Mo-Doped in

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Hybrid-Functional Study of Native Defects and W/Mo-Doped in Monoclinic-Bismuth Vanadate Patompob Pakeetood, Pakpoom Reunchan, Adisak Boonchun, Sukit Limpijumnong, Ratiporn Munprom, Rajeev Ahuja, and Jiraroj T-Thienprasert J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 22 May 2019 Downloaded from http://pubs.acs.org on May 28, 2019

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The Journal of Physical Chemistry

Hybrid-functional Study of Native Defects and W/Mo-doped in Monoclinic-bismuth Vanadate Patompob Pakeetood,† Pakpoom Reunchan,†, ¶ Adisak Boonchun, †, ¶ Sukit Limpijumnong, Ratiporn Munprom,§ Rajeev Ahuja,, Jiraroj T-Thienprasert*, †, ¶ †Department ¶Thailand

of Physics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand

Center of Excellence in Physics, Commission on the Higher Education, 328 Si Ayutthaya Road, Bangkok 10400, Thailand

The

Institute for the Promotion of Teaching Science and Technology, 924 Sukhumvit Road, Phra Khanong, Klong Toei, Bangkok 10110, Thailand

§Department

of Materials Engineering, Faculty of Engineering, Kasetsart University, Bangkok 10900, Thailand

Condensed

Matter Theory Group, Materials Theory Division, Department of Physics and Astronomy, Uppsala University, Box 530, SE75121 Uppsala, Sweden Department

of Materials Science and Engineering, Royal Institute of Technology, SE-10044 Stockholm, Sweden

ABSTRACT: Monoclinic scheelite (ms) BiVO4 is recognized as one of the most promising photocatalyst materials due to its band gap as well as band-edge positions. Several theoretical and experimental works have been dedicated to improve the photocatalytic activity of ms-BiVO4. It has been reported that doping ms-BiVO4 with either W or Mo can enhance its photocatalytic activity comparing to undoped one. Further, codoping with W and Mo can further improve the photocatalytic activity. Here, we systematically investigate all native and W/Mo related defects in ms-BiVO4 by using density functional theory with hybrid functional. For undoped ms-BiVO4, we reveal that vacancies are the most dominant intrinsic defects and these defects compensate themselves leading to moderate n-type conductivity in O-poor growth condition. For W/Mo-doped ms-BiVO4, W and Mo are likely to substitute for V atom under all crystal growth conditions. While WV defect is a shallow donor, MoV defect creates a defect level below the conduction band edge. This implies that doping with W can gain more photocatalytic efficiency, which agrees well with experiment. Interestingly, we find that two donors, i.e., WV and MoV defects, prefer to form a complex defect becoming a shallow double donor. This can improve the electrical conductivity of W/Mo codoped ms-BiVO4, which helps enhance its photocatalytic performance. In addition, the formation of donor-donor complexes is quite stable and helps improve material property.

1. INTRODUCTION

key role for this phenomenon. Zhao et al.11 firstly reported that the photocurrent of Au/Ag-TiO2 can be generated by using only visible-light illumination and this enhancement is later ascribed to LSPR-induced hot-electron generation at nanoparticle/metal-oxide interface. Beside metal oxides, carbon nitride (CN) 2D material has attracted much attention due to its promising applications ranging from (photo)catalysis and photoelectrochemistry to biosensors.11 It has been revealed that doping is an essential method to modulate the electronic structure of semiconductors. For example, phosphorous-doped CN can increase the electrical conductivity by up to 4 orders of magnitude and improve the photocurrent generation by a factor of up to 5. Regarding ternary metal oxides, It has been reported that bismuth vanadate (BiVO4) exhibits a promising performance for photocatalytic O2 evolutions and organic compound degradation under visible-light irradiation due to its small band gap of ~2.4 – 2.5 eV and its proper band-edge positions.12-21 In addition, Wang et al. revealed that BiVO4 could be applied for visible-light driven photocatalytic inactivation of E. coli.22 Due to a variety of applications, BiVO4 has been attracted much attention for many researchers.

