Hybrid Density Functional Theory Study of Native Defects and Nonmetal (C, N, S, and P) Doping in a Bi₂WO₆ Photocatalyst

Abstract

Native defects and nonmetal doping have been shown to be an effective way to optimize the photocatalytic properties of Bi₂WO₆. However, a detailed understanding of defect physics in Bi₂WO₆ has been lacking. Here, using the Heyd–Scuseria–Ernzerhof hybrid functional defect calculations, we study the formation energies, electronic structures, and optical properties of native defects and nonmetal element (C, N, S, and P) doping into Bi₂WO₆. We find that the Bi vacancy (Bi_vac), O vacancy (O_vac), S doping on the O site (S_O), and N doping on the O site (N_O) defects in the Bi₂WO₆ can be stable depending on the Fermi level and chemical potentials. By contrast, the substitution of an O atom by a C or P atom (C_O, P_O) has high formation energy and is unlikely to form. The calculated electronic structures of the Bi_vac, O_vac, S_O, and N_O defects indicate that the band-gap reduction of O_vac²⁺, Bi_vac, and S_O defects is mainly due to forming shallow impurity levels within the band gap. The calculated absorption coefficients of O_vac²⁺, Bi_vac, and S_O show strong absorption in the visible light region, which is in good agreement with the experimental results. Hence, O_vac²⁺, Bi_vac, and S_O defects can improve the adsorption capacity of Bi₂WO₆, which helps enhance its photocatalytic performance. Our results provide insights into how to enhance the photocatalytic activity of Bi₂WO₆ for energy and environmental applications through the rational design of defect-controlled synthesis conditions.

1. Introduction

Visible-light-driven photocatalysts are promising candidates for solving the energy crisis and environmental pollution problems because of their high efficiency and clean and renewable characteristics.¹⁻⁵ Recently, Bi³⁺-based oxides such as BiOCl,⁶⁻⁹ Bi₂MoO_6,¹⁰ and Bi₂WO₆¹¹⁻¹³ are fascinating and of practical importance for visible-light-driven photocatalysts. Among these materials, Bi₂WO₆, as an n-type semiconductor with a 2.80 eV¹³ band gap, is an interesting Aurivillius phase of perovskite layers inserted between Bi₂O₂ layers. Its potential applications, including solar cells, electrode materials, an excellent photocatalyst for water splitting, and photodegradation of organic pollutants.^11,14−17

However, the visible-light-responsive photocatalytic application of Bi₂WO₆^11,18,19 is limited by rapid recombination of excitonic pairs, ineffective charge separation, and poor visible-light absorption. Various improvement methods have been developed to improve the photocatalytic activity, for example, semiconductor coupling,²⁰ morphology control,^21,22 noble metal deposition,²³ and metal or nonmetal ion doping.²⁴⁻³³ All these methods can improve the photocatalytic activity of Bi₂WO₆. Nonmetallic element doping is regarded as an efficient approach to enhance the activity. For example, Hoang et al.³⁰ synthesized N-doped Bi₂WO₆ by using a two-step microwave-assisted and hydrothermal method. It was found that 0.25% (atomic ratio) N-doped Bi₂WO₆ exhibited the best photocatalytic activity. This is due to the most significant decrease in the recombination rate of photogenerated electron–hole pairs. Fu et al.²⁹ reported that doping Bi₂WO₆ with 0.5% B displayed the highest photocatalytic activity under visible-light irradiation. This is because the doped B atoms could act as electron traps and facilitate the separation of photogenerated electron–hole pairs. Shang et al.³¹ demonstrated that doping Bi₂WO₆ with N could significantly enhance photocatalytic activities. The reasons are that N doped into Bi₂WO₆ not only broadens the range of light absorption in the visible region but also inhibits the photogenerated electron–hole recombination losses and increases the transfer rate. However, the nature of the promoting effects remains elusive. A complete understanding of the nonmetallic-induced photocatalytic activity of Bi₂WO₆ is still lacking.

The formation of intrinsic defects (such as Bi vacancy, W vacancy, O vacancy, and so on) may compensate the extrinsic nonmetallic doping into Bi₂WO₆. Therefore, the intrinsic defects of Bi₂WO₆ had been studied both theoretically and experimentally. For example, Huo et al.³⁴ showed that the photocatalytic NO oxidation activity was enhanced by introducing oxygen vacancy defects into Bi₂WO₆. Using the GGA (generalized gradient approximation) + U method, they reported that oxygen vacancies narrow band gaps compared with perfect Bi₂WO₆. Di et al.¹⁵ had engineered bismuth vacancies into Bi₂WO₆ using a highly efficient template-directed strategy. They found that bismuth vacancies favor water oxidation reactions. Their PBE (Perdew–Burke–Ernzerhof) calculations suggest that bismuth vacancies in Bi₂WO₆ would induce new energy levels in the band gap, increasing its conductivity.

