Improving photocatalytic properties of SrTiO₃ through (Sb, N) codoping: a hybrid density functional study

Abstract

A systematic study using hybrid density functional theory has been carried out to investigate the synergistic effect of Sb and N doping on the photocatalytic properties of SrTiO₃ under visible light. The calculated band gap (3.19 eV) for SrTiO₃ with the Heyd, Scuseria, and Ernzerhof hybrid functional is found to be very close to the experimentally observed value of 3.2 eV. Although doping with N is able to enhance the visible light activity by reducing the effective band gap to 2.31 eV, the localized occupied and unoccupied states in the forbidden region may affect the photocatalytic activity. However, the presence of Sb not only passivates those unoccupied states completely, but also shifts the localized occupied states near the valence band to form a continuum band structure. The introduction of N into the SrTiO₃ crystal structure is favored by the presence of Sb. In the codoped system charge compensation is established, thereby unwanted vacancy formation will be minimized. The absorption curve for the (Sb, N)-codoped SrTiO₃ is found to shift towards the visible region due to reduction in band gap to 2.66 eV. Moreover, the band alignment shows that the (Sb, N)-codoping makes SrTiO₃ thermodynamically more suitable for hydrogen production as compared to the undoped system. Based on the present study, we can propose (Sb, N)-codoping as one of the effective approaches to improve the photocatalytic activity of SrTiO₃ for water splitting under visible light irradiation.

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1. Introduction

Photo splitting of water under sunlight is one of the most promising ways to generate hydrogen which has been widely accepted as an alternative energy carrier.¹ The biggest challenge is to find a suitable catalyst for this purpose. To date numerous efforts have been made towards developing semiconductor based photocatalysts.^2–4 Among the perovskites, SrTiO₃ has been extensively studied for its potential applications in this field. Since the band gap of SrTiO₃ is 3.2 eV, its photoactivity is limited to the UV region of the solar spectrum.⁵ There have been made several experimental as well as theoretical attempts by doping with foreign element/elements to improve the visible light activity of SrTiO₃. These include cationic doping either at the Sr lattice site⁶ or at the Ti lattice site^7–16 as well as anionic doping at the oxygen lattice site.^17–23 Among the transition metal doped systems, Cr-doped SrTiO₃ has been extensively studied due to its potential application to split water and organic compounds under visible light.^7–11 However, there exists some major issues that limit the photocatalytic efficiency of Cr-doped SrTiO₃. Improved photocatalytic activity has been observed only when chromium is in trivalent state (Cr³⁺), although chromium is more stable in hexavalent state (Cr⁶⁺).⁸ Hence keeping chromium in trivalent state is a challenge as it has tendency to be converted in the hexavalent state. Secondly, localized mid gap states introduced due to Cr doping not only hinder the mobility of the charge carriers, but also bring significant changes in the band edge positions, thus affect overall water splitting property.¹¹ Owing to attractive visible light activity Rh-doped SrTiO₃ has been found to be studied by several groups.^12–16 However, photoactivity of Rh-doped SrTiO₃ is limited by the presence of Rh⁴⁺ species, which plays significant role in the electron–hole recombination.¹⁶ Doping with non-metal elements are also extensively studied for the band gap engineering of the oxide based semiconductor photocatalysts. Among them N-doping has attracted immense interest for extending the absorption curve to the desirable range. Wang et al. observed that the photocatalytic activity under visible light is significantly improved due to N doping and the visible light absorption increases with increasing amount of N into the SrTiO₃ crystal structure.²¹ However, this is due to the presence of localized N 2p states which appear above the valence band (VB) reducing the effective band gap.²² Another major challenge in case of monodoping is to avoid charge compensating defects, which are well known to diminish photocatalytic efficiency. There have been shown many efforts using codoping approach to overcome the undesirable consequences associated with those localized states and the additional charge introduced due to N-doping. Miyauchi et al.²⁴ and Wang et al.²⁵ successfully synthesized (La, N)-codoped SrTiO₃, which shows improved photocatalytic activity under visible light. However, this photoactivity has been found to be limited to the decomposition of organic compounds. Although, it has been shown in the theoretical study of Wei et al. that codoping of either nonmetal (H, F, Cl, Br, I) or metal (V, Nb, Ta, Sc, Y, La) is able to passivates the N-induced discrete states, their applicability for the photo-splitting of water is still to be explored.²⁶ Recently, Yu et al. synthesized (Cr, N)-codoped SrTiO₃, which has been shown to generate only H₂ during water splitting under visible light.²⁷ In the present study, we employ Sb as codopant to improve the photoactivity of N-doped SrTiO₃ under visible light. The advantages for choosing Sb as codopant are: (a) being very similarity in ionic radius (Sb⁵⁺: R_ef = 0.60 Å; Ti⁴⁺: R_ef = 0.605 Å),²⁸ Sb can be easily fitted at the Ti lattice site without causing major lattice distortion in the host crystal structure; (b) introduction of Sb into the N-doped system is expected to maintain charge balance in the codoped SrTiO₃ (Ti⁴⁺ + O²⁻ = Sb⁵⁺ + N³⁻); (c) use of a non transition metal (Sb) may be more preferable over transition metal to avoid localized ‘d’-states in the forbidden region. It has been successfully shown in the earlier reports that introduction of Sb as a codopant significantly increases the photocatalytic property of the monodoped entity.^16,29–36 As for example, codoping of Sb into the Rh-doped SrTiO₃ effectively reduces the electron–hole recombination rate by fixing Rh oxidation state to +3 forming a charge compensated system.¹⁶ Similarly, codoping of Sb into the Cr-doped SrTiO₃ has been found to enhance the photoactivity for H₂ evolution by suppressing the formation of hexavalent chromium (Cr⁶⁺) as well as vacancy, which are known to diminish the photoactivity of SrTiO₃.²⁹ However, detailed theoretical studies exploring the effect of Sb on the electronic structure of SrTiO₃ are rare. Here, we present a systematic study to investigate the synergistic effect of both N (as a substituent of O) and Sb (as a substituent of Ti) as codopants, and compare the results with that of the N-doped, Sb-doped and undoped SrTiO₃, using density functional theory as a tool. Since the use of Heyd, Scuseria, and Ernzerhof (HSE)³⁷ functional is known to successfully reproduce the experimental band gap for undoped SrTiO₃, we employ the same functional in our calculations. Conclusions have been drawn by analyzing the band structure, partial density of states (PDOS), optical spectrum, and band alignment with respect to the water redox levels.

