density at the conduction band minimum (CBM) is shown in Figure a. This implies shallow-level doping as the wave function is delocalized. The reason for this is that shallow levels have delocalized wave functions, whereas deep levels have localized ones.[31]Figure c shows the TDOS and PDOS of MoBi-doped BiVO4. There is an occupied state in the band gap at −0.45 to −0.71 eV below the Fermi energy. This occupied surface state is primarily dominated by O 2p, V 3d, and Mo 4d states. In the absence of occupied states, the band gap is 2.25 eV. This is evident in Figure b, which shows the partial charge density in the energy range between −0.45 and −0.71 eV below the Fermi level, indicating that the wave function is localized, especially around the Mo atom. The occupied state is considered to be a deep-level feature. It is likely that this deep level functions as a center of recombination for photoinduced e– and h+ during photocatalysis as it can easily trap carriers generated by photons.[44] This behavior is consistent with findings from previous studies.[45,46] For MoV-doped BiVO4, the DOS (Figure d) and partial charge density (Figure c) are similar to that of FO-doped BiVO4. This suggests that the Mo atom occupies the position of the V atom and that no impurity state appears in the band gap. This result is consistent with that of our previous calculations.[11]

Figure 3

Partial charge density of (a) FO, (b) MoBi, (c) MoV, (d) FOMoBi, and (e) FOMoV-doped BiVO4. The isosurface values are 0.007 e/Å3. The purple, green, red, black and blue spheres represent Bi, V, O, Mo and F atoms, respectively.

For FOMoBi-doped BiVO4, as shown in Figure e, the impurity state appears near the bottom of the conduction band edge and would also behave as a donor. A significant reduction in band gap from 2.4 to 2.05 eV is observed. The partial charge density at the CBM (Figure d) shows that the wave function is delocalized, implying shallow-level doping. However, as shown in Table , the formation energy of FOMoBi-doped BiVO4 is the highest under O-poor and O-rich conditions. They are unlikely to form. This indicates that the FOMoBi defect in BiVO4 is challenging to form.

Finally, for FOMoV-doped BiVO4, as shown in Figure f, similar to that of FOMoBi-doped BiVO4, the impurity state appears near the bottom of the conduction band edge and would also behave as a donor. Its band gap is 2.25 eV, smaller than that of bulk BiVO4 (2.4 eV). This suggests that visible light absorptions with red shifts of the optical band gap transition are expected compared with undoped BiVO4, which will be discussed in section . The partial charge density at the CBM (Figure e) shows that the wave function is delocalized, mainly over the V atoms and the Mo atom, which implies shallow-level doping. Thus, this shallow level doping state can promote the charge carrier mobility and photocatalytic activity of FOMoV-doped BiVO4 instead of the deep-level state. More importantly, under O-poor conditions, the formation energy of FOMoV-doped BiVO4 is the lowest (energetically favorable). This means that shallow-level doping and the lowest formation energy can explain the experimental observation of the FOMoV-doped BiVO4 enhanced photocatalytic efficiency.[16]

Optical Properties

In general, the optical absorption properties of photocatalytic semiconductor materials are closely related to their electronic band structure. It is a significant factor affecting the photocatalytic activity.[47] Due to their large formation energies, the optical absorption properties of MoBi and FOMoBi are not discussed in this paper. The frequency-dependent absorption coefficients[8,48,49] of the FO-, MoV-, and FOMoV-doped BiVO4 can be obtained from the frequency-dependent complex dielectric function:where ε1(ω) and ε2(ω) are the real and imaginary parts of the dielectric function, respectively, and ω is the phonon energy. The imaginary part ε2(ω) of the dielectric function ε(ω) is calculated using the standard formulation:[48]where V is the cell volume, ℏω is the incident photon’s energy, p is the momentum operator, |nk⟩ denotes the electronic state k in band n, and f is the Fermi occupation function. The real part ε1(ω) is related to ε2(ω) by the Kramer–Krönig transformation. The absorption coefficient α(ω) can be derived from ε1(ω) and ε2(ω) as follows:[8,49]

The frequency-dependent absorption coefficients along the [100], [010], and [001] directions between 1.5 and 3.5 eV are shown in Figure using the HSE method. It is shown that the doping effect on optical absorption coefficients along the [001] (Figure c) is larger than that along [100] and [010] directions (Figure a,b). Therefore, we focus on the optical absorption coefficients of the FO-, MoV-, and FOMoV-doped BiVO4 along the [001] direction. In Figure c, it can be seen that the optical absorption coefficients of the FOMoV-doped BiVO4 exhibit one main peak at 2.15 eV. This is due to a transition between nodes occupying the O 2p valence band and states occupying the V 3d and Mo 4d states. Among the main peaks, this one exhibits the most optical absorption (FO, MoV, and FOMoV). The results are also consistent with the aforementioned electronic properties. When the energy is greater than 2.4 eV, the optical absorption coefficient for the MoV-doped BiVO4 is significantly higher than the FOMoV-doped BiVO4. Further, this result shows that the MoV-doped BiVO4 highly effectively improves optical absorption in the visible region. This agrees with the experimental[14] and theoretical results.[11]

Figure 4

Calculated optical absorption spectra of the FO-, MoV-, and FOMoV-doped BiVO4 using the HSE method along with the (a) [100], (b) [010], and (c) [001] directions.