Several metal oxide-based semiconductors are recognized as promising photocatalysts, which can be used to harvest solar energy to split water into hydrogen and oxygen for renewable and storable energies or for the purpose of water purification. Titanium dioxide (TiO2) is one of the most interesting metal oxide-based semiconductors for using in a water-splitting process due to its strong photo-induced redox power, high photocorrosion resistance and nontoxicity; however, the efficiency of TiO2 photocatalyst is limited to an ultraviolet light, which is a small fraction of the sunlight’s spectrum, due to its large band gap of 3.2 eV.1-3 To obtain the best photocatalytic activity, the band gap of chosen materials should be ~2.0 eV, which is responsive to a visible light region being a significant portion of the spectrum. Therefore, there are many literatures trying to search for metal oxide-based materials with suitable band gaps as well as band-edge positions.2, 4-9 Recently, it has been reported that the photocatalyst activity of metal-oxide can be enhanced by using nanoparticle, such as Au/Ag-TiO2, Au-ZnO, and Au-CeO2.10 The localized surface plasmon resonance (LSPR) at interface of nanoparticle/metal-oxide plays a

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Figure 1 (Color online) Illustration of (a) 24-atom ms-BiVO4 unit cell where the blue and pink shades represent the VO4 tetrahedra and BiO8 dodecahedra and (b) 96-atom ms-BiVO4 supercell used in the defect calculations with (c) their local structures. The values shown are in angstrom unit. Pink, blue and red balls represent Bi, V, and O atoms, respectively

BiVO4 can crystalize in three different crystal structures, namely, tetragonal zircon (tz), tetragonal scheelite (ts), and monoclinic scheelite (ms).23 It is noteworthy that monoclinic scheelite BiVO4 can also conventionally be defined as monoclinic clinobisvanite structure. It has been revealed that, among all three structures, ms-BiVO4 exhibits the best photocatalytic activity.21, 24-26 This is because tz-BiVO4 has a large band gap of ~2.9 eV, while the band gaps of ts- and ms-BiVO4 are ~2.3 and 2.4 eV, respectively.20 The difference in photocatalytic activity between ts- and ms-BiVO4 has been attributed to the difference in their crystal structures.27 However, the efficiency of photocatalyst ms-BiVO4 is still low due to the electron-hole recombination process limiting the usage of this material.28-29 To overcome this problem, it has been experimentally demonstrated that doping BiVO4 with Mo or W could enhance the water photo-oxidation activity as well as organic compound degradation.30-32 In addition, co-doping with Mo and W in BiVO4 reveals a remarkably high photocatalytic activity over undoped and W-doped BiVO4.13, 33 However, there is ambiguity in the role of doping, in particular, in altering atomic and electronic structures. In order to gain more understanding about the atomic and electronic structures of undoped and W/Mo-doped BiVO4, first-principles calculations based on density functional theory (DFT) has been carried out. Regarding undoped BiVO4, Walsh et al. used DFT with generalized gradient approximation parameterized by Perdew-Burke-Ernzerhof (GGA-PBE) to investigate the electronic density of states and band structure of bulk ms-BiVO4 showing a direct band gap at A point

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with light holes and light electron effective masses (~0.3 me).15 However, by using DFT with GGA-PBE functional, Zhao et al. considered more k paths in the Brillouin zone and found that actually bulk ms-BiVO4 has an indirect band gap located along the k-point path from M to L. Its optical properties were also studied.34 Yin et al. used DFT with GGA functional to study some intrinsic and extrinsic defects in ms-BiVO4 by calculating the defect formation energies. They found that Bi and O vacancies are the most dominant intrinsic defects leading to moderate n-type and p-type conductivities at Bi-rich/Opoor and O-rich growth conditions, respectively.35 They further suggested that excellent n-type conductivity could be obtained by doping with Mo or W. Beyond GGA or GGA-PBE functional, Kweon and Hwang used hybrid functional proposed by Heyd-Scuseria-Ernzerhof (HSE) to study structural and electrical properties of pure ms-BiVO4 and ts-BiVO4 by varying the Hatree-Fock (HF) exchange fraction.27 They found that HF-25% gives lattice parameters very close to the experiment, but at HF-25% the calculated band gap (~ 3 eV) is larger than the experimental band gap of ~2 eV. To our knowledge, there have been no theoretical studies on native point defects in ms-BiVO4 using HSE functional, which provide more direct comparison with experiments than other functionals. In addition, the effect of W- and Mo-doping in ms-BiVO4 on the enhancement of photocatalytic activity is still unclear, especially in the case of W/Mo co-doping in msBiVO4. In this paper, we used DFT with HSE functional to investigate the structural and electronic properties of bulk ms-BiVO4. Then, native defects in ms-BiVO4 were investigated by considering the defect formation energy under several crystal growth conditions. The effects of dominant native point defects on the photocatalytic properties were elucidated. After that, we investigated W and Mo related defects in ms-BiVO4 under several growth conditions and explained why doping with W resulted in better photocatalytic activity than doping with Mo. Last, we investigated the likelihood of complexdefect formations, including donor-acceptor and donor-donor complexes. We found an unusual behavior of the donor-donor complex formation, i.e., WV-MoV complex, which can further enhance the photocatalytic activity of W/Mo co-doped msBiVO4.

