Electronic Structure and Optical Properties of N/Si-Codoped Anatase TiO<sub><b>2</b></sub> Evaluated Using First Principles Calculations

Lin, Huey-Jiuan; Wu, Hsuan-Chung

doi:https://doi.org/10.1155/2014/342132

International Journal of Photoenergy

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Abstract Introduction Methods Results and Discussion Conclusions Acknowledgments Supplementary Materials References Copyright Related Articles

Research Article | Open Access

Volume 2014 | Article ID 342132 | https://doi.org/10.1155/2014/342132

Electronic Structure and Optical Properties of N/Si-Codoped Anatase TiO₂ Evaluated Using First Principles Calculations

Huey-Jiuan Lin¹and Hsuan-Chung Wu^2,3

Academic Editor: Pramod H. Borse

Received13 Nov 2013

Revised09 Feb 2014

Accepted03 Mar 2014

Published27 Apr 2014

Abstract

First principles calculations were used to evaluate the electronic structure and optical properties of N/Si-monodoped and N/Si-codoped TiO₂ to further understand their photocatalytic mechanisms. In accordance with the atomic distance between N and Si dopants, this study considered three N/Si codoping configurations, in which the N dopant had a tendency to bond with the Si dopant. The calculations showed that the bandgaps of the N/Si codoping models were narrow, in the range 3.01–3.05 eV, redshifting the intrinsic absorption edge. The Si 3p orbital of N/Si-codoped TiO₂ plays a key role in widening the valence band (VB), thereby increasing carrier mobility. In addition, the N-induced impurity energy level in the forbidden band appears in all three N/Si codoping models, strengthening absorption in the visible region. The bandgap narrowing, VB widening, and impurity energy levels in the forbidden band are beneficial for improving the photocatalytic activity of N/Si-codoped TiO₂.

1. Introduction

Since the pioneering work of Fujishima and Honda in 1972 [1], titanium dioxide (TiO₂) has been widely studied as a promising photocatalytic material because of its excellent properties (e.g., it is nontoxic, inexpensive, and chemically stable). However, pure anatase TiO₂ has a wide bandgap of 3.2 eV and only absorbs in the UV region (~5%) of solar energy. Therefore, its solar energy use is restricted. Much research has recently been devoted to developing methods of extending the optical absorption of TiO₂-based materials into the visible region.

Doping TiO₂ with various dopants including transition metals such as Mo [2], Co [3], and Au [4] and nonmetals such as N [5–9], Si [10–14], P [15], and S [16] is a popular method of enhancing the characteristics of TiO₂. Since the report of Asahi et al. in 2001 [5], N has been considered the most effective nonmetallic elemental dopant and has been studied further [5–9]. Doping with Si is also effective for enhancing the photocatalytic activity of TiO₂ [10–14]. Doping TiO₂ with two dopants (i.e., codoping) has recently been developed as a method to enhance photocatalytic activity, and promising results have been reported for codoping TiO₂ with nitrogen and silicon (N/Si) [17–19]. Ozaki et al. [17, 18] fabricated nitrogen-doped silica-modified TiO₂, which showed strong absorption in the 400–500 nm visible region and exhibited high photocatalytic activity toward visible-light-induced acetaldehyde decomposition. They indicated that the amount of Si added significantly increased the amount of N and the visible-light-induced photocatalytic activity. Hou et al. [19] found that N-doped SiO₂/TiO₂ exhibited higher photocatalytic activity than N-doped TiO₂ when the weight ratio of SiO₂/TiO₂ was in the range 0.05–0.20. Shi et al. [20] performed first principles calculations to evaluate the energies and electronic properties of N/Si-codoped TiO₂. The calculated energies indicated that Si doping increases the concentration of N in N/Si-codoped TiO₂. The bandgap of Si/N-codoped TiO₂ was significantly narrowed to 1.63 eV. However, the calculated bandgap of pure anatase TiO₂ (2.18 eV) was underestimated owing to the limitations of standard density functional theory (DFT). A few approaches such as DFT + U (Hubbard U) and hybrid functionals have been used to investigate TiO₂-based materials in order to overcome this limitation. Long and English [21] used Heyd-Scuseria-Ernzerhof (HSE06) hybrid DFT calculations to investigate the effects of N/Si codoping on the electronic properties of anatase TiO₂. Their calculated bandgap of anatase TiO₂ was 3.2 eV, which was consistent with the experimentally obtained bandgaps. The calculated results suggest that double-hole coupling plays a key role in ensuring high photocatalytic activity in the visible region for TiO₂-based photocatalysts.

