Theoretical studies on the form and effect of N-doping in an ZnGa₂O₄ photocatalyst

Abstract

In the present work, hybrid density functional theory calculations were employed to analyze the electronic structures of ZnGa₂O₄ with different N impurity concentrations. The electronic transition energies in N-doped ZnGa₂O₄ with a molar ratio N/O of ∼3% were 3.35 and 1.43 eV for substituted and interstitial N-doping, respectively, which were much smaller than the value of 4.25 eV of pure ZnGa₂O₄. In 2N-doped ZnGa₂O₄ with a molar ratio N/O of ∼6%, three models with different N-doping sites (2N_s, 2N_i, and N_s + N_i) are analyzed. The calculated result indicated that the N impurity atoms preferred to form an N–N dimer rather than two apart N atoms in all three models. The electronic transition energies decreased by about 1.52, 0.91, and 2.51 eV for 2N_s-, 2N_i-, and N_s + N_i-doped ZnGa₂O₄, respectively, which mainly originated from the N–N π* states in the midgap. The half-filled impurity levels, which originated from the single electron of N-doping, were passivated due to the interaction of the two impurity atoms. The defect formation energies indicated that the oxygen vacancy would promote the introduction of a nitrogen impurity. Urea was recommended as a nitrogen source to easily achieve 2N_s-doping forms. Based on the present calculations, 2N_s-doped ZnGa₂O₄ was considered as the better photocatalyst due to a smaller band gap for visible light response and a suitable redox couple for overall water splitting. Our work provided a theoretical explanation for the origin of the enhanced visible light photocatalytic activity of N-doped ZnGa₂O₄.

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1. Introduction

One of the promising ways to solve energy and environmental issues is to utilize photocatalytic technology to split water to give H₂ and degrade organic pollutants with solar energy. Since Inoue et al. first presented studies about p-block metal oxides of MIn₂O₄, M₂SnO₄ and M₂Sb₂O₇ (M = Ca, Sr), demonstrating them as good photocatalysts for water decomposition under UV light,¹ semiconductors with a d¹⁰ electronic configuration (In³⁺, Ga³⁺, Ge⁴⁺, and Sn⁴⁺ etc.) have been considered as good photocatalysts and showed promising applications.^2–8 Among the p-block metal oxide photocatalysts studied, cubic spinel ZnGa₂O₄ is also a good photocatalyst for water splitting,^9–15 organic pollutant degradation,^16–21 and CO₂ reduction.^22–25 However, pure ZnGa₂O₄ still has a low solar energy utilization due to its wide band gap of about 4.1–4.5 eV.^11,14,15 Therefore, broadening the light absorption of the ZnGa₂O₄ photocatalyst by tuning the band gap energy has become one study aspect.

To reduce the large band gap, some transition metals (TM) have been introduced in ZnGa₂O₄. Zhang's group synthesized Zn_1−xCd_xGa₂O₄ solid solution photocatalysts with better UV light activity for the methylene blue degradation, which exhibited the band gaps between 4.8 and 3.6 eV by different Cd components.²⁶ Xu et al. narrowed the band gaps of ZnGa₂O₄ from 4.7 to 3.1 eV by introducing Cr to substitute Ga ions (ZnGa_2−xCr_xO₄), presenting a better photocatalytic H₂ production activity.²⁷ Irie et al. demonstrated that Rh-doped ZnGa₂O₄ with a good visible light activity for water splitting had a 600 nm light adsorption onset due to the impurity states in the midgap.²⁸ However, TM-doped materials have some disadvantages for efficient photocatalytic reactions, such as rapid electron–hole recombination and thermal instability. To solve these questions, nonmetal doping gives some promising advantages. Hereinto, the N-doped semiconductor photocatalysts, which displays favorable visible light activity, are the most widely investigated.^29–34 N-Doped spinel ZnGa₂O₄ photocatalysts prepared by Parida et al. through solid–solid reaction method based on different N-precursors, which gave the band gap energy of minimal 2.6 eV.³⁵ Lobo et al. also achieved N-doped ZnGa₂O₄ photocatalysts by combining sol–gel and nitridation steps, presenting the band gap energy of minimal 2.4 eV.^9,15 Interestingly, in Parida's work, a significant band gap change from 3.0 to 2.6 eV was observed corresponding to the nitrogen content change from 0.04% to 0.15%. However, N-doped ZnGa₂O₄ prepared by nitridation steps gives a slight band gap variation from 2.47 to 2.40 eV when the nitrogen content increases from 0.58% to 2.85%. The result suggests that the different nitrogen sources and contents will influence the effect of N-doping on the band structure of ZnGa₂O₄. Although the effect of N-doping in the semiconductor photocatalyst was discussed by previous experimental and theoretical work, the form of N-doping and the origin of the improved visible light adsorption were still in debate. For example, the form of N-doping in TiO₂ was speculated to be substituted, interstitial, NO_x or NH_x depending on experimental conditions.^30–38 Experiments and theoretical calculations also noted that the forms of N-doping were connected with synthesis conditions.^34,39 Lobo's work noted that the band gap narrowing of N-doped ZnGa₂O₄ should be contributed to the mixing states of N 2p and O 2p above the valence band, inducing by the substituted N-doping. However, Batzill's work and Li's work illustrated the p orbital energy of N was close to that of O, which induced less band gap narrowing.^40,41 The fact suggests that the large band gap narrowing of about 2.0 eV of N-doped spinel ZnGa₂O₄ is still complicated and unclear. Therefore, further studies are necessary to reveal the origin of the experimentally observed large red shift.

