Synergistic effect of C, Ag-codoped TiO₂ photocatalyst within the GGA + U framework

Abstract

The electronic structures and optical properties of C, Ag-codoped TiO₂ were investigated within the GGA + U framework. Different doping concentration and different dopant distance (C_sAg_s (near and far), C_2sAg_s (near and far), and C_3sAg_s (near and far)) models were constructed. According to the formation energy results of these codoped systems, it was found that low concentration codoping was more stable than high concentration codoping. Therefore, we chose the C_sAg_s (near and far) codoped TiO₂ to calculate further electronic structures and optical properties. It was found that near distance codoping could narrow the band gap to 2.81 eV, and far distance codoping decreased the band gap to 2.66 eV. Meanwhile, it was found that far distance codoping preferred to form more localized states near the top of the valence band, while near distance codoping could induce more significant hybrid states in the band gap. Optical property showed that C and Ag codoping could induce a synergistic effect compared with single C and single Ag doping. After codoping, the visible absorption was stronger for both the near and far distance codoped systems than those of the single doped systems, moreover, the far distance codoping configuration could induce both more significant band edge shift and stronger visible optical absorption than that of the near distance codoping configuration.

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Introduction

TiO₂ is a highly efficient photocatalytic material for energy and environmental applications due to its strong oxidizing power, high chemical inertness, low cost, and long-term stability.^1–3 Unfortunately, the band gap of TiO₂ is large (3.2 eV for anatase and 3.0 eV for the rutile structure), and absorbs very little visible light, which prevents its wide application in the visible region.⁴ To utilize solar light, it is necessary to enhance the visible optical absorption of TiO₂.

Band gap narrowing and introducing gap states are two effective routes to improve the visible optical absorption of TiO₂. Nonmetal doping can create electronic states near the valence band or behave as part of the valence band, and thus can narrow the band gap of TiO₂.^5–8 For example, N doping is an effective route to create N 2p electronic states near the top of the valence band, and lots of experiments have confirmed the enhancement of the visible light response of N-doped TiO₂.^9–15 In addition, C-doped TiO₂ showed 0.12–0.3 eV 2p electronic states near the top of the valence band, and X-ray photoelectron spectroscopy showed an increased electron density of states above the valence band of TiO₂.^16–18 In contrast, metal doping prefers to produce electronic states in the band gap, and thus induce the visible optical absorption centre.^19–21 It has also been shown that metal-doped TiO₂ has visible photocatalytic properties.^22,23

Due to the individual benefits of metal and nonmetal doping, it has been proposed that metal and nonmetal codoping can combine the two benefits and thus can induce some interesting results.²⁴ It was reported that codoping could improve the photoactivity of TiO₂ by introducing gap states and band gap narrowing.^24–29 For example, Gai et al. calculated the band structure and electronic state density of metal and nonmetal codoped TiO₂ in detail, and they predicted C, Mo-codoped TiO₂ could be conceived as a visible photocatalyst.²⁸ The band edges of TiO₂ could be modified by passivated C, Mo-codopants to shift the valence band edge up significantly, while leaving the conduction band edge almost unchanged, thus satisfying the stringent requirements. Subsequently, the experiment confirmed that C, Mo-codoping could enhance the photocatalytic activity of TiO₂.³⁰ In another independent work, Zhu et al. reported that noncompensated n–p codoping effectively narrows the band gap, and N, Cr-codoping could be a good candidate for enhancing the visible photoactivity of TiO₂.^31,32