The DFT + U is a method of correcting the underestimation of the bandgap and involves adding an orbital-dependent term to the DFT potential; it has previously been used to describe the electronic structures of transition-metal oxides [22–25]. Thus, we used the DFT + U method to more accurately represent the electronic structure and optical properties of N/Si-codoped TiO₂. The N/Si codoping system included three N-Si-distance-based models, which were compared with the N-monodoped, Si-monodoped, and pure TiO₂ models to further understand the mechanism of N/Si-codoping-induced photocatalytic activity enhancement. The optimized structures and Mulliken charges of the N-, Si-, and N/Si-doped TiO₂ were also analyzed and compared with corresponding values in the literature.

2. Calculation Models and Methods

Figure 1 shows the 2 × 2 × 1 48-atom anatase TiO₂ supercell model considered in this study. The N-monodoping and Si-monodoping models were constructed by substituting one O atom (from the O1 site) with one N atom ( model) and substituting one Ti atom (from the Ti1 site) with one Si atom ( model), respectively. The corresponding concentrations of N and Si were both 2.08 at.% (dopant atoms/total atoms). In addition, we considered three N/Si codoping configurations in which the O1 atom was substituted with one N atom. The Ti1, Ti2, or Ti3 sites were substituted with one Si atom in the N/Si-1, N/Si-2, or N/Si-3 models, respectively. Our calculations showed that the enthalpy of the N/Si-1 model was the lowest (−37865.04 eV), indicating that the N/Si-1 structure was more stable than the N/Si-2 (−37864.71 eV) and N/Si-3 (−37864.73 eV) ones. This implies that the Si in the N/Si codoping model tends to bond with the N (forming Ti-N-Si bonds), which is consistent with the formation energy calculation results in the literature [20].

CASTEP software was used to perform the first principles calculations [26]. The potentials of ion core and valence electrons were modeled using ultrasoft pseudopotentials in the Vanderbilt form [27]. The valence electron configurations of the atoms were 2s²2p³ for N, 2s²2p⁴ for O, 3s²3p² for Si, and 3s²3p⁶3d²4s² for Ti. The wave functions of the valence electrons were expanded through a plane-wave basis set, and the cut-off energy was set to 400 eV. The Monkhorst-Pack-scheme-based K-point grid sampling was set at (i.e., <0.04 Å⁻¹) [28]. The convergence threshold for self-consistent iterations was set to eV. The optimization parameters were set as follows: energy change = eV/atom, maximum force = 0.03 eV/Å, maximum stress = 0.05 GPa, and maximum displacement tolerance = 0.001 Å.

We previously used the DFT + U method and the following formalism to describe the exchange and correlation potential [6, 24]: where denotes the spin ()-polarized on-site density matrix. The spherically averaged Hubbard parameter, , describes the increase in energy caused by placing an extra electron at a particular site, and the parameter (1 eV) represents the screened exchange energy. The effective Hubbard parameter, , accounts for the on-site Coulomb repulsion for each affected orbital. Here, the effective on-site Coulomb interaction is eV for Ti 3d in the DFT + U approach (see Figure S1 in Supplementary Material available online at http://dx.doi.org/10.1155/2014/342132).

3. Results and Discussion

3.1. Structural Optimization

Table 1 summarizes the average optimized bond length and the volume difference ratios of all the doping models and the pure anatase TiO₂. In the pure anatase TiO₂, each Ti atom is horizontally and vertically surrounded by four and two adjacent O atoms, respectively; the average length of the Ti–O bond is 1.992 Å. When an O atom is substituted with one N atom ( model), the Ti–O (1.994 Å) and Ti–N (2.045 Å) bonds were longer than the Ti–O bond in the pure TiO₂, expanding the volume. Because the ionic radius and electronegativity of N (1.71 Å for N³⁻ and 3.04) are larger and smaller than those of O (1.32 Å for O²⁻ and 3.44) [29, 30], respectively, the Ti–N bond is longer than the Ti–O one in the model [6]. Conversely, the Ti–O and Si–O bonds in the model are both shorter than the Ti–O bond in the pure anatase TiO₂, thereby shrinking the lattice because the Si⁴⁺ radius and Si electronegativity (0.40 Å for Si⁴⁺ and 1.90) are smaller and higher than those of Ti⁴⁺ and Ti (0.61 Å for Ti⁴⁺ and 1.54) [30, 31], respectively. This result is consistent with the previously obtained experimental results [10, 11] and theoretical calculations [20].