2. Computational methods

Spin-polarized DFT calculations have been carried out using Vienna ab initio simulation package (VASP)³⁸ electronic structure code. The electron-ion interaction has been treated by projector augmented wave (PAW) potential,³⁹ which is widely used for the studies of electronic structure of semiconductor materials. For the Brillouin zone integration we employ Monkhorst and Pack scheme to generate gamma-centered k-point sets.⁴⁰ The mono-doped system is modeled by replacing either one of the Ti or O atoms by Sb or N, respectively from a 2 × 2 × 2 supercell (40 atoms) of the cubic (space group: Pm3̄m) SrTiO₃ crystal structure. In the case of codoping, we simultaneously introduce both Sb and N into SrTiO₃. This corresponds to Sb concentration of 12.5% and N concentration of 4.17%. The exchange and correlation energy density functionals were defined by generalized gradient approximation (GGA) with Perdew–Burke–Ernzerhof (PBE) scheme⁴¹ during geometry optimization. K-point mesh of 8 × 8 × 8 was found to be sufficient to attain convergence. The total energy convergence tolerance was set to 10⁻⁶ eV per atom for the self consistent iteration. Electronic structure calculations have been carried out by employing the HSE hybrid functional, where the short-range interactions are calculated with exact exchange mixing in both HF and DFT. The exchange-correlation energy is expressed as

