International Journal of Photoenergy

Volume 2014 (2014), Article ID 816234, 7 pages

http://dx.doi.org/10.1155/2014/816234

Research Article

Electronic Structures of S/C-Doped TiO₂ Anatase (101) Surface: First-Principles Calculations

Qili Chen,¹ Min Liu,² Kaihua He,¹ and Bo Li³

¹School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China

²Central China Normal University Press, Wuhan 430074, China

³Faculty of Mechanical and Electronic Information, China University of Geosciences, Wuhan 430074, China

Received 18 February 2014; Accepted 10 March 2014; Published 2 June 2014

Academic Editor: Jiaguo Yu

Copyright © 2014 Qili Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

The electronic structures of sulfur (S) or carbon (C)-doped TiO₂ anatase (101) surfaces have been investigated by density functional theory (DFT) plane-wave pseudopotential method. The general gradient approximation (GGA) + U (Hubbard coefficient) method has been adopted to describe the exchange-correlation effects. All the possible doping situations, including S/C dopants at lattice oxygen (O) sites (anion doping), S/C dopants at titanium (Ti) sites (cation doping), and the coexisting of anion and cation doping, were studied. By comparing the formation energies, it was found that the complex of anion and cation doping configuration forms easily in the most range of O chemical potential for both S and C doping. The calculated density of states for various S/C doping systems shows that the synergistic effects of S impurities at lattice O and Ti sites lead a sharp band gap narrowing of 1.35 eV for S-doped system comparing with the pure TiO₂ system.

1. Introduction

Many researchers have paid much attention on titanium dioxide (TiO₂). As a promising photocatalytic semiconductor for environmental treatment, it has excellent functionality, long-term stability, and nanotoxicity [1]. However, TiO₂ is a kind of wide band gap semiconductor (3.2 eV for anatase phase and 3.0 eV for rutile phase [2]). It needs ultraviolet (UV) radiation to excite the electrons from valence band (VB) to conduction band (CB). Unfortunately, the energy of UV light accounts for only small fraction of the sunlight. Then, how to enhance the ability of visible light (VIS) absorption of TiO₂ is critical to enable the utility of TiO₂ photocatalyst materials.

Many efforts have been made to achieve this purpose, including introducing metal or nonmetal species for doping. S and C species are special among nonmetal species. For these two species, both cation and anion doping could be formed in TiO₂. The group of Umebayashi [3, 4] have synthesized S-doped TiO₂ by ion implantation and oxidation annealing of TiS₂. They found that the S atoms occupied oxygen sites to form Ti-S bonds and lead a decrease in the band-gap energy. Based on the theoretical analyses using ab initio band calculations, they thought that mixing of the S 3p states with the valence band contributes to the band gap narrowing. Ohno’s group [5] have synthesized S-doped TiO₂ photocatalysts chemically in which S (S⁴⁺) substitute some of the lattice titanium atoms, which showed strong absorption for visible light and high activities for degradation of methylene blue, 2-propanol in aqueous solution, and partial oxidation of adamantane under irradiation at wavelengths longer than 440 nm. Long et al. [6] have discussed the structural and electronic properties of S-doping configurations by substitution and adsorption at the rutile TiO₂ (110) surface with first-principles density functional theory calculations. Their results indicate that S dopants replace surface O atoms or bind to Ti atoms preferentially. S-cation doping led to relatively small reductions of the photon transition energy, while S-anion doping and adsorption on the surface resulted in significant red shifts of the optical absorption edge. For C-doped TiO₂, some experimental researches have been done by Nakano et al. [7]. They have prepared C-doped TiO₂ film by oxidative annealing of sputtered TiC films at 550°C in flowing O₂ gas. Deep-level optical spectroscopy measurements revealed three deep levels located at 0.86, 1.30, and 2.34 eV below the CB. They thought the 2.34 eV band introduced by the C-doping contributes to band gap narrowing by mixing with the O 2p valence band. Both anion doping and cation doping have been studied by Kamisaka et al. [8] for C-doped TiO₂. It was found that neither in-gap impurity states nor visible-light absorbance were observed in the case of cation doping, while a density-of-states analysis revealed three in-gap impurity states for anion doping. Kesong et al. [9] have also discussed the structural and electronic properties of two possible substitutional carbon-doped structures of anatase and rutile TiO₂. They found that the band gap changes slightly for C-anion doping and the optical absorption energy is reduced by about 0.18 and 0.3 eV for cation C-doped anatase and rutile TiO₂, respectively. Lee et al. [10] presented first-principles density-functional calculations for the electronic properties anion C-doped TiO₂. They found that three C 2p bands appear in the band gap; they were located at 0.52, 0.96, and 1.48 eV away from the VB maximum of TiO₂. The energy gap between the highest O 2p band and the lowest Ti 3d band is 2.42 eV, close to 2.39 eV in undoped TiO₂.

