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J. Phys. Chem. B 2006, 110, 17866-17871
DFT Description on Electronic Structure and Optical Absorption Properties of Anionic S-Doped Anatase TiO2 FengHui Tian and ChengBu Liu* Institute of Theoretical Chemistry, Shandong UniVersity, Jinan, 250100 China ReceiVed: April 15, 2006; In Final Form: June 7, 2006
Plane-wave-based pseudopotential density functional theory (DFT) calculations are used to characterize the doping effect of S substituting for O in anatase TiO2. Through band structure calculation, a direct band gap is predicted in TiO2-xSx. Electronic structure analysis shows that the doping S could substantially lower the band gap of TiO2 by the presence of an impurity state of S 3p on the upper edge of the valence band. Excitations from the impurity state of S 3p to the conduction band may be responsible for the red shift of the absorption edge observed in the S-doped TiO2. The band gap lowering and red shift of the absorption edge are found to increase as the sulfur concentration increases.
1. Introduction Titanium dioxide (TiO2) has received a lot of attention as a promising semiconductor photocatalyst since it was found to be efficient for water splitting.1 Nevertheless, it is only activated upon UV excitation (about 3% of the solar spectrum) because of its wide band gap (3.2 eV for anatase). To utilize solar energy effectively, many methods are used to engineer the band gap of TiO2. Recently, non-metal-doped TiO2 received a lot of attention since the doping of nonmetals (S, N, C, B, P, F, etc.) could efficiently extend the photoresponse of TiO2 to the lowenergy (visible) region.2-11 At first, Asahi et al. reported their results on N-doped TiO2.2 It was described that N was substituted on the lattice O site, displaying as an anion in TiO2-xNx with significant visible light photocatalytic activity. After that, TiO2-xNx became the aim of a large number of experimental3,4 and theoretical investigations.5-7 Anionic S-doped TiO2 had been synthesized successfully by Umebayashi et al.12,13 They suggested that S doped on the lattice oxygen site in TiO2 induces visible light response for the material. Good performance reported subsequently made Sdoped TiO2 deserving of being investigated in a detailed manner. Sathish et al.4 described in their investigation on N-doped TiO2 that the as-prepared N-doped TiO2 is only approximately 50% active compared to S-doped TiO213 after normalizing variables. Asahi et al.2 evidenced that the substitutional doping of N or S for O in the anatase TiO2 was the most effective among several nonmetals because their p states contribute to the band gap narrowing by effective mixing with O 2p states, based on a theoretical calculation under local density approximation (LDA). S-doped ZnO nanowires (4 atom % of sulfur) have also been synthesized successfully by Bae et al.; in their job S-doping is expected to modify the electrical and optical properties effectively because of the large electronegativity and size differences between S and O.14 It is mentioned that band gap engineering might be possible because of the larger band gap of ZnS (3.66 eV) compared to that of ZnO. In this regard, the smaller band gap of TiS2 (0.3 eV or so)15 can be helpful in the band gap lowering of TiO2. On the microscopic side, exploring factors dominating photocatalytic activities, providing useful information for the * Corresponding author. E-mail:
[email protected].