E^HSE_XC = aE^SR_X(μ) + (1 − a)E^PBE,SR_X(μ) + E^PBE,LR_X(μ) + E^PBE_C (1)

where, ‘a’ stands for the mixing coefficient. The screening parameter μ defines the short ranged (SR) and long ranged (LR) part of the interaction. In the present study, we use the mixing exchange parameter of 28% and standard screening parameter of 0.2 Å⁻¹ to reproduce the experimental band gap of SrTiO₃.¹¹ K-point mesh of 3 × 3 × 3 was set for the hybrid functional calculations. The valence states considered during the calculations are: Sr (4s²4p⁶5s²), Ti (4s²3d²), Sb (5s²5p³), O (2s²2p⁴), and N (2s²2p³). The energy cutoff of 600 eV has been chosen for the plane wave basis sets. To investigate the absorption behavior frequency-dependent dielectric function calculation has been carried out for the codoped and undoped SrTiO₃.

3. Results and discussion

Salient features of the electronic structure of undoped SrTiO₃, monodoped SrTiO₃ using N and Sb as dopants, and (Sb, N)-codoped SrTiO₃ are discussed below.

3.1. SrTiO₃

Cubic SrTiO₃ is described by a framework of TiO₆ perfect octahedron, where the center position is occupied by Ti. Fig. 1a shows the band structure plot for the undoped SrTiO₃ along high symmetric k-path of the Brillouin zone (the horizontal dashed line represents the Fermi level). The calculated band gap (3.19 eV) shows excellent agreement with the experimental value (3.2 eV).⁵ Analysis of the projected density of states (Fig. 2) indicates that the valence band maximum (VBM) is dominated by O 2p states while conduction band minimum (CBM) is composed of Ti 3d states. We will now discuss the effect of doping and codoping on the electronic structure of SrTiO₃.

Fig. 1 Electronic band structure along the high symmetry k-path of the Brillouin zone for (a) undoped SrTiO₃ (b) N-doped SrTiO₃ (c) Sb-doped SrTiO₃ (d) (Sb, N)-codoped SrTiO₃. The horizontal dashed lines represent the Fermi level.

Fig. 2 DOS and PDOS plots for undoped SrTiO₃. The vertical dashed lines indicate the Fermi level.

3.2. N-doped SrTiO₃

Since, doping of nitrogen in the oxide based material mainly involves replacement of oxygen by nitrogen, we consider only substitutional doping. From the optimized cell structure, obtained in our calculation, it is found that N doping does not make any significant change in the SrTiO₃ crystal structure. The Ti–N bond length (1.976 Å) in N-doped SrTiO₃ is slightly higher than the Ti–O bond length (1.974 Å) in undoped crystal. This leads to increase in lattice parameter by only a small extent.

Introduction of N (2s²2p³) in place of O (2s²2p⁴) is found to bring significant changes in the electronic structure of SrTiO₃. The N-doped SrTiO₃ is deficient by one electron. Comparison of band structure plot of the N-doped SrTiO₃ (Fig. 1b) with that of the undoped SrTiO₃ (Fig. 1a) shows that, some occupied and unoccupied states are introduced above the VB. Analysis of PDOS plot (Fig. 3a) indicates that these states are formed due to mixing of N 2p state with O 2p state along with small contribution from Ti 3d state. Consequently, the band gap (energy difference between the occupied impurity states and the conduction band) is reduced to 2.31 eV, which is responsible for the visible light absorption of N-doped SrTiO₃. However, these localized states are highly undesirable for the photocatalytic purpose as they may hinder the mobility of the charge carriers. Therefore one needs to introduce a codopant to passivate these discrete states for better photocatalytic property. Since the CBM of SrTiO₃ (prominent Ti 3d character), is located just 0.8 eV above the water reduction level (H⁺/H₂), we carefully choose Sb as the codopant, which is expected not to perturb the conduction band (CB) level largely. Before discussing the results of the codoped system, it will be instructive to first discuss the monodoped system with Sb as the dopant.

Fig. 3 DOS and PDOS plots for (a) N-doped SrTiO₃ (b) Sb-doped SrTiO₃. The vertical dashed lines indicate the Fermi level.