2. CALCULATION METHOD We used first-principles calculations based on DFT with a plane-wave basis set as implemented in the Vienna Ab-Initio Simulation Package (VASP) codes.36 The interactions between core and valence electrons were described by the projector augmented wave method and the energy cutoff for expanding the plane-wave basis set was set at 500 eV.37 The Hybrid functional proposed by HSE was employed for accurately describing the exchange-correlation energy.38 For kspace integrations, the Monkhorst-Pack scheme was carried out with a sampling k-points mesh of 5×5×5 for bulk calculations. The amount of nonlocal Fock-exchange was chosen at 12.4% resulting in the calculated band gap of 2.60 eV in agreement with the experimental band gaps of 2.5 – 2.7 eV.3940 The calculated lattice parameters of ms-BiVO4 are a = 7.267 Å, b = 11.687 Å, and c = 5.135 Å, which are in good agreement with the experimental values of a = 7.247 Å, b = 11.697 Å, and c = 5.090 Å.34 To study the defects in msBiVO4, a supercell approach with a supercell size of 96 atoms

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Figure 2 (Color online) Illustration of the possible range of Bi, V, and O chemical potentials for the thermodynamic equilibrium growth of ms-BiVO4 where the O chemical potentials are projected onto Bi–V chemical potential plane. All values shown are referenced to their natural phases, i.e., metallic Bi, metallic V, and O2 gas.

as represented in Fig. 1 was used. This is large enough to suppress the fictitious interactions arising from the defects in the neighboring cells due to the periodic boundary conditions.41 For supercell calculations, the k-points sampling mesh was reduced to 2×2×2. All atoms in the supercell were allowed to relax until the forces acting on each atom became less than 0.02 eV/Å. The likelihood of a defect formation can be determined by its formation energy defined by41

HF (Dq ) Etot (Dq ) Etot (bulk)  ni i  q(E F  EVBM )  q ,

(1)

i

where Etot(Dq) and Etot(bulk) are the total energy of the supercell containing the defect D in charge state q and the total energy of a defect-free supercell, ni is the number of atom species X being added (removed) to (from) a supercell to create the defect D with corresponding atomic chemical potentials μi as described below, EF is the Fermi energy referenced to the valence band maximum EVBM, and Δq represents the finite-size correction term.42-43 The concentration of defect is inversely proportional to the exponential of the defect formation energy defined in Eq. (1). This means that the defect with lower formation energy exists in higher concentration in a crystal. To grow ms-BiVO4 crystal under thermodynamic equilibrium, the following condition must be satisfied,

Etot (BiVO4 )  Bi   V  4 O ,

(2)

where Etot(BiVO4) is the total energy per formula unit of msBiVO4, μBi, μV, and μO are the atomic chemical potentials for Bi, V, and O, respectively. The above equation implies that the chemical potentials can be any values lying on the plane in a 3-D chemical potential space satisfied Eq. (2). However, we need to prevent undesired phases, which might form during the crystal growth process, such as metallic-Bi, metallic-V, O2 gas, Bi-oxides, and V-oxides; Bi  Etot (metallic-Bi),  V  Etot (metallic-V), O  Etot (O2 )/2 Bi  Etot (BiO) O , Bi  Etot (BiO2 ) 2O , Bi  (Etot (Bi2O3 ) 3O )/2  V  Etot (VO) O , V  Etot (VO2 ) 2O ,  V  (Etot (V2O3 ) 3O )/2

V  (Etot (V2O5 )5O )/2

(3) Consequently, the infinite plane determined by Eq. (2) is limited to a finite plane imposed by Eq. (3) as illustrated in Fig. 2, in which the oxygen chemical potential O is projected onto a plane of Bi and V chemical potentials and all values

Figure 3 (Color online) The calculated band structures along several high symmetry paths where the valence band maximum is set to zero. The arrows indicate the direct and indirect transitions. The blue and dashed gray lines represent the calculations with HSE and PBE functionals, respectively.