In addition, atom configuration can play a very important role in a codoped system. For a codoped system, the far distance configuration of the doping atoms can avoid the formation of hybrid electronic states,³³ and will benefit band gap engineering. However, sometimes, some hybrid electronic states caused by near distance doping can form some special structures which could induce some unexpected optical phenomena and thus improve the visible photoactivity.³⁴ For example, for the N, B-codoped system, the electronic states at the top of the valence band and in the band gap will be significantly different for different doping distances.^35,36 Besides, it was reported that the distance between dopant atoms in carbon nanotubes had a significant effect on the electronic structure.³⁷ Thus, we conceived that different doping configurations will have a significant influence on the electronic structure and optical properties of codoped TiO₂, which can provide some information for the development of visible photocatalytic and water splitting materials. In this work, in order to guarantee the reliability of the results, we constructed models with different doping concentrations and different dopant distance (C_sAg_s (near and far), C_2sAg_s (near and far), and C_3sAg_s (near and far)), however, the formation energy results indicated that the configuration with a high codoping concentration was unstable. Therefore, we presented the electronic structures and optical properties of C, Ag-codoped anatase TiO₂ with the low doping concentration (C_sAg_s (near and far)). Meanwhile, the GGA + U method was employed to correct the band gap.

Computational methods

All the calculations were based on density functional theory (DFT), within the plane-wave-pseudo-potential approach, together with the Perdew–Burke–Ernzerhof (PBE) exchange correlation functional.^38,39 The interaction between the valence electrons and the ionic core was described by ultrasoft pseudopotential, which used 2s²2p⁴, 3d²4s², 2s²2p² and 4d¹⁰5s¹ as the valence electron configurations for the O, Ti, C, and Ag atoms, respectively. We chose the energy cut off of 340 eV for the pure and C, Ag-codoped TiO₂ systems. The Brillouin-zone sampling mesh parameters for the k-point set were 1 × 2 × 2.⁴⁰

Firstly, geometry optimization was performed by the GGA method, because the geometry parameters calculated by the GGA method are closer to the experiments than those calculated by the GGA + U method.⁴¹ In this way, atomic positions and lattice parameters were optimized. The equilibrium lattice constants and fractional atomic coordinates were deduced from the total-energy minimization using the BFGS geometry optimization method. Relaxation of the lattice parameters and atomic positions was carried out under the constraint of the unit-cell space group symmetry. Energy–volume relationships were obtained by varying the unit-cell volume and the fitted results were obtained using the Murnaghan equation of state:

From the fitted results, the estimate of the static bulk modulus B₀ at zero pressure, and the first-order pressure derivative of the bulk modulus B^′₀ were obtained. In the optimization process, the energy change, maximum force, maximum stress and maximum displacement tolerances were set as 2 × 10⁻⁵ eV per atom, 0.05 eV Å⁻¹, 0.1 GPa and 0.002 Å, respectively.

Then, the electronic structure and optical properties of C, Ag-codoped TiO₂ were calculated using the GGA + U method.⁴² The GGA + U approach introduces an intra-atomic electron–electron interaction as an on-site correction in order to describe systems with localized d states, which can produce a better band gap relative to the GGA method.⁴³ In previous work, we calculated the U value dependent band gap, and found that the band gap with U = 6.6 eV was close to the real band gap and also didn’t induce unphysical results.⁴⁴ Meanwhile, this U value has also been tested by another group.⁴⁵ Thus, to account for the strongly correlated interactions of the Ti 3d electrons, a moderate on-site Coulomb repulsion U = 6.6 eV was applied to the further calculations of the electronic structures and optical properties in the present work.⁴⁶ All parameters, such as k-point and the cut off energy were the same as the structural optimization.

To calculate the electronic structures and optical properties of pure and C, Ag-codoped anatase TiO₂, a supercell was used, which contained 72 atoms. The substitution method was taken into account in this paper. Our study was based on a supercell with 72 atoms, as a 2 × 3 × 1 repetition of the primitive anatase unit cell. For the C, Ag-codoped anatase TiO₂, different numbers of O atoms were replaced with C atoms, and one Ti atom was replaced with a Ag atom. Substitution models were formed with configurations of Ti₂₃O₄₇C₁Ag₁, Ti₂₃O₄₆C₂Ag₁, and Ti₂₃O₄₅C₃Ag₁. Substitution models are presented in Fig. 1.