3.3. Sb-doped SrTiO₃

Previous experimental reports show that, Sb occupies exclusively Ti lattice site in the Sb-doped SrTiO₃ as the ionic size of Sb⁵⁺ (R_ef = 0.60 Å) is closer to the ionic size of Ti⁴⁺ (R_ef = 0.605 Å) than that of Sr (R_ef = 1.44 Å).^{16,29,35,36,42} The optimized structure shows that the introduction of Sb into the Ti lattice site does not lead to much change in the lattice structure. As the stable oxidation state for Sb is the pentavalent state (Sb⁵⁺), it leaves one extra electron to the system. This is manifested in the band structure plot (Fig. 1c), with the Fermi level located in the conduction band. Analysis of PDOS plot (Fig. 3b) clearly indicates that the defects states are contributed by Ti 3d state. This is due to localization of the extra unpaired electron in the Ti 3d orbital. One more thing we should point out is that the respective band edges are still dominated by the O 2p and Ti 3d states, as observed in the case of undoped SrTiO_3. The contribution of the Sb 5s and 5p states to the band edges is found to be less significant. This may be due to more ionic character of the Sb–O bond as indicated in the study of Wang et al.⁴² This is again supported by the analysis of Bader charge density.⁴³ In the case of undoped SrTiO₃, the calculated Bader charges on Ti and O centers are 2.04|e| and −1.23|e|, respectively, while, for Sb-doped SrTiO₃, the values on the Sb and O centers are 2.80|e| and −1.29|e|, respectively.

3.4. (Sb, N)-codoped SrTiO₃

Before going to the discussion on the electronic structure of (Sb, N)-codoped SrTiO_3, we calculate the defect pair binding energy (E_b) using the relation⁴⁴

E_b = E_Sb-SrTiO3 + E_N-SrTiO3 − E_{(Sb,N-SrTiO3)} − E_SrTiO3 (2)

where, E_N-SrTiO3, E_Sb-SrTiO3, E_{(Sb,N)-SrTiO3} and E_SrTiO3 represent the energy of the N-doped, Sb-doped, (Sb, N)-codoped, and undoped SrTiO₃ supercell, respectively. The positive value of the defect pair binding energy (1.58 eV per supercell) indicates that the codoped system is sufficiently stable.

Let us discuss the synergistic effect of both N and Sb on the electronic structure of SrTiO₃. The band structure plot (Fig. 1d) for the codoped SrTiO₃ shows that the Fermi level resides above the VBM, similar to that of an intrinsic semiconductor. It is interesting to observe that the band gap reduces significantly to 2.66 eV, which ensures the absorption of visible light. This is the consequence of elevation of VB edge associated with the formation of (N 2p, O 2p) hybridized state (Fig. 4). The discrete acceptor states as appearing in the case of N-doped SrTiO₃ are completely passivated, resulting into a continuum band structure. This is due to the presence of Sb which compensates for the electron deficiency introduced through N-doping. It has been quantified by Bader charge analysis, which indicates a higher electronic charge on the N centre in the (Sb, N)-codoped SrTiO₃ (−1.36|e|) as compared to that in N-doped SrTiO₃ (−1.15|e|). On the other hand, the Ti 3d defect states arising in the case of Sb-doped SrTiO₃ is no longer present in the (Sb, N)-codoped SrTiO₃. Presence of both Sb and N leads to formation of charge compensated system, which will minimize formation of undesired defects and thus reduce charge carrier loss.

Fig. 4 DOS and PDOS plots for (Sb, N)-codoped SrTiO₃. The vertical dashed lines indicate the Fermi level.