However, these theoretical and experimental studies are not enough to give a clear insight of the real mechanism for VIS sensitivity of S/C-doped TiO₂. In this paper, we demonstrated a relatively more comprehensive investigation on the effects of S/C impurities on the electronic structures of TiO₂. Firstly, the surface models were adopted to calculate the band structure of S/C-doped TiO₂ anatase. To our opinion, the surface model is more suitable to simulate synthesized powder or film samples than bulk model. Of the anatase single-crystalline surfaces, the (101) surface is the predominant face that is exposed on anatase minerals and polycrystalline powders, and theory calculations also show that it is thermodynamically the low-energy surface [1, 11]. Moreover, besides the isolated anion and cation doping that have been discussed in our calculations, the case of anion and cation codoping with two S/C atoms (lattice O and Ti atoms are replaced by S/C atoms synchronously) has also been studied. Furthermore, because the local density approximation (LDA) and general gradient approximation (GGA) which are generally used to describe the exchange-correlation effects always lead to a severe underestimation of the band gap [12] for transition metal oxides, GGA + U (Hubbard coefficient) was used in this present work to compensate for the limitation for those strongly correlated systems [13] which introduces an additional term based on a simple Hubbard model for electron on-site repulsion.

2. Methods and Models

2.1. Computational Details

The computational calculations have been performed by density-functional theory (DFT) plane-wave pseudopotential method [14], as implemented in the CASTEP 5.0 codes [15]. GGA + U was used for describing the exchange-correlation effects. Within GGA + U, the Coulomb correlation interaction of Ti 3d electrons has been taken into account. The U = 8.50 eV of Ti 3d electrons was adopted in all energy calculations which has been confirmed by our previous works [16–18]. The ultrasoft pseudopotential was used to describe electron-ion interactions. The kinetic energy cutoff for the plane-wave basis was chosen as 380.0 eV. The Brillouin zone sampling was restricted to the point in surface geometry optimization. In energy calculations, it was set to 1 × 2 × 4. Structure optimization was performed by minimizing the total energy and the ionic force, until all the components of the residual forces were less than 0.01 eV·Å⁻¹. The energy and the displacement tolerance were set to 5.0 × 10⁻⁶ eV·atom⁻¹ and 5.0 × 10⁻⁴ Å, respectively.

2.2. Models

The TiO₂ (hereafter referring to the anatase structure exclusively) (101) surfaces were modeled by vacuum slabs. According to our previous computational results [19] and some references [20, 21], we have selected a slab of Ti₂₄O₄₈(TO) with surface area of 11.15 × 7.55 Å² and slab thickness of 3 layers (see Figure 1(a)). The surface species, namely, the bridging two-fold coordinated oxygen atom , three types of three-fold coordinated oxygen atom (, , and ), and five/six-fold coordinated titanium atoms ( and ), are denoted in Figure 1(a) as well.

(a)

(b)

Figure 1: (a) Relaxed structure of Ti₂₄O₄₈ surface cell (TO) with surface area of 11.15 × 7.55 Å², the first layer is in the dashed line. (b) Relaxed structure of the first layer of TO, the bond length of with its neighboring O atoms and with its neighboring Ti atoms are labeled. Ti and O atoms are represented by grey and red spheres, respectively.

The models of anion doping surfaces Ti₂₄O₄₇S(A-STO) and Ti₂₄O₄₇C(A-CTO) were built by replacing a surface oxygen atom with a sulfur or carbon atom in the slab of TO (the configuration of an S or C atom substituting an O atom is denoted SO or CO). There are four types of surface oxygen site, namely, the , , , and site (as shown in Figure 1(a)), for a sulfur or carbon atom to substitute. For the models of cation doping surfaces Ti₂₃SO₄₈(C-STO) and Ti₂₃CO₄₈(C-CTO), there are two possible surface sites, and site, for a sulfur or carbon atom to substitute (the configuration of a S or C atom substituting a Ti atom is denoted STi or CTi). By comparing the total energy of the optimized slabs for S/C doping (the values are shown in Table 1), it was clear that the site and site are energetically favored for anion and cation doping, respectively. Long’s results also show that S dopants replace surface O atoms preferentially [6].