Fig. 1 Pure and substitution models of C_sAg_s, C_2sAg_s, and C_3sAg_s-codoped TiO₂.

Results and discussion

To evaluate the feasibility of codoped systems, studies on the optimization, lattice distortion, and formation energies were carried out. We first checked the structural properties of C_sAg_s, C_2sAg_s, and C_3sAg_s-codoped TiO₂. Table 1 gives the lattice parameters a and c of the pure and codoped TiO₂ systems. For pure TiO₂, the lattice constants were 3.776 Å for a and 9.486 Å for c, which were very close to the other calculation result and the experimental data.^47–49 After doping, a and c were 3.815 and 9.845 Å for the far C_sAg_s-codoped TiO₂, and 3.673 and 10.390 Å for the near C_sAg_s-codoped TiO₂, respectively. Furthermore, the lattice constant a increased to 3.941 and 3.959 Å for the far C_2sAg_s and C₃Ag_s-codoped TiO₂, but decreased to 3.648 and 3.638 Å for the near C_2sAg_s and C₃Ag_s-codoped TiO₂. Generally, it could be seen that the far distance codoping induced less lattice distortion than that of the near distance codoping. Meanwhile, the C_sAg_s-codoping suffered less lattice distortion at a low concentration of C. However, with the increase of C doping concentration, c increased sharply. This indicates that high concentration may induce large lattice distortion and potential instability.

Table 1 Calculated lattice constants of TiO₂, and C_sAg_s, C_2sAg_s, and C_3sAg_s-codoped TiO₂

	a (Å)	c (Å)
Pure TiO2	3.776	9.486
CsAgs far	3.815	9.845
CsAgs near	3.673	10.390
C2sAgs far	3.941	10.042
C2sAgs near	3.648	10.591
C3sAgs far	3.959	10.146
C3sAgs near	3.638	10.691

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Then, we calculated the formation energy. For a supercell, the formation energy of a doped system is defined as:^41,50–52

E_f = E_(codoped) − E_(pure) − nμ_C − μ_Ag + nμ_O + μ_Ti

where E_(codoped) and E_(pure) are the total energies of the codoped system and pure TiO₂. n is the doping atom number. μ is the chemical potential of the atom and it was obtained by calculating the stable element. We calculated the formation energies under O-rich and Ti-rich conditions (Fig. 2). Under Ti-rich conditions, it could be seen that the formation energies of the far and near C_sAg_s-codoped TiO₂ were −8.96 and −7.69 eV, respectively. In contrast, under O-rich conditions, the formation energies were −3.82 and −2.7 eV corresponding to the far and near C_sAg_s-codoped TiO₂, respectively. The negative value of the formation energy indicated high stability. However, with the increase of C doping concentration, the formation energy sharply increased. The formation energies of the far and near C_2sAg_s-codoped TiO₂ were 15.21 and 16.0 eV under O-rich conditions and 10.22 and 11.09 eV under Ti-rich conditions, respectively. Furthermore, the formation energies of the far and near C_3sAg_s-codoped TiO₂ increased to above 30 eV under both O- and Ti-rich conditions. It was obvious that the stability of the codoped system got worse under high doping concentration. Thus, combining the lattice distortion and the formation energy it was found that a low concentration of C_sAg_s was stable, so we performed further electronic structure calculations using this model.

Fig. 2 Formation energies of C_sAg_s, C_2sAg_s, and C_3sAg_s-codoped TiO₂ under Ti-rich and O-rich conditions.