Theoretically, intrinsic defects and nonmetallic doping in Bi₂WO₆ have been calculated with the GGA-PBE and DFT + U method.^{15,28,34−36} However, they only focus on neutral impurities and their electronic properties. Note that the formation energy of a neutral defect is independent of the position of the Fermi level. Whether an impurity or defect becomes electrically active or instead remains inactive often depends on the growth conditions (e.g., the presence of native defects) and cannot directly be inferred from a DFT calculation on a neutral defect alone.³⁷ In addition, GGA-PBE yield significantly underestimated band gaps, i.e., 1.85–1.95 eV, compared to the experimental value of 2.80 eV.¹³ Moreover, the GGA + U correction was only employed for W’s d electrons, whereas all other components were treated within GGA. Hence, quantitatively more reliable calculations are required. As proposed by Heyd, Scuseria, and Ernzerhof (HSE06),^38,39 it provides the best overall performance compared to GGA-PBE and GGA + U. More importantly, previous results have shown that the HSE06 hybrid functional is a reliable method to calculate transition levels and formation energies of defects.⁴⁰

This paper systematically studies the doping properties for both intrinsic and nonmetal (C, N, S, and P) doping of Bi₂WO₆ and understands how they can change the electronic structure and optical absorption properties using the HSE06 hybrid approach. We calculate the transition energies and formation energies of intrinsic and impurity defects and Fermi-level pinning positions. The Bi_vac, O_vac, S_O, and N_O have rather low formation energies. Due to C_O and P_O having higher formation energies, they are unlikely to form. The calculated electronic structures of Bi_vac, O_vac, S_O, and N_O defects implied that O_vac²⁺, Bi_vac, and S_O defects can narrow the band gap of Bi₂WO_6, and no recombination centers occurred, which can improve photocatalysis of Bi₂WO₆. The calculated absorption coefficients of O_vac²⁺, Bi_vac, and S_O show strong absorption in the visible region. Our results suggest that O_vac²⁺, Bi_vac, and S_O doping is able to narrow the band gap, and thus these defects are good dopant candidates to tailor the visible light absorption property of Bi₂WO₆ photocatalysts.

2. Results and Discussion

2.1. Formation Energy

For vacancy calculations, one atom is removed from the supercell, and the remaining atoms are allowed to relax. Here, we consider three types of intrinsic defects in the Bi₂WO₆ lattice for various possible charge states, including Bi_vac, W_vac, and O_vac. The substitutional defect X_O is created by replacing a lattice O by X (X = C, N, S, and P). The defect formation energies for various charge states in Bi₂WO₆ are plotted as a function of the electronic Fermi energy for five representative chemical potential conditions with the finite size corrections in Figure 1. As shown in Figure 1, all the defects’ formation energies depend on the growth condition and the Fermi level. The energy of a defect with a charge state is only shown for the range of Fermi levels where the charge state has the lowest energy. In Figure 1, the line’s slope is associated with the most stable charge state of a defect, and the transition levels lie where the slopes change. Moreover, Figure 1 depicts that the formation energies of intrinsic defects and nonmetal-doped (C, N, S, and P) defects in the charge-neutral charge states are constant regardless of the variations in Fermi energy.

Figure 1.

Defect formation energy calculations of Bi₂WO₆ supercells with various types of point defects in different charge states using the HSE06 method as a function of the Fermi level (referenced to valence band maximum) under (a) C, (b) D, (c) E, (d) F, and (e) M growth conditions (see Figure 5). The energetic value of the Fermi level pinning was indicated by red dashed lines. The slope of the curves indicates the charge state, and the kinks in the curves indicate the transition of charge states. The numbers in the plot indicate the defect charge state; parallel lines imply equal charge states. For each defect, only the charge states that are energetically most favorable at a given Fermi energy are shown.