Previously, many photocatalysts were prepared and studied with considerable photocatalytic activity. However, the number of visible-light-sensitive photocatalysts with overall water splitting ability is limited due to the strict demand of the band relative positions. That is the conduction band minimum (CBM) must be higher than the hydrogen producing potential and the valence band maximum (VBM) must be lower than the water oxidation potential. Therefore, a great deal of effort has been spent on finding semiconductors with suitable band structures. The potentials of VBM and CBM of ZnGa₂O₄ are ca. 3.0 and −1.2 V (vs. SHE), respectively, which indicates the ZnGa₂O₄ has a suitable redox couple for overall water splitting.⁴² Although some transition metals (TM) and nonmetals have been introduced into ZnGa₂O₄ to reduce the large band gap of 4.2 eV to response visible light, the influence of impurities on the VBM and CBM relative positions is unclear. Generally, the TM-doping introduces some d impurity states in the gap of semiconductor photocatalysts. Although the d states narrowed the original bandgap and simultaneously retains the potential, others depressed the CBM to suppress the reduction potential for H₂ production. The redox ability of photogenerated electron–hole pairs decreases as Cd concentration increases in Zn_1−xCd_xGa₂O₄ due to the CB and VB shift to Fermi level.²⁶ Irie's work demonstrates that the introduction of Rh-doping in a regular octahedral coordination (Ga sites) creates fully occupied t⁶_2g and empty e⁰_g midgap states due to ligand-field splitting of the octahedrally coordinated Rh³⁺, and these midgap states had suitable potentials to produce hydrogen/oxygen under visible-light irradiation.²⁸ The nonmetal-doping, such as N, and C introduces p impurity states in the gap of semiconductor photocatalysts. N-Doping induces the VB contraction and stronger oxidation potential in rutile TiO₂ and a slight VB extension in anatase TiO₂.⁴³ The carbon self-doping in g-C₃N₄ could shift the potentials of both valence and conduction bands positively, which would increase the photooxidation ability and reduce the photoreduction ability.⁴⁴ These previous studies indicate that the doping in ZnGa₂O₄ requires careful design for the visible-light sensitive photocatalyst toward overall water splitting.

