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.

Since Honda and Fujishima first disn class="Chemical">covered the photocatalytic <pan> class="Chemical">span class="Chemical">water sppan>>litting into H2 and O21, the photocatalysis of <spn>an class="Chemical">water splitting has become an active research field and a potential way to solve the severe environmental crisis and energy shortage issues23. TiO2 is the earliest photocatalyst used in water splitting, the intrinsic wide band gap of pure TiO2 (~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 solutions5.

Recently, Ye et al. reported that cubic structure semin class="Chemical">conductor <pan> class="Chemical">span class="Chemical">Ag3PO4, which exhibits strong oxidation power leading to O2 production from <sppan>>an class="Chemical">water, and its quantum yield achieve up to nearly 90% under visible light6. This is intriguing because most photocatalysts give much poorer quantum yields of ~20%7. Theoretical studies have also been performed to understand their origin7891011. Reunchan and Umezawa suggest that native point defects are unlikely to be responsible for an intrinsic conductivity of Ag3PO4, which an n-type character was observed in the previous report, but Ag3PO4 could feasibly be doped in n-type fashion7.

First-principles density functional theory (DFT) calculations have been n class="Chemical">commonly used to study the electronic properties of <pan> class="Chemical">span class="Disease">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 functional14, 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 physics15161718.

In this paper, we perform first-principles calculations based on the hybrid HF density functional to investin class="Chemical">gate the influence of n class="Chemical">N, C, F, Cl, and S impurities on the electronic properties of <span class="Chemical">Ag3PO4. 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 (VAn class="Chemical">SP)1920. Inpan>teraction between the valence and n class="Chemical">core electrons was described using the projector augmented wave (PAW) approach21. 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 (<n class="Chemical">spanpan> class="Genpan>e">HSEpan>>06)1422, which adopts a screened Coulomb potential. Hence, greatly improving the description of structural properties and band structures, including band gaps. Both of these aspn>ects are particularly important for defects. The <span class="Gene">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 as4.

Where a is the mixing n class="Chemical">coefficient and ω is the range-separation parameter. A n class="Chemical">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 <span class="Gene">HSE06 functional24. We find that a proportion of 33% HF exchange with 67% PBE exchange produces accurate values for lattice constants and the band gap in <span class="Chemical">Ag3PO4.

We used a 128-atom supercell n class="Chemical">constructed by 2 × 2 × 2 replication of the cubic <pan> class="Chemical">span class="Chemical">Ag3PO4 unit cell (sppan>>ace group ), which ensures sufficient spn>atial separation between the periodic images of the impurities. Various dopings of <span class="Chemical">Ag3PO4 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-points25. 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 ∆Hf(α, q) as a function of the electron Fermi energy27 EF as well as the atomic chemical potentials2829 μi is as follows:

Where

E(α, q) is the total energy for the studied supercell n class="Chemical">containing defect α in charge state q anpan>d E (host) is the total enpan>ergy of the same supercell without the defect. n indicates the number of atoms of type i (<pan> class="Chemical">span class="Disease">host atoms or impurity atoms) that have been added to (n < 0) or removed from (n > 0) the supercell , and q is the number of electrons transferred from the supercell to the reservoirs in forming the defect cell. EF is the electron Fermi level referenced to the valence-band maximum (VBM) of host, εVBM(host), and varies from the valence-band maximum to the conduction-band minimum (CBM). μi is the chemical potential of constituent i referenced to its elemental solid or gas with energy E(i).

The defect transition energy level ε(q/q′) is the EF in Eq. (1), at which the formation energy ∆Hf(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 n class="Chemical">combine the advanpan>tages of both pan> class="Chemical">special k-points and Γ-point-only approaches12. In this scheme, for acceptor level (q < 0), the transition energy level with respect to VBM is given by:

For <n class="Chemical">span class="Species">donorn> level (q >0), the <spn>an class="Disease">ionization energy referenced to the CBM is given by:

Where εDk(0) and εDΓ(0) are the defect levels at the special k-points (averaged) anpan>d at the Γ-point, repan> class="Chemical">spectively; εVBMΓ(host) and εCBMΓ(host) are the VBM and CBM energies, respectively, of the host at the Γ-point; and εgΓ(host) is the calculated bandgap at the Γ-point.The formation energy of a charged defect is then given by

Where ∆Hf(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 desn class="Chemical">cribed elsewhere30.