shown are referenced to their natural phases. As shown in Eq. (1), the defect formation energy obviously depends on the atomic chemical potentials. This causes a lot of conditions to be considered. For simplicity and convenience to relate with the experiment, we consider only the formation energy at three points on the boundary, i.e., point a, b, and c (as labeled in Fig. 2) representing the O-poor, O-rich/Bi-poor, and O-rich/Vpoor growth conditions, respectively. Regarding W- and Morelated defects in ms-BiVO4, we also need to prevent the formation of their undesired phases including W-metal, WO2, WO3, Mo-metal, MoO2, and MoO3. We found that the chemical potential of W is determined by W = Etot(WO3) – 3O under all growth conditions, while that of Mo is determined by Mo = Etot(MoO2) – 2O for O-poor condition and Mo = Etot(MoO3) – 3O for both O-rich/Bi-poor and O-rich/V-poor conditions.

3. RESULTS AND DISCUSSION 3.1. Crystal and Electronic structures of ms-BiVO4. The optimized conventional cell of ms-BiVO4 is represented in Fig. 1. In Figure 1(a), we depicted the crystal structure of 24-atom ms-BiVO4 unit cell with C2/c space group. This unit cell is composed of four bismuth (Bi) atoms, four vanadium (V) atoms, and sixteen oxygen (O) atoms. Each Bi atom is surrounded by eight O atoms with slight differences in bond lengths forming distorted dodecahedron (see Fig. 1a and 1c). The eight Bi-O bond lengths can be classified into four groups by symmetries, i.e., 2.430, 2.437, 2.478, and 2.495 Å, as illustrated in Fig. 1c. Each V atom is surrounded by four oxygen atoms with little differences in bond lengths forming tetrahedron (see Fig. 1a and 1c). For O atoms, there are two types of in-equivalent O atoms, named O1 and O2, both of which are coordinated with 2 Bi and a V with slight differences in bond lengths as seen in Fig. 1c. The values in the parenthesis represent the bond length for O2 species. Each O atom at the corner of a tetrahedron is shared with that of a dodecahedron as depicted in Fig. 1a. It has been reported that a slight distortion of VO4 tetrahedron causes an internal electric field facilitating the electron-hole pair separation, which helps improving the photocatalytic activity of the sample.20, 34, 44 However, the difference in the calculated two V-O bond lengths is only 0.004 Å, which is quite small compared with the experimental


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Figure 4 (Color online) Total and site projected density of states of Bi, V, and O atoms in ms-BiVO4. The valence band maximum is set to zero as indicated by the vertical dotted line.

value, specifically ~0.02 Å.45 Consistently, the distortion of a Bi-O dodecahedron is also small when compared with experiment. This may be attributed to two reasons: (1) the experiment performed at room temperature, while the calculations were carried out at absolute zero temperature, and (2) the coupling of Bi 6s and O 2p in the calculation is too weak, even though HSE functional was taken in the calculation as described in Ref.[46]. The calculated band structures of ms-BiVO4 along several high symmetry points accompanying with its Brillouin zone are illustrated in Fig. 3, in which the blue and gray lines represent the band structures calculated with HSE and PBE functionals, respectively, and the top of valence band maximums (VBM) is set to zero. We clearly see that the features of the band structures calculated with HSE functional are quite similar to that with PBE functional except the width of band gap as expected. The calculated energy band gaps for indirect and direct transitions are 2.05 eV and 2.10 eV, respectively, for PBE functional, and 2.60 eV and 2.66 eV, respectively, for HSE functional. The latter provides the values closer to the experimental band gap of ~ 2.5 - 2.7 eV.39-40 These results are in good agreement with the prior calculated results13, confirming that the VBM is located along V- line while the conduction band minimum (CBM) is located along the -(0.5,0.5,0) line. The high curvature at VBM and CBM points implies the low effective hole and electron masses. Therefore, the hole and electron mobilities of ms-BiVO4 are expected to be very high, providing greater probability for charge carriers to reach the surface reaction sites within their life-time. In order to gain more understanding about the electronic structure of ms-BiVO4, the total density of states and the angular momentum projected partial density of state (PDOS) on Bi, V, and O atoms are illustrated in Fig. 4. Regarding the valence band states, the lowest band centered at ~-18 eV is mostly composed of O s, while the middle band centered at ~9 eV is mostly composed of Bi s. In addition, the highest band located at ~ -5 – 0 eV is mainly contributed by O p orbital mixing with V d and some Bi s. For conduction band states, they are mainly composed of V d hybridized with some Bi s and O s. The VBM and CBM are mainly from O s and V d states, respectively. Therefore, during the photo-absorption process, the photo-generated carriers can transfer from O atom to V atom due to the internal electric field created in the distorted

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Figure 5 (Color online) Calculated formation energy of all native point defects as a function of Fermi energy under (a) O-poor, (b) O-rich/Bi-poor, and (c) O-rich/V-poor growth conditions. The slope of each line indicates the charge state of the defect.