In Figure 1a,c,e, at chemical potentials C, E, and M, the results show that the dominant native acceptor is Bi_vac, while the primary native donor is O_vac. The Fermi level is pinned (where the formation energy lines cross the energy overlap of the lowest-energy donor and acceptor) by Bi_vac and O_vac. However, the position of the Fermi level pinning is different. At chemical potentials C, the Fermi level is pinned to be at ∼1.1 eV above VBM, showing a p-type conductivity. At chemical potential E, as O_vac is positively charged and Bi_vac is negatively charged for Fermi level within the band gap, these defects self-compensate, and the Fermi level is pinned roughly around the midgap, resulting in the intrinsically insulating property. At chemical potential M, the Fermi level is pinned to be at ∼0.75 eV below CBM within the n-type region. These results imply that it is possible to control the growth condition to obtain the conductivity from p-type to good n-type. At chemical potentials C and E, the formation energy of the W_vac defect is similar to that of O_S and O_N. Whereas, at chemical potential M, the formation energy of the W_vac defect significantly increased. These results indicated that the oxygen-rich environment could promote the formation of W vacancies. Moreover, under these conditions (chemical potentials C, E, and M), the formation energy of O_p, and O_c is very high, > 9 eV, which means that it is difficult to dope C and P into Bi₂WO₆. For PBE results, as shown in Figure S2 of the Supporting Information, the transition trends of formation energy as a function of the Fermi level are almost identical with the transition trends calculated by the HSE method. However, the energy of the pinned Fermi level is different. This is because the PBE method underestimates the band gap of Bi₂WO₆.

However, in Figure 1b,d, under the oxygen-poor/bismuth-rich conditions (chemical potentials D and F), we find that the formation energy of Bi_vac increases evidently when the formation energy of O_N and O_S both decrease. Thus, the lowest-formation energy defects are V_O as E_F < 1.55 eV. When E_F > 1.55 eV formation energies of O_vac and O_S are almost identical, which is the lowest-formation energy defects between these ranges. We notice that the formation energy of O_N is also low in the same range of E_F. Therefore, it is easy to synthesize N-doped bismuth tungstate experimentally.^30,31,41 Under these conditions, the Fermi level is pinned by O_vac and O_N, which is to be at ∼0.79 eV below CBM, within the n-type region. Meanwhile, the formation energy of the W_vac defect is the highest than others for the Fermi level within the band gap. Moreover, O_P’s and O_C’s formation energies both decrease, but the value is about 6 eV, which is still very high. These results suggested that W_vac, O_P, and O_C defects are unlikely to form.

The transition (ionization) levels of low-energy defects depend on free carrier generation and its contribution to the electrical conductivity,⁴² which can be derived according to the turning points in Figure 1. We are concerned about the transition level of Bi_vac, O_vac, and O_N defects due to lower formation energy compared with the other defects. The ε(−/0) thermodynamic transition level (ionized from neutral to −1 charged) of Bi_vac is located at 0.17 eV above VBM, thereby demonstrating its shallow donor character, which agrees with the experimental observation.¹⁵ For O_vac, the donor (+2/+1) transition level is observed at 0.45 eV above VBM, while (+1/0) donor levels appear to be localized deep into the band gap 1.50 eV above VBM. Unlike the O_vac, the density of states (DOS) for O_vac²⁺ show delocalized distribution (we will address this issue in Section 2.2). This suggests that the O_vac acceptor state is not a deep, localized state. Such shallow levels not only extend the absorption spectra of O_vac²⁺ in Bi₂WO₆ but also play a role as trap levels, which increase the carrier lifetime.^43,44 For all the chemical potentials, the formation energy of the donor O_vac is the lowest when the conductivity is p-type. Therefore, the ionization of the dominant O_vac²⁺ with a high concentration can produce an evident amount of hole carriers, resulting in good p-type conductivity. Moreover, the acceptor (−1/0) level associated with O_N appears to be localized deep at 1.38 eV above VBM, which may act as recombination centers.

2.2. Electronic Structure with HSE06

In Figure 2, we present the total density of states (TDOS) and partial density of states (PDOS) for different native defects of Bi₂WO₆ between −5 and 6 eV using the HSE06 functional. We focus on the defects O_vac, O_vac⁺, O_vac, Bi_vac^2–, Bi_vac, N_O, N_O^–, and S_O. This is because these defects have the lowest formation energies under different chemical conditions for a certain range of Fermi level. The electronic properties of pure Bi₂WO₆ were also calculated to compare with native defects of Bi₂WO₆, as shown in Figure 2a. For pure Bi₂WO₆, the valence band maximum (VBM) of the Bi₂WO₆ is predominantly composed of O 2p states, which hybridize with the Bi 6s 6p and W 5d states of relatively lower density. Unlike the VBM, the conduction band minimum (CBM) has nearly identical contributions from the O 2p orbitals and the W 5d orbitals. These results are in good agreement with previous theoretical results.^28,36,45

Figure 2.

