Insight into the enhanced photocatalytic activity of Mo and P codoped SrTiO₃ from first-principles prediction

Abstract

In this study, the synergistic effect of cation codoping (Mo and the cation P) on the band structure of SrTiO₃ is demonstrated to enhance its photocatalytic activity. The electronic structure and optical properties of (Mo + P) codoped SrTiO₃ are examined by performing GGA + U calculations. The results show that the strong hybridization between the Mo 4d states and the O 2p states assisted by the non-metal P leads to the formation of fully occupied and delocalized intermediate states (IBs) near the valence band of SrTiO₃. The proximity of IBs to the valence band resulted in the ability to separate photo-excited electrons from reaction holes, which helps to ensure efficient electron replenishment reducing the probability of trapping electrons from the CB. This kind of metal Mo and non-metal P-compensated codoping can efficiently narrow the band gap and enhance the visible-light absorption. Moreover, the positions of the band edges after codoping (Mo + P) are found to be thermodynamically favorable for water splitting.

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1. Introduction

Perovskite, SrTiO₃, has attracted intense attention as a promising material in the fields of photocatalysis and water splitting, since it presents excellent properties such as low cost and long term stability.^1,2 Due to the large band gap of SrTiO₃ (3.25 eV),³ it is, however, not able to show photocatalytic activity in the visible-light region, and can absorb only ultraviolet light (only 5% of solar energy). Besides the long term stability, an ideal photocatalyst should also have a narrow band gap to utilize cheaper visible-light, and appropriate band edge positions to meet the requirements for water splitting.^4,5 As such, there has been ever-growing interest in the band structure engineering of SrTiO₃. Enabling SrTiO₃ to absorb the more abundant visible-light is a crucial prerequisite for enhancing the photoconversion efficiency by reducing its band gap below 2.0 eV.^6–8

In exploring the enhanced photocatalytic activity of SrTiO₃-based materials to the visible-light region, there have been many reports that have adopted different strategies for optimizing the band gap and extending the light absorption of SrTiO₃ by different doping schemes.^9–15 Among them, the codoping approach is an effective means for lowering the band gap and improving the visible-light response, involving either cation–anion,^16–18 cation–cation,^19–21 or anion–anion^22,23 pairs. In the case of cation–cation codoping, the substitution of transition metal cations (Cr, Fe, Rh, Mo, W, etc.) at the host Ti sites in SrTiO₃ has shown to lower the band gap by introducing localized 3d impurity states, shifting the absorption spectra threshold towards the visible region.^24–27 Recently, the substitution of non-metal and metal cations at the Ti sites in TiO₂ has stimulated great interest in enhancing the visible-light absorption and photocatalytic activity by including (Fe + Si), (Mo + P) and (W + P) codoping.^28–30 However, to the best of our knowledge, there is no reported experimental or theoretical work focusing on the synergistic effects of (Mo + P) codoped SrTiO₃ on the band gap engineering.

The present work investigates the role of Mo and P cation codoping in SrTiO₃ using first-principles calculations. The substitutional positions of both the Mo and P dopants are incorporated at the Ti sites. The stabilities and optical properties of codoped systems were first determined. The electronic structure of the codoped system was analyzed and compared to gain insight into the intermediate states for lowering the band gap. To explore the synergistic effects on the redox capacity for photocatalytic water splitting, the band edge alignments were carefully carried out. These prediction results indicate that the band structure engineering of SrTiO₃ by codoping with metal and non-metal cations (Mo + P) is a promising strategy for enhancing photocatalytic activity.