development of new highly active photocatalyst materials, is of value and importance. Umebayashi et al.12 have ever pointed out that the mixing of S 3p with O 2p on the upper edge of the valence band helps the doped material to be active under visible light irradiation based on a calculation in a two-unit-cell supercell. Yamamoto et al.16 reported their theoretical results on S-doped rutile TiO2. There is a need to investigate S-doped anatase TiO2 more thoroughly. In this article, we will provide a systematical study of the S-doped anatase TiO2 system to complete three tasks: first, provide electronic structure analysis, to make clear how doping S affects the material; second, disclose the optical absorption behavior changed by doping S; third, check the situation under different doping levels to explore the concentration-dependent behavior of electronic and optical absorption properties of TiO2. 2. Computational Details The plane-wave-based density functional theory (DFT) calculation was performed using the CASTEP program17 with the core orbitals replaced by ultrasoft pseudopotentials, and a kinetic energy cutoff of 300 eV. The doping effects are modeled by replacing oxygen atom with one sulfur atom. We considered 72, 48, and 24 atom supercells denoted as (b), (c), and (d) to simulate doping concentration of 0.0139, 0.0208, and 0.0417, respectively. Pure TiO2 denoted as (a) was also calculated for comparison. The Monkhorst-Pack k-point sampling is set as 5 × 5 × 2, 5 × 3 × 2, 3 × 3 × 2, and 3 × 2 × 2 for supercells from (a) to (d). All the electronic structures and the optical absorption spectra were calculated on the corresponding optimized crystal geometries. The generalized gradient approximation (GGA) with the PBE exchange correlation functional was adopted. Test calculations showed that an increase in the number of k-points yields no significantly different results to the total energy (0.3 × 10-2 or so for (b) and 0.2 × 10-3 or so for (d)) at cutoff energy of 300 eV. Optimized structural parameters of a, c, and u (u ) dap/c, dap is the apical Ti-O bond length) for pure anatase TiO2 are listed in Table 1, which shows very good, consistent with experimental18 and theoretical predication.21 A scissors operator of 1.40 eV was introduced to shift the conduction levels to be consistent with the measured value of the band gap.2,7
10.1021/jp0635462 CCC: $33.50 © 2006 American Chemical Society Published on Web 08/22/2006
Properties of Anionic S-Doped Anatase TiO2
J. Phys. Chem. B, Vol. 110, No. 36, 2006 17867
TABLE 1: Structural Parameters of Anatase TiO2 this work a (Å) c (Å) u
3.885 9.690 0.208
experimental 3.782 9.502 0.208
18
theoretical
21
3.692 9.671 0.206
The absorption curves can be obtained from the imaginary part of the dielectric constant from CASTEP calculation. The imaginary part of the dielectric constant 2 is described as
2(pω) )
2e2π Ω0
|〈Ψkc|uˆ ‚r|ΨkV〉|2δ[Ekc - EkV - pω] ∑ ∑ c,ν k
where Ω is the volume of the elementary cell, k represents the k point, ω is the frequency of the incident light, c and ν represent the conduction and valence bands, respectively. Ψkc and ΨkV are the eigenstates, r is the momentum operator, and uˆ is the external field vector. 3. Results and Discussions 3.1. Electronic Structure. Band structure plots for pure and doped TiO2 (taking model (d) as an example) are presented in Figure 1. It indicates that pure TiO2 (Figure 1a) is an indirect band gap semiconductor with a minimum band gap between M and G, which is very consistent with most of the theoretical7,19 and experimental results.20 Although a direct band gap is supported in a FLAPW calculation, it is also mentioned in the job that the band gap that is direct or indirect is quite sensitive to the crystal configuration.21 The band gap transformation between pure and S-doped TiO2 disclosed here seems to be coincident with the band gap configuration-dependent argument. It is clear that S-doped anatase TiO2 (Figure 1d) is turned into a direct band gap semiconductor at G, which is also true for S-doped rutile TiO2.16 Further analysis shows that the direct
band gap property is retained for anatase TiO2 at different S-doping concentration (see Supporting Information). For a semiconductor photocatalyst, effective absorption is one of the most important properties. So this kind of transformation will be a significant advantage for the doped material to perform better in photocatalysis. Density of states plots calculated for TiO2 with different levels of S doping are presented in Figure 2 and indicate how the band gap of the system varies with sulfur content. (CASTEP takes the energy of the highest occupied orbital as the energy zero by default.) Concentration-dependent behavior of band gap energy is evident. Band gap energies of 3.203, 2.753, 2.669, and 2.545 eV are corresponding to doping levels of 0.0000, 0.0139, 0.0208, and 0.0417 (Table 2 and Figure 2), respectively. Compared with the band gap of pure TiO2, the lowering values by different S-doping levels of 0.0000, 0.0139, 0.0208, and 0.0417 are 0.000, 0.450, 0.534, and 0.658, respectively (Table 2). An almost linear reduction of band gap energy with the doping concentration enhancement can be found just as disclosed in the N doping case.7 We also find that the width of the valence band increases with the doping concentration increasing.16 Moreover, the lower doping concentration is considered to be more significant in the practical application.7 The higher doping levels such as those considered in the S-doped rutile system (0.50, 0.75, 1.00, etc.) can be regarded as O-doped TiS2,16 which in our consideration may to some extent deviate from the scope of S-doped materials. So our calculation concentrated on the lower doping levels. In Figure 2, contributions from each of the related orbitals to total density of states are displayed by partial density of states (PDOS). Comparison between doping cases from (b) to (d) with pure (a) indicated that the engineering to the band gap of TiO2 is actualized by the presence of the S 3p state localizing slightly above the upper edge of the valence band. Excitations from the impurity state of S 3p to a conduction band may be responsible
Figure 1. Band structure plots for pure (a) and S-doped anatase TiO2 at 0.0417 doping concentration (d).