VO4 tetrahedron as described above. This could help reduce the electron-hole recombination rate enhancing the photocatalytic activity in ms-BiVO4. Note that electron small polaron is reported to be stable and localized on V atom.47-48 The formation of small polaron can result in poor electron transport, which degrades the photocatalytic activity of undoped msBiVO4. 3.2. Native point defects in ms-BiVO4. In this section, we investigated the likelihood of each native point defect formations in ms-BiVO4 by considering the defect formation energy as a function of Fermi energy under different chemical potentials, which reflect different experimental growth conditions varying from O-poor to O-rich as described in the previous section. We can then determine the effect of dominant native point defects on electronic property of ms-BiVO4, which could affect its photocatalytic activity. The native point defects included in this studies are vacancy, interstitial, and antisite defects. The formation energies of vacancy defects in ms-BiVO4 including Bi vacancy (VacBi), V vacancy (VacV), and O vacancy (VacO) defects as a function of Fermi energy under O-poor, Orich/Bi-poor, and O-rich/V-poor growth conditions are illustrated in Fig. 5a, 5b, and 5c, respectively. The black, red, and green lines represent the formation energies of VacBi, VacV, and VacO defects, respectively. The slope of each line indicates the charge state of the defects. Regarding VacBi defect, we found that it is a shallow acceptor with two defect transition levels at (-1/-2) = 0.10 eV and (-2/-3) = 0.17 eV and its formation energy is quite low at the Fermi level position high above the VBM, especially under O-rich/Bi-poor and Orich/V-poor growth conditions. Similarly, VacV defect is also an acceptor with two transition levels at (0/-1) = 0.23 eV and (-1/-5) = 0.66 eV. Its formation energy is somewhat higher than that of VacBi, except for the Fermi-level above 2.17 eV under O-rich/V-poor growth condition. On the other hand, VacO defect is a shallow donor with a defect transition level at (0/+2) = 2.51 eV and its formation energy is at the Fermilevel near the VBM, especially under O-poor growth condition.


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Figure 6 (Color online) Calculated formation energy of W and Mo related defects as a function of Fermi energy under (a) O-poor, (b) O-rich/Bi-poor, and (c) O-rich/V-poor growth conditions. The slope of each line indicates the charge state of the defect. The dashed lines represent the dominant native defects, i.e. VacBi and VacV.

For interstitial defects, Bi interstitial (Bii), V interstitial (Vi), O interstitial (Oi), and O split-interstitial (two O atoms share an O’s site; Oisplit) defects were studied. The formation energies of these interstitial defects are illustrated in Fig. 5. Bii is a donor with two defect transition levels at (+3/+2) = 2.11 eV and (+2/+1) = 2.55 eV. Vi is also a donor with four defect transition levels at (+5/+4) = 1.03 eV, (+4/+3) = 1.30 eV, (+3/+2) = 1.99 eV, and (+2/+1) = 2.15 eV. The formation energy of Vi is lower than that of Bii, except when the Fermilevel rises above 0.75 eV under O-rich/V-poor growth condition. Oi is a deep double acceptor with a defect transition level at (0/-2) = 1.24 eV, but Oisplit turns to be a double donor with a defect transition level at (+2/0) = 0.69 eV. The formation energy of Oisplit is lower than that of Oi when the Fermi-level is lower than 1.72 eV. However, their formation energies are quite high under all crystal growth conditions. For antisite defects, we considered Bi substituting for V (BiV), V substituting for Bi (VBi), O substituting for Bi (OBi), and O substituting for V (OV) defects as depicted in Fig. 5. We found that VBi and OV are amphoteric with defect transition levels: (+2/+1) = 0.66 eV, (+1/0) = 1.15 eV, and (0/-1) = 1.87 eV for VBi and (+1/-1) = 0.30 eV, (-1/-2) = 1.06 eV, and (-2/-4) = 2.46 eV for OV. On the other hand, OBi and BiV are acceptors with defect transition levels: (-1/-2) = 0.11 eV and (-2/-3) = 0.88 eV for OBi and (0/-1) = 1.46 and (-1/-2) = 1.66 eV for BiV. From Fig. 5, it is clearly seen that the formation energy of antisite defects including OBi, OV, and VBi are somewhat high. This is because the ionic radii of O (126 pm) and Bi (117 pm)/V (68 pm) are very different making O difficult to substitute for Bi or V atom and vice versa. However, under O-rich/V-poor growth condition, the formation of BiV defect becomes plausible due to its reasonably low formation energy. By considering all dominant native defects, we could determine the pinned Fermi-level from charge neutrality condition: p – n +  qC(Dq ) = 0, where p and n are intrinsic hole and