2. Computational methods

All the spin-polarized calculations were performed using the CASTEP package in Materials Studio 8.0.³¹ The exchange and correlation interaction was treated with the generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE). The interactions between the valence electrons and ionic core were approximated by the ultra-soft pseudopotentials (USPP). To reproduce the experimental band gap of 3.25 eV in SrTiO₃, the GGA + U_p + U_d approach was adopted to describe the correlation effects, which can predict the corrected electronic structure and optical properties.^32–34 The on-site corrections are typically applied to the d or f orbitals of transition metal oxides; however, the band gaps are still underestimated with respect to the experimental values. Theoretical studies have revealed that the corrected band electronic structures of metal oxides can be obtained by simultaneously using the on-site Coulomb corrections on the d states of transition metals and the 2p orbital of oxygen atoms. Ma et al. theoretically found that the simultaneous application of the on-site Coulomb corrections on the Zn-3d (U_d) and O-2p (U_p) orbitals lead to a corrected band structure of ZnO.³² It has been also reported that the pair of U_d (10 eV) and U_p (7 eV) was identified as an optimal choice for the correct band structure of W-doped ZnO; in this work, we chose the GGA + U_d + U_p method to discuss the correction effects on the electronic structure of SrTiO₃ oxide materials. Based on the previous theoretical predictions, we firstly fit the U_d (2.3 eV) of Ti-3d states,³⁵ then discuss the effects of different U_p values on the band structures. It was found that the band gaps were 3.11, 3.22 and 3.48 eV for bulk SrTiO₃ system as using the U_p values (7, 8 and 9 eV) for O-2p orbitals, respectively. The correct band gap was 3.22 eV within U_p = 8 eV, which agrees well with the experimental results. We note that a U_p value of 8 eV is the best choice, which is somewhat larger than the U value used in previous work.³² Taking into account the transition metal Mo dopant, we also calculated the band gap of Mo-doped SrTiO₃ by using Coulomb corrections on the Mo-4d. The indirect spin-down band gap is about 1.75 eV within U_d = 4 eV, which is very close to the band gap (1.86 eV) calculated by the HSE hybrid density functional.³⁶ Therefore, for a better description of the localized transition, we used the on-site repulsion U_eff = 2.3 eV and 4 eV on the Ti 3d and Mo 4d states as in previous theoretical investigations,^35,37,38 and the U of the O 2p states was set to 8 eV. Spin-polarized calculations were performed for pure and different doped SrTiO₃ systems. The energy cut-off for the wave function expanded in plane waves was chosen to be 400 eV, and k-point mesh with 3 × 3 × 3 was used for the supercell calculation. Both the lattice parameters and the atomic positions were fully relaxed until the residual forces were smaller than 0.03 eV Å⁻¹, and the convergence tolerance for the optimized electronic energy was set to 1 × 10⁻⁵ eV.

To explore the optical properties, the absorption coefficients (α_abs(ω)) were simulated according to the following relation:³⁹

where ω is the angular frequency of the photon, ε₁(ω) and ε₂(ω) are the real and imaginary parts of the complex dielectric function ε, respectively. Considering the tensor nature of ε(ω) in the cubic structure, the ε(ω) are the x, y, z components in the tensor matrix. The imaginary part ε₂(ω) of the dielectric tensor is calculated using summation over the empty states, while the real part ε₁(ω) of the dielectric tensor is obtained from the Kramers–Kronig transformation, as implemented in CASTEP. Taking into account the crystal anisotropy, in the present study, the spectra along the c-axis are analyzed because the strongest absorption is along the c-axis direction.

3. Results and discussion

The presence of one electron and one hole per dopant is essential for modeling the charge compensation synergistic effect. Intense attention has been paid to B–B sites for metal–metal elements codoping (i.e., Cr/Ta, Ta/Ni, and W/Cd),^40,41 which provide one electron as the donor dopant and one hole as the acceptor dopant, thus keeping the charge balance in codoping systems. The substitution of metal and non-metal dopants on the Ti sites can also introduce the charge balance. To model the Mo and P dopants codoping in SrTiO₃, a 2 × 2 × 2 periodic supercell within 40 atoms was constructed, as shown in Fig. 1. Before investigating the electronic and optical properties of the (Mo + P) codoped SrTiO₃ systems, we first optimized the primitive SrTiO₃. The optimized lattice parameters a, b, c were 3.952 Å, consistent with previous theoretical and experimental results.⁴² The GGA + U_p + U_d calculated band gap of SrTiO₃ was 3.22 eV, which also agrees well with the experimental (3.25 eV) and HSE calculation values (3.19 eV) due to the partial correction of the band gap by suitable U values. These results show that the parameters and computational methods (GGA + U) employed here are suitable for describing different monodoped and codoped SrTiO₃ systems.

Fig. 1 The 2 × 2 × 2 supercell structures of pure SrTiO₃ cubic crystal (a), the (Mo + P) codoped SrTiO₃ with the near configuration (b), the medium configuration (c), and the far configuration (d). The dark green, gray and red balls represent the Sr, Ti and O atoms, respectively. The Mo and P dopants are marked in violet and blue, respectively.