Spin-polarized density of the states (DOS) for the (a) bulk Bi₂WO₆, (b) Bi_vac^2–, (c) Bi_vac, (d) O_vac (e) O_vac¹⁺, and (f) O_vac defect. The red dotted lines denote the Fermi level. Positive (negative) values of the DOS denote spin up (down).

For the Bi_vac^2– defect, as shown in Figure 2b, we find that an occupied state in the gap (at about 0.1 eV below the Fermi level) and an isolated empty band (at about 0.9 eV above the Fermi level). These two states are mainly composed of O 2p orbitals, which may act as recombination centers when electron–hole pairs are generated. This is consistent with a previous theoretical result,¹⁵ where they only focus on the neutral bismuth vacancy. Moreover, there is a shallow defect level underneath the CBM concerning that of the pure Bi₂WO₆. An attempt to add an electron, for the Bi_vac defect, we observe from Figure 2c that the Fermi level is at the edge of the conduction band, which exhibits typical n-type characteristics. There are two occupied states (one is spin up, and another is spin down) near the Fermi level. Its localization character is fragile. This suggests that the band gap of Bi_vac^3–:Bi₂WO₆ is narrower than the band gap of undoped Bi₂WO₆, and thus the photoabsorption probability increases.

In addition, these delocalization characters of the defect level and enhanced DOS will favor the electron transition into the conduction band under the irradiation, leading to a higher carrier concentration and an increasing electronic conductivity.^46,47 It has been reported that bismuth vacancy-rich Bi₂WO₆ exhibits significantly increased visible-light photocatalytic oxygen evolution activity than that of pristine Bi₂WO_6.¹⁵ This activity can be explained by the formation of the Bi_vac^3– defect. This is because not only the formation energy of Bi_vac is the lowest under oxygen-rich conditions when E_F > 2.31 eV, but also it has a narrow band gap, such that its absorption is increased. More importantly, there is no recombination centers that occurred.

For the neutral oxygen vacancy, as shown in Figure 2d, there are two spin-degenerated occupied states (the positive is spin up, and the negative is spin down) in the vicinity of midgap. These two states are dominated by Bi 6p orbitals, serving as a recombination center, which decreases the efficiency of charge separation. As shown in Figure 2e, the DOS of O_vac¹⁺ is similar to the DOS of Bi_vac. There is an occupied state in the gap (at about 0.1 eV below the Fermi level) and an isolated empty band (at about 0.9 eV above the Fermi level), which also act as recombination centers. However, as shown in Figure 2f, for O_vac²⁺, the Fermi level is at the edge of the valence band, which exhibits typical p-type characteristics. There are two empty states (one is spin up, and another is spin down) near the Fermi level, which shows the delocalization character. This suggests that the band gap of O_vac/Bi₂WO₆ is narrower than the band gap of pristine Bi₂WO_6, and its absorption is increased. The O_vac^2– defect can enhance the photocatalytic activity, while O_vac and O_vac degrade, and it is desirable to induce the former one as much as possible and suppress the latter. This can be achieved by controlling E_F < 0.45 eV under any environment (Figure 2), as discussed in the previous section.

In Figure 3, we plot the TDOS and PDOS for different nonmetal elements (N and S) doping into Bi₂WO₆ between −5 and 6 eV using the HSE06 functional. For the N_O defect, as shown in Figure 3a, we found an isolated empty band (at about 1.0 eV above the Fermi level). This state is mainly composed of N 2p orbitals, which may act as recombination centers when electron–hole pairs are generated. This is consistent with the localized deep (−1/0) transition level of O_N that appears to be at 1.38 eV above VBM. Based on the previous analysis, this defect is not natural to be formed because the formation energy of N_O is higher than that of compensated defect O_vac under any conditions. When one more electron is injected, the empty band of O_N is occupied by the extra electron (Figure 3b). The occupied states are moved below the Fermi level. These states are mainly composed of N 2p orbitals, which results in a higher degree of delocalization and a correspondingly reduced band gap of pure Bi₂WO₆. As shown in Figure 2, under the oxygen-poor/bismuth-rich conditions, the formation energy of N_O^– is almost the same as the lowest formation energy (O_vac and O_S). Therefore, experimentally synthesized N-doped Bi₂WO₆ samples^30,31,41 may be N_O. This explains the experimental observations of a better photocatalysts efficiency performance of N-doped Bi₂WO₆.

Figure 3.

Spin-polarized DOS for the (a) N_O, (b) N_O^1–, and (c) S_O defects using the HSE06 functional. The red dotted lines indicate the Fermi level. Positive (negative) values of the DOS denote spin up (down).