Chemical potentials

Under thermal equilibrium growth n class="Chemical">conditions, the steady production of host material, <pan> class="Chemical">span class="Chemical">Ag3PO4, should satisfy the following equation:

where μAg, μP, and μO are the chemical potentials of Ag, P, and O source, ren class="Chemical">spectively, anpan>d ∆Hf is the formation enpan>ergy for <pan> class="Chemical">span class="Chemical">Ag3PO4 per formula. In order to avoid the precipitation of the host elements, the chemical potential μ must be bound by

To avoid the formation of sen class="Chemical">condary phases (such as <pan> class="Chemical">span class="Chemical">Ag2O and <sppan>>an class="Chemical">P2O5), μAg, μP, and μO must satisfy further constrains:

n class="Chemical">Considering Eqs. (6)–(9), , , , the accessible ranpan>ges for μAg, μP, anpan>d μO are limited anpan>d are presenpan>ted as the shaded area in Fig. 1. As shownpan> in Eqs. (5), the calculated formation enpan>ergies of charged defects depenpan>d senpan>sitively on the selected values for μAg, μP, anpan>d μO anpan>d the Fermi-level positions. Here, the calculated values at two represenpan>tative chemical potenpan>tial points are labeled as O-rich anpan>d O-poor in Fig. 1. The exact value of chemical potenpan>tials at points O-rich pan> class="Chemical">condition and O-poor condition are (−0.84, −7.93, 0) and (0, −3.71, −1.69) for μAg, μP, and μO, respectively.

Figure 1

Accessible range of chemical potentials (shaded region) of equilibrium growth condition for Ag3PO4.

For impurity doping, the chemical potentials of impurities also need to satisfy other n class="Chemical">constraints to avoid the formation of impurity-related phases, for example

The formation enthalpies of the <n class="Chemical">spanpan> class="Chemical">AgClpan>>, <spn>an class="Chemical">Ag2SO4, AgF, and CO2 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.

Table 1

The formation enthalpies (in eV) of Ag2O, P2O5, AgCl, Ag2SO4, AgF, and CO2 molecules calculated from the HSE06 hybrid functional.

	HSE06	Experiment
ΔHf (Ag2O)	−0.32	−0.3231
ΔHf(P2O5)	−15.86	−15.6032
ΔHf (AgCl)	−1.20	−1.3231
ΔHf(Ag2SO4)	−7.06	−7.4231
ΔHf (AgF)	−2.03	−2.1331
ΔHf(CO2)	−3.82	−4.0831

The experimental values are also listed for comparison.

Results and Discussion

Bulk properties

We first present the results for the structural and electronic properties of defect-free bulk <n class="Chemical">spanpan> class="Chemical">Ag3PO4pan>>. The crystal structure of <spn>an class="Chemical">Ag3PO4 has a cubic structure with space group , its basic structural unit is constructed by PO4 tetrahedron and AgO4 tetrahedron. The interaction between phosphorus and oxygen is mainly by covalent bond, while the interaction between silver and oxygen is formed mainly by ionic bond8. The optimized cell parameters are a = b = c = 6.02 Å, and excellent agreement with the experimental values of a = b = c = 6.00 Å8. The P-O, Ag-O, and Ag-Ag bond lengths are calculated to be 1.56 Å (experimental value11: 1.56 Å), 2.37 Å (experimental value11: 2.36 Å), 3.01 Å (experimental value11: 3.00 Å), respectively. The calculated indirect band gap (M−Γ) is 2.33 eV, and the direct gap at Γ is 2.45 eV, in excellent agreement with the experimental value of 2.36 eV and 2.43 eV6, respectively.

N, C, F, Cl, and S impurities in Ag3PO4

In this section, we discuss the different impurities in <n class="Chemical">spanpan> class="Chemical">Ag3PO4pan>> individually. The calculated thermodynamic transition energy levels for all impurities are listed in Fig. 2.

Figure 2

Thermodynamic transition levels for N, C, F, Cl and S impurities in Ag3PO4 (Unit: eV).

Nitrogen

The electronic properties of substitutional n class="Chemical">N at O sites (n class="Chemical">NO) has been confirmed by several reports4533. The conductivity of a semiconductor depends not only on the thermodynamic transition levels of donor and acceptors, but also on their formation energies. The thermodynamic transition level corresponds to the intersection of the formation energies for the different charge states. Formation energy as a function of Fermi level for NO in the O-rich and O-poor limit are shown in Fig. 3. When the Fermi level is low, the neutral charge state (NO0) is energetically preferable, as the Fermi level rises, above the Fermi level of 0.46 eV, the negative charge state (NO−1) 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 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 NO0 induces a localized defect state.

Figure 3

Calculated formation energies for N substituting on the O site as a function of Fermi level at O-rich and O-poor conditions.

Figure 4

Spatial distribution of the squared wave functions of the neutral defect states created by (a) NO, (b) CO, (c) FO, (d) ClO, (e) SP, where the isosurface values34 are 0.05, 0.05, 0.005, 0.005, 0.005 e/Å3, respectively. The silver, pink, red balls represent Ag, P, O atoms, respectively.

The n class="Chemical">N 2p orbital enpan>ergy is 1.9 eV higher thanpan> the O 2p orbital enpan>ergy, this imply that upon pan> class="Chemical">N substitution on O, the N 2p will create a partially filled impurity state at the Fermi level35. Thus, we examined the total density of states and projected density of states of <span class="Chemical">NO0 (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 <span class="Chemical">NO0 and NO−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 class="Chemical">spanpan> class="Chemical">pan> class="Chemical">NO0 is more stable than NO−1 under O-poor condition but still relatively high even the Fermi level is near the conduction band. The high formation energy of the NO indicates that the N-<sppan>>an class="Chemical">doped Ag3PO4 system using an N2 source may not readily to produce p-type conductivity, which is consistent with the N-doped ZnO system36.