In the N/Si-2 and N/Si-3 models, the N-Si distance is longer, weakening the atomic interactions between the N and Si atoms. Therefore, the Ti–N and Si–O bond lengths in the N/Si-2 and N/Si-3 models are closer to those in the monodoping models ( and ). In the N/Si-1 model, the bond lengths vary in descending order as follows: Ti–N > Ti–O > Si–N > Si–O. The Ti–N bond in the N/Si-1 model (2.099 Å) is longer than that in the N/Si-2 and N/Si-3 models (both = 2.042 Å); the Si–O bond in the N/Si-1 model (1.818 Å) is shorter than that in the N/Si-2 and N/Si-3 models (both = 1.830 Å). Consequently, the volume difference ratios of these three codoping models are almost identical (−1.5%) and are between those of the (0.4%) and (−2.0%) models.

3.2. Mulliken Population

Table 2 summarizes the average Mulliken atomic and bond populations of each N/Si model. The average atomic populations of the Ti and O atoms in the pure anatase TiO₂ are 1.48 and , respectively, suggesting that the Ti atoms tend to lose electrons and the O atoms tend to gain them. The Mulliken population of N atoms () is larger than that of O atoms () in the model because of the former’s smaller electronegativity. The atomic population of Si atoms () is larger than that of Ti atoms () in the model, indicating that Si atoms transfer more electrons to the surrounding O atoms thereby reducing the average atomic population of O atoms.

The atomic population of Si atoms () in the N/Si-1 model is slightly smaller than that of those in the model because N atoms are less electronegative than O atoms. Further, the atomic population of N atoms in the N/Si-1 model () is smaller than that of N atoms in the N/Si-2 and N/Si-3 models (), suggesting that N atoms can gain more electrons from the Si atoms in the N/Si-1 model because the N atoms are directly bonded to the Si atoms. The atomic populations of N atoms () in the N/Si-2 and N/Si-3 models are the same as those in the model, implying that there is, again, almost no interaction between N and Si atoms in the N/Si-2 and N/Si-3 models.

The Ti–O bond population was larger than the Ti–N one, indicating that Ti–O bonds are more covalent than Ti–N ones. Further, the Si–N and Si–O bond populations in each model are in the range 0.402–0.500 , meaning that Si–N and Si–O bonds were more covalent than the Ti–N and Ti–O ones.

3.3. Electronic Structure

Figure 2 shows the band structures calculated for the N/Si-monodoped and codoped TiO₂ models. The Fermi level, indicated by the dotted line, was set to zero. The bandgap obtained for the pure anatase TiO₂ was 3.21 eV, as shown in Figure 2(a), and is consistent with experimentally obtained bandgaps. The bandgap in the model (Figure 2(b)) was 3.09 eV, which was less than that of the pure anatase TiO₂. An isolated impurity energy level resulting from the empty N-2p orbital above the valence band maximum (VBM) at 1.44 eV caused the TiO₂ to absorb in the visible region. The valence band (VB) of the model is 4.6 eV wide, which is slightly wider than that of pure anatase TiO₂ (4.5 eV). The bandgap narrowed to 3.05 eV in the model (Figure 2(c)). There is no impurity energy level in the forbidden band because the Si and Ti atoms showed equal valencies. It should be noted that the VB of the model (5.3 eV) is wider than that of pure anatase TiO₂ and the model. A wider VB results in higher photogenerated carrier mobility [20]. The bandgaps were narrowed to 3.01–3.05 eV and the VBs were 5.3 eV wide in the N/Si codoping models (Figures 2(d)–2(f)). All three codoping models showed the impurity energy levels; the N/Si-1 model impurity energy level was the highest.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 3 shows the total density of states (TDOS) and projected density of states (PDOS) near the Fermi level of N/Si-doped TiO₂. They help explain the distribution of each related orbital associated with the constituent elements. The VB mainly consists of the O 2p and a few Ti 3d and N 2p states while the conduction band (CB) comprises the Ti 3d and a few O 2p states in the model (Figure 3(a)). The empty N 2p state mainly contributes to the impurity energy levels in the forbidden band. The Si 3s electrons appear in the range (−7)–(−6.5) eV in the model (Figure 3(b)). The Si 3p orbital mainly contributes to the bottom of the VB, thus significantly widening it. In the N/Si-1 model (Figure 3(c)), the N 2p orbital is hybridized not only with the Si 3s orbital in the range (−7)–(−6.5) eV but also with the Si 3p orbital in the VB. Therefore, the Si–N bond is more covalent than the Ti–N and Ti–O ones, as mentioned in Section 3.2. In addition, adding Si atoms produced a wider VB and a narrower bandgap in the N/Si-1 model than in the one. Figure 3(d) shows the DOS of the N/Si-2 model, which is similar to that of the N/Si-3 one. It should be reemphasized that the Si 3p state, not the N 2p one, contributes to widening the VB; therefore, the Si 3p state played a key role in widening the VB.