Table 1: Energy differences for S and C dopant at different substitutional doping site on TiO₂ anatase (101) surface. A-STO and A-CTO denote anion doping surfaces Ti₂₄O₄₇S and Ti₂₄O₄₇C; C-STO and C-CTO denote cation doping surfaces Ti₂₃SO₄₈ and Ti₂₃CO₄₈, respectively.

Substitutional doping site

O2C

Ti5C
Ti6C

A-STO
0.00
0.45
1.51
2.47
—
—

A-CTO
0.00
0.06
0.17
0.21
—
—

C-STO
—
—
—
—
0.00
1.16

C-CTO
—
—
—
—
0.00
1.13

Unit: eV.

Figures 2(a), 2(b), 2(d) and 2(e) exhibit the relaxed configurations of SO, CO and STi, CTi. It can be seen from the structures that S atom substituting Ti atom at site (see Figure 2(d)) and C substituting O atom at site (see Figure 2(b)) do not lead significant lattice distortion, while substitutional S atom at site extends upwards and tends to leave the surface (see Figure 2(a)) and substitutional C atom at site seems to be attracted by O atoms at and site strongly (see Figure 2(e)), forming two short C−O bond with distance of 1.360 and 1.387 Å, which is consistent with [6].

(a)

(b)

(c)

(d)

(e)

(f)

Figure 2: Relaxed structure of the first layer of S/C-doped surfaces: (a) Ti₂₄O₄₇S(A-STO), (b) Ti₂₃SO₄₈(C-STO), (c) Ti₂₃SO₄₇S(AC-STO), (d) Ti₂₄O₄₇C(A-CTO), (e) Ti₂₃CO₄₈(C-CTO), and (f) Ti₂₃CO₄₇C(AC-CTO). The bond length of S or C dopants with its neighboring Ti or O atoms is labeled. Ti and O atoms are represented by grey and red black spheres, respectively. Substitutional S and C dopants are represented by yellow and green spheres.

According to the above discussions, the model of anion and cation codoping surface with two S atoms, Ti₂₃SO₄₇S(AC-STO), or that with two C atoms, Ti₂₃CO₄₇C(AC-CTO), was created by one S or C atom substituting an O atom at site and the other S or C atom substituting a Ti atom at site in the slab of TO. For the case of coexistent SO and STi or CO and on TO surface, there are four sites around a site, which could be distinguished by distance, namely, the nearest one, the next nearest one, the next next nearest one, and the farthest one. For S doping, the total energy differences are 0.14, 0.08, 0.07, and 0.00 eV of the optimized slabs, for C doping, and the total energy differences are 0.00, 0.04, 0.07, and 0.12 eV of each optimized configuration. It was found that SO and STi tend to be apart, while CO and CTi tend to be close; the optimized C–C bond length is only 1.360 Å. Figures 2(c) and 2(f) exhibit the relaxed configuration of and .

3. Results and Discussion

3.1. Defect Formation Energy

In order to evaluate the relative stability of various doping configurations under deferent oxygen atmosphere, the defect formation energies of each doping configuration as a function of O chemical potential has been calculated and the results were exhibited in Figure 3. Taking S doping, for example, the calculation scheme was displayed as follows.

(a)

(b)

Figure 3: (a) The formation energies of the STi, SO, and complexes as a function of O chemical potential. The zero in the vertical axis corresponds to the formation energy of STi. (b) The formation energies of the CTi, CO, and complexes as a function of O chemical potential. The zero in the vertical axis corresponds to the formation energy of CTi.

Firstly, for the neutral SO, STi defect, and the complex defect, the substitutional formation energies are calculated as the following equations [22]:

where (TO), (A-STO), (C-STO), and (AC-STO) are the total energies of TO, A-STO, C-STO, and AC-STO, respectively. μ(S), μ(Ti), and μ(O) are the chemical potentials of S, Ti, and O atom, respectively.