electron, and C(Dq) is the concentration of defect D at charge state q. We found that the Fermi-level positions are pinned at 2.28 eV, 1.07 eV, and 1.24 eV for O-poor, O-rich/Bi-poor, and O-rich/V-poor growth conditions, respectively. We have to note that Fermi-level represents the average energy used to remove electrons or holes from the material. Consequently, ntype semiconductor material with high Fermi-level (close to CBM) should be better than that with low Fermi-level because of less energy required to remove an electron. At a certain temperature, n-type semiconductor material with high Fermi level can provide more electrons than that with low Fermi level. These electrons can possibly move to the surface and interact with the oxygen in the environment to produce some reactive oxygen species (ROS). It is clearly seen that n-type semiconductor material with high Fermi level provides better photocatalytic activities than that with low Fermi level. The most dominant defects at pinned Fermi-level are: (1) VacO, and VacBi defects for O-poor and O-rich/Bi-poor conditions and (2) VacO, VacBi, and BiV defects for O-rich/V-poor condition. Under O-poor growth condition, we found that msBiVO4 behaved like a moderate n-type semiconductor due to donor VacO, which are compensated by acceptor VacBi. Under O-rich/Bi-poor and O-rich/V-poor growth conditions, the electrical conductivity of ms-BiVO4 becomes very poor because the pinned Fermi-level is around middle gap. As mentioned before, the low Fermi-level should reduce the photocatalytic activities of ms-BiVO4 grown under these conditions. In addition, it is surprised that BiV defect has the lowest formation energy under O-rich/V-poor condition; indicating that the antisite defect in ms-BiVO4 is unavoidable in some crystal growth conditions. Comparing with the previous theoretical work35, our calculated defect transition levels are different from their results because the functional and finite-size correction method employed are different. The HSE functional employed here is likely to provide more realistic results due to proper interaction treatments. Finally, we reveal that undoped ms-BiVO4 can exhibits moderate n-type conductivity when it is growth under O-poor condition. This facilitates its photocatalytic activity. However, under O-rich growth condition, the compensating VacBi defect becomes dominant resulting in a poor electrical conductivity in undoped ms-BiVO4, which could degrade its photocatalytic activity. Based on the vacuum growth process, we suggest growing ms-BiVO4 under O-poor condition to promote the formation of donor VacO defects and impede the formation of compensating VacBi defects. 3.3. W- or Mo- doped in ms-BiVO4. To enhance the photocatalytic activity of ms-BiVO4, it has been reported that samples codoping with W/Mo give a better photocatalytic activity than undoped sample (>10 times).13 However, theoretical studies supporting this observation are still limited and the previous computations are mostly based on GGA functional. In addition, the experiments showed that W-doped msBiVO4 has better photocatalytic activity than Mo-doped msBiVO4, but the reason for this finding is still ambiguous.13 In this section, we employed HSE functional to systematically investigate the preferred sites of W- and Mo-related defects in ms-BiVO4 under different growth conditions by considering the formation energies of defects in various forms, including substitution for Bi atom (WBi/MoBi), substitution for V atom (WV/MoV), and interstitial (Wi/Moi). For substitution on Bi site, we found that both WBi and MoBi are amphoteric with quite high formation energies under three extreme growth conditions as illustrated in Fig. 6. Their high


