The electronic properties of impurities (N, C, F, Cl, and S) in Ag3PO4: A hybrid functional method study

The transition energies and formation energies of N, C, F, Cl, and S as substitutional dopants in Ag3PO4 are studied using first-principles calculations based on the hybrid Hartree-Fock density functional, which correctly reproduces the band gap and thus provides the accurate defect states. Our results show that NO and CO act as deep acceptors, FO, ClO, and SP act as shallow donors. NO and CO have high formation energies under O-poor condition therefore they are not suitable for p-type doping Ag3PO4. Though FO, ClO, and SP have shallow transition energies, they have high formation energies, thus FO, ClO, and SP may be compensated by the intrinsic defects (such as Ag vacancy) and they are not possible lead to n-type conductivity in Ag3PO4.


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, the photocatalysis of water splitting has become an active research field and a potential way to solve the severe environmental crisis and energy shortage issues 2,3 . TiO 2 is the earliest photocatalyst used in water splitting, the intrinsic wide band gap of pure TiO 2 (~3.2 eV for anatase and ~3.0 eV for rutile) confines its photon absorption to the ultraviolet (UV) region, severely limiting solar energy utilization to ~5% 4 . Metal oxides are considered as potential candidates for photoelectrochemical (PEC) water splitting because of their resistance to oxidization and possible stability in aqueous solutions 5 .
Recently, Ye et al. reported that cubic structure semiconductor Ag 3 PO 4 , which exhibits strong oxidation power leading to O 2 production from water, and its quantum yield achieve up to nearly 90% under visible light 6 . This is intriguing because most photocatalysts give much poorer quantum yields of ~20% 7 . Theoretical studies have also been performed to understand their origin [7][8][9][10][11] . Reunchan and Umezawa suggest that native point defects are unlikely to be responsible for an intrinsic conductivity of Ag 3 PO 4 , which an n-type character was observed in the previous report, but Ag 3 PO 4 could feasibly be doped in n-type fashion 7 .
First-principles density functional theory (DFT) calculations have been commonly used to study the electronic properties of point defects insulators and semiconductors. The local density approximation (LDA) 12 or the generalized gradient approximation (GGA) 13 functional are typically employed to describe the exchange-correlation energy within DFT. A major shortcoming of LDA and GGA calculations is the large uncertainty in the position of defect levels (and hence also formation energies) due to the severe underestimation of the semiconductor band gap. Heyd et al. recently proposed hybrid Hartree-Fock (HF) density functional 14 , the hybrid functional has been used to accurately reproduce the band gap of insulators and semiconductors, therefore, the use of the hybrid functional is rationalized for the description of defect physics [15][16][17][18] .
In this paper, we perform first-principles calculations based on the hybrid HF density functional to investigate the influence of N, C, F, Cl, and S impurities on the electronic properties of Ag 3 PO 4 . Because interstitials of these impurities usually have large formation energies, we will only consider substitutional defects. The paper is organized as follow: Details of the calculations are provided in Sec. II. The electronic properties of each impurity are described in Sec. III. Finally, Sec. IV summarizes the results.

Methodology
The density functional calculations were performed in the Vienna ab initio simulation package (VASP) 19,20 . Interaction between the valence and core electrons was described using the projector augmented wave (PAW) approach 21 . A plane-wave basis set was used to expand the wave functions up to a kinetic energy cutoff value of 300 eV.
We used the Heyd-Scuseria-Ernzerhof hybrid functional (HSE06) 14,22 , which adopts a screened Coulomb potential. Hence, greatly improving the description of structural properties and band structures, including band gaps. Both of these aspects are particularly important for defects. The HSE exchange is derived from the PBE0 (Perdew-Burke-Ernzerhof (PBE) functional containing 25% exact exchange) 23 exchange by range separation and then by elimination of counteracting long-range contributions as 4 .
Where a is the mixing coefficient and ω is the range-separation parameter. A consistent screening parameter of ω = 0.2 Å −1 is used for the semilocal PBE exchange as well as for the screened nonlocal exchange as suggested for the HSE06 functional 24 . We find that a proportion of 33% HF exchange with 67% PBE exchange produces accurate values for lattice constants and the band gap in Ag 3 PO 4 . We used a 128-atom supercell constructed by 2 × 2 × 2 replication of the cubic Ag 3 PO 4 unit cell (space group P n 43 ), which ensures sufficient spatial separation between the periodic images of the impurities. Various dopings of Ag 3 PO 4 have been modeled by substitution of S at P or Y (Y = N, C, F, Cl) at O sites. For geometry optimizations and electronic structure calculations, the Brillouin zone was sampled with a 2 × 2 × 2 mesh of Monkhorst-Pack special k-points 25 . Both the atomic positions and cell parameters were optimized until residual forces were below 0.01 eV/Å.