(a)

(b)

(c)

(d)

3.4. Optical Properties

The optical properties of materials can be obtained using the dielectric function, , whose imaginary part, , is calculated using the following expression [32]: where , , , , and and represent the electronic charge, unit cell volume, vector defining the polarization of the incident electric field, light frequency, and the wave functions of the conduction and VBs, respectively. Kramers-Kronig relations can be used to calculate the real part of the dielectric function, , from . The absorption coefficient, , can be obtained from and .

Figure 4 shows the absorption spectra computed for the N/Si-doped TiO₂. The pure anatase TiO₂ did not show any absorption in the visible region because it shows a wide bandgap of 3.21 eV. Doping the TiO₂ with Si narrowed the bandgap, thereby redshifting the intrinsic absorption edge toward higher wavelengths (Figure 4 inset). The N-doped TiO₂ showed a redshifted intrinsic absorption edge due to the band gap narrowing and the absorption had extended into the visible and infrared (IR) regions, owing also to the N 2p impurity energy level that occurs in the forbidden band mentioned previously in Section 3.3. The forbidden band contained the N 2p impurity energy level in all three N/Si codoping models. Therefore, the codoping models exhibited stronger absorption than the pure anatase or Si-doped TiO₂ in the visible region, thereby enhancing photocatalytic activity. It should be noted that the N/Si-1 model shows the stablest structure of the three codoping models and exhibits the strongest absorption between 400 and 500 nm, which is consistent with the previously reported experimental results [17, 18].

4. Conclusions

First principles calculations were performed to study the optimized structure, Mulliken population, electronic structure, and optical properties of N/Si-codoped TiO₂ models. The N/Si-1 model exhibited the stablest structure, whose bond lengths are arranged in descending order as follows: Ti–N > Ti–O > Si–N > Si–O. The bandgaps of the N/Si codoping models were narrowed to 3.01–3.05 eV, and the VBs were widened to 5.3 eV; the Si 3p orbital played a key role in extending VB width. All three N/Si codoping models showed the N-induced impurity energy level in the forbidden band; therefore, these models exhibited stronger absorption than the pure anatase TiO₂ and the monodoped models in the visible region and thus showed enhanced photocatalytic activity. According to our theoretical calculations, the bandgap narrowing, VB widening, and impurity energy level in the forbidden band all aid in improving the photocatalytic activity of N/Si-codoped TiO₂.

Conflict of Interests

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

Acknowledgments

The authors are grateful for the support of the National Science Council in Taiwan (NSC 102-2221-E-131-008). The authors also acknowledge the National Center for High-Performance Computing for computer time and the use of its facilities.

Supplementary Materials

Determination of an appropriate effective Hubbard U_eff parameter is necessary in DFT+U calculations to correctly interpret the intra-atomic electron correlation. For anatase TiO2 phases, the band gap widens when the effective Hubbard U_eff is increased. The band gap of anatase can be effectively widened by increasing U_eff from 0 to 8 eV. Here, the effective on-site Coulomb interaction is U_eff = 8.4 eV for Ti 3d in the DFT + U approach, and the calculated band gap of pure anatase is 3.21 eV, which is very close to the experimental value.