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Figure 2. Density of states plots for different levels of S doping in anatase TiO2. The unit for density of states is states/eV‚unit cell, y: doping concentration.
for the red shift of the absorption edge observed in the S-doped TiO2.12-13 S 3s, whose contribution is mainly embodied in the peak at -11 eV or so, does not take part in the bonding. So is the O 2s orbital at about -17 eV. Ti 3p and Ti 3s are located at a much lower energy level far from the valence band. O 2p,
Ti 3d, and S 3p consist of valence and conduction bands for the doped TiO2 of (b), (c), and (d). For the pure TiO2 (a), the upper edge of the valence band is dominated by the O 2p orbital and the bottom of the conduction band is mainly due to the Ti 3d orbital. Then, the position of the S 3p state reveals that the
Properties of Anionic S-Doped Anatase TiO2
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TABLE 2: Band Gap Energy of Pure and S-Doped TiO2, the Value after Correction of Scissor Operator (+1.4 eV), the Lowering Value of Band Gap Corresponding to the Band Gap of Pure TiO2, ∆, the Calculated Absorption Edge Based on the Band Gap Energy, and the Distance from the Bottom of the Impurity State Band Arising from S Doping to the Upper Edge of the Valence Band
model
concn
pure TiO2 (b) (c) (d)
0.0000 0.0139 0.0208 0.0417
scissor band gap operator (eV) (+1.4 eV) 1.803 1.353 1.269 1.145
3.203 2.753 2.669 2.545
∆ (eV)
absorption edge (nm)
D (eV)
0.450 0.534 0.658
387 451 465 488
0.208 0.066 0.002
TABLE 3: Population on the S Atom, the Three Ti Atoms Bonded to the S Atom, and Bond Lengths of the Three S-Ti Bonds in Different Models model
S population
Ti population
(b) (c) (d)
-0.10 -0.11 -0.15
0.74(2), 0.80 0.74(2), 0.80 0.76(2), 0.81
S-Ti bond length (Å) 2.219(2) 2.219 (2) 2.255 (2)
2.323 2.331 2.360
alteration of the band gap of TiO2 by S substituting for O is realized by the interaction between S 3p and O 2p.2,12 To check the existing type of the S 3p state, an examination of the distance from the bottom of the S 3p state band to the upper edge of the valence band was made. We found that the distance reduces with the increasing of doping concentration (Table 2, the last column). Moreover, at higher doping concentration of 0.0417 they are nearly mixing together with a very small separation up to 0.002 eV. So it can be concluded that S 3p is slightly localized above the valence band O 2p at low doping concentration, and then they gradually become mixed with the increasing doping concentration. Umebayashi et al.12 have ever calculated S-doped anatase TiO2 in a twounit-cell supercell, which should be the case at a higher doping level. So the explanation that the mixing of S 3p and O 2p extends the width of the valence band so as to induce visible light activity for TiO2 is accepted. In this regard, our results are very consistent with their results. Lin et al.7 also found in their study of N-doped TiO2 that at the doping concentration of at least 20% the N 2p states would mix with the O 2p valence band. In this work, a mixing between S 3p and O 2p can be found at about 4.2% for S-doped anatase TiO2, which is a positive factor for the carrier transfer, just as Asahi et al. emphasized.2 In the S-doped rutile system, S 3p is found to play almost the same role with similar existing type,16 which impressed to us that the S 3p orbital seems to be very suitable in both energy and electron structure to interact with the O 2p orbital in the semiconductor oxides. When S substitutes on the O site, three S-Ti bonds are formed. From the inorganic chemistry point of view, we make bond analysis to help check the doping effect of S. The lengths of three S-Ti bonds are listed in Table 3. Among them, two are degenerate and shorter, and one is longer. Because S 3s did not take part in bonding, the S-Ti bonds should form between S 3p and Ti 3d orbitals. Taking S 3p in the (d) plot of Figure 2 as an example, the small peak on the upper edge of the valence band should be a bonding peak. The one at -3.5 eV or so is another bonding peak. According to the relationship between bond length and bond strength, the former peak corresponds to the longer S-Ti bond; the latter correlates to the shorter two. With a weaker bond and a higher energy level, the former bonding peak separates from the O 2p valence band a little to localize in the band gap. As far as bonding type is concerned,
TABLE 4: Relation of V/V0 ∼ Doping Concentration doping level V/V0
0.0000 1.000
0.0139 1.026
0.0208 1.035
0.0417 1.057
a Note: V, the volume of the optimized structure for doped models; V0, the volume of the optimized structure for the undoped models of the same dimension; V/V0, the ratio of the optimized volume before and after doping.