Theoretical calculations based on local density functional theory (DFT) are considered as a benefit tool to analyze the properties of semiconductors. However, although the structural parameters are agreement with experiments, the band gaps are severely underestimated by the DFT calculations.⁴⁵ The band gaps of ZnGa₂O₄ calculated by local density approximation (LDA) and generalized gradient approximation (GGA) are about 2.6–2.8 eV,^46,47 which are much less than the experimental value. Some methods, such as GW, LDA + U, hybrid and screened functionals, were developed and used to correct the gap underestimated problem. The GW approximation⁴⁸ based on the many-body perturbation theory is to date the top method for calculating quasiparticle band structures. Dixit's work gives the band gap of about 4.6 eV of ZnGa₂O₄ using the GW approximation, which is in good agreement with experiments.⁴⁹ However, although the GW approximation shows methodological advances, DFT is still widely used for investigating electronic structure features due to much more computationally demanding by the GW calculations. The LDA + U method,^50–53 which includes the on-site Coulomb interaction in the Hamiltonian, has been used to descript the effect of the d-electrons. The band gap of ZnGa₂O₄ calculated by the LDA + U method was about 3.1 eV,⁴⁶ which slightly suppressed the error of the LDA calculation. However, the underestimate of band gap is still severe in the LDA + U calculations. Hybrid and screened functionals, which mix a fraction of nonlocal potentials such as Hartree–Fock (HF) exchange potentials or screened nonlocal exchange potentials within Kohn–Sham type approaches, go beyond the local and semi-local approximations of DFT.⁵⁴ A new class of calculations based on hybrid and screened functionals have been reported to give good band gaps in semiconductors.^55,56 These researches suggest that the combination of local DFT and nonlocal functionals will be favorable for accurately calculating the band structure of ZnGa₂O₄ and its changes induced by N-doping.

In the present paper, theoretical calculations with different local, nonlocal, screened exchange and hybrid functionals are implemented to achieve the accurate band structure of cubic spinel ZnGa₂O₄. Based on the calculated results, the Perdew–Burke–Ernzerhof (PBE0) hybrid functional is employed to obtain microscopic insight into the effect of N-doping on the electronic properties of ZnGa₂O₄ correlated with N impurity forms and content. The results provide a solid basis for the rationalization of the experimentally observed red shift and the changes of the VB and CB potentials as a result of N-doping in ZnGa₂O₄.

2. Computational details and structural aspects

DFT calculations supplied the accurate description of the total energy and equilibrium structure of the crystals. Therefore, to achieve the equilibrium structure of the cubic spinel ZnGa₂O₄ (56 atoms), the exchange and correlation interactions were dealt with the GGA-PBE functional.⁵⁷ The norm conserving pseudo-potential was used to deal with the core electrons and the valence atomic configurations were 3d¹⁰4s² for Zn, 3d¹⁰4s²4p¹ for Ga, 2s²2p⁴ for O, and 2s²2p³ for N. The plane wave cut off was set to 800 eV. The k mesh of 4 × 4 × 4 achieved by the Monkhorst–Pack scheme⁵⁸ was used to achieve accurate structural parameters. The convergence tests of the plane wave cut off and the k points were given in Fig. S1 of the ESI.† In the geometrical optimization, all forces on atoms were converged to less than 0.03 eV Å⁻¹, the maximum ionic displacement was within 0.001 Å and the total stress tensor was reduced to the order of 0.05 GPa. The optimized lattice parameters were a = b = c = 8.567 Å, which were in good agreement with the experimental and the other theoretical values.^59–62 all calculations were performed using Cambridge Sequential Total Energy Package (CASTEP).

The N-doped models were constructed based on the fully relaxed pure ZnGa₂O₄. For the substitutional N-doped model, one oxygen atom in the ZnGa₂O₄ crystal structure was replaced by one nitrogen atom labeled as N_s. For the interstitial N-doped model, one nitrogen atom was set at the interstitial sites of the ZnGa₂O₄ crystal lattice labeled as N_i. For the higher N impurity concentration, two nitrogen atoms were introduced in the lattice labeled as 2N_s, 2N_i, and N_s + N_i. Different doping positions of two nitrogen atoms were tested, and the relative stability of the doped models was studied to find the most stable structure according to N–N distance. All the electronic structures were calculated on the corresponding optimized models. The local, nonlocal, screened and hybrid functionals are implemented to calculate the band structures of the pure ZnGa₂O₄ as shown in Fig. S2.† The calculated results suggest that the hybrid PBE0 functional⁶³ will be favorable for analyzing the changes of the electronic structures of ZnGa₂O₄ induced by N-doping.

To examine the thermodynamic stability of the different N-doped models, the formation energies (E_f) were calculated according to the following equation,^64–67

E_f = E_t(Doping) + n_Oμ_O − E_t(Pure) − n_Nμ_N,

where E_t(Doping) was the total energy of the structures with the N impurity, and E_t(Pure) was the total energy of the ideal cell. n_O was the number of O atom being removed from the cell, and n_N was the number of N impurity introduced into the lattice. μ_O and μ_N were the chemical potentials of N and O, respectively. In the present work, μ_O was fixed at the energy of half an O₂, while μ_N was calculated based on the different nitrogen sources.