Band-Edge Potential

In general, the edge potentials of the conduction band (CB) and valence band (VB) significantly impact photocatalysis. The Mulliken electronegativity theory[50] can predict the CB and VB potentials of bulk BiVO4 and FO-, MoBi-, MoV-, FOMoBi-, and FOMoV-doped BiVO4: ECB = χ – Ec – 0.5Eg (or EVB = χ – Ec + 0.5Eg), where ECB (EVB) is the conduction (valence) band potential, χ is the absolute electronegativity of bulk BiVO4, and FO-, MoBi-, MoV-, FOMoBi-, and FOMoV-doped BiVO4, Ec is the energy of the free electron in the hydrogen scale (approximately 4.5 eV), and Eg is the band gap energy of the bulk BiVO4, and FO, MoBi, MoV, FOMoBi, FOMoV-doped BiVO4. The band position and photoelectric thresholds for several compounds have been calculated.[9,11,51,52]

Using the calculation method based on our previous literature,[52] we obtained the Mulliken electronegativity (χ) of Bi, V, O, F, and Mo from these data, which are 4.12, 3.60, 7.54, 10.40, and 4.05 eV, respectively.[53,54] The χ value for BiVO4 is 6.04 eV. Therefore, the ECB value of BiVO4 was calculated to be +0.33 eV, and the EVB value was estimated to be +2.73 eV, which agreed well with our previous calculation.[9]

The band-edge positions for bulk BiVO4 and FO-, MoBi-, MoV-, FOMoBi-, and FOMoV-doped BiVO4 are presented in Figure . As shown in Figure , the CBM of the FO-doped BiVO4 is shifted by 0.07 eV toward positive potential, and the VBM is lowered by 0.03 eV relative to that of the bulk BiVO4. Results showed that the oxidizing capacity of the VB and the reducing capacity of the CB both decreased. For MoBi-doped BiVO4, the CBM shifts by 0.07 eV toward positive potential, and the VBM is lowered by 0.08 eV compared to the bulk BiVO4, suggesting that both the VB’s and CB’s reducing capacities will decrease. In addition, one occupied state is introduced into the band gap. Consequently, its photocatalytic activity is negligible owing to its recombination center function. The CBM of MoV-doped BiVO4 is shifted by 0.05 eV toward positive potential, and the VBM is lowered by 0.05 eV compared to that of bulk BiVO4. The VB’s oxidizing capability and CB’s reducing capability are unchanged as a result of this study. CBM and VBM for FOMoBi-doped BiVO4 are shifted by 0.19 eV toward positive potential and 0.16 eV toward negative potential, respectively, suggesting that the VB’s oxidizing capacity and CB’s reducing capacity will both be significantly reduced. The band gap is 2.05 eV, which is the reason. Furthermore, for FOMoV-doped BiVO4, the CBM is shifted by 0.10 eV toward positive potential. The VBM is lowered by 0.05 eV, leading to a slight decrease in the oxidizing capacity of the VB and the reducing capacity of the CB. Under visible light irradiation, it exhibits high photocatalytic efficiency and a wide light response range. Its shallow-level doping leads to a small intrinsic band gap and the lowest formation energy.

Figure 5

Calculated band gaps and band edge positions of bulk BiVO4, MoBi, MoV, FOMoBi, and FOMoV doped using the HSE method. The VBM and CBM values are given concerning the standard redox potentials for water splitting.

Conclusion

This study calculates the formation energy, electronic properties, and photocatalytic activity of FOMoV codoped BiVO4 based on the HSE hybrid functional. From the calculated formation energies, we find that Mo atoms prefer to replace V atoms, whereas F atoms prefer to replace O atoms under oxygen-poor conditions. More importantly, BiVO4 doped with FOMoV is found to be shallow-level doped, with the occurrence of some continuum states above the conduction band edge. Moreover, FOMoV-doped BiVO4 shows absorption stronger than that of pure BiVO4 in the visible spectrum. Finally, based on the band-edge calculation, BiVO4 doped with FOMoV retains a high oxidizing capacity. The present results show consistency with the relevant experimental observations.