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J. Phys. Chem. C 2009, 113, 650–653
Geometric and Electronic Properties of Sn-Doped TiO2 from First-Principles Calculations Run Long, Ying Dai,* and Baibiao Huang School of Physics, State Key Laboratory of Crystal Materials, Shandong UniVersity, Jinan 250100, People’s Republic of China ReceiVed: May 17, 2008; ReVised Manuscript ReceiVed: NoVember 18, 2008
We systemically investigated the effects of Sn doping on the geometrical and electronic properties of TiO2 by means of first-principles electronic structure calculations. Our results indicate a band gap reduction of 0.12 eV when Sn is substituted for Ti in rutile TiO2, leading to a red-shift of the optical adsorption edge. However, the band gap increases with increasing the Sn doping level. In contrast, when O is replaced by Sn, though this substitutional doping is not energetically preferred, the excitation energy increases slightly compared with the undoped case due to the well-known “band-filling mechanism”, leading to a blue-shift of the optical absorption edge. For doped anatase TiO2, the substitution of Sn for Ti may also increase the band gap and hence the optical gap. The results provide explanations not only for the red-shift and blue-shift of the optical absorption edge in different experiments, but also for the different electronic properties between Sn-doped anatase and rutile TiO2, with a certain Sn content resulting in the transformation of the two phases. 1. Introduction Titanium dioxide (TiO2) has received much attention as a good photocatalyst for the remediation of organic pollutants and the photogeneration of hydrogen from water.1,2 However, TiO2 has a serious disadvantage in that only UV light, about 3% of the solar spectrum, can be used for its photocatalytic activity due to large band gap (3.0 eV for rutile structure3 and 3.2 eV for anatase structure4). To utilize a wider range of the solar spectrum, the band gap needs to be narrowed. Recently, it has been suggested that the substitution of a nonmetal atom such as N,5-11 C,12-14 or S15-18 leads to high photocatalytic activity under visible light owing to a band gap narrowing. In addition, some groups have made an attempt to improve the photocatalytic activity of TiO2 and extend its optical absorption to the visible-light region by doping with Si and Sn.19-27 For Sn-doped TiO2, Li et al.24 showed that Sn4+ ions can be incorporated linearly into TiO2 lattices, accompanied by a phase transformation from anatase to rutile depending on the amount of the dopant. Pure anatase TiO2 has an optical band gap of 3.22 eV. With the inclusion of a small amount of Sn dopants, the band gap is raised to 3.35 eV, while maintaining the same anatase phase. When more Sn4+ ions are introduced, the crystal structure (anatase and rutile) of the mixed oxide nanoshperes is transformed to the rutile phase. Furthermore, the optical band gap of rutile TiO2 still increases with increasing content of Sn4+ ions. The observed dependence of the band gap on the concentration of doped Sn25,26 has been ascribed to the shifting of the conduction band toward a higher energy.25 Additionally, Lin et al.27 reported that the substitution of Sn for Ti in rutile TiO2 leads to a blue-shift of the optical absorption edge, indicating an increase in the band gap of the semiconductor. It is puzzling that the doping effects of substitutional Sn should actually lead to red-shift or blue-shift in different experiments. However, until now, there has been no report on the geometrical and electronic properties of Sn-doped TiO2 so that the physical and chemical origin of the enhanced photo* Corresponding author.