The monodoped and codoped systems were constructed from the relaxed 2 × 2 × 2 supercell. Considering the effect of the oxidation states of Mo and P cations on the ground states of the codoped SrTiO₃, we calculated the total energy of different oxidation state configurations with the pairs of (Mo⁵⁺, P³⁺), (Mo⁵⁺, P⁵⁺), (Mo⁶⁺, P³⁺) and (Mo⁶⁺, P⁵⁺) codoping. For simplicity, the energy of the (Mo⁵⁺, P³⁺) codoped configuration was set to zero, and the energies of (Mo⁵⁺, P⁵⁺), (Mo⁶⁺, P³⁺) and (Mo⁶⁺, P⁵⁺) codoped configurations were 6.7, 31.6 and 32.3 meV, respectively. It is noted that the (Mo⁵⁺, P³⁺) codoped configuration possesses the lowest total energy, which is considered to be the ground state. We used one Mo⁵⁺ cation to substitute for a Ti⁴⁺ host site to produce an electron per supercell, while one P³⁺ cation substituted for a Ti⁴⁺ site to introduce a hole per supercell. For the Mo or P-monodoped SrTiO₃ system, there was only one doping configuration due to the symmetry of the cubic crystal, thus the Mo or P was substituted at the Ti1 site as labeled in Fig. 1(a). According to the relative substitute positions of Mo and P dopants, there are three different configurations for the (Mo + P) codoping. For the convenience of discussion, the three configurations are defined as the “near”, “medium” and “far” configurations, respectively, as shown in Fig. 1(b)–(d). For the near configuration, the Mo and P dopants occupy the nearest neighboring Ti sites at Ti1 and Ti2 sites, respectively. While for the medium and far configurations, the (Mo, P) dopant pairs substitute at (Ti1, Ti3) and (Ti1, Ti4), respectively. For the cases of three (Mo + P) codoped SrTiO₃ systems, the near configuration was found to be energetically more stable by 0.07 and 0.22 eV than the medium and the far configurations, respectively. Although the nearest neighbour codoping configuration was found to be more energetically attainable in experimental techniques such as hydrothermal and sol–gel methods,^43,44 the dopants will enter the lattice sites randomly in the supersonic cluster beam deposition techniques.⁴⁵ Therefore, to provide a theoretical basis for the design and fabrication of new photocatalysts, in the following sections, we discuss the electronic structure and optical properties of all three codoped configurations.

To obtain detailed insight into the doping effect of the Mo/P on the electronic structure of SrTiO₃, we first calculated the total DOS and partial DOS (PDOS) of pure and monodoped models, as shown in Fig. 2. For the pure SrTiO₃, the valence band maximum (VBM) and conduction band minimum (CBM) were mainly contributed by the O 2p states and Ti 3d states, respectively, as shown in Fig. 2(a). The Mo monodoped SrTiO₃ was modeled by introducing one Mo dopant at the host Ti1 site. The highest occupied orbital energy level was shifted to near the CBM after Mo doping, which is ascribed to the downward shift of the VBM and CBM. Here, the Fermi level was set at zero energy (CASTEP takes the energy of the highest occupied orbitals as the energy zero by default). That is to say, the Mo-doped SrTiO₃ system shows a typical n-type semiconductor nature due to the electron doping. The CBM was significantly downward shifted to lower energy, and some mid-gap impurity states appeared as isolated states within the forbidden gap, which can greatly narrow the band gap of SrTiO₃, as shown in Fig. 2(b). Analysis of PDOS showed that these localized impurity states originated from the strong hybridization of the Mo 4d and O 2p states. The lower energy of the Mo 4d orbital than the Ti 3d orbital induced the spin-up partially occupied states 0.74 eV above the VB and unoccupied states 0.23 eV below the CB, which can be interpreted by the different valence electron configurations of Mo (5s²4d⁴) and Ti (4s²3d²). Substitution of a Ti⁴⁺ site with a Mo⁵⁺ dopant leads to the intrinsic donor defects in SrTiO₃, which typically acts as trapping centers for charge carriers to depress the photocatalytic activity. In the case of P cation doping, there was no variation in the VBM but a slight upward shifting of the CBM, as shown in Fig. 2(c), which displays p-type doping character. In this case, the band gap expands slightly to 3.34 eV. Some spin states lying above the CBM do not originate from the P 3p impurity orbitals but from the Ti 3d states due to lattice distortion. Due to the large differences in ionic radius between the dopant P (0.44 Å) and the host Ti (0.605 Å) elements, the perturbation in the lattice structure is relatively large. Based on these results, we considered the charge compensation effects of the Mo and P codoping on SrTiO₃ to solve the above problems, and then enhance the photocatalytic performance.