3. Results and discussion

3.1 N_s- and N_i-doped ZnGa₂O₄

A. Geometrical structures. Cubic spinel ZnGa₂O₄ has a closed packed face-centered-cubic structure with space group Fd3̄m, in which the Zn atoms are located at tetrahedral sites with the Wyckoff positions 8a (1/8, 1/8, 1/8), while Ga atoms are located at octahedral sites with the 16d (1/2, 1/2, 1/2) and the O atoms at 32e (u, u, u). The lengths of the O–Ga bonds and the O–Zn bonds are 2.030 Å and 2.060 Å, respectively. For the N_s structure as shown in Fig. 1b, the lengths of the optimized N_s–Ga and N_s–Zn bonds are 2.019 and 1.956 Å, respectively, which are slightly shorter than the original O–Ga and O–Zn bonds in the pure ZnGa₂O₄. For the N_i structure as shown in Fig. 1c, the N_i-doping induces a large local lattice distortion after full structural relaxation. The lattice O atom is pushed away from the original position by the N_i atom, forming a new N–O bond with bond length of about 1.368 Å.

Fig. 1 The geometrical structures and electron density of (a) pure, (b) N_s-doped, and (c) N_i-doped ZnGa₂O₄. The unit of the electron density labeled in the table is e Å⁻³.

To study the variation of chemical bonding induced by the N-doping for ZnGa₂O₄, we calculate the total electron density and Mulliken charge population (as shown in Table 1) for the N_s and N_i models. For the pure ZnGa₂O₄, Fig. 1a shows that the O ions connect with adjacent Ga ions through a common electron cloud, presenting covalent O–Ga bonds. For the N_s-doped ZnGa₂O₄, Fig. 1b shows more electron cloud between N_s ion and Ga cations (0.672 e Å⁻³) than that between O ions and Ga cations (0.609 e Å⁻³), which is consistent with the shorter N_s–Ga and N_s–Zn bonds after geometrical optimization. The charges of −0.87 |e| on the N_s ion are close to −0.84 |e| on the original O ions. The result suggests that N²⁻ ion is localized in the lattice, which will introduce one acceptor level in the ZnGa₂O₄. For the N_i-doped ZnGa₂O₄, Fig. 1c shows a covalent interaction between the N_i ion and the adjacent O ion. The charges on the N_i ion and the O ion are −0.48 |e| and −0.50 |e|, respectively. The total charges of −0.98e on the NO species suggests that the NO²⁻ species exist in the lattice.

Table 1 The bond lengths and Mulliken charge populations for pure, N_s-, N_i-, 2N_s-, 2N_i-, N_s + N_i-, and 2N_s + V_O-doped ZnGa₂O₄

Models	Bond lengths (Å)				Charges (|e|)
	O/N–Ga	O/N–Zn	N–O	N–N	Ga	Zn	O	N
Pure	2.030	2.060			1.20	0.97	−0.84
Ns	2.019	1.956			1.21	0.96	−0.84	−0.91
Ni	1.960	1.951	1.368		1.22	0.96	−0.50	−0.48
2Ns	1.994	1.950		1.696	1.20	0.93	−0.84	−0.77
	1.987	1.945						−0.77
2Ni		2.084	1.797	1.176	1.22	0.93	−0.75	−0.21
		2.014						−0.13
Ns + Ni	1.971	2.160		1.284	1.20	0.97	−0.84	−0.46
	1.975	2.131						−0.46
2Ns + VO	1.918/1.945/1.988	1.929			1.21	0.95	−0.84	−1.00
	1.932/1.962/1.978	1.996

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B. Electronic structures. Fig. 2 gives the band structures, the total density of states (TDOS), and the project density of states (PDOS) of pure, N_s-, and N_i-doped ZnGa₂O₄. For the pure ZnGa₂O₄, the calculated band gap is about 4.25 eV using hybrid PBE0 functional, which is in good agreement with the experimental 4.1–4.5 eV.^11,14,15 The valance band maximum (VBM) of the pure phase are predominantly contributed by the O 2p states. The conduction band minimum (CBM) basically originates from the Ga 4s states with small O 2p states. The result indicates that the p–s electronic transition is responsible for the optical absorption onset of the pure ZnGa₂O₄. In the present work, the energy of the VBM of pure ZnGa₂O₄ is set as the reference (zero energy) to study the changes of the redox ability of N- and 2N-doped models. The redox potentials of water splitting are labeled in all band structures (3.05 eV for H₂/H₂O and 1.82 eV for H₂O/O₂).