We then moved to the energy band structure calculation. Fig. 3 shows the band structures of the near and far C_sAg_s-codoped TiO₂. It was shown that the band gap of the near C_sAg_s-codoped TiO₂ was 2.81 eV, which was lower than 2.89 eV of pure TiO₂. Meanwhile, doped states could be found in the band gap. In contrast, the band gap of the far C_sAg_s-codoped TiO₂ was decreased to 2.66 eV. Similarly, some discrete energy could also be found in the band gap. These band gap states are close to previously reported codoped systems, such as N, Cr-codoped TiO₂.⁵³ It is necessary to investigate the electronic states in the gap in detail.

Fig. 3 Energy band structure of the near and far C_sAg_s-codoped TiO₂. The blue line represents up spin and the red line represents down spin.

To explore the electronic states of the pure, near and far distance C_sAg_s-codoped TiO₂, we calculated the density of states (DOS), which are presented in Fig. 4. Compared with pure TiO₂ (Fig. 4a), C and Ag codoping could induce mid-gap states in both the spin-up and spin-down bands at low C concentration, which were mainly composed of the C 2p and Ag 4d electronic states in the valence band maximum (Fig. 4b). The energy level of the middle states was deeper for the near distance codoping. Meanwhile, both the far and near distance codoping induced some C 2p states to behave as part of the valence band, which was consistent with previous work. It has been widely reported that C 2p states could enhance the electronic states near the valence band.⁴⁵ In addition, spin asymmetry could be observed for the codoped system, but was more significant for the far codoped system.

Fig. 4 DOS of pure and C_sAg_s-codoped TiO₂.

To investigate the partial density of states (PDOS) of the C_sAg_s-codoped system, we further analyzed the Ag 4d and C 2p states (Fig. 5). It was clear that the C 2p of the near C_sAg_s-codoped TiO₂ showed very good spin symmetry. In contrast, the C 2p from the far codoped TiO₂ showed significant spin asymmetry. Meanwhile, Ag 4d states from the near codoped TiO₂ also showed better spin symmetry than that of the far codoped TiO₂. It could be concluded that the far distance codoping induced the significant spin asymmetry of C 2p and Ag 4d.

Fig. 5 PDOS of the far and near C_sAg_s-codoped TiO₂.

Band gap narrowing was observed for the near and far distance C_sAg_s-codoped systems. The nature of this phenomenon was similar. Combining band structure and DOS, mid-gap states and band gap narrowing were both observed in the two codoped systems. However, for the near distance codoped system, the middle states were wider and deeper in gap. For the far distance codoped system, in contrast, the middle states were more narrow and induced a smaller band gap. Inspired by the electronic structure, it was of interest to further investigate the optical properties.

To investigate the optical transition of C_sAg_s-codoped TiO₂, it is necessary to investigate the imaginary part of the dielectric function (ε₂), because ε₂ is important for describing the optical properties of any material. Optical transitions between occupied and unoccupied states are caused by the electric field of the photon. The spectra from the excited states can be described as a joint DOS between the valence and conduction bands. Optical transition peaks correspond to optical transitions between two states, and the intensity of the peaks is proportional to the density of states. For the pure TiO₂, the 4.29 eV optical transition (E_g) was observed only (Fig. 6). After C and Ag codoping, the optical transition from the band gap decreased to 3.92 eV for the far distance C, Ag-codoped system, and 4.07 eV for the near distance C, Ag-codoped system. The redshift of the optical transition indicated that the band gaps of the C_sAg_s-codoped systems were decreased, which was in good agreement with the result of DOS. Moreover, the optical transition peak around 2 eV could be observed for the C_sAg_s-codoped TiO₂ systems, which indicated that C and Ag codoping could induce a visible optical transition. The optical transition peak at 0.4 eV was observed for the near distance C, Ag-codoped TiO₂, but this peak does not contribute to the visible light response. In addition, the optical properties of the single C and single Ag doped TiO₂ were also investigated. It was found that C and Ag codoping could produce a synergistic effect which could further increase the visible absorption compared with single doping. Especially, the far distance codoping showed a stronger intensity visible optical transition compared to the near distance codoping, which was interesting. It is necessary to investigate the visible absorptions of the codoped systems.