the three bonds can be speculated upon as two are σ bonds between S 3p and Ti 3d and one is a d-p π coordination bond with two electrons all coming from S 3p. The two σ bonds formed degenerately with a stronger strength and lower energy level. The d-p π coordination bond is weaker with a higher energy level. They are all components of the valence band in the doped TiO2. From the distribution of density of states (Figure 2) of the two related orbitals S 3p and Ti 3d, we can see that this explanation is creditable. For the bonding peak at the upper edge of the valence band, contribution from the Ti 3d orbital is negligible. Besides, Mulliken population analysis shows that, independent of its concentration in the crystal, the charge on the S ion was about -0.11 as shown in Table 3. The same situation of the almost identical population for the N atom at different doping level is also reported for the N-doped system.7 The population values are -0.44 for the O site in the pure TiO2. The much lowered charge population value indicates a large oxidation occurred. It is obvious that the doping atom suffered serious effect from its environment in the crystal. And the three bonding Ti atoms are reduced slightly. The population on the three Ti atoms are decreased to +0.76(2) and +0.80 or so as shown in Table 3, which is +0.88 in the pure TiO2. This indicates to us that the oxidation is mostly due to neighboring oxygen ions. And we believe that the larger ion radius and lower electronegativity of S than O play an important role in it.14 Geometrically, the direct effect of the substitution of O by S with a larger ion radius should be an expansion of the unit cell of TiO2, which can be a probe of the creditability of the calculations. To validate it, we checked the volume of the optimized supercells before and after S doping. Calculation results show that the expansion of the unit cell due to S doping is present regardless of doping level and becomes more evident with the increase of the doping concentration (Table 4). An almost linear relationship between doping level (0.0000, 0.0139, 0.0208, and 0.0417) and volume ratio V/V0 before and after doping (1.000, 1.026, 1.035, and 1.057) was disclosed. This result is consistent with the expectation for the larger ion radius substitution of S for O. Calculations on the S-doped rutile system have also disclosed the same law.16 It confirmed that our simulation on the S-doped anatase TiO2 systems is creditable. For a doping impurity, it usually functions through the differences in both macroscopic (geometrical) and microscopic (electronic) structures. Co-effect of these two kinds of structures determines the properties of the doped system. Except for the native differences of S atoms and O atoms in electronic structure, the alternation in geometrical structure can be attributed to one of the origins of the modification of the electron structure of the whole system. An extra calculation seems to be powerful evidence to this (Figure 3). Taking (d) as an example, constructing a (d)-u model by substituting one O atom with one S atom in an optimized pure TiO2 lattice of the same dimension as (d) without further geometry optimization, we found in the subsequent band structure analysis that the direct band gap property can still be achieved in this (d)-u model with a larger band gap of 1.407 eV, which is much narrower (1.145 eV, Table 2) for the optimized (d) model. The effect of geometry change on the
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Figure 3. Band structure plots for (d) and (d)-u, the unoptimized (d) model.