catalytic activity and the longer wavelength optical absorption remains unexplained. In the present work we performed density functional theory (DFT) calculations for Sn-doped TiO2 with the aim of elucidating two outstanding problems: (I) the origin of narrowing and broadening of the band gap in Sn-doped TiO2 and (II) the effects of Sn content on the change in the band gap. Our theoretical analysis provides a probable explanation for the experimentally observed red and blue shifts in the optical absorption edge of Sn-doped TiO2. The thermodynamical properties of Sn-doped TiO2 are also discussed by calculating the formation energies of the substitutional defects. 2. Computational Details To explore the effect of Sn doping on the microscopic mechanism of the band gap change and photoactivities of TiO2, the calculations were performed with the CASTEP code based on first-principles density functional theory.28 The exchange and correlation interactions were modeled by using the generalized gradient approximation of Perdew, Burke, and Ernzerhof.29 The Vanderbilt ultrasoft pseudopotential30 was used with the cutoff energy of 340 eV. For the geometry optimization of doped rutile TiO2, the Monkhorst-Pack31 k-point set 2 × 2 × 3 was used for the 48-atom 2 × 2 × 2 supercell, and the k-point set 2 × 4 × 3 for the 24-atom 2 × 2 × 1 supercell. Finer k-point sets 3 × 3 × 4 and 3 × 5 × 4 were employed for calculating the electronic properties of doped rutile TiO2. For the geometry optimization and the electronic property calculations for doped anatase TiO2, the k-points sets 3 × 3 × 2 and 3 × 3 × 4 were used for the 48-atom 2 × 2 × 2 supercell. In the geometry optimizations, all forces on the atoms were converged to less than 0.03 eV/Å, the maximum ionic displacement was within 0.001 Å, and the total stress tensor was reduced to the order of 0.05 GPa. 3. Results and Discussion 3.1. Optimized Structures. To examine how the concentration of Sn dopant affects the electronic properties, the Sn-doped structures were constructed by using the 48-atom 2 × 2 × 2
10.1021/jp8043708 CCC: $40.75 2009 American Chemical Society Published on Web 12/17/2008
Properties of Sn-Doped TiO2
J. Phys. Chem. C, Vol. 113, No. 2, 2009 651
Figure 1. Optimized partial structures using the 48-atom 2 × 2 × 2 supercell: (a) pure rutile TiO2, (b) doped rutile TiO2 with the substitution of Sn for O, and RSn-O model, and (c) doped rutile TiO2 with the substitution of Sn for Ti. The white spheres represent Ti atoms; the red spheres represent O atoms, and the dark spheres represent Sn atoms. The unit in bond length is Å.
and the 24-atom 2 × 2 × 1 supercells with one Ti or O atom replaced by one Sn atom, which corresponds to the Sn content of 2.08% and 4.17%, respectively. The two possible substitutional Sn sites (i.e., Sn for Ti and Sn for O) are considered to provide abundant theoretical analysis for understanding experiments. The optimized partial structures, taken from the 48-atom 2 × 2 × 2 supercell and the 24-atom 2 × 2 × 1 supercells, are shown in parts a-c of Figure 1, respectively. For pure rutile TiO2 (Figure 1a), the optimized Ti-O bond lengths are 2.009 and 1.956 Å, respectively. For substitutional Sn doping for O (Figure 1b), in which Sn should exist as an anion to maintain the charge balance, the Sn-Ti bond lengths increase to 2.325 and 2.025 Å. The latter are substantially longer than the Ti-O bonds of pure rutile TiO2 since the atomic radius of Sn is larger than that of O, so that the substitution of Sn for O would induce a significant local structure distortion and have a high formation energy. This viewpoint is confirmed by the subsequent calculated formation energy. On the other hand, for the substitution of Sn for Ti (Figure 1c), the Sn ion forms six Sn-O bonds with adjacent six O atoms. The four Sn-O bond lengths are 2.016 Å and the other two Sn-O bond lengths are 2.029 Å, which also slightly increase by about 3.1% and 1% compared with the case of pure TiO2, respectively. The distortions found for the Sn for Ti substitution are weaker than those for the Sn for O substitution. This indicates the substitution of Sn for Ti requires a relatively small formation energy. We will clarify this prediction in the subsequent text. 3.2. Formation Energies. To probe the stabilities of the doped systems, we calculated the formation energies (Eform) for the doped systems according to the formula
Eform ) E(doped) - [E(pure) + µSn - µX)]
(1)
where E(doped) and E(pure) are the total energies of the supercells with and without dopants, respectively. µSn is the chemical potential of the impurity Sn taken as the free energy of one Sn atom in bulk Sn. Under equilibrium conditions, the concentration of a point defect is controlled by its formation energy, which depends on the chemical potentials of the host and impurity atoms. For TiO2, the chemical potentials of O and Ti satisfy the relationship µTi + 2µO ) µTiO2, µO e µO2/2, and metal . The chemical potential µO is determined by the µTi e µTi energy of an O2 molecule in the O-rich growth condition (corresponding to a high value of µO). By referencing µO to the energy of an O atom in the O2 molecule, µTi in the Ti-rich condition (corresponding to a high value of µTi) amounts to the energy of one Ti atom in bulk Ti. The calculated formation energies in Sn-doped rutile TiO2 are summarized in Table 1, which reveals three features: (a) The formation energy for the substitution of Sn for Ti is much lower than that for O under both O-rich and Ti-rich conditions. (b) Under the O-rich growth
TABLE 1: Defect Formation Energies in Sn-Doped Rutile TiO2 under O-Rich and Ti-Rich Conditions (corresponding to high µO and µTi) Calculated by Using the 48-atom 2 × 2 × 2 Supercell. Eform (eV)
O-rich
Ti-rich
Sn for O in rutile Sn for Ti in rutile Sn for Ti in anatase
12.61 -6.35 (-6.31)a -6.05
7.59 3.71 (3.75)a 4.01
a
The numbers in parentheses represent the calculations by using the 24-atom 2 × 2 × 1 supercell.