Supplementary Figure

References

A. Fujishima and K. Honda, “Electrochemical photolysis of water at a semiconductor electrode,” Nature, vol. 238, no. 5358, pp. 37–38, 1972.
View at: Publisher Site | Google Scholar
Y. K. Du, Y. Q. Gan, P. Yang, F. Zhao, N. P. Hua, and L. Jiang, “Improvement in the heat-induced hydrophilicity of TiO₂ thin films by doping Mo(VI) ions,” Thin Solid Films, vol. 491, no. 1-2, pp. 133–136, 2005.
View at: Publisher Site | Google Scholar
M. Subramanian, S. Vijayalakshmi, S. Venkataraj, and R. Jayavel, “Effect of cobalt doping on the structural and optical properties of TiO₂ films prepared by sol-gel process,” Thin Solid Films, vol. 516, no. 12, pp. 3776–3782, 2008.
View at: Publisher Site | Google Scholar
M. Zhou, J. Zhang, B. Cheng, and H. Yu, “Enhancement of visible-light photocatalytic activity of mesoporous Au-TiO₂ nanocomposites by surface plasmon resonance,” International Journal of Photoenergy, vol. 2012, Article ID 532843, 10 pages, 2012.
View at: Publisher Site | Google Scholar
R. Asahi, T. Morikawa, T. Ohwaki, K. Aoki, and Y. Taga, “Visible-light photocatalysis in nitrogen-doped titanium oxides,” Science, vol. 293, no. 5528, pp. 269–271, 2001.
View at: Publisher Site | Google Scholar
H.-C. Wu, S.-W. Lin, and J.-S. Wu, “Effects of nitrogen concentration on N-doped anatase TiO₂: density functional theory and Hubbard U analysis,” Journal of Alloys and Compounds, vol. 522, pp. 46–50, 2012.
View at: Publisher Site | Google Scholar
J. Qian, G. Cui, M. Jing, Y. Wang, M. Zhang, and J. Yang, “Hydrothermal synthesis of nitrogen-doped titanium dioxide and evaluation of its visible light photocatalytic activity,” International Journal of Photoenergy, vol. 2012, Article ID 198497, 6 pages, 2012.
View at: Publisher Site | Google Scholar
H. Fu, G. Shang, S. Yang, and T. Xu, “Mechanistic study of visible-light-induced photodegradation of 4-chlorophenol by TiO₂-_xN_x with low nitrogen concentration,” International Journal of Photoenergy, vol. 2012, Article ID 759306, 9 pages, 2012.
View at: Publisher Site | Google Scholar
M.-C. Wang, H.-J. Lin, C.-H. Wang, and H.-C. Wu, “Effects of annealing temperature on the photocatalytic activity of N-doped TiO₂ thin films,” Ceramics International, vol. 38, no. 1, pp. 195–200, 2012.
View at: Publisher Site | Google Scholar
X. Yan, J. He, D. G. Evans, X. Duan, and Y. Zhu, “Preparation, characterization and photocatalytic activity of Si-doped and rare earth-doped TiO₂ from mesoporous precursors,” Applied Catalysis B: Environmental, vol. 55, no. 4, pp. 243–252, 2005.
View at: Publisher Site | Google Scholar
R. Jin, Z. Wu, Y. Liu, B. Jiang, and H. Wang, “Photocatalytic reduction of NO with NH3 using Si-doped TiO₂ prepared by hydrothermal method,” Journal of Hazardous Materials, vol. 161, no. 1, pp. 42–48, 2009.
View at: Publisher Site | Google Scholar
M. Sun, X. Zhang, J. Li, X. Cui, D. Sun, and Y. Lin, “Thermal formation of silicon-doped TiO₂ thin films with enhanced visible light photoelectrochemical response,” Electrochemistry Communications, vol. 16, no. 1, pp. 26–29, 2012.
View at: Publisher Site | Google Scholar
S. Iwamoto, S. Iwamoto, M. Inoue, H. Yoshida, T. Tanaka, and K. Kagawa, “XANES and XPS study of silica-modified titanias prepared by the glycothermal method,” Chemistry of Materials, vol. 17, no. 3, pp. 650–655, 2005.
View at: Publisher Site | Google Scholar
Y. Zhang, X. Li, D. Chen, N. Ma, X. Hua, and H. Wang, “Si doping effects on the photocatalytic activity of TiO₂ nanotubes film prepared by an anodization process,” Scripta Materialia, vol. 60, no. 7, pp. 543–546, 2009.
View at: Publisher Site | Google Scholar
Y. Lv, L. Yu, H. Huang, H. Liu, and Y. Feng, “Preparation, characterization of P-doped TiO₂ nanoparticles and their excellent photocatalystic properties under the solar light irradiation,” Journal of Alloys and Compounds, vol. 488, no. 1, pp. 314–319, 2009.