It is shown that the band gap of S-doped Bi₂WO₆ is about 2.33 eV in Figure 4c, which is reduced by 0.46 eV comparing with pure Bi₂WO₆. The substitution S mainly modifies the valence band edge and forms the O 2p and S 2p hybridization states on the valence band’s band edge. Thus, the S doping narrows the band gap of Bi₂WO₆ without localized gap states, which yields a clean band gap by maintaining the stability of the photocatalyst and avoids the formation of the recombination centers, leading to better photocatalytic performance. Therefore, the S–Bi₂WO₆ may be good candidates for visible-light photocatalysis.

Figure 4.

Square of the wave functions corresponding to the defect states near the Fermi level in the band gap created by (a) Bi_vac^2–, (b) Bi_vac, (c) O_vac, (d) O_vac¹⁺, (e) O_vac, (f) N_O, (g) N_O^1–, and (h) S_O defects. The isosurface value is 0.003 e/ų. The purple, gray, red, blue, and yellow spheres represent Bi, W, O, N, and S atoms, respectively.

It is known that the shallow levels have delocalized wave functions. On the other hand, deep levels have localized ones.⁴⁸⁻⁵⁰ As shown in Figure 4, we have plotted the wave-function squares of the Bi_vac^2–, Bi_vac, O_vac, O_vac¹⁺, O_vac, N_O, N_O^1–, and S_O defect states near the Fermi level in the band gap. Figure 4b,e,h plots the wave-function square of the Bi_vac, O_vac²⁺, and S_O defect states. The wave function of the defect states distributes not only around the defects but also around O atoms away from the W atom, indicating a delocalized feature, which is consistent with the result that Bi_vac, O_vac²⁺, and S_O are shallow defects near the Fermi level in the band gap. Figure 4a,c,d,f,g plots the wave-function square of the Bi_vac, O_vac, O_vac¹⁺, N_O, and N_O defect states near the Fermi level in the band gap, respectively. It is seen that the wave function is localized around defects, consistent with the deep-level feature.

Generally, the conduction band (CB) and valence band (VB) edge potentials of a semiconductor play a vital role in the photocatalysis process. The Mulliken electronegativity theory⁵¹ can predict the conduction band and valence band potentials of Bi₂WO₆: E_CB = χ – E^c – 0.5E_g, (or E_VB = χ – E^c + 0.5E_g), where E_CB (E_VB) is the conduction (valence) band potential, the χ is the absolute electronegativity of bulk Bi₂WO₆, E^c is the energy of the free electron in the hydrogen scale (approximately 4.5 eV),⁵² and E_g is the band gap energy of the Bi₂WO₆ (2.79 eV). Using the Mulliken electronegativities, the band position and photoelectric thresholds for many compounds have been calculated.⁵³⁻⁵⁵

For the Mulliken electronegativity (χ) of compound A_aB_bC_c can be calculated according to the following equation:^56,57, where χ (A), χ (B), and χ (C) are the absolute electronegativity of the A atoms, B atoms, and C atoms respectively; the a, b, c are the number of A atoms, B atoms, C atoms in an A_aB_bC_c compound, respectively. According to the Mulliken definition, per atom’s absolute electronegativity is equal to the arithmetic mean of the atomic electron affinity (A) and the first ionization energy (I).⁵⁶ From these data, we obtained the Mulliken electronegativity of Bi, W, O, N, and S that are 4.12, 4.40, 7.54, 7.24, and 6.22 eV, respectively.^58,59 The χ value for Bi₂WO₆ is 6.2 eV. Hence, the E_CB value of Bi₂WO₆ was calculated to be +0.31 eV, and the E_VB value was estimated to be +3.10 eV, which agreed well with the previous calculation.⁶⁰

To evaluate the defects’ influence on the photocatalytic activity of Bi₂WO₆, the CBM and VBM of the Bi_vac^3–, O_vac, and S_O defects concerning the Bi₂WO₆ are presented in Figure 5. As sown in Figure 5, for the Bi_vac^3– defect, the VBM is raised by 0.08 eV, and the CBM is lowered by 0.03 eV relative to that of the pure Bi₂WO₆. This result indicated that the oxidizing capacity of the VB and the reducing capacity of the CB are reduced. Meanwhile, some defect states are introduced in the band gap, and the electron transition among the VB, CB, and these gap states leads to the visible-light absorption. For O_vac defects, the CBM does not change, and the VBM is reduced by 0.24 eV relative to that of the pure Bi₂WO_6, which suggests that the oxidizing capacity of VB will decrease. This is due to the band gap is reduced to 2.84 eV. Only one spin up and one spin down defect states appear in the band gap. Immensely, for the S_O defect, the CBM does not change, and the VBM is raised by 0.25 eV relative to that of the pure Bi₂WO₆. This result suggested that the oxidizing capacity of the VB is improved. One occupied state and one unoccupied state are introduced in the band gap, improving the visible-light absorption capacity of Bi₂WO₆.