Formation energies and transition levels.
To determine the defect formation energies and defect transition energy levels, we follow the procedure in Ref. 26. The defect formation energy ∆H f (α, q) as a function of the electron Fermi energy 27 E F as well as the atomic chemical potentials 28,29 μ i is as follows: is the total energy for the studied supercell containing defect α in charge state q and E (host) is the total energy of the same supercell without the defect. n i indicates the number of atoms of type i (host atoms or impurity atoms) that have been added to (n i < 0) or removed from (n i > 0) the supercell , and q is the number of electrons transferred from the supercell to the reservoirs in forming the defect cell. E F is the electron Fermi level referenced to the valence-band maximum (VBM) of host, ε VBM (host), and varies from the valence-band maximum to the conduction-band minimum (CBM). μ i is the chemical potential of constituent i referenced to its elemental solid or gas with energy E(i).
The defect transition energy level ε α (q/q′) is the E F in Eq. (1), at which the formation energy ∆H f (α, q) of defect α in charge state q is equal to that of another charge q′ of the same defect, i.e., In this paper, we used a hybrid scheme to combine the advantages of both special k-points and Γ -point-only approaches 12 . In this scheme, for acceptor level (q < 0), the transition energy level with respect to VBM is given by: For donor level (q > 0), the ionization energy referenced to the CBM is given by: Where ε D k (0) and ε D Γ (0) are the defect levels at the special k-points (averaged) and at the Γ -point, respectively; ε VBM Γ (host) and ε CBM Γ (host) are the VBM and CBM energies, respectively, of the host at the Γ -point; and ε g Γ (host) is the calculated bandgap at the Γ -point.The formation energy of a charged defect is then given by Where ∆H f (α, 0) is the formation energy of the charge-neutral defect. More details of calculation methods for formation energies and transition energies of defects are described elsewhere 30 .
Chemical potentials. Under thermal equilibrium growth conditions, the steady production of host material, Ag 3 PO 4 , should satisfy the following equation: where μ Ag , μ P , and μ O are the chemical potentials of Ag, P, and O source, respectively, and ∆H f is the formation energy for Ag 3 PO 4 per formula. In order to avoid the precipitation of the host elements, the chemical potential μ i must be bound by To avoid the formation of secondary phases (such as Ag 2 O and P 2 O 5 ), μ Ag , μ P , and μ O must satisfy further constrains: Considering Eqs. For impurity doping, the chemical potentials of impurities also need to satisfy other constraints to avoid the formation of impurity-related phases, for example The formation enthalpies of the AgCl, Ag 2 SO 4 , AgF, and CO 2 compounds obtained using the present HSE06 functional are listed in Table 1. The formation enthalpies obtained with the present HSE06 functional calculations are agreement with the experimental values.