condition, the formation energies are negative, indicating that the substitution of Sn for Ti is energetically favorable. The radius of Sn4+ is slightly larger than that of Ti4+, so the substitution requires a relatively small formation energy. (c) The formation energy increases with increasing the Sn content (24-atom supercell). Therefore, it is understandable that the incorporation of more Sn atoms into the TiO2 lattice needs a greater formation energy. However, it should be noted that the substitution of Sn for O may exist due to the particular preparation conditions employed. 3.3. Electronic Properties. The density of states (DOS) and projected density of states (PDOS) calculated for Sn-doped rutile TiO2 using the 48-atom 2 × 2 × 2 supercell are shown in Figure 2. The DOS and PDOS plots of pure rutile TiO2, given in parts a and a′ in Figure 2, indicate that the O 2p states dominate the valence band while the conduction band is mostly composed of Ti 3d states. The calculated band gap for the undoped rutile phase, 1.95 eV, is much smaller than the experimental band gap of 3.0 eV. This underestimation of the band gap is due to the well-known shortcoming of the DFT. Compared with the case of pure rutile, the substitution of Sn for O (Figure 2, parts b and b′) raises the valence band maximum by about 0.15 eV and lowers the conduction band edge by about 0.32 eV. Most Sn 5p states are located in the conduction band, so that the substitution of Sn for O puts the Fermi level in the conduction band about 0.64 eV above the conduction band bottom, showing a typical n-type metallic behavior. (Note that the charge balance requires the presence of Sn2-.) Consequently, the electron excited by a UV-visible photon from the valence band must go into the empty states of the conduction band above the Fermi level. This means that, since the substitution of Sn for O occasionally occurs in the doped rutile TiO2, the optical absorption may show a blue-shift of about 0.17 eV. The latter may provide an explanation for the blue-shift in substitutional Sn-doped TiO2 observed by Lin et al.27 This is the well-known “band-filling mechanism” associated with the optical properties of an n-type semiconductor.32 The substitution of Sn for Ti (Figure 2, parts c and c′) does not shift the valence band maximum but lowers the conduction
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Figure 2. DOS and PDOS plots calculated for undoped rutile TiO2 and Sn-doped rutile TiO2: (a) pure rutile model, (b) rutile TiO2 with substitution of Sn for O using the 48-atom 2 × 2 × 2 supercell, (c) rutile TiO2 with substitution of Sn for Ti using the 48-atom 2 × 2 × 2 supercell, and (d) rutile TiO2 with substitution of Sn for Ti using the 24-atom 2 × 2 × 1 supercell. The energy is measured from the top of the valence band of pure rutile TiO2, and the dotted line represents the Fermi level for the case of the substitution of Sn to Ti. The Fermi level for the substitution of Sn for O is separately denoted by the solid line.