Fig. 2 TDOS and PDOS of (a) pure SrTiO₃, (b) Mo monodoped SrTiO₃, and (c) P monodoping. The Fermi level is set at zero energy.

To evaluate the relative difficulty for the incorporation of dopants into the host lattice in experiments, we calculated the formation energies (E_f) of different (Mo + P) codoping configurations. The smaller the formation energy, the easier the substitutional doping is;⁴⁶ that is to say, the stability of the doped SrTiO₃ with different substitutional sites is determined by the relative formation energy. The formation energies of monodoped Mo and P, and the codoped (Mo + P) SrTiO₃ systems are defined as follows:

E_f = E_monodoped − E_pure + μ_Ti − μ_Mo/P (2)

and

E_f = E_codoped − E_pure + 2μ_Ti − μ_Mo − μ_P (3)

where the E_pure, E_monodoped and E_codoped are the total energy of pure SrTiO₃, Mo or P monodoped, and (Mo + P) codoped SrTiO₃ systems, respectively. μ_Ti, μ_Mo and μ_P denote the chemical potentials of Ti, Mo and P atoms, respectively; the formation energies can vary as a function of the oxygen chemical potential for doped systems.⁴⁷ In this study, we also considered the effect of the oxygen environment (either O-rich or Ti-rich growth conditions) on the formation energy. At the equilibrium conditions between the SrTiO₃ and the reservoirs of Sr, Ti and O elements, the following relation must be satisfied:

μ_Sr + μ_Ti + 3μ_O = μ_SrTiO3 (4)

where μ_Sr, μ_Ti and μ_O are the chemical potentials of Sr, Ti, O elements. In the present study, the μ_Sr and μ_Ti were calculated from the energy per atom in the respective bulk crystals. Under O-rich growth conditions, μ_O was simulated from the energy of one O atom in the O₂ molecule placed at the centre of a 15 × 15 × 15 ų cubic box, and the μ_Ti was determined by formula (4). Under Ti-rich conditions, μ_Ti amounts to the energy of one Ti atom in bulk Ti and the μ_O is assumed by the formula (4). The calculated formation energies of doped SrTiO₃ systems are listed in Table 1. For Mo monodoping, the E_f values were −8.987 and 3.599 eV under O-rich and Ti-rich conditions, respectively, implying that for the monodoping of Mo in SrTiO₃, it is difficult for Mo to enter into the lattice under Ti-rich conditions in experiments. In contrast, for P cation monodoping, the predicted E_f under O-rich and Ti-rich conditions are −15.349 and −2.762 eV, respectively, which indicates that the substitution of one Ti⁴⁺ by a P³⁺ cation can be more easily realized under O-rich conditions than that under Ti-rich conditions. Compared with the monodoping, we found that the E_f decreases after codoping. In the cases of three (Mo + P) codoped configurations, E_f is negative for all of them under O-rich conditions, suggesting that the synthesis of (Mo + P) codoped SrTiO₃ is feasible in an O-rich environment. However, for (Mo + P) codoping under the Ti-rich conditions, the synthesis may be rather difficult due to the positive E_f values.

Table 1 Calculated defect formation energies of Mo/P monodoped and codoped SrTiO₃ in the O-rich and Ti-rich conditions, which are denoted as E_f^O–rich and E_f^Ti–rich (eV), respectively. The defect pair binding energies (E_b, in eV) of the three (Mo + P) codoped SrTiO₃ configurations are also listed

Dopants	E^O-richf (eV)	E^Ti-richf (eV)	Eb (eV)
Mo	−8.987	3.599	—
P	−15.349	−2.762	—
(Mo + P)-near	−24.768	0.405	0.433
(Mo + P)-medium	−24.696	0.478	0.359
(Mo + P)-far	−24.549	0.625	0.213

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To examine the coupling strength between the Mo–P dopant pairs in the codoped models, we calculated the defect pair binding energy (E_b), according to the following equation:

E_b = E_Mo + E_P − E_Mo+P − E_pure (5)

where E_Mo, E_P, E_Mo+P, and E_pure represent the total energies of the Mo monodoped SrTiO₃, the P monodoped SrTiO₃, the (Mo + P) codoped SrTiO₃, and the pure SrTiO₃, respectively, calculated using the same supercell. The calculated binding energies of the three (Mo + P) codoped configurations are also summarized in Table 1. A positive E_b implies that the defect pair is stable with respect to the isolated defect. For three codoped configurations, E_b was predicted to be 0.433, 0.359 and 0.213 eV, respectively, indicating that donor–acceptor Mo–P pairs are more stable as compared to the corresponding isolated impurities in SrTiO₃, which may be attributed to the electron transfer from the P to Mo impurity. We found that the E_b value decreased with the increase in the distance from the defect pairs, which is ascribed to the reduced charge transfer from non-metal P to metal Mo.