Fig. 2 The band structures, and density of states of (a) pure, (b) N_s-doped, and (c) N_i-doped ZnGa₂O₄. The dash line presents the Fermi level.

For the N_s-doped ZnGa₂O₄, as shown in Fig. 2b, the electronic transition energy decreases to about 3.35 eV due to three impurity levels localized at the VBM. The host band gap of 4.35 eV from the host VBM to CBM is slightly larger than 4.25 eV of the pure ZnGa₂O₄. We contribute the larger band gap to a reduction of the Coulomb repulsion and a contraction of the band, resulting from the removal of one electron when one N atom replaces one O atom in the cell. The PDOS shows that the impurity levels are mainly contributed by the mixing states of N 2p states with little O 2p states. It is clear that the substituted N-doping improve the solar energy utilization of ZnGa₂O₄ through some continuous states above the VBM, and N_s-doped ZnGa₂O₄ still shows overall water splitting ability. However, the narrowing of the electronic transition energy is still not enough to response the visible light, which demands the energy of less than 2.8 eV.

For the N_i-doped ZnGa₂O₄, Fig. 2c shows two isolated impurity levels in the gap. The theoretical gap from the host VBM to the CBM has a slight increasing of about 0.18 eV, which is contributed to the p–p repulsion of the N_i-doping and the VBM. However, the electron excited energy from the top impurity level to the CBM is about 1.43 eV, which is much smaller than 4.25 eV of pure phase. The PDOS indicates that the two midgap levels are mainly originated from the mixing states of N 2p states and O 2p states. The further highest occupied molecular orbital (HOMO) analysis as shown in Fig. 3c shows a remarkable NO π-antibonding character. Therefore, we conclude that the electronic excitations from the NO π* states are one of the reasons of the visible light response in N_i-doped ZnGa₂O₄. Importantly, the calculated band structure indicates that the overall water splitting ability of ZnGa₂O₄ has been break due to the deep impurity levels. In addition, the calculated band structures of N_s- and N_i-doped ZnGa₂O₄ show the top impurity level crossing the Fermi level presents half occupied characteristic, which is agreement with the charge population analysis. However, the partially occupied impurity states go against the photocatalytic activity of semiconductors because these states can act as recombination centers to suppress the photogenerated current and reduce the UV light activity. Thus, the passivated approach is desired to compensate the half occupied impurity states.

Fig. 3 The highest occupied molecular orbital (HOMO) of (a) pure, (b) N_s-doped, and (c) N_i-doped ZnGa₂O₄.

3.2 2N_s-, 2N_i- and N_s + N_i-doped ZnGa₂O₄

A. Geometrical structures. To achieve the most stable configuration of 2N_s-, 2N_i- and N_s + N_i-doped ZnGa₂O₄, the different lattice sites are tested for the two N-doping atoms. The relative energies of these models are calculated and shown in Fig. S3–S5.† As shown in Fig. 4, all the most stable configurations of the three 2N-doped ZnGa₂O₄ give a N₂ dimer structure formed by the two adjacent N-doping atoms. This result is agreement with the theoretical work of 2N-doped TiO₂ and MgTa₂O₆.^39,68 For the 2N_s-doped ZnGa₂O₄, the two N_s atoms attract each other, which induces one initial N–Ga bond disappearing and forms one N_s–N_s bond with bond length of 1.696 Å. The bonds between N_s-doping ions and adjacent Ga ions are 1.994 and 1.987 Å, which are slightly shorter than that in pure ZnGa₂O₄. For the 2N_i-doped ZnGa₂O₄, the two N_i atoms are also bounded together with the bond length of about 1.176 Å, and a large local distortion of lattice is induced by the 2N_i-doping. Meanwhile, the N_i–N_i dimer together with one lattice O atoms forms –N_i–N_i–O– structure, which gives N–O bond length of 1.797 Å. For the N_s + N_i-doped ZnGa₂O₄, the N_i atom pushes the N_s atom away from the original lattice site to form a new –N₂– structure with the N_s–N_i bond length of 1.284 Å. These calculated results note that the N₂ dimer is common in N-doped ZnGa₂O₄, especially for higher nitrogen impurity content.