Figure 3. DOS and PDOS plots calculated for (a) pure anatase TiO2 and (b) for Sn-doped anatase TiO2 with substitution of Sn for Ti using the 48-atom 2 × 2 × 2 supercell. The energy is measured from the top of the valence band of pure anatase TiO2 and the dotted line represents the Fermi level.
band bottom by about 0.12 eV, compared with that of pure rutile. Some gap states are located close to and are mixed with the conduction band edge. The PDOS analysis indicates that the gap states are mostly composed of the Sn 5s orbitals, and the Fermi level is pinned at the valence band maximum (zero energy). This reflects that the Sn at the Ti site exists as Sn4+.
Thus a red-shift of the absorption edge should appear for the substitution of Sn for Ti. It has been reported24 that, as the extent of Sn doping is increased, anatase TiO2 is converted to rutile TiO2 leading to an increase in the optical band gap. To verify this observation, we calculated the DOS and PDOS plots of Sn doped rutile TiO2
Properties of Sn-Doped TiO2 for the substitution of Sn for Ti using the 24-atom 2 × 2 × 1 supercell (Sn content of 4.17%) (Figure 2, parts d and d′). It can be clearly seen that the band gap increases by about 0.06 eV compared with the value obtained for the 48-atom 2 × 2 × 2 supercell (Sn content of 2.08%), which may be due to stronger interactions between the Sn 4p and Ti 3d orbitals. This is consistent with the observation that the increase in the content of Sn doping leads to a band gap increase.20 However, it should be noted that the band gap value of 1.89 eV calculated for the substitution of Sn for Ti by using the 24-atom supercell is smaller than that for pure rutile of 1.95 eV, still corresponding to a red-shift of the optical absorption edge. To verify another experimental observation that Sn-doping may result in a blue-shift of the optical absorption edge of anatase TiO2, we calculated the DOS and PDOS plots of undoped anatase TiO2 as well as Sn-doped anatase TiO2 using the 48-atom 2 × 2 × 2 supercell with the substitution of Sn for Ti (Figure 3). For the doped system (Figure 3, parts b and b′), most Sn 5s states are located at the bottom of the conduction band and are mixed with the Ti 3d states. Thus, the extension of the optical absorption edge into the visible-light region is not expected. The top of the valence band has no obvious shift while the conduction band bottom has a slightly upward shift of about 0.06 eV compared with that of the pure anatase. Consequently, the energy of electron excitation from the valence band to the conduction band has an increase of about 0.06 eV, which corresponds to a blue-shift of the optical absorption edge. This result may explain the experimental finding reported in ref 20. The formation energies calculated for the substitution of Sn for Ti are slightly larger in anatase TiO2 than in rutile TiO2 under both O-rich and Ti-rich conditions (Table 1). 4. Conclusions We have studied the electronic structures of substitutional Sn-doped TiO2 based on DFT calculations. The calculated formation energies indicate that the substitution of Sn for Ti is energetically favored over that for O. The substitution of Sn for Ti in rutile TiO2 leads to a band gap decrease due to the Sn 5s gap states in the conduction band. The substitution of Sn for O atom in rutile TiO2 introduces gap states of Sn 5p character close to the bottom of the conduction band, and the excitation from the valence band to the empty states above the Fermi level results in a blue-shift of the absorption edge. In rutile TiO2 with substitution of Sn for Ti, the band gap was calculated to increase as the extent of Sn doping increases. Furthermore, the substitution of Sn for Ti in anatase TiO2 is also found to increase the band gap. Consequently, the observed red-shift of the absorption edge in the Sn-doped TiO2 may arise from different kinds of Sn doping. Acknowledgment. This work is supported by the National Basic Research Program of China (973 program, Grant No.