The optical absorption of the codoped SrTiO₃ is strongly related to its photocatalytic activity. Here, we calculated the optical absorption coefficients of three codoped SrTiO₃ systems and compared them with the results of pure SrTiO₃; the results are shown in Fig. 3. The calculated optical absorption spectra of pure SrTiO₃ is consistent with previous experimental and theoretical results.^48,49 The pure SrTiO₃ can only respond to UV light, which has no absorption activity in the visible-light region. The gradient curves with their absorption edges all extend into the visible-light region for three (Mo + P) codoped SrTiO₃ configurations, and a new optical absorption peak was observed in the wavelength range of 365–650 nm. In comparison, the medium configuration and the far configuration had even higher absorption efficiencies than that in the near case, due to narrower band gaps. The maximum absorption edges can be extended to 649 nm for the far configuration. The (Mo + P) codoped SrTiO₃ system showed significantly improved absorption performance, which indicates its potential for application as a visible-light-driven photocatalyst. These prominent visible absorptions from our predicted calculations are comparable to previous works on SrTiO₃ with different codoping.⁵⁰

Fig. 3 Optical absorption spectra for the pure and (Mo + P) codoped SrTiO₃.

In general, the optical properties of codoped SrTiO₃ are mainly determined by their electronic band structures.⁵¹ As shown in Fig. 4, we first calculated the band structure of monodoped Mo/P, codoped (Mo + P) SrTiO₃ systems, and compared them with that of pure SrTiO₃. For the Mo monodoped case, there are several spin-up partially occupied impurity bands just below the CB, as shown in Fig. 4(b), which can be ascribed to the presence of one more electron in the shell of the Mo dopant (5s²4d³) than that in the host Ti (4s²3d²). Since donor states are localized near to the CBM, we assumed that the band gap was calculated as the direct gap between the impurity states and the VBM of about 0.74 eV. Attractive candidates for photocatalytic water splitting must have a suitable band gap ranging from 1.5 to 3.0 eV, although the Mo monodoped SrTiO₃ can efficiently narrow the band gap; note that a relatively smaller band gap is not suitable for water splitting. For the P monodoped case, one P³⁺ cation is substituted at the host Ti⁴⁺ of perovskite SrTiO₃, which will introduce one hole into the system. From Fig. 4(c), we see that the bandwidth of the P monodoped SrTiO₃ is even higher than that of pure SrTiO₃, which is also not suitable for water splitting. In view of the band structure engineering, the formation of the charge non-compensation defects and the partially occupied impurity bands in Mo or P monodoped SrTiO₃ can facilitate the formation of recombination centers, which will decrease the photocatalytic performance.

Fig. 4 Band structure of SrTiO₃ before and after doping: (a) pure SrTiO₃, (b) Mo-doped SrTiO₃, (c) P-doped SrTiO₃, (d) (Mo + P) codoped SrTiO₃ within near configuration, (e) (Mo + P) codoped SrTiO₃ within medium configuration, and (f) (Mo + P) codoped SrTiO₃ within far configuration.