Nextly, the atom chemical potentials of Ti and O must satisfy the boundary conditions and μ(Ti) ≤ μ(Ti metal), where μ(O₂) and μ(Ti metal) are the chemical potentials of oxygen gas and titanium metal, respectively. Under the oxygen-rich (metal-poor) condition,  μ(O) is set as 1/2μ(O₂). While, under the oxygen-poor (metal-rich) condition,  μ(Ti) = μ(Ti metal). Correspondingly μ(Ti) or μ(O) is derived from the relation μ(Ti) + 2μ(O) = μ(TiO₂ bulk) [23–25].  μ(TiO₂ bulk) is the chemical potentials of TiO₂ anatase bulk.

Figure 3(a) exhibits the formation energies of SO, STi and the complex , as a function of , with the zero of the vertical scale corresponding to the formation energy of STi. is always lower than , only under the sufficient O-poor (Ti-rich) growth condition; is larger than , which indicates that in the most range of , the complex forms much more easily. Thus, SO and STi could be created synchronously in S-doped TiO₂ samples.

For the case of C doping, the defect formation energies are calculated in the same way. Figure 3(b) shows the formation energies of CO, CTi and the complex , as a function of , with the zero of the vertical scale corresponding to the formation energy of CTi. Namely, in the most range of , is lower than and is always the lowest in all the range of μ(O), which shows that isolated CTi forms more easily than isolated CO and has the most possibility to be on the C-doped TiO₂ surfaces.

3.2. Electronic Structures of Substitutional S/C-Doped Surfaces

The density of the states (DOS) for TO is shown in Figure 4, with the Fermi level being 0 eV on the energy axis. For the pure surface TO, the calculated band gap energy is about 2.64 eV which is smaller than 3.2 eV calculated for bulk structure. The valence band (VB) consists of Ti 3d and O 2p orbits with the width of 5.40 eV, and the conductive band (CB) consists of Ti 3d states mainly.

Figure 4: Density of the states (DOS) calculated for the pure surface Ti₂₄O₄₈(TO). Fermi level is at 0 eV and is 8.50 eV for Ti 3d electrons.

The calculated partial density of the states (PDOS) of S-doped surfaces is shown in Figure 5. In the PDOS of A-STO (Figure 5(a)), S 3p states are localized; a part of them are lying at the Femi level and adjacent to the TiO₂ VB maximum, which leads an expansion of VB from 5.40 to 5.80 eV. The electron excitation energy from the occupied VB states to the CB minimum shortens to 2.00 eV. However, in the PDOS of C-STO (see Figure 5(b)), the majority of S 3p states locates far away from the Femi level; only a few of them disperse and mix with O 2p and Ti 3d VB states. There is a slight change for the band gap energy from 2.64 eV to 2.45 eV. The conclusion accords with [6] that S-anion doping leads significant red shifts of the optical absorption edge.

(a)

(b)

(c)

Figure 5: Density of the states (DOS) calculated for S-doped surfaces: (a) Ti₂₄O₄₇S(A-STO), (b) Ti₂₃SO₄₈(C-STO), and (c) Ti₂₃SO₄₇S(AC-STO). Fermi level is at 0 eV and is 8.50 eV for Ti 3d electrons. The 3p states of S dopant at site and that of S dopant at site are represented by dark grey and black area, respectively.

For the AC-STO, the PDOS (Figure 5(c)) shows that the localized S 3p states introduced by S dopant at site still appear at the top of VB, and S dopant at site provides some localized 3p states at the bottom of CB; thus the width of VB states expands to 6.10 eV and the band gap energy decreases to 1.45 eV, which indicates a great decrease of excited energy for electronic transition and a red shift of the optical absorption for S-doped TiO₂. Obviously, the electronic properties of codoped systems are not a mechanical mixture of those of both single-doped systems, but the coupling contribution of surface S impurities at and sites, which is consistent with [26, 27].

The calculated PDOSs of C-doped surfaces are shown in Figure 6. Figure 6(a) exhibits the PDOS of A-CTO. A part of localized C 2p states locate at the TiO₂ VB maximum, which leads a slight expansion of VB from 5.40 to 5.50 eV, the band gap energy has a very small shortness of 0.14 eV. Additionally, another part of localized C 2p is lying in the gap and 1.70 eV away from the Femi level. In the PDOS of C-CTO (Figure 5(b)), C dopants do not introduce any states around the Femi level, and the calculated band gap energy is almost equal to that of TO. These conclusions are similar with [8].