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formation energies suggest that both W and Mo atoms are unlikely to substitute for Bi atom. This could be attributed to the large difference between the ionic radii of dopants, W (76 pm)/Mo (75 pm), and that of Bi (117 pm). Regarding the substitution on V site, we found that WV defect is a shallow donor without any defect level in the band gap. However, MoV defect is a shallow donor with one defect transition level at (+1/0) = 2.38 eV. These results are different from previous theoretical study which found that both WV and MoV create defect levels inside the band gap.35 Previous study was carried out by using GGA functional, which is known to give the formation energies of charged defects too low. Note that, the formation energies of WV and MoV are quite low under three extreme growth conditions as shown in Fig. 6. Such low formation energies reflects that the substitution of W or Mo on V site is likely. For W and Mo interstitial, these defects are donors with the defect transition levels at: (+6/+5) = 1.01 eV, (+5/+3) = 1.65 eV, (+3/+2) = 1.72 eV, (+2/+1) = 2.21 eV, and (+1/0) = 2.50 eV for Wi and (+6/+5) = 0.95 eV, (+5/+4) = 1.24 eV, (+4/+3) = 1.40 eV, (+3/+2) = 1.47 eV, (+2/+1) = 2.15 eV, and (+1/0) = 2.40 eV for Moi. The formation energies of these interstitials defects are somewhat high, except under O-poor growth condition with the Fermilever less than ~1.25 eV. For Mo-doped ms-BiVO4, by including all dominant Mo and native point defects (dashed lines) in charge neutrality calculation, as illustrated in Fig. 6, we found that the Fermilevels are pinned at 2.38 eV, 1.25 eV, and 1.68 eV, for O-poor, O-rich/Bi-poor, and O-rich/V-poor growth conditions, respectively. Similarly, for W-doped ms-BiVO4, the pinned Fermi levels are 2.50 eV, 1.15 eV, and 1.60 eV. At pinned Fermilevel, we found that W or Mo atom are likely to substitute only for V atom under all crystal growth conditions. The distinct physical properties under different growth conditions can be related to the formation of unintentionally compensating native point defects, especially VacBi defect, which has low defect formation energy. As mentioned above, WV and MoV defects are both donors, but only the later creates the defect transition level at (+1/0) = 2.38 eV. This differs with the prior theoretical study which reports that both WV and MoV defects created the defect transition level at (+1/0) = 2.49 and 2.46, respectively.35 In the experiment, they found that Wdoped ms-BiVO4 revealed better photocatalytic activity than Mo-doped ms-BiVO4.13 This agrees well with our calculated results reporting that WV defect can be more easily ionized or generated more electrons than MoV defect. Once these electrons move to the surface, they can interact with the oxygen to produce some ROS at the surface. Therefore, WV doped msBiVO4 can generate more ROS at the surface resulting in better photocatalytic activity than Mo-doped ms-BiVO4. In addition, under O-poor condition the formation energy of WV defect is somewhat lower than that of MoV, while the compensating defect, i.e. VacBi, possesses quite high formation energy. Therefore, W- or Mo-doped ms-BiVO4 grown under O-poor condition can be a good n-type semiconductor (high Fermilevel), which could help reduce the electron-hole recombination rate and facilitate its photocatalytic activity. Doping with W or Mo in ms-BiVO4 under O-rich/Bi-poor and O-rich/Vpoor cannot enhance the photocatalytic activity due to the low formation energy of compensating VacBi defect. Therefore, we suggest that growing W- or Mo doped ms-BiVO4 crystal under O-poor condition is the best choice to enhance its photocatalytic properties.

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Figure 7 (Color online) Calculated formation energy of complex defects as a function of Fermi energy under (a) O-poor, (b) Orich/Bi-poor, and (c) O-rich/V-poor growth conditions. The slope of each line indicates the charge state of the defect. The dashed lines represent the dominant acceptor native defects, i.e. VacBi and VacV.

3.4. W and Mo codoped in ms-BiVO4. It has been reported that W and Mo codoped ms-BiVO4 can further enhance the photocatalytic activity.13 However, there is no clear explanation for this enhancement. In this section, we therefore investigated the likelihood of complex defect formation related to W and Mo in ms-BiVO4. As showed in the previous section, W and Mo prefer to substitute for V site under all crystal growth conditions considered; becoming a shallow donor defect. Because both WV and MoV defects are donor, the formation of complex defects between donor and acceptor (VacBi) could be expected owing to a coulomb attraction, i.e., WVVacBi and MoV-VacBi complex defects. To investigate the likelihood of complex defect formations, we calculate the binding energy of the complex, which is defined by, Eb[(A  B)q ] H f [(A  B)q ]  H f (Aq ) H f (B q ) , (4)