Results and Discussion
Bulk properties. We first present the results for the structural and electronic properties of defect-free bulk Ag 3 PO 4 . The crystal structure of Ag 3 PO 4 has a cubic structure with space group P n 43 , its basic structural unit is constructed by PO 4 tetrahedron and AgO 4 tetrahedron. The interaction between phosphorus and oxygen is mainly by covalent bond, while the interaction between silver and oxygen is formed ) becomes more favorable. The thermodynamic transition level of ε(− /0) is located at 0.46 eV above VBM. To obtain further details, the squared wave function e 2 ψ of the neutral defect state at Γ point is visualized in Fig. 4(a). The neutral defect state is highly confined around the N atom, which suggests that N O 0 induces a localized defect state. The N 2p orbital energy is 1.9 eV higher than the O 2p orbital energy, this imply that upon N substitution on O, the N 2p will create a partially filled impurity state at the Fermi level 35 . Thus, we examined the total density of states and projected density of states of N O 0 (not shown). The neutral defect state has the main contribution from s orbitals and d orbitals of Ag, p orbitals of N and O, minor contribution from p orbitals of P. We also analyzed the local lattice relaxations around N O 0 and N O −1 . In the neutral state, the neighboring Ag atoms relax inward, resulting in a N-Ag bond length (2.11 Å) that is 11% shorter than the equilibrium O-Ag bond length, while the N-P bond length (1.65 Å) become 6% longer  than the equilibrium O-P bond length. In the negative state, the N-Ag bond length is 2.11 Å, while the N-P bond length 1.64 Å. Figure 3 shows that the formation energy of N O 0 is more stable than N O −1 under O-poor condition but still relatively high even the Fermi level is near the conduction band. The high formation energy of the N O indicates that the N-doped Ag 3 PO 4 system using an N 2 source may not readily to produce p-type conductivity, which is consistent with the N-doped ZnO system 36 . Carbon. As carbon atom has four valence electrons which is two electrons less than oxygen atom, the substitution of C on O site (C O ) will act as a double acceptor. The 2p orbital energy of carbon is 3.8 eV higher than the O 2p orbital 35 . Consequently, C O has two distinct transition levels in the band gap: a ε(− /0) transition at 1.54 eV above the VBM and a ε(2− /0) transition at 1.39 eV above the VBM as shown in Fig. 2. This implies that C O in Ag 3 PO 4 is a negative-U system. A defect often has a negative U if the atomic position of the defect depends sensitively on its charge state 37 , U refers to the additional energy upon charging of the defect with an additional electron 38 . In the neutral charge state (C O 0 ), the three Ag nearest neighbors relax inward by 13% (of the equilibrium O-Ag bond length) while one nearest P atom slightly relaxes outward by about 13% (of the equilibrium O-P bond length). Figure 4(b) plots the squared wave function of the neutral C O defect level. One can see that the squared wave function is localized around C atom, consistent with the deep level feature. The neutral defect state has p orbitals of C and O, s orbitals and d orbitals of Ag contribute primarily, p orbitals of P contribute in a small part. The formation energies of C O in the neutral, − 1, and − 2 charge states as a function of the Fermi level are shown in Fig. 5. Even the formation energies of C O under O-poor condition is significantly lower than under O-rich condition but still relatively high, therefore C is not suitable for p-type doping Ag 3 PO 4 .    Chlorine. Chlorine atom is a famous n-type dopant 37,39 . The formation energy of substitutional Cl (Cl O ) against the Fermi level is shown in Fig. 7 for the two extreme cases. For Cl O , no transition level is find in the gap (a ε(0/+ ) transition at 0.14 eV above the CBM) and the + 1 charge state is energetically favorable for the whole range of the Fermi level. The extra electron from Cl O 0 occupies a conduction-band-like state, i.e., an extended state that is only slightly perturbed by the presence of the impurity 33 . Therefore, Cl O is a shallow donor.
We have plotted the squared wave function of the neutral defect state at the Γ point in Fig. 4(d). It is seen that the squared wave function associated with the donor level distributed not only around Cl atom, but also around O atoms and Ag atoms away from the Cl atom, indicating a delocalized feature, which is consistent with the result that Cl O is a shallow donor. The defect state has main contribution from s and d orbitals of Ag followed by s and p orbitals of Cl, O, and P. The formation energy of Cl O is relatively high even under O-poor condition, therefore chlorine is not suitable for n-type doping Ag 3 PO 4 . Sulfur. Sulfur is a possible candidate for n-type doping when substituted for P 7 . In the case of the S substituting on the P site, the transition level ε(0/+ ) is located at 2.37 eV (0.08 eV below the CBM). The defect state is spatially away from S P 0 [ Fig. 4(e)], which is consistent with the result that S P is a shallow donor. The defect state has main contribution from s and d orbitals of Ag followed by s orbitals of S, O, and P. It is also clearly from the shape of wave function that s and d orbitals are the main contributor to the defect state.
Sulfur is surrounded by four O atoms, for S P 0 these four nearest neighbor O atoms relax inward by 4% of the equilibrium P-O bond length. Formation energies of S P in its various charge state are shown in Fig. 8. We note, S P has lower formation energy than F O and Cl O for both O-rich and O-poor conditions. When the Fermi level near the VBM, S P is stable in the + 1 charge state. In n-type Ag 3 PO 4 , where the Fermi level is near the CBM, S P is stable in the neutral charge state, but the formation energies in the n-type regime are high under O-poor condition for this sulfur is not suitable candidate for n-type doping Ag 3 PO 4 .

Conclusion
Using hybrid density functional calculations we have investigated the electrical properties of N, C, F, Cl, and S impurities in Ag 3 PO 4 . We found that N O and C O act as deep acceptors, F O , Cl O , and S P act as shallow donors. N O and C O have high formation energies even under most equilibrium condition (O-poor condition) therefore they are not suitable for p-type doping Ag 3 PO 4 . Though F O , Cl O , and S P have shallow transition energies, they have high formation energies, thus F O , Cl O , and S P may be compensated by Ag vacancy and they are not possible lead to n-type conductivity in Ag 3 PO 4 .