3.5. Defect formation energy

In order to find favorable growth condition for doping of the individual element as well as both, we calculate defect formation energy in each case.^45,46 The defect formation energy relates chemical potential of the elements as

ΔH_f = E_doped + n_Oμ_O + n_Tiμ_Ti − E_SrTiO3 − n_Nμ_N − n_Sbμ_Sb (3)

where, E_doped represents total energy for the doped/codoped SrTiO₃ supercell. μ stands for chemical potential of the element. n is the number of elements inserted or removed for the construction of doped/codoped structure. At the equilibrium condition between the reservoir of Sr, Ti and O and SrTiO₃ eqn (4) must be satisfied

μ_Sr + μ_Ti + 3μ_O = μ_SrTiO3(bulk) (4)

The chemical potential of the element cannot exceed that of the respect bulk (Sr/Ti) or gaseous (O) state, i.e. μ_Sr ≤ μ_Sr(bulk), μ_Ti ≤ μ_Ti(bulk) and μ_O ≤ μ_O(gas).

The expression for the heat of formation SrTiO₃ is given by

Δ = μ_SrTiO3(bulk) − μ_Sr(bulk) − μ_Ti(bulk) − 3μ_O(gas) (5)

Since the heat of formation for SrTiO₃ is a negative quantity we can write

μ_Sr(bulk) + Δ ≤ μ_Sr ≤ μ_Sr(bulk) (6a)

μ_Ti(bulk) + Δ ≤ μ_Ti ≤ μ_Ti(bulk) (6b)

3μ_O(gas) + Δ ≤ 3μ_O ≤ 3μ_O(gas) (6c)

The chemical potential, μ_Sr(bulk), μ_Ti(bulk), and μ_Sb have been calculated from the energy of an atom in the respective bulk structure. On the other hand, μ_O(gas) and μ_N have been calculated from the energy of an oxygen atom (1/2E_O2) and nitrogen atom (1/2E_N2) in the corresponding gaseous molecule confined at the centre of a 20 × 20 × 20 ų cubic box.

The calculation of the formation energy (Fig. 5a and b) indicates that in both the cases substitutional doping is energetically more favored in comparison to the interstitial doping. Fig. 5a shows the variation of formation energy for N-doped SrTiO₃ as a function of oxygen chemical potential (μ_O − μ_O(gas)). Under O-rich condition the formation energy has a large positive value, which shows a decreasing trend as we proceed towards O-poor condition. As shown in Fig. 5b, that the formation energy for Sb-doping is highly positive under Ti-rich condition. This indicates that the doping with individual element is highly unfavorable under host rich condition, may be due to requirement of large energy for vacancy formation in the substitution process. However, this is found to be feasible in presence of both the dopant elements as shown in Fig. 5c. The calculation indicates that the O-rich condition is more suitable than the Ti-rich condition for the growth of the (Sb, N)-codoped SrTiO₃.

Fig. 5 The variation of defect formation energy with the chemical potential of O (μ_O − μ_O-gas) and Ti (μ_Ti − μ_Ti-bulk) for (a) N-doped SrTiO₃ (b) Sb-doped SrTiO₃ (c) (Sb, N)-codoped SrTiO₃. The color lines (5c) corresponds to different formation energies for the (Sb, N)-codoped SrTiO₃. The codoped system cannot be formed in the lower half of the diagonal axis (large white region) in the case of 5c because the chemical potential of Sr (μ_Sr) is exceeded (eqn (6a)).

3.6. Optical property

To investigate the absorption property we calculate the frequency dependent dielectric function, ε(ω) = ε₁(ω) + iε₂(ω). The real part (ε₁) and imaginary part (ε₂) of the dielectric tensor are obtained from Kramers–Kronig transformation, and using summation over the empty states, respectively, as implemented in VASP. The absorption coefficient α(ω) has been evaluated using the formula⁴⁷

Fig. 6 shows that the absorption curve for the undoped SrTiO₃ is limited to the UV region, while it is shifted towards the visible region in presence of both Sb and N dopants. This observation supports the band gap reduction of SrTiO₃ due to codoping with Sb and N as discussed in the earlier section.

Fig. 6 The calculated optical absorption curves for the undoped and codoped SrTiO₃.