Fig. 6 Imaginary parts of the dielectric function of pure, single C doped, single Ag doped, and C_sAg_s-codoped TiO₂.

Fig. 7 presents the optical absorptions of pure, single C doped, single Ag doped, and C_sAg_s-codoped TiO₂. It was shown that the optical band edges of the single C doped and C_sAg_s-codoped TiO₂ shifted to the visible light region compared to pure TiO₂. It is well known that the relationship between the optical band gap and the absorption coefficient is given by^54,55

αhv = c(hv − E_g)^1/2

where h is Planck’s constant, c is the constant for a direct transition, v is the frequency of radiation and α is the optical absorption coefficient. The optical band gap E_g can be obtained from the intercept of (αhv)² versus photon energy (hv). By using the extrapolation, the optical band gap of the C_sAg_s-codoped system can be obtained. It was found that the calculated optical band gaps decreased from 3.27 eV for pure TiO₂ to 2.68 eV for the far distance C, Ag-codoped TiO₂, and 3.0 eV for the near distance C, Ag-codoped TiO₂. The optical band gap of the single C-doped TiO₂ also decreased, while that of the single Ag-doped TiO₂ did not. Meanwhile, the optical absorptions between 450–800 nm were enhanced for both the near and far distance codoped systems compared with pure and single doped TiO₂. Especially, the absorption intensity of the far distance codoped TiO₂ was obviously higher than that of the near distance codoped TiO₂. We calculated the optical properties of N, B-codoped TiO₂ using the GGA + U method, and found visible absorption was in the range of 400–700 nm. It was also found that C-doped TiO₂ could form localized states and thus induce significant visible optical absorption.²⁸ Besides, a recent investigation also showed that B, Ag-codoped TiO₂ could present stronger visible light absorption in the range of 400–800 nm than B or Ag single doped TiO₂.⁵⁶ Our work used the GGA + U method to correct the band gap and clearly showed that the visible optical absorption of C, Ag-codoped TiO₂ should be reliable. Importantly, C and Ag codoping induced the synergistic effect both for the far distance codoping and the near distance codoping.

Fig. 7 Optical absorption of pure, single C doped, single Ag doped, and C_sAg_s-codoped TiO₂.

Conclusion

In summary, the electronic structures and optical properties of single C doped, single Ag doped, and C, Ag-codoped TiO₂ were calculated based on the GGA + U method. It was found that both far and near distance codoping induced band gap narrowing and visible optical absorption, and C and Ag codoping could produce an obvious synergistic effect compared with single C and single Ag doping. After codoping, visible absorption in the 450–800 nm range was sharply increased, moreover, the far distance codoping induced more significant band gap narrowing and visible optical absorption. Therefore, it is conceivable that C, Ag-codoped TiO₂ would be useful for visible photoactivity.

Acknowledgements

The author would like to thank Prof. Yanni Li, School of Chemical Engineering and Technology at Tianjin University, for providing the computational plat. This work is supported by the National Natural Science Foundation of China (Grant no. 11304220).