(a)

(b)

(c)

Figure 6: Density of the states (DOS) calculated for C-doped surfaces: (a) Ti₂₄O₄₇C(A-CTO), (b) Ti₂₃CO₄₈(C-CTO), and (c) Ti₂₃CO₄₇C(AC-CTO). Fermi level is at 0 eV and is 8.50 eV for Ti 3d electrons. The 2p states of C dopant at site and that of C dopant at site are represented by dark grey and black area, respectively.

For the AC-CTO, the PDOS (Figure 6(c)) shows that the C dopant at site still provides two parts of localized 2p states: one is at the bottom of VB and the other is in the gap, 1.23 eV away from the Femi level. The band gap energy decreases from 2.64 eV to 2.23 eV, and the VIS absorption of C-doped TiO2 could be improved by the decrease of intrinsic absorption energy. On the other hand, extrinsic absorption from VB states to unoccupied gap states contributes to the VIS sensitivity of C-doped TiO₂, either. However, the gap states may also act as the electron-cavity recombination centers, thus reducing the photocatalytic efficiency.

4. Conclusions

In this present work, all spin-polarized density-functional theory plane-wave pseudopotential method has been adopted to investigate the electronic properties of TiO₂ anatase (101) surfaces with S and C doping. (Hubbard coefficient) method has been used to describe exchange-correlation effects. For the case of S doping, our calculations demonstrated that the formation energy of the complex is lower than that of the isolated STi or SO in the most range of chemical potentials of O, which indicates that the complex may form more easily under most of conditions for S-doped TiO₂. The calculated density of the states of anion and cation codoping surface AC-STO shows that there is a sharp decrease for the band gap energy from 2.64 to 1.45 eV due to the synergistic effect of SO and STi defects. Thus, the ability of VIS absorption for S-doped TiO₂ could be improved greatly. For the case of C doping, the formation energy of the complex is the lowest in all the range of chemical potentials of O. The calculated density of the states of anion and cation codoping surface AC-CTO also shows a decrease for the band gap energy from 2.64 to 2.23 eV and the VIS absorption could be improved by the decrease of intrinsic absorption energy appreciably, but the gap states induced by CO defect may act as the electron-cavity recombination centers, thus reducing the photocatalytic efficiency.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

The project was supported by the National Natural Science Foundation of China (41340048), and the Fundamental Research Funds for the Central Universities (CUG120110).

References

U. Diebold, “The surface science of titanium dioxide,” Surface Science Reports, vol. 48, no. 5–8, pp. 53–229, 2003.

D. P. Norton, “Synthesis and properties of epitaxial electronic oxide thin-film materials,” Materials Science and Engineering R, vol. 43, no. 5-6, pp. 139–247, 2004.

T. Umebayashi, T. Yamaki, S. Yamamoto et al., “Sulfur-doping of rutile-titanium dioxide by ion implantation: photocurrent spectroscopy and first-principles band calculation studies,” Journal of Applied Physics, vol. 93, no. 9, pp. 5156–5160, 2003.

T. Umebayashi, T. Yamaki, H. Itoh, and K. Asai, “Band gap narrowing of titanium dioxide by sulfur doping,” Applied Physics Letters, vol. 81, no. 3, pp. 454–456, 2002.

T. Ohno, M. Akiyoshi, T. Umebayashi, K. Asai, T. Mitsui, and M. Matsumura, “Preparation of S-doped TiO₂ photocatalysts and their photocatalytic activities under visible light,” Applied Catalysis A, vol. 265, no. 1, pp. 115–121, 2004.

R. Long, N. J. English, and Y. Dai, “First-principles study of s doping at the rutile TiO₂ (110) surface,” Journal of Physical Chemistry C, vol. 113, no. 40, pp. 17464–17470, 2009.

Y. Nakano, T. Morikawa, T. Ohwaki, and Y. Taga, “Electrical characterization of band gap states in C-doped TiO₂ films,” Applied Physics Letters, vol. 87, no. 5, Article ID 052111, 2005.

H. Kamisaka, T. Adachi, and K. Yamashita, “Theoretical study of the structure and optical properties of carbon-doped rutile and anatase titanium oxides,” Journal of Chemical Physics, vol. 123, no. 8, Article ID 084704, 2005.

Y. Kesong, D. Ying, H. Baibiao, and W. Myung-Hwan, “Density functional characterization of the visible-light absorption in substitutional C-anion- and C-cation-doped TiO₂,” Journal of Physical Chemistry C, vol. 113, no. 6, pp. 2624–2629, 2009.