To overcome these problems, we studied the effect of (Mo + P) compensated codoping on the band gap of SrTiO₃. The obtained energy band structures of (Mo + P) codoped SrTiO₃ configurations are plotted and shown in Fig. 4. For the near configuration, there is a spin-up intermediate bands (IBs) with a width of 0.86 eV, which is located below the Fermi level, as shown in Fig. 4(d). The intrinsic forbidden gap is divided into two sub-gaps by the presence of such IBs. In this case, the host band gap decreased significantly to 1.73 eV. Compared with the narrow band gap of about 0.74 eV in Mo monodoped SrTiO₃, the (Mo + P) codoped system exhibited an indirect band gap with an ideal value. On the one hand, the IBs can be stepping stones to improving the excitation of electrons to the CB under low photon energy, which will promote the absorption efficiency. On the other hand, the IBs can also act as a trapping center, which will promote the electron and hole recombination. However, the excitation or recombination depends on the energy difference between the VB and IBs or CB and IBs. Usually, the shallow impurity states near the VB are beneficial for the charge separation; in contrast, the deep impurity states near the CB can easily become recombination centers. As seen from Fig. 5, the energy difference between the VBM and the IBs minimum is much smaller than that between the CBM and the IBs maximum. This means that the probability for a VB hole to pump up into the IBs will be greater than the probability for a CB electron to combine with a hole in the IBs;⁵² i.e., the IBs can facilitate electron excitation and enhance the photocatalytic efficiency. We also noted that the IBs that appeared below the Fermi level in (Mo + P) codoped system are fully occupied states. By the introduction of Mo and P dopants, these fully filled IBs near the VBM can lead to photo-excitation from the IBs to the CB directly, reducing the chance of electron–hole recombination. Here, we also find that the partially occupied bands of Mo monodoped SrTiO₃ preferred to be located near the CBM, which can act as a carrier-trapping center. For the (Mo + P) codoped cases, the fully occupied IBs were moved to the nearby VBM due to the synergistic effect of charge compensation codoping. As shown in Fig. 4(e) and (f), for the medium and far configurations cases, there are also some fully occupied IBs below the energy zero level. Moreover, the CBMs of both configurations showed slight downward shifts as compared with the near configuration, which further narrowed the band gap.

Fig. 5 TDOS and the corresponding PDOS of Ti 3d, O 2p, Mo 4d and P 3p electrons. (a) (Mo + P) codoped SrTiO₃ within near configuration, (b) (Mo + P) codoped SrTiO₃ within medium configuration, and (c) (Mo + P) codoped SrTiO₃ within far configuration. The Fermi level is set at zero energy.

To further understand the origin of the enhanced optical performance of SrTiO₃, we calculated the total DOS and partial DOS of (Mo + P) codoped SrTiO₃ and compared them with that of pure SrTiO₃, as shown in Fig. 5. For three (Mo + P) codoped SrTiO₃ configuration cases, all of the VBMs and CBMs positions shifted towards the low-energy direction, inducing narrowed band gaps of 1.73, 1.59 and 1.49 eV, respectively. These narrowed band gaps are greatly helpful for exciting electrons from the VB to the CB and broadening the optical absorption spectra edge. As seen from Fig. 5, there are IBs located near the VBs in the three codoping cases, and they appeared as non-continuous states above the VBM, which is located below the Fermi level, suggesting that the IBs are fully occupied. The partial DOS results imply that the IBs mainly originated from the hybridization of Mo 4d and O 2p states, as shown in the bottom panel of Fig. 5(a)–(c). The impurity Mo 4d states appeared far below the CBMs due to the more negative energy of the Mo 4d orbital than the Ti 3d orbital. However, for the three codoping cases, the presence of the partially occupied Mo 4d states in the CB can facilitate the formation of the CB with Mo 4d character, which is different from the Ti 3d character in the pure SrTiO₃. Interestingly, within the band gap of the CBs, there is slight hybridization from the P 3p and O 2p states, indicating weak P–O coupling in the (Mo + P) codoped SrTiO₃, which also leads to the CBM shifting to the low-energy direction. For the (Mo + P) codoped SrTiO₃ system, the delocalized and fully occupied IBs formed by the p–d coupling can effectively narrow the band gap and induce the band downward shift to about 1.9 eV as compared with that of the pure SrTiO₃. These can lead to a decrease in the photo-excitation energy; thus the absorption edge is extended to the visible light region due to the synergistic effect of the Mo and P codoping. In particular, some photo-generated electrons were excited directly from the IBs to the CB in the presence of both Mo and P dopants, which could be responsible for the fact that the new absorption peaks (365–650 nm) appeared in the above optical spectra (see Fig. 3).