3.7. Photocatalytic activity

As we know, reduction in the band gap is necessary to improve the visible light activity, but not sufficient to achieve high photocatalytic activity for water splitting. The band edges must be in proper position with respect to the water redox levels for spontaneous release of hydrogen as well as oxygen from water splitting. The conduction band potential should be more positive than the H⁺/H₂ potential and the valence band potential should be more negative than the H₂O/O₂ potential, i.e. CB should be located above the water redox potential (H⁺/H₂) and VB should be located below the water oxidation level (H₂O/O₂). To check this criterion for our proposed system we align the positions of the band edges with respect to that of the undoped SrTiO₃. For undoped SrTiO₃ the CBM is located 0.8 eV above the water reduction (H⁺/H₂) level and the VBM is 1.17 eV below the water oxidation level (H₂O/O₂).⁴⁸ The VBM and CBM for the (Sb, N)-codoped SrTiO₃ is now placed by considering the relative shifts of the corresponding electronic energy levels with respect to that of the undoped SrTiO₃. As can be seen from Fig. 7, that the VBM of (Sb, N)-codoped SrTiO₃ is located 0.20 eV below the water oxidation level and the CBM position is 1.23 eV above the water reduction level. Hence, overall water splitting is thermodynamically feasible in the (Sb, N)-codoped SrTiO₃. Interestingly, the CBM of the (Sb, N)-SrTiO₃ is located even 0.43 eV above the CBM of the undoped SrTiO_3. This implies that the modified system should be more feasible for H₂ evolution due to enhancement of reducing power with respect to the undoped SrTiO₃.

Fig. 7 The band alignment of the undoped, and codoped SrTiO₃ with respect to the water redox levels.

3.8. Effect of supercell size

To investigate the effect of supercell size, we have also considered larger supercell (2 × 2 × 3). The formation energy has been calculated following the same procedure as discussed in the case of 2 × 2 × 2 supercell. Fig. 8 shows the formation energy variation as a function of chemical potential of Ti and O. The calculated formation energy for (Sb, N)-codoped SrTiO₃ using 2 × 2 × 2 (Fig. 5c) and 2 × 2 × 3 supercell (Fig. 8) has been found to be almost similar. This justifies the choice of supercell size used in the calculation.

Fig. 8 The variation of defect formation energy with the chemical potential of O (μ_O − μ_O-gas) and Ti (μ_Ti − μ_Ti-bulk) for (Sb, N)-codoped SrTiO₃ using 2 × 2 × 3 supercell. The color lines corresponds to different formation energies for the (Sb, N)-codoped SrTiO₃. The codoped system cannot be formed in the lower half of the diagonal axis (large white region) because the chemical potential of Sr (μ_Sr) is exceeded (eqn (6a)).

4. Conclusion

The hybrid DFT calculations reported here reveal the significance of codoping of Sb and N into SrTiO₃ for improving the photocatalytic activity under visible light. The positive defect pair binding energy indicates that the (Sb, N)-codoped SrTiO₃ is sufficiently stable. The band gap is reduced significantly without introducing any isolated midgap states. As the codoped system is charge compensated, it is expected to reduce undesirable vacancy formation, and consequently defect assisted carrier loss can be avoided. Presence of Sb also facilitates the introduction of N into the SrTiO₃ crystal structure by reducing formation energy. The band alignment for the codoped SrTiO₃ is such that both the photo-oxidation and photo-reduction processes associated with water splitting are thermodynamically feasible. Moreover, the reducing power of the modified SrTiO₃ is higher than that of the undoped material, making it more suitable for H₂ generation. Hence we can propose that the codoping of Sb and N into the SrTiO₃ crystal is one of the promising approaches to enhance the efficiency for photo-splitting of water using visible light.

Acknowledgements

We thank the BARC computer centre for providing the high performance parallel computing facility. The authors like to acknowledge Dr A. K. Samanta, Dr C. Majumder and Dr D. Karmakar for valuable discussions. We also thank Dr B. N. Jagatap for his encouragement and support. The work of Prof. Swapan K. Ghosh is supported through Sir J. C. Bose Fellowship from the Department of Science and Technology, India.

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