J. Y. Lee, J. Park, and J. H. Cho, “Electronic properties of N- and C-dopedTiO₂,” Applied Physics Letters, vol. 87, Article ID 011904, 2005.

T. Ihara, M. Miyoshi, Y. Iriyama, O. Matsumoto, and S. Sugihara, “Visible-light-active titanium oxide photocatalyst realized by an oxygen-deficient structure and by nitrogen doping,” Applied Catalysis B, vol. 42, no. 4, pp. 403–409, 2003.

C. Stampfl and C. G. Van De Walle, “Density-functional calculations for III-V nitrides using the local-density approximation and the generalized gradient approximation,” Physical Review B, vol. 59, no. 8, pp. 5521–5535, 1999.

S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, “Electron-energy-loss spectra and the structural stability of nickel oxide: an LSDA+U study,” Physical Review B, vol. 57, no. 3, pp. 1505–1509, 1998.

M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” Reviews of Modern Physics, vol. 64, no. 4, pp. 1045–1097, 1992.

S. J. Clark, M. D. Segall, C. J. Pickard et al., “First principles methods using CASTEP,” Zeitschrift für Kristallographie, vol. 220, no. 4, pp. 567–570, 2005.

Q. L. Chen, G. Zheng, K. H. He, and B. Le, “First-principles calculations on electronic structures of TiO₂ anatase (101) surfaces with N impurities,” Modern Physics Letters B, vol. 25, p. 119, 2011.

Q.-L. Chen and C.-Q. Tang, “First-principles calculations on electronic structures of N/F-doped and N-F-codoped TiO₂ anatase (101) surfaces,” Acta Physico-Chimica Sinica, vol. 25, no. 5, pp. 915–920, 2009.

Q. Chen, C. Tang, and G. Zheng, “First-principles study of TiO₂ anatase (101) surfaces doped with N,” Physica B, vol. 404, no. 8-11, pp. 1074–1078, 2009.

Q. L. Chen, B. Li, G. Zheng, K. H. He, and A. S. Zheng, “First-principles calculations on electronic structures of Fe-vacancy-codoped TiO₂ anatase (101) surface,” Physica B, vol. 406, no. 20, pp. 3841–3846, 2011.

E. Finazzi, C. Di Valentin, A. Selloni, and G. Pacchioni, “First principles study of nitrogen doping at the anatase TiO₂ (101) surface,” Journal of Physical Chemistry C, vol. 111, no. 26, pp. 9275–9282, 2007.

Y. W. Xu, K. Chen, S. H. Liu, M. J. Cao, and J. Q. Li, “Interaction of photoactive catechol with TiO₂ anatase (101) surface: a periodic density functional theory study,” Chemical Physics, vol. 331, pp. 275–282, 2007.

X. Y. Cui, J. E. Medvedeva, B. Delley, A. J. Freeman, and C. Stampfl, “Spatial distribution and magnetism in poly-Cr-doped GaN from first principles,” Physical Review B, vol. 75, no. 15, Article ID 155205, 2007.

F. Wang, Z. Pang, L. Lin, S. Fang, Y. Dai, and S. Han, “Theoretical study of the magnetic interaction of Cr-doped ZnO with and without vacancies,” Journal of Magnetism and Magnetic Materials, vol. 321, no. 19, pp. 3067–3070, 2009.

F. Gao, J. Hu, J. Wang, C. Yang, and H. Qin, “Ferromagnetism induced by intrinsic defects and carbon substitution in single-walled ZnO nanotube,” Chemical Physics Letters, vol. 488, no. 1–3, pp. 57–61, 2010.

A. Debernardi and M. Fanciulli, “The magnetic interaction of Fe doped ZnO with intrinsic defects: a first principles study,” Physica B, vol. 401-402, pp. 451–453, 2007.

J. Yu, P. Zhou, and Q. Li, “New insight into the enhanced visible-light photocatalytic activities of B-, C- and B/C-doped anatase TiO₂ by first-principles,” Physical Chemistry Chemical Physics, vol. 15, no. 29, pp. 12040–12047, 2013.

P. Zhou, J. G. Yu, and Y. X. Wang, “The new understanding on photocatalytic mechanism of visible-light response N–S codoped anatase TiO₂ by first-principles,” Applied Catalysis B, vol. 142-143, pp. 45–53, 2013.