To describe the hybridization in the (Mo + P) codoped SrTiO₃, we plotted the charge density distribution in the (010) planes for pure SrTiO₃, codoped within the near and the medium configurations and in (011) planes for the far configuration, as shown in Fig. 6. The distances between the neighbouring elements on the same surface were obtained from CASTEP outcome files, while the distances between other elements were graphically measured linear distances. For comparison, the charge density of the pure SrTiO₃ is plotted in Fig. 6(a). It was found that the Ti–O bonds were in the form of covalent bonds in pure SrTiO₃. Checking the inner part of the optimized geometry of the pure SrTiO₃, the labeled atom positions correspond to that in Fig. 1(a), the Ti1–Ti2, Ti1–Ti3, and Ti1–Ti4 distances were 3.922, 5.546, and 6.793 Å, respectively and the Ti1–O1 bond length was 1.961 Å. For the three (Mo + P) codoped systems, the Mo atom substituted for the Ti1 atom, and the P atom replaced the Ti2, Ti3 and Ti4 atoms in the three cases, respectively. The optimized Mo–P distances in the three cases were 3.899, 5.512, 6.755 Å, respectively, showing obvious contractions as compared with those corresponding to the Ti–Ti distances in pure SrTiO₃. Moreover, the Mo–O bonds in the three codoped models were 2.207, 2.017 and 2.007 Å, respectively, which are larger than that of the Ti1–O1 bond (1.961 Å) before codoping, indicating that the covalency of the Mo–O bond is weaker than that of Ti–O bond. In contrast, due to the relatively small atomic radius of the P atom, the entered P dopant generated a large lattice distortion. This could be because the P–O bond lengths in the three codoped cases were 1.682, 1.715 and 1.734 Å, respectively, which are significantly smaller as compared to those of the Ti1–O1 bonds in pure SrTiO₃. Such the relatively shortened P–O bond lengths indicate that the P dopant is strongly bonded to the nearest O atom. As shown in Fig. 6(b)–(d), after (Mo + P) codoping, the Mo–O bond showed the typical covalent nature, and there was charge transfer from the nearest neighboring O atoms to the Mo dopants. Moreover, the P–O bonds in the three codoped configurations displayed a significant degree of covalency. We observed that the charge density around the P dopant was lower than that of the near O atoms, which is mainly due to the relatively large electronegativity of the O atom.

Fig. 6 Charge density distribution in the (010) plane for (a) pure SrTiO₃, (b) the near codoped configuration, and (c) the medium codoped configuration. Charge density distribution in the (011) plane for (d) the far codoped configuration.

It is well known that the photoconversion efficiency of a semiconductor for water splitting to produce hydrogen is governed by the position of the band edge with respect to the redox potential. Theoretically, the relevant potential level of donor dopants is required to be more negative than the valence band potential, while the potential level of acceptor species needs to be more positive than the conduction band potential. In order to describe the oxidation and reduction capacity of the (Mo + P) codoped SrTiO₃ systems, the CBM (E_CB) and VBM (E_VB) are calculated empirically according to the following formula:

where E_g is the band gap, X is the absolute electronegativity of the perovskite oxide catalyst, and E₀ is the energy of free electrons on the hydrogen scale (∼4.5 eV). The valence band tops (E_VB) were calculated from the respective band gaps.

To estimate the water reduction performance of different (Mo + P) codoped systems, the band alignments with respect to the water redox levels of three different codoped SrTiO₃ systems as well as pure SrTiO₃ were calculated and plotted on one diagram, as shown in Fig. 7. For the pure SrTiO₃ system, the calculated band gap is 3.22 eV, in which the VBM is located 1.17 eV below the water oxidation (H₂O/O₂) level and the CBM lies 0.82 eV above the water reduction (H⁺/H₂) level, and this is consistent with the experimental results.⁵³ For three (Mo + P) codoped SrTiO₃ configurations, there were IBs in the forbidden band with band widths of 0.86, 1.05 and 0.95 eV, respectively. These fully occupied IBs can be considered as stepping-stones to bridging the VBM and the CBM, thus photo-generated electrons are directly excited from the IBs to the CB. As seen from Fig. 7, the (Mo + P) codoping can effectively narrow the band gap by introducing the delocalized energy levels, and also greatly perturb the positions of both the VBM and CBM. As for the three (Mo + P) codoped SrTiO₃ configurations, the band edge positions of both the VBM and CBM straddle the water redox potential levels, which meet the thermodynamic criterion for hydrogen production in solar-light-driven water splitting.

Fig. 7 The band edge alignment of the pure and codoped SrTiO₃ systems with respect to the water redox band edge position potentials.