Figure 5.

Calculated VBM and CBM positions of pure Bi₂WO₆, Bi_vac^3–, O_vac, and S_O defects in Bi₂WO₆ obtained from HSE06 calculations. The VBM and CBM values are given concerning the normal hydrogen electrode (NHE) potential. The black and green arrowheads represent the occupied and unoccupied states of defect states, respectively.

2.3. Optical Properties

Generally, the optical absorption properties of photocatalytic semiconductor material are closely related to its electronic band structure. This is a significant factor affecting the photocatalytic activity.⁵⁴ In this study, we focus on the Bi_vac^3–, O_vac, and S_O defects. This is because these defects narrow the band gap of Bi₂WO₆, and no recombination centers are formed. The calculated absorption coefficients along the [001] direction for Bi_vac^3–, O_vac, and S_O defects in Bi₂WO₆ are shown in Figure 6. For comparison, the absorption coefficient of Bi₂WO₆ was also calculated. Figure 6 indicates that pure Bi₂WO₆ cannot absorb the visible light effectively due to its wide band gap. After Bi_vac^3–, O_vac, and S_O doping, the absorption coefficients in the visible-light region are enhanced, and a redshift is observed on the absorption edge. The high optical absorption results from the narrow band gap and the weak electron–hole recombination, as mentioned already. In the energy region between 1.5 and 2.75 eV, the absorption coefficients of Bi_vac^3–, and O_vac are more extensive than that of S_O. When the energy is higher than 2.8 eV, the absorption coefficient is enhanced by about four times as compared with pure Bi₂WO₆. This is caused by absorption between the 2p orbital of O in the valence bands and the 5d orbital of W in the conduction bands according to the PDOS in Figures 2 and 3. Therefore, the enhanced absorption of incident photons will enhance the photocatalytic efficiency of Bi_vac^3–, O_vac, and S_O doping Bi₂WO₆ in the near-ultraviolet region. These results are also in good agreement with the electronic properties mentioned above and previous experimental reports.

Figure 6.

Calculated frequency-dependent optical absorption spectra for the pure Bi₂WO₆, Bi_vac^3–, O_vac, and S_O defects using the HES06 method.

3. Conclusions

Using the HSE06 hybrid approach, we calculate the formation energies, electronic structure, and optical properties of native defects and nonmetals (C, N, S, and P) doping in a Bi₂WO₆ photocatalyst. We find that the formation energies strongly depend on the impurity charge states and Fermi level position. The calculated formation energies and transition levels demonstrate that Bi_vac, O_vac, S_O, and N_O have relatively low formation energies. However, C_O and P_O are more challenging to form than S_O and N_O due to the higher formation energies. The calculated electronic structures of Bi_vac, O_vac, S_O, and N_O defects reveal that the O_vac²⁺, Bi_vac, and S_O defects facilitate the delocalization of electrons. This leads to narrow band gaps of Bi₂WO₆ and hinders the formation of recombination centers, which would improve the photocatalysis performance of Bi₂WO₆. We reveal that the semiconductor nature of Bi₂WO₆ can be tuned from p-type to n-type by changing the growth conditions. The calculated absorption coefficients of O_vac²⁺, Bi_vac, and S_O show strong absorption in the visible region, which is in good agreement with the experimental results. Based on these results, we suggest that O_vac²⁺, Bi_vac, and S_O doping are good dopant candidates to tailor the visible-light absorption property of Bi₂WO₆ photocatalysts. Our results provide a comprehensive investigation of the charged defect of the Bi₂WO₆, which provides a useful strategy for further optimizing the photocatalytic performance of Bi₂WO₆ and its future applications.