J. Phys. Chem. C, Vol. 113, No. 2, 2009 653 2007CB613302), National Natural Science Foundation of China under Grant No. 10774091, Natural Science Foundation of Shandong Province under Grant No. Y2007A18, and the Specialized Research Fund for the Doctoral Program of Higher Education 20060422023. References and Notes (1) Hoffmann, M. R.; Martin, S. T.; Wonyong, C.; Bahnemann, D. W. Chem. ReV. 1995, 95, 69–96. (2) Arntz, F.; Yacoby, Y. Phys. ReV. Lett. 1966, 17, 857–860. (3) Tang, H.; Le´vy, F.; Berger, H.; Schmid, P. E. Phys. ReV. B 1995, 52, 7771–7774. (4) Asahi, R.; Morikawa, T.; Ohwaki, T.; Aoki, K.; Taga, Y. Science 2001, 293, 269–271. (5) Valentin, C. Di.; Pacchioni, G.; Selloni, A.; Livraghi, S.; Giamello, E. J. Phys. Chem. B 2005, 109, 11414–11419. (6) Burda, C.; Lou, Y.; Chen, X.; Samia, A. C.; Stout, J.; Gole, J. L. Nano Lett. 2003, 3, 1049–1051. (7) Irie, H.; Watanabe, Y.; Hashimoto, K. J. Phys. Chem. B 2003, 107, 5483–5486. (8) Khan, S. U. M.; Al-Shahry, M., Jr Science 2002, 297, 2243–2245. (9) Diwald, O.; Thompson, T. L.; Zubkov, T.; Goralski, E. G.; Walck, S. D.; Yates, J. T., Jr J. Phys. Chem. B 2004, 108, 6004–6008. (10) Yang, K.; Dai, Y.; Huang, B. B.; Han, S. H. J. Phys. Chem. B 2006, 110, 24011–24014. (11) Yang, K.; Dai, Y.; Huang, B. B. J. Phys. Chem. C 2007, 111, 12086–12090. (12) Sakthivel, S.; Kisch, H. Angew. Chem., Int. Ed. 2003, 42, 4908– 4911. (13) Umebayashi, T.; Yamaki, T.; Itoh, H.; Asai, K. Appl. Phys. Lett. 2002, 81, 454–456. (14) Valentin, C. Di.; Pacchioni, G.; Selloni, A. Chem. Mater. 2005, 17, 6656–6665. (15) Umebayashi, T.; Yamaki, T.; Yamamoto, S.; Miyashita, A.; Tanaka, S. J. Appl. Phys. 2003, 93, 5156–5161. (16) Yu, J. C.; Ho, W.; Yu, J.; Yip, H.; Wong, P. K.; Zhao, J. EnViron. Sci. Technol. 2005, 39, 1175–1182. (17) Yang, K.; Dai, Y.; Huang, B. B. J. Phys. Chem. C 2007, 111, 18985–18994. (18) Chen, X.; Burda, C. J. Am. Chem. Soc. 2008, 130, 5018–5019. (19) Yang, K.; Dai, Y.; Huang, B. B. Chem. Phys. Lett. 2008, 456, 71– 75. (20) Luo, H.; Takata, T.; Lee, Y.; Zhao, J.; Domen, K.; Yan, Y. Chem. Mater. 2004, 16, 846–849. (21) Oh, S.-M.; Kim, S. S.; Lee, J. E.; Ishigaki, T.; Park, D.-W. Thin Solid Films 2003, 435, 252–258. (22) Ozaki, H.; Iwamoto, S.; Inoue, M. Chem. Lett. 2005, 34, 1082– 1085. (23) Ozaki, H.; Iwamoto, S.; Inoue, M. Catal. Lett. 2007, 113, 95–98. (24) Li, J.; Zeng, H. C. J. Am. Chem. Soc. 2007, 129, 15839–15847. (25) Uchiyama, H.; Imai, H. Chem. Commun. 2005, 48, 6014–6016. (26) Mahanty, S.; Roy, S.; Sen, S. J Cryst. Growth 2004, 261, 77–81. (27) Lin, J.; Yu, J. C.; Lo, D.; Lam, S. K. J. Catal. 1999, 183, 368– 372. (28) Segall, M. D.; Lindan, P. J. D.; Probert, M. J.; Pickard, C. J.; Hasnip, P. J.; Clark, S. J.; Payne, M. C. J. Phys., Condens. Matter 2002, 14, 2717– 2744. (29) Vanderbilt, D. Phys. ReV. B 1990, 41, 7892–7985. (30) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865–3868. (31) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188–5192. (32) Pankove, J. I. Optical Processes in Semiconductors; Dover: New York, 1975; p 39.
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