References

1. A. L. Linsebigler, G. Lu and J. T. Yates Jr, Chem. Rev., 1995, 95, 735–758.
2. S. U. Khan, M. Al-Shahry and W. B. Ingler, Science, 2002, 297, 2243–2245.
3. S. Song, B. Y. Xia, J. Chen, J. Yang, X. Shen, S. Fan, M. Guo, Y. Sun and X. Zhang, RSC Adv., 2014, 4, 42598–42603.
4. T. Umebayashi, T. Yamaki, H. Itoh and K. Asai, Appl. Phys. Lett., 2002, 81, 454–456.
5. R. Asahi, T. Morikawa, T. Ohwaki, K. Aoki and Y. Taga, Science, 2001, 293, 269–271.
6. J. Yu, Q. Xiang and M. Zhou, Appl. Catal., B, 2009, 90, 595–602.
7. M. Guo, X. Zhang and C. Liang, Phys. B, 2011, 406, 3354–3358.
8. M. L. Guo, X. D. Zhang, C. T. Liang and G. Z. Jia, Chin. Phys. Lett., 2010, 27, 057103.
9. K. Yang, Y. Dai and B. Huang, J. Phys. Chem. C, 2007, 111, 12086–12090.
10. S. Hoang, S. P. Berglund, N. T. Hahn, A. J. Bard and C. B. Mullins, J. Am. Chem. Soc., 2012, 134, 3659–3662.
11. F. Spadavecchia, G. Cappelletti, S. Ardizzone, M. Ceotto and L. Falciola, J. Phys. Chem. C, 2011, 115, 6381–6391.
12. R. Long and N. J. English, Appl. Phys. Lett., 2009, 94, 132102.
13. M. Harb, P. Sautet and P. Raybaud, J. Phys. Chem. C, 2011, 115, 19394–19404.
14. Z. Lin, A. Orlov, R. M. Lambert and M. C. Payne, J. Phys. Chem. B, 2005, 109, 20948–20952.
15. J. Tao, L. Guan, J. Pan, C. Huan, L. Wang, J. Kuo, Z. Zhang, J. Chai and S. Wang, Appl. Phys. Lett., 2009, 95, 06250.
16. J. Yu, P. Zhou and Q. Li, Phys. Chem. Chem. Phys., 2013, 15, 12040–12047.
17. F. Dong, S. Guo, H. Wang, X. Li and Z. Wu, J. Phys. Chem. C, 2011, 115, 13285–13292.
18. X. Chen and C. Burda, J. Am. Chem. Soc., 2008, 130, 5018–5019.
19. W. Choi, A. Termin and M. R. Hoffmann, J. Phys. Chem., 1994, 98, 13669–13679.
20. X. Zhang, M. Guo, C. Liu, W. Li and X. Hong, Appl. Phys. Lett., 2008, 93, 012103.
21. M. Guo and J. Du, Phys. B, 2012, 407, 1003–1007.
22. B. Liu, H. M. Chen, C. Liu, S. C. Andrews, C. Hahn and P. Yang, J. Am. Chem. Soc., 2013, 135, 9995–9998.
23. Y. Ni, Y. Zhu and X. Ma, Dalton Trans., 2011, 40, 3689–3694.
24. S. In, A. Orlov, R. Berg, F. García, S. Pedrosa-Jimenez, M. S. Tikhov, D. S. Wright and R. M. Lambert, J. Am. Chem. Soc., 2007, 129, 13790–13791.
25. J. Zhang, Y. Wu, M. Xing, S. A. K. Leghari and S. Sajjad, Energy Environ. Sci., 2010, 3, 715–726.
26. Y.-F. Li, D. Xu, J. I. Oh, W. Shen, X. Li and Y. Yu, ACS Catal., 2012, 2, 391–398.
27. H. Kato and A. Kudo, J. Phys. Chem. B, 2002, 106, 5029–5034.
28. Y. Gai, J. Li, S.-S. Li, J.-B. Xia and S.-H. Wei, Phys. Rev. Lett., 2009, 102, 036402.
29. L. Mi, P. Xu, H. Shen, P.-N. Wang and W. Shen, Appl. Phys. Lett., 2007, 90, 171909.
30. J. Zhang, C. Pan, P. Fang, J. Wei and R. Xiong, ACS Appl. Mater. Interfaces, 2010, 2, 1173–1176.