Fig. 4 The geometrical structures and electron density of (a) 2N_s-doped, (b) 2N_i-doped, and (c) N_s + N_i-doped ZnGa₂O₄. The unit of the electron density labeled in the table is e Å⁻³.

Fig. 4 shows that the two N-doping ions are bounded together by a common electron cloud, presenting a strong covalent-like characteristic. For 2N_s-doped ZnGa₂O₄, more electrons are shared by N_s-doping and Ga ions (more than 0.672 e Å⁻³), which give stronger N_s–Ga covalent bonds. The interaction of the two N_s ions reduces the charges on each N_s ion to −0.77 |e|. For 2N_i-doped ZnGa₂O₄, the total electron density map indicates that the N_i–O bonds are much weaker than that in N_i-doped ZnGa₂O₄. This result is consistent with the smaller total charges of −0.34 |e| on the two interstitial N ions, which is contributed to the interaction of the two N_i ions. For N_s + N_i-doped ZnGa₂O₄, the effect of the N₂ dimer is similar to the original O ions. However, the two N–Ga bonds present stronger covalent-like characteristic by capturing more electrons (−0.92 |e|). The present results give strong interaction between the two N-doping for the three 2N-doped models, which will significantly affect the electronic structures of ZnGa₂O₄.

B. Electronic structures. Fig. 5a for 2N_s-doped ZnGa₂O₄ shows that two isolated impurity levels localize in the gap, and the other two impurity levels are above the VBM. The electronic transition energy from the highest occupied level to the CBM is about 2.73 eV. The host band gap is about 4.45 eV from the host VBM to CBM. The increase of about 0.20 eV of band gap in 2N_s-doped ZnGa₂O₄ is larger than that in N_s-doped ZnGa₂O₄. This phenomenon is contributed to the more reduction of the Coulomb repulsion and the more contraction of the valence band due to the more electronic losing of the two N_s-doping atoms. In addition, the band structure shows that 2N_s-doped ZnGa₂O₄ still keeps overall water splitting ability. The DOS and PDOS indicate that the two isolated impurity levels are mainly contributed to the N 2p states with a little O 2p states, while the other two impurity levels are dominated by the O 2p states mixing with a little N 2p states. The further HOMO analysis (see Fig. 6a) gives the frontier orbital level of 2N_s-doped ZnGa₂O₄, presenting a remarkable N_s–N_s π-antibonding character. Especially, no half-filled levels are observed in 2N_s-doped ZnGa₂O₄, which is contributed to the interaction of the two N-doping. Based on the calculated results, we conclude that the midgap states originated from the N–N π* states are favorable for improving the visible light absorption of ZnGa₂O₄ and are one of reasons for the observed red shift of the absorption edge in experiments.

Fig. 5 The band structures and density of states of (a) 2N_s-doped, (b) 2N_i-doped, and (c) N_s + N_i-doped ZnGa₂O₄. The dash line presents the Fermi level.

Fig. 6 The highest occupied molecular orbital (HOMO) of (a) 2N_s-doped, (b) 2N_i-doped, and (c) N_s + N_i-doped ZnGa₂O₄.