Carbon

As <n class="Chemical">spanpan> class="Chemical">carbonpan>> atom has four valence electrons which is two electrons less than <spn>an class="Chemical">oxygen atom, the substitution of C on O site (CO) will act as a double acceptor. The 2p orbital energy of carbon is 3.8 eV higher than the O 2p orbital35. Consequently, CO 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 CO in Ag3PO4 is a negative-U system. A defect often has a negative U if the atomic position of the defect depends sensitively on its charge state37, U refers to the additional energy upon charging of the defect with an additional electron38. In the neutral charge state (CO0), 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 n class="Chemical">CO defect level. One can see that the squared wave function is localized around C atom, n class="Chemical">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 CO 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 CO 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 <span class="Chemical">Ag3PO4.

Figure 5

Calculated formation energies for C substituting on the O site as a function of Fermi level at O-rich and O-poor conditions.

Fluorine

Shifting the Fermi level towards the n class="Chemical">conduction banpan>d, or in other words n-type pan> class="Chemical">conditions, likely enhance the photocatalytic activities in <span class="Chemical">Ag3PO47. In contrast to the NO and CO, the substitutional F at O site (FO) exhibits distinct characteristics. Unlike the NO and CO, where the defect states are highly localized at impurities, the defect state induced by FO is spatially distributed away from F as the delocalized state [see Fig. 4(c)]. The defect state has main contribution from s and d orbitals of Ag followed by s orbitals of F, O, and P. For FO0 the three nearest neighbor Ag atoms relax outward by 17%, while for FO+1 the relaxation are outward by 18% of the equilibrium Ag-O bond length.

The formation energy of FO in different charge states as a function of the Fermi level is shown in Fig. 6. When the Fermi level is low, the positive charge state (FO+1) is energetically preferable, as the Fermi level rises, the formation energy approaches that of the neutral charge state (FO0), above the Fermi level of 2.41 eV, the neutral charge state becomes more favorable. The thermodynamic transition level of ε(0/+) is located 2.41 eV above the VBM (0.04 eV below the CBM). Though the Fermi level drops to the VBM the formation energy of FO becomes very small for the favorable growth condition (O-poor condition), but when the Fermi level is near the CBM, the formation energy of FO is still relatively high, thus, FO may be compensated by Ag vacancy and it is not possible lead to n-type conductivity in <span class="Chemical">Ag3PO4.

Figure 6

Calculated formation energies for F substituting on the O site as a function of Fermi level at O-rich and O-poor conditions.

Chlorine

<n class="Chemical">spanpan> class="Chemical">Chlorinepan>> atom is a famous n-type dopant3739. The formation energy of substitutional Cl (<spn>an class="Chemical">ClO) against the Fermi level is shown in Fig. 7 for the two extreme cases. For ClO, 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 ClO0 occupies a conduction-band-like state, i.e., an extended state that is only slightly perturbed by the presence of the impurity33. Therefore, ClO is a shallow donor.

Figure 7

Calculated formation energies for Cl substituting on the O site as a function of Fermi level at O-rich and O-poor conditions.

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 <n class="Chemical">spanpan> class="Species">donorpan>> 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 <spn>an class="Chemical">ClO 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 ClO is relatively high even under O-poor condition, therefore chlorine is not suitable for n-type doping Ag3PO4.

Sulfur

<n class="Chemical">spanpan> class="Chemical">Sulfurpan>> is a possible candidate for n-type doping when substituted for P7. 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 spn>atially away from <span class="Chemical">SP0 [Fig. 4(e)], which is consistent with the result that <span class="Chemical">SP is a shallow <span class="Species">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.

<n class="Chemical">span class="Chemical">Sulfurn> is surrounded by four O atoms, for <spn>an class="Chemical">SP0 these four nearest neighbor O atoms relax inward by 4% of the equilibrium P-O bond length. Formation energies of SP in its various charge state are shown in Fig. 8. We note, SP has lower formation energy than FO and ClO for both O-rich and O-poor conditions. When the Fermi level near the VBM, SP is stable in the +1 charge state. In n-type Ag3PO4, where the Fermi level is near the CBM, SP 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 Ag3PO4.

Figure 8

Calculated formation energies for S substituting on the P site as a function of Fermi level at O-rich and O-poor conditions.

Conclusion

Using hybrid density functional calculations we have investin class="Chemical">gated the electrical properties of pan> class="Chemical">N, C, F, Cl, and S impurities in Ag3PO4. We found that NO and CO act as deep acceptors, FO, ClO, and SP act as shallow donors. NO and CO have high formation energies even under most equilibrium condition (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 Ag vacancy and they are not possible lead to n-type conductivity in Ag3PO4.

Additional Information

How to cite this article: Huang, Y. et al. The electronic properties of impurities (n class="Chemical">N, C, F, Cl, anpan>d S) in <pan> class="Chemical">span class="Chemical">Ag3PO4: A hybrid functional method study. Sci. Rep. 5, 12750; doi: 10.1038/srep12750 (2015).