31. W. Zhu, X. Qiu, V. Iancu, X.-Q. Chen, H. Pan, W. Wang, N. M. Dimitrijevic, T. Rajh, H. M. Meyer, M. P. Paranthaman, G. M. Stocks, H. H. Weitering, B. Gu, G. Eres and Z. Zhang, Phys. Rev. Lett., 2009, 103, 226401.
32. M. E. Kurtoglu, T. Longenbach, K. Sohlberg and Y. Gogotsi, J. Phys. Chem. C, 2011, 115, 17392–17399.
33. L. Huang, A. Rosa and R. Ahuja, Phys. Rev. B: Condens. Matter Mater. Phys., 2006, 74, 075206.
34. W.-J. Yin, S.-H. Wei, M. M. Al-Jassim and Y. Yan, Phys. Rev. Lett., 2011, 106, 066801.
35. M. Guo, X.-D. Zhang and J. Du, Phys. Status Solidi RRL, 2012, 6, 172–174.
36. N. Feng, A. Zheng, Q. Wang, P. Ren, X. Gao, S.-B. Liu, Z. Shen, T. Chen and F. Deng, J. Phys. Chem. C, 2011, 115, 2709–2719.
37. D. Carroll, P. Redlich, X. Blase, J.-C. Charlier, S. Curran, P. Ajayan, S. Roth and M. Rühle, Phys. Rev. Lett., 1998, 81, 2332.
38. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865.
39. M. C. Payne, M. P. Teter, D. C. Allan, T. Arias and J. Joannopoulos, Rev. Mod. Phys., 1992, 64, 1045–1097.
40. H. J. Monkhorst and J. D. Pack, Phys. Rev. B: Solid State, 1976, 13, 5188–5192.
41. R. Long and N. J. English, Chem. Phys. Lett., 2009, 478, 175–179.
42. L. Li, W. Wang, H. Liu, X. Liu, Q. Song and S. Ren, J. Phys. Chem. C, 2009, 113, 8460–8464.
43. V. I. Anisimov, F. Aryasetiawan and A. Lichtenstein, J. Phys.: Condens. Matter, 1997, 9, 767–808.
44. M. Guo and J. Du, Int. J. Mod. Phys. B, 2013, 27, 1350123.
45. K. Yang, Y. Dai, B. Huang and M.-H. Whangbo, J. Phys. Chem. C, 2009, 113, 2624–2629.
46. H. J. Kulik, M. Cococcioni, D. A. Scherlis and N. Marzari, Phys. Rev. Lett., 2006, 97, 103001.
47. S. Na-Phattalung, M. F. Smith, K. Kim, M.-H. Du, S.-H. Wei, S. Zhang and S. Limpijumnong, Phys. Rev. B: Condens. Matter Mater. Phys., 2006, 73, 125205.
48. A. Janotti, J. Varley, P. Rinke, N. Umezawa, G. Kresse and C. Van de Walle, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 81, 085212.
49. Y. Wang, H. Liu, Z. Li, X. Zhang, R. Zheng and S. Ringer, Appl. Phys. Lett., 2006, 89, 042511.
50. F. Oba, A. Togo, I. Tanaka, J. Paier and G. Kresse, Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 77, 245202.
51. J. Li, S.-H. Wei, S.-S. Li and J.-B. Xia, Phys. Rev. B: Condens. Matter Mater. Phys., 2006, 74, 081201.
52. X. Cui, J. Medvedeva, B. Delley, A. Freeman, N. Newman and C. Stampfl, Phys. Rev. Lett., 2005, 95, 256404.
53. M. Chiodi, C. P. Cheney, P. Vilmercati, E. Cavaliere, N. Mannella, H. H. Weitering and L. Gavioli, J. Phys. Chem. C, 2011, 116, 311–318.
54. X. Zhang, M. Guo, W. Li and C. Liu, J. Appl. Phys., 2008, 103, 063721.
55. V. Srikant and D. R. Clarke, J. Appl. Phys., 1998, 83, 5447.
56. N. Feng, Q. Wang, A. Zheng, Z. Zhang, J. Fan, S.-B. Liu, J.-P. Amoureux and F. Deng, J. Am. Chem. Soc., 2013, 135, 1607–1616.

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