Fig. 5b gives the band structure of 2N_i-doped ZnGa₂O₄. Only one isolated level localizes in the gap, which induces the electronic transition energy decrease to 3.34 eV. The host band gap has a slight change of about 0.08 eV, and there are no half-filled levels in the band. The calculated band structure shows a significant difference compared with that of N_i-doped ZnGa₂O₄, in which two isolated levels, smaller electronic transition energy of 1.43 eV and larger host band gap increasing of 0.18 eV are observed. The DOS and PDOS of 2N_i-doped ZnGa₂O₄ show that the midgap level is mainly contributed by O 2p states with little N 2p states. The HOMO analysis as shown in Fig. 6b gives an –N_i–N_i–O– mixing characteristic, which consists of N_i–N_i π* and N_i–O σ orbitals. Importantly, some N 2p states localize above the Ga 4s states of the CBM mixing with empty states. Based on the calculated results and combined with charge analysis, we conclude that the unpaired electrons of the N_i-doping are paired, which induce one empty anti-bond molecular orbital moving up and the other occupied anti-bond molecular orbital moving down. The up orbital results in the weakening of the p–p repulsion between the midgap states and the VBM. Thus the broadening of the host band gap is smaller than that in N_i-doped ZnGa₂O₄. The down orbital increases the electronic transition energy of about 1.91 eV from the impurity states to CBM compared with that in N_i-doped ZnGa₂O₄. Therefore, although the N_i–N_i impurity induces the electronic transition energy decreasing than pure phase, the interaction of two N_i-doping atoms goes against the further improving of the visible light response of N-doped ZnGa₂O₄.

The band structure of N_s + N_i-doped ZnGa₂O₄ as shown in Fig. 5c gives the host band gap of 4.46 eV and no half-filled level localizes in the band structure. One isolated level localizes in the gap, and the electronic transition energy from the level to CBM is 1.74 eV, which is much smaller than 4.25, 3.35, 3.34, and 2.73 eV of pure, N_s-, 2N_i-, and 2N_s-doped ZnGa₂O₄, and just larger than 1.43 eV of N_i-doped ZnGa₂O₄. The DOS and PDOS show the N 2p states are responsible for the midgap level. The HOMO analysis presents a remarkable N_s–N_i π anti-bonding character. Therefore, the electronic transition of π*–s is one of reasons that inducing visible light absorption in experiments. The character is agreement with that in 2N_s-doped ZnGa₂O₄, while is different to that in 2N_i-doped ZnGa₂O₄. In addition, there are some N 2p impurity states localizing above the Ga 4s states of the CBM. Obviously, this character is similar to that in 2N_i-doped ZnGa₂O₄, which originates from the charge compensation of the two N-doping. Although the charge compensation may lower the impurity levels to broaden the electronic transition energy as discussed above, two effects play a positive role to narrow the energy in N_s + N_i-doped ZnGa₂O₄. One is that the N_i-doping introduces more electrons resulting in a strong p–p repulsion of the impurity states and valence bands, the other is that the mixing of the N 2p states and conduction bands as shown in Fig. 5c lowers the CBM. Therefore, based on the calculated results, we conclude that the N_s + N_i-doping units the advantages of substituted and interstitial N-doping, which is favorable for improving the solar energy utilization of ZnGa₂O₄. However, the redox potentials of the impurity levels indicate that N_s + N_i-doped ZnGa₂O₄ has no O₂ producing ability.

3.3 2N_s + V_O-doped ZnGa₂O₄

In consideration of the fact that the oxygen vacancy (V_O) is common in oxide semiconductors, the synergetic effect of N impurity and V_O on the geometrical and the electronic structures are calculated and analyzed. The V_O will attract the interstitial N impurity to form the substituted N-doping after structural relaxation. Thus, only 2N_s + V_O-doped model is considered in the present work. Fig. 7a shows the optimized structure of 2N_s + V_O-doped ZnGa₂O₄, which gives the shortest two N–Ga bonds with 1.918 and 1.932 Å in N-doped models. The result indicates the oxygen vacancy strengths the interaction between N-doping and adjacent cations. The electron density map as shown in Fig. 7b shows that more electrons are common in cloud than that in pure phase and also that in N_s-doped model. Mulliken population listed in Table 2 gives the charges of −1.00 |e| on each N ion, showing more electrons transferring from adjacent cations compared with −0.84 |e| of O ion and −0.91 |e| of N_s ion in N_s-doped ZnGa₂O₄. Therefore, we conclude that the oxygen vacancy induces the N³⁻ ions formation in the lattice of 2N_s + V_O-doped ZnGa₂O₄ due to the electron transferring between V_O donor and N_s acceptor.

Fig. 7 (a) The geometrical structure, (b) the electron density, and (c and d) the electronic structures of 2N_s + V_O-doped ZnGa₂O₄. The unit of the electron density labeled in the table is e Å⁻³. The dash line presents the Fermi level.