The calculated CBM and VBM potentials vs. NHE for the different systems are listed in Table 2. The calculated E_CB and E_VB of pure SrTiO₃ are −1.17 and 2.05 eV, respectively, which possesses a strong reducing ability under UV light due to its more negative CBM than the water reduction potential (0 eV vs. NHE at pH 0). Moreover, its VBM is more positive than the water oxidation potential level (1.23 eV vs. NHE). Therefore, it has the capacity for photocatalytic water splitting. As mentioned previously in the literature, the enhanced oxidation or reduction capacity depends on the downward shift of the VBM or the upward shift of the CBM, respectively.^54,55 In the cases of the three (Mo + P) codoped configurations, the CBMs shifted upward by 0.83, 0.90 and 0.95 eV, respectively, as compared to the pure SrTiO₃, which implies that the photo-reduction ability is enhanced, and the absorption edges move towards the visible light region. The VBMs of the three codoped systems moved downward as compared to that of pure SrTiO₃ by 0.66, 0.73 and 0.78 eV, respectively, which means that the oxidation ability is also improved. From the calculated E_CB and E_VB in Table 2, we can deduce that splitting water into H₂ with the (Mo + P) codoped SrTiO₃ photocatalyst is thermodynamically feasible. The results show that the (Mo + P) codoped SrTiO₃ system possessed the more suitable band gap and band edge positions for photocatalytic water splitting.

Table 2 Calculated CBM (eV) and VBM (eV) potentials vs. NHE for the pure and (Mo + P) codoped cases

Model	SrTiO3	(Mo + P)-near	(Mo + P)-medium	(Mo + P)-far
ECB (eV)	−1.17	−0.34	−0.27	−0.22
EVB (eV)	2.05	1.39	1.32	1.27

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Solar energy provides an attractive way to produce hydrogen via water splitting. When the energy of the incident light is larger than the band gap of the SrTiO₃-based catalytic materials, electrons and holes are generated in the VB and CB, respectively. The photo-generated electrons (e⁻) and holes (h⁺) that migrate from the bulk of the semiconductor towards the reaction sites on the photocatalyst surface without recombination can reduce and oxidize water molecules to produce hydrogen and oxygen, respectively. A schematic diagram of the (Mo + P) codoped SrTiO₃ photocatalyst for water splitting is shown in Fig. 8. Based on the above electronic band structure, the introduction of Mo and P dopants in metal oxide will generate new IBs energy levels between the VBM and CBM, resulting in the narrowed minimum light absorption energy gap of the host lattice. This will reduce the photon excitation energy from the VB to CB, thus extending its range of optical absorption to the visible-light region. Furthermore, the proximity of IBs to the VB allows for efficient electron replenishment, which possesses ability to separate photoexcited electrons from reaction holes, reducing the probability of trapping electrons from the CB, so the photocatalytic activity of the (Mo + P) codoped SrTiO₃ system will be good. As schematically depicted in Fig. 8, the band edge potential of the (Mo + P) codoped SrTiO₃ photocatalyst by theoretical prediction is appropriate for water-oxidation/-reduction processes.

Fig. 8 Schematic plot of the energy band alignment of the (Mo + P) codoped SrTiO₃ Photocatalyst and the redox potential of the water-splitting reaction.

4. Conclusion

We have explored the metal/non-metal (Mo + P) codoping effects on the electronic structure and photocatalytic performance of SrTiO₃ based on first principles predictions. Theoretical results indicate that the (Mo + P) codoped SrTiO₃ is feasible in O-rich environments due to low formation energy. The (Mo + P) codoping leads to a strong hybridization between Mo 4d and O 2p, which induces the fully occupied and delocalized IBs near the valence band, possessing the ability to separate photo-excited electrons from reaction holes and reducing the probability of trapping electrons from the CB. We found that both the strong Mo–O hybridization and weak P–O coupling can narrow the band gap of SrTiO₃, and also improve its photocatalytic performance. The calculated optical absorption spectra of the (Mo + P) codoped SrTiO₃ also verified the improved visible light absorption by donor–acceptor pair codoping. The band edge positions of the (Mo + P) codoped SrTiO₃ system also satisfy the criterion for water splitting.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work is supported by the Key Projects of Natural Science Foundation of Colleges and Universities of Anhui Province (KJ2019A0117), Stand-up Fund for Talent Introduction of Anhui University of Science and Technology, the College Physics Teaching Team of Anhui Province (2019jxtd046), the Top Talents of Colleges and Universities of Anhui Province (GxbjZD14), and the Key Technologies R&D Program of Anhui Province of China (1604a0802122 and 17030901091).

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