View at: Publisher Site | Google Scholar
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.
View at: Publisher Site | Google Scholar
H. Ozaki, S. Iwamoto, and M. Inoue, “Enhanced visible light sensitivity of nitrogen-doped nanocrystalline si-modified titania prepared by the glycothermal method,” Chemistry Letters, vol. 34, no. 8, pp. 1082–1083, 2005.
View at: Publisher Site | Google Scholar
H. Ozaki, S. Iwamoto, and M. Inoue, “Effects of amount of Si addition and annealing treatment on the photocatalytic activities of N- and Si-codoped titanias under visible-light irradiation,” Industrial and Engineering Chemistry Research, vol. 47, no. 7, pp. 2287–2293, 2008.
View at: Publisher Site | Google Scholar
Y. D. Hou, X. C. Wang, L. Wu et al., “N-Doped SiO₂/TiO₂ mesoporous nanoparticles with enhanced photocatalytic activity under visible-light irradiation,” Chemosphere, vol. 72, no. 3, pp. 414–421, 2008.
View at: Publisher Site | Google Scholar
W. Shi, Q. Chen, Y. Xu, D. Wu, and C. Huo, “A first-principles calculation on the electronic properties of Si/N-codoped TiO₂,” Applied Surface Science, vol. 257, no. 7, pp. 3000–3006, 2011.
View at: Publisher Site | Google Scholar
R. Long and N. J. English, “Band gap engineering of (N, Si)-codoped TiO₂ from hybrid density functional theory calculations,” New Journal of Physics, vol. 14, Article ID 053007, 11 pages, 2012.
View at: Google Scholar
G. Shao, “Red shift in manganese- and iron-doped TiO₂: a dft+u analysis,” Journal of Physical Chemistry C, vol. 113, no. 16, pp. 6800–6808, 2009.
View at: Publisher Site | Google Scholar
X. Ma, B. Lu, D. Li, R. Shi, C. Pan, and Y. Zhu, “Origin of photocatalytic activation of silver orthophosphate from first-principles,” Journal of Physical Chemistry C, vol. 115, no. 11, pp. 4680–4687, 2011.
View at: Publisher Site | Google Scholar
H. C. Wu, Y. S. Lin, and S. W. Lin, “Mechanisms of visible light photocatalysis in N-doped anatase TiO₂ with oxygen vacancies from GGA+U calculations,” International Journal of Photoenergy, vol. 2013, Article ID 289328, 7 pages, 2013.
View at: Publisher Site | Google Scholar
H. C. Wu, Y. C. Peng, and T. P. Shen, “Electronic and optical properties of substitutional and interstitial si-doped ZnO,” Materials, vol. 5, no. 11, pp. 2088–2100, 2012.
View at: Google Scholar
M. D. Segall, P. J. D. Lindan, M. J. Probert et al., “First-principles simulation: ideas, illustrations and the CASTEP code,” Journal of Physics Condensed Matter, vol. 14, no. 11, pp. 2717–2744, 2002.
View at: Publisher Site | Google Scholar
D. Vanderbilt, “Soft self-consistent pseudopotentials in a generalized eigenvalue formalism,” Physical Review B, vol. 41, no. 11, pp. 7892–7895, 1990.
View at: Publisher Site | Google Scholar
H. J. Monkhorst and J. D. Pack, “Special points for Brillouin-zone integrations,” Physical Review B, vol. 13, no. 12, pp. 5188–5192, 1976.
View at: Publisher Site | Google Scholar
Z. Zhao and Q. Liu, “Mechanism of higher photocatalytic activity of anatase TiO₂ doped with nitrogen under visible-light irradiation from density functional theory calculation,” Journal of Physics D: Applied Physics, vol. 41, no. 2, Article ID 025105, 10 pages, 2008.
View at: Publisher Site | Google Scholar
D. R. Lide, Ed., CRC Handbook of Chemistry and Physics, Taylor & Francis, Boca Raton, Fla, USA, 2006.
R. D. Shannon, “Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides,” Acta Crystallographica, vol. 32, pp. 751–767, 1976.
View at: Google Scholar
R. Chowdhury, S. Adhikari, and P. Rees, “Optical properties of silicon doped ZnO,” Physica B: Condensed Matter, vol. 405, no. 23, pp. 4763–4767, 2010.
View at: Publisher Site | Google Scholar

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Copyright © 2014 Huey-Jiuan Lin and Hsuan-Chung Wu. 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.

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