Table 2 The electronic transition energies (E_tr) and the defect formation energies (E_f) based on the different nitrogen sources of the different N-doped models

Models	Etr (eV)	Ef (eV)
		N2	NH3	N2H4	Urea	Hexamine
Pure	4.25
Ns	3.35	5.28	3.83	4.84	2.47	4.43
Ni	1.43	5.12	3.67	4.68	2.41	4.27
2Ni	2.73	6.80	3.90	5.93	1.39	5.10
2Ns	3.34	9.62	6.62	8.75	4.21	7.92
Ns + Ni	1.74	7.17	4.27	6.30	1.76	5.47
2Ns + VO	3.38	3.25	0.35	2.38	−2.16	1.55

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The oxygen vacancy has a significant effect on the band structure of N-doped ZnGa₂O₄. As shown in Fig. 7c, some impurity levels form a continuous impurity band and extend the width of about 0.8 eV of the VB. The band gap decreases to 3.38 eV and the half-filled level induced by N_s-doping disappears. Obviously, the electron transferring between oxygen vacancy and N_s-doping will be favor of improving the photocatalytic activity. Fig. 7d shows the impurity levels are mainly contributed by the mixing states of N 2p states and O 2p states. The energy of the mixing states is lower, which suggests stronger oxidizing ability of than that in N_s-doped model VB. In addition, the calculated band structure indicates that 2N_s + V_O-doped ZnGa₂O₄ still keep the overall water splitting ability.

3.4 Formation energy

The defect formation energies of N-doped ZnGa₂O₄ are listed in Table 2. It is clear that the nitrogen impurity atoms are inclined to enter into the interstitial sites in the lattice of ZnGa₂O₄. This should be contributed to the large interspace of the spinel lattice and the strong interaction between the interstitial N and the lattice O. The N_s-doping is also possible because the E_f of 5.28, 3.83, 4.84, 2.47, and 4.43 eV is close to 5.12, 3.67, 4.68, 2.41, and 4.27 eV of N_i-doping under the different nitrogen sources. The result is agreement with the analysis of N-doped TiO₂, which gives the interstitial N first and the substituted N following.³⁴ The formation energies of the 2N_s + V_O-doped ZnGa₂O₄ are much smaller than that of other 2N-doped models. The result indicates the oxygen vacancy will promote the introduction of nitrogen impurity. In most cases, the formations of 2N_s-, 2N_i-, and N_s + N_i-doping are difficult than that of N_s-, and N_i-doping. However, using urea as nitrogen source, the calculated formation energies of 1.39, 2.21, and 1.76 eV for 2N_i-, 2N_s-, and N_s + N_i-doping are smaller than the formation energies of N_s- and N_i-doping, which indicate the N–N dimer could be preferentially formed in a suitable environment. The above calculated electronic structures with the different N-doping forms suggest that the 2N_s-doped ZnGa₂O₄ has a smaller band gap for absorbing visible light and a suitable redox couple for overall water splitting. Therefore, urea is recommended as nitrogen source to easily achieve the 2N_s-doping from the view of thermodynamics.

4. Conclusions

The geometrical structures and electronic structures of N-doped and 2N-doped ZnGa₂O₄ are discussed based on the PBE0 calculations. The present work notes that the interstitial N impurity is prior on thermodynamics and induces a larger decrease of the electronic transition energies in N-doped ZnGa₂O₄ due to the midgap NO π* states. In 2N-doped ZnGa₂O₄, the two N impurity atoms form N₂ dimer structure in the lattice, and the electronic transition energy has a significant decrease, which is contributed to the N–N π* states in the midgap. The oxygen vacancy will promote the introduction of 2N_s-doping in the lattice of ZnGa₂O₄. Our work provides a theoretical analysis for the visible light photocatalytic activity induced by nitrogen impurity in ZnGa₂O₄ photocatalyst.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 51402169 and 51502076), the Natural Science Foundation of Shandong Province, China (Grant No. 51402169), and the China Postdoctoral Science Foundation (Grant No. 2013M530322). The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center, Shandong University, Weihai.

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Footnote

† Electronic supplementary information (ESI) available: The convergence tests, the band structures of the pure ZnGa₂O₄ calculated by different functionals, the relative energies of 2N-doped ZnGa₂O₄ with different doping sites. See DOI: 10.1039/c6ra09655g

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