4. Computational Methods

First-principles calculations based on the density functional theory (DFT) were performed using the projected augmented wave (PAW)⁶¹ method implemented in the Vienna ab initio simulation package (VASP).^62,63 The Kohn–Sham one-electron states are expanded using the plane-wave basis set with a kinetic energy cutoff of 500 eV. The Perdew–Burke–Ernzerhof (PBE)⁶⁴ exchange-correlation (XC) functional within the GGA was employed for the geometrical optimization. Since the GGA approach usually underestimates semiconductors’ band gap, we used the screened hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE)^38,39 for a more accurate description of the electronic structure. We tested the energy gap of pristine Bi₂WO₆ by adjusting the Hartree–Fock mixing parameter from 0.15 to 0.35. It was found that when α = 0.15, the calculated band gap is 2.79 eV for Bi₂WO₆, closely to the experimental band gap 2.80 eV.¹³ Therefore, in our calculations, we chose the mixing parameter equals 0.15 for the short-range Hartree–Fock exchange instead of the commonly used value of 0.25. The PAW potentials with the valence electrons 6s²6p³ for Bi, 5d⁴6s² for W, 2s²2p⁴ for O, 2s2²p² for C, 2s²2p³ for N, 3s²3p³ for P, and 3s²3p⁴ for S have been employed. The Monkhorst–Pack k-point meshes⁶⁵ for the 36-atom pure Bi₂WO₆ primitive cell is 6 × 2 × 6. Vacancy and doping defects calculations were performed in a 2 × 1 × 2 supercell (144 atoms). For these systems, we used a 2 × 1 × 2 k-point, which was found to be sufficient to reach convergence for bulk calculations and used for geometry optimization and electronic property calculations. For defects calculations, the supercells’ sizes were kept, but the atomic positions were relaxed until forces were smaller than 0.03 eV/Å, corresponding to the energy convergence smaller than 0.0001 eV. For all calculations, spin polarization was taken into consideration. The experimental atomic positions⁶⁶ were employed as the starting points of relaxation, and the following calculations were performed using the relaxed atomic positions.

The formation energy of a defect X in charge state q is defined as^67,68

1

where E_tot(X^q) is the total energy of the Bi₂WO₆ in the presence of a defect X in charge state q in the supercell, and E_tot(bulk) is the total energy of pristine Bi₂WO₆ in the absence of a defect in the supercell. For charged defects (q ≠ 0), the formation energy depends on the Fermi level (E_F), which varies from the valence-band maximum (VBM) to the calculated conduction-band minimum (CBM). In this study, E_F at the VBM is set to 0 eV, and CBM is set to 2.79 eV, respectively. E_V is the energy cost in removing an electron from the pure supercell. ΔV is determined by aligning O atoms’ 1s core levels far away from the defect center in defective cells to the pure bulk. Additionally, E_corr is a correction term to account for supercell errors such as image–charge interactions. This is because of the supercell and periodical boundary conditions used in the DFT calculations. Following the approach given by Lany and Zunger,^69,70 the image–charge correction term is written as

2

where f is a shape factor related to the supercell geometries,⁷⁰q is the total charge, α is the Madelung constant, ε is the static dielectric constant of the pristine bulk,⁷¹ and L is the linear dimension of the supercell (L = V^1/3, V is the volume of the supercell). n_i corresponds to the number of atoms added to (n_i > 0) or taken from (n_i < 0) the system to form the X. Defects with lower formation energies will form more easily and occur in higher concentrations. μ_i = E_i + Δμ_i is the chemical potentials of the constituent i in the reservoir, where E_i denotes the calculated standard state energies.⁷² The values of Δμ_i can vary depending on the environmental conditions in thermodynamic equilibrium but are restricted by the relation¹²

3

where ΔH_f(Bi₂WO₆) is the formation enthalpy of per formula of Bi₂WO₆, which is equal to −14.98 eV according to our HSE06 calculations. This result is very close to previous −15.50 eV estimates using the PBE method¹² but higher than the experimental value of −11.52 eV.⁷³ The upper bound is Δμ_i ≤ 0 as, at this point, precipitation of element i̇ to its standard state occurs. Thereby, the non-formation of the pure solids Bi and W or O₂ gas, requires

4

The following relationships should be satisfied to avoid the formation of other oxide phases (such as WO₂, WO₃, and Bi₂O₃):

5

6

7

Eqs 3–7 determine the phase diagram of Bi₂WO₆ as a two-dimensional panel with two independent variables, Δμ_Bi, and Δμ_W. The PBE- and HSE06-calculated stable regions for Bi₂WO₆ in the phase diagram are shown as the light green and light blue shaded quadrilateral in Figure S1 and Figure 7, respectively. The values inside of these regions induce no precipitation of the second phase. Our PBE result is in excellent agreement with the previous theoretical studies.^12,74,75 The stability regions are estimated by the PBE and HSE06 methods, having almost the same shape and size. Thus, the coordinates of C, D, E, and F in Figure S1 are not much different from those of C, D, E, and F in Figure 7. This indicates that the calculated results of the two methods agree with each other.

Figure 7.