tion, so as to create absorption edge red shift and visible light activity in the range of 400-500 nm. 4. Conclusions Based on all of the above, we can see that anionic S doping is an efficient way to induce visible light activity for anatase TiO2 by providing S 3p state on the upper edge of the valence band. The doping concentration-dependent behavior of the band gap energy and the red shift of the absorption edge were evidenced. Acknowledgment. This work was supported by the National Natural Science project (20373033) and Project 973 (2004CB719902) of China. Figure 4. Absorption spectra of TiO2 with different S-doping concentration (pure and three doping cases with doping levels of 0.0000, 0.0139, 0.0208, and 0.0417).
electronic structure is obvious.16 The larger ion radius of S is favorable to the band gap lowering.14 In addition, the still retained direct band gap property in the (d)-u model clearly indicates that the native difference of S and O in the electronic structure is the origin of the indirect to direct band gap transformation. Thus, it is both the geometrical and electronic structures functioning externally and internally that determine the property of the doped system. 3.2. Absorption Spectra. Correspondingly, Figure 4 indicates the variation of absorption with sulfur content. Red shift of the absorption edge can be found for the anionic S doping, regardless of doping concentration. The absorption edge is 387, 451, 465, and 488 nm for the pure (a), (b), (c), and (d) models, corresponding to the doping level of 0.0000, 0.0139, 0.0208, and 0.0417, respectively (Table 2). It can be speculated that the presence of the S 3p state on the upper edge of the valence band reduced the electron transition distance for optical absorp-
Supporting Information Available: Band structure plots for S-doped anatase TiO2 at 0.0139 and 0.0208 doping levels. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Fujishima, A.; Honda, K. Nature 1972, 238, 37. (2) Asahi, R.; Morikawa, T.; Ohwaki, T.; Aoki, K.; Taga, Y. Science 2001, 293, 269. (3) Lindgren, T.; Mwabora, J. M.; Avendano, E.; Jansson, J.; Hoel, A.; Granqvist, C.-G.; Lindquist, S.-E. J. Phys. Chem. B 2003, 107, 5709. Irie, H.; Watanabe, Y.; Hashimoto K. J. Phys. Chem. B 2003, 107, 5483. Gole, J. L.; Stout, J. D.; Burda, C.; Lou, Y.; Chen, X. J. Phys. Chem. B 2004, 108, 1230. Diwald, O.; Thompshon, T. L.; Zubkov, T.; Goralski, E. G.; Walck, S. D.; Yates, J. T., Jr. J. Phys. Chem. B 2004, 108, 6004. Nakamura, R.; Tanaka, T.; Nakato, Y. J. Phys. Chem. B 2004, 108, 10617. Sakthivel, S.; Kisch, H. ChemPhysChem 2003, 4, 487. (4) Sathish, M.; Viswanathan, B.; Viswanath, R. P.; Gopinath, Ch. S. Chem. Mater. 2005, 17, 6349. (5) Di Valentin, C.; Pacchioni, G.; Selloni, A. Phys. ReV. B 2004, 70, 085116. (6) Di Valentin, C.; Pacchioni, G.; Selloni, A.; Livraghi, S.; Giamello, E. J. Phys. Chem. B 2005, 109, 11414.
Properties of Anionic S-Doped Anatase TiO2 (7) Lin, Zh.; Orlov, A.; Lambert, R. M.; Payne, M. C. J. Phys. Chem. B 2005, 109, 20948. (8) Khan, S. U. M.; Al-Shahry, M.; Ingler, W. B., Jr. Science 2002, 297, 2243. (9) Zhao, W.; Ma, W.; Chen, Ch.; Zhao, J.; Shuai, Zh. J. Am. Chem. Soc. 2004, 126, 4782. (10) Lin, L.; Lin, W.; Zhu, Y.; Zhao, B.; Xie, Y. Chem. Lett. 2005, 34, 284. (11) Li, D.; Haneda, H.; Hishita, Sh.; Ohashi, N. Chem. Mater. 2005, 17, 2596. (12) Umebayashi, T.; Yamaki, T.; Itoh, H.; Asai, K. Appl. Phys. Lett. 2002, 81, 454. (13) Umebayashi, T.; Yamaki, T.; Tanaka, S.; Asai, K. Chem. Lett. 2003, 32, 330. (14) Bae, S. Y.; Seo, H. W.; Park, J. J. Phys. Chem. B 2004, 108, 5206.
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