where Eb[(A–B)q ] is the binding energy of the A–B complex defect in charge state q, H f [(A  B)q ] is the calculated formation energy of A–B complex defect in charge state q, and the last term in the parenthesis is the sum of the formation energy of isolated defects A and B. The more negative value of binding energy means the higher opportunity of isolated defects A and B to form A–B complex defect.49 In opposite, the positive value indicates that the complex defect is unlikely to form. The formation energies of the complexes between donor and compensating acceptor defects, i.e., WV-VacBi and MoV-VacBi complexes as a function of Fermi energy are illustrated in Fig. 7. We found that both complex defects are shallow double acceptor without any energy level in the band gap. If these complexes form, they act as a compensating defect, which reduces the photocatalyst activity of the sample. To determine the stability of the complex, we plot the binding energy of the complex as a function of Fermi energy as depicted in Fig. 8. The binding energy of WV-VacBi and MoV-VacBi complexes depends on the Fermi energy position and their highest values are only around -0.15 eV, which is rather low. This indicates


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Figure 8 (Color online) Calculated binding energy of complex defects as a function of Fermi energy.

that if these complexes form, their concentrations should be very low. Therefore, the formation of these complexes should not have significant effect on the photocatalyst activity of the sample. We further investigated the likelihood of donor-donor complex formation by investigating WV-MoV complex, where WV and MoV defects are placed in the nearest positions of each other (~3.85 Å). The formation energy and binding energy of WV-MoV complex are shown in Fig. 7 and 8, respectively. We found that WV-MoV complex is a shallow double donor with a defect transition level at (+2/0) = 2.55 eV and the binding energy of the complex is -0.34 eV, which is higher than that of WV/MoV-VacBi complex defects. This means the formation of WV-MoV complex is more likely to form than the donoracceptor complex defects. This is surprising because the coulomb interaction between the donor and donor defects should be a repulsive interaction making it prefer to stay away from each other. This result was rechecked by replacing W or Mo on a different V site resulting in a longer distance between WV and MoV defects (~5.06 Å) in the supercell. The calculated total energy is slightly increased (by 0.11 eV) compared to the initial complex studied. This confirms that WV defect prefers to stay close to MoV defect. As depicted in Fig. 7, the defect transition level of WV-MoV complex is much closer to the CBM than that of MoV defect. Thus, the formation of WVMoV complex could help reduce the ionization energy of MoV defect. Once the ionization energy is reduced, the number of electrons moving to the surface is also increased. Consequently, ROS at the surface are more generated resulting in an improvement of photocatalytic activity of W/Mo codoped msBiVO4. To our knowledge, the formation of donor-donor complex has never been previously studied in ms-BiVO4. We hope that this finding will draw attentions to examine more unexpected donor-donor complex and paves the new way to enhance or improve physical properties of materials by codoping donor with another donor.

4. Conclusion Based on DFT with hybrid functional, we found that msBiVO4 has an indirect band gap, where the VBM is along V- direction and the CBM is along -(0.5,0.5,0) direction. The high curvatures at VBM and CBM indicate the high mobilities of hole and electron. For undoped ms-BiVO4, vacancy defects play an important role for its photocatalytic activity. We suggest that growing undoped ms-BiVO4 under O-poor condition should provide the best photocatalytic properties due to a

small amount of unintentional compensating VacBi defects. To enhance the photocatalytic performance of ms-BiVO4, doping with W/Mo has been previously reported to give the best activity. We found that both W and Mo dopants prefer to substitute for V’s site under all crystal growth conditions studied. Doping with W should give better photocatalytic activity than doping with Mo because WV defect does not introduce any level inside the gap. This agrees well with the experimental finding that W-doped ms-BiVO4 gives higher photocatalytic activity than Mo-doped ms-BiVO4. In the case of W/Mo codoped ms-BiVO4, we found that WV defect is likely to bind with MoV defect becoming WV-MoV complex defect, which can further improve its photocatalytic activity over W-doped msBiVO4. It is interesting to note that, the WV-MoV complex, which is a donor-donor complex, binds stronger than WV/MoV-VacBi, which is a donor-acceptor complex.

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected] (J.T.)

ACKNOWLEDGMENT P.P. is supported by The Graduate School, Kasetsart University. J.T., A.B., and P.R. acknowledge the financial support from Kasetsart University Research and Development Institute (KURDI). SNIC and HPC2N are acknowledged for providing the computing facilities.

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