Ranges of chemical potentials showing the formation of different competing phases under thermodynamic equilibrium calculated by HSE06. The light-blue-shaded quadrilateral CDEF is the region where Bi₂WO₆ is stable without forming other phases. Specific points C, D, E, F, and M are chosen as the representative chemical potentials for the following defect formation energy calculation.

Five representative chemical potentials points C, D, E, F, and M were selected in the light-blue-shaded regions to calculate defect formation energies. C and E represent oxygen-rich conditions, D and F indicate oxygen-poor and bismuth-rich conditions, and M in the stable region represents condition between O-rich conditions and O-poor/bi-rich conditions, respectively. Moreover, we obtained the values of Δμ_Bi, Δμ_W, and Δμ_O and then calculated the values of corresponding chemical potentials using μ_i = E_i + Δμ_i; the results are listed in Table 2.

Table 2. Chemical Potentials Used to Represent Growth Conditions (C, D, E, F, and M ) for Bi₂WO₆^a.

	chemical potentials (eV)
condition	μBi	μW	μO	μC	μN	μP	μS
C	–7.62	–22.63	–6.16	–13.87	–9.68	–13.21	–8.88
D	–4.29	–15.97	–8.38	–9.96	–9.47	–7.66	–5.34
E	–7.22	–23.43	–6.16	–13.87	–9.68	–13.21	–8.88
F	–4.29	–17.59	–8.11	–9.97	–9.47	–8.34	–5.34
M	–6.29	–20.31	–6.99	–12.21	–9.47	–11.14	–6.39

^aM is one point in the Bi₂WO₆ stability region.

When considering impurity (C, N, P, and S) doping, impurities’ chemical potentials should also be considered. The following constraints are enforced to avoid the formation of impurity-related phases:

8

9

10

11

12

13

For example, for N doping at C chemical potentials, Δμ_N= −0.21 eV. In this case, the μ_N= −9.68 eV is used for the calculation of formation energy for N-doping defects. The derived upper-limit chemical potentials for C, N, P, and S by HSE06 are listed in Table 1, considering the special growth conditions.

Table 1. Calculated Enthalpy of Formation Per Formula Unit of Bi₂WO₆ and the Possible Limiting Phases by HSE06 Calculation^a.

compound	ΔHf (eV)	experiment
Bi2WO6	–14.98	–11.5273
Bi2O3	–5.86	–5.9576
WO2	–5.75	–6.1176
WO3	–8.32	–8.7476
CO	–0.71	–1.1476
CO2	–3.91	–4.0876
P2O5	–14.38
SO2	–3.06	–3.0876
SO3	–4.13
Bi2S3	–1.78	–1.4876
WC	–0.41
N2O5	–0.42	–0.4576

^aExperimental values at 298 K are provided for comparison (unit: eV).

The formation energy (given per formula unit) calculated by HSE06 for the various possible competing phases (Bi₂O₃, WO₂, WO₃, CO, CO₂, P₂O₅, SO₂, SO₃, and Bi₂S₃ WC N₂O₅) are shown in Table1 together with the available experimental values. It is seen that the calculated values are in good agreement with the experimental results.

We further calculated the thermodynamic transition energy levels ε(q/q ′ ) of the defect in Bi₂WO₆ using the following expression:

14

where E_f(X^q) and E_f(X^q′) represent formation energies of the doped Bi₂WO₆ in the charge states q and q′, respectively. Ε(q/q′) refers to the Fermi level at which the formation energies of the defect in charge q and q′ cross.

The imaginary part ε₂(ω) of the dielectric function ε(ω) is calculated using the standard formulation

15

where V is the cell volume, ℏω is the energy of the incident photon, p→ is the momentum operator, |nk→> denotes the electronic state k→ in band n, and f_nk→ 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:⁷⁷

16

It should be noted that many-body perturbation GW (“G” is the one-body Green’s function, which describes the propagation of a particle in an interacting system, and “W” is the linear response dynamically screened Coulomb interaction) approximation is used to calculate quasiparticle excitations in semiconductors and insulators, as measured by direct and inverse photoemission experiments.⁷⁸ For the optical spectrum, the Bethe–Salpeter equation (BSE) is solved to include the effects of electron–hole interactions.⁷⁹ However, more GW and BSE calculations for doped Bi₂WO₆ are limited by their expensive computational time in this paper.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.0c03685.

• Ranges of chemical potentials for Bi₂WO₆ under thermodynamic equilibrium calculated by PBE and defect formation energy calculations of Bi₂WO₆ supercells with various types of point defects in different charge states using the PBE-DFT method as a function of the Fermi level (PDF)

Author Contributions

^§ J.Z. and P.D. contributed equally to this paper.

The authors declare no competing financial interest.