Impurity Concentration Dependence of Optical Absorption for

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Impurity Concentration Dependence of Optical Absorption for Phosphorus-Doped Anatase TiO2 Yanhua Peng, Jingfu He, Qinghua Liu, Zhihu Sun, Wensheng Yan, Zhiyun Pan, Yanfei Wu, Suzhen Liang, Weiren Cheng, and Shiqiang Wei* National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei, Anhui 230029, People’s Republic of China ABSTRACT: The efficient absorption of visible light is crucial for improving the photocatalytic activity of foreign species-doped TiO2. With first-principles calculations, we explore the effects of phosphorus doping on mediating the photocatalytic activity of anatase. It is found that the P impurity tends to occupy the cation site in TiO2; more importantly, there exists a critical phosphorus concentration of about 0.7% for maximizing the absorption of solar light. The optical energy gap is narrowed by ∼0.3 eV at the low doping concentration of 0.7%, whereas it increases with P concentration at the higher P concentration region of 0.7
3.1 atm. %. These results suggest that the dopant concentration dependence might be responsible for numerous seeming controversies of optical absorption observed in experiments. This finding points to a possibility of tailoring the optical absorption of TiO2 by varying the dopant content.

I. INTRODUCTION Semiconductor photocatalysis has attracted considerable research efforts since the discovery of photoelectrochemical splitting of water on TiO2 electrodes.1 However, the large intrinsic band gap of TiO2 (∼3.2 eV) allows only the absorption of ultraviolet light with wavelengths less than 387 nm, but prohibits the effective absorption of visible light.2,3 Hence, there are still serious problems, especially the low photoelectrochemical efficiency and the difficulty in utilizing the visible light, to be solved. This obstacle makes the solar conversion efficiency of pure TiO2 rather low.4
6 To overcome this obstacle, many approaches have been tried to realize the cost and energy savings in converting sunlight into electric power or chemical energies.2,7 Among them, doping of foreign species, such as metal atoms,8
11 nonmetal ions,12
24 or codoping,25
27 to modify the electronic properties of TiO2 has been frequently used for extending the optical absorption edge into the visible light region. It turns out that doping nonmetal atoms, such as B,21 N,12 and C13 anion doping and S,14 I,16 and P15,17 cation doping, seems to be more successful. Among numerous potential cation dopants, phosphorus doping in TiO2 deserves special attention because it presents a novel photocatalysis activity.17,19 However, the actual effect of P doping on the optical property is still a matter of active debate. Yu et al.15 reported that phosphated mesoporous titania showed a blue shift in the UV
vis absorption band edge because of the quantum-size effect. K€or€osi et al.17 also observed that the absorption edge was shifted to a shorter wavelength after phosphoric acid treatment on titania due to a higher band gap. On the contrary, Zheng and co-workers28 observed a red shift of the absorption edge in the visible light region with band-gap r 2011 American Chemical Society

narrowing. Lin et al.18 reported that P doping improved absorption in the visible range and its band-gap energy moved to 3.05 eV. The theoretical methods have long been used as an efficient way to clarify these controversial results of experiments. Many publications have reported the dopant concentration influence on the absorption of visible light with different dopants in TiO2.29
32 However, the microscopic insight into the effect of P doping concentration on the photocatalytic activity of anatase is not completely performed, which demands an accurate analysis of atomic and electronic structures of P-doped TiO2 from both theoretical and experimental aspects. In this work, we have performed density functional theory (DFT) calculations to exploit the atomic occupation of phosphorus dopant and electronic structures on phosphorus-modified anatase TiO2. We find an interesting phenomenon that the electronic structure and optical energy gap of titania are strongly dependent on the phosphorus concentration. This finding provides a uniform interpretation on the seemingly controversial experimental observations on the photoactivity of P-doped TiO2.

II. COMPUTATIONAL DETAILS The first-principles DFT calculations were performed by the Vienna Ab-initio Simulation Package (VASP)33,34 based on the plane-wave method. Our calculations employed a generalized gradient approximation, the Perdew
Wang 91 exchange-correlation functional,35 and the ultrasoft pseudopotential.36 The basis Received: January 11, 2011 Revised: March 5, 2011 Published: April 06, 2011 8184

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Table 1. Optimized Structural Parameters of P CationDoped Anatase TiO2 a (Å)

b (Å)

c (Å)

undoped (exptl)

3.776

3.776

9.486

undoped (calcd) P-doped

3.800 3.798

3.800 3.798

9.581 9.574

P
O (Å)

P
O (Å)

1.940 1.727

2.001 1.779

Table 2. Calculated Formation Energies for P-Doped Anatase TiO2 formation energy (eV) type

subP
O

subP
Ti

Ti-rich O-rich

10.52 15.48

11.26 1.32

Figure 1. Schematic of the phosphorus cation-doped anatase supercell. The red spheres represent O atoms, the silver spheres represent Ti atoms, and the yellow sphere represents the P atom. The dotted circles denote schematically the positions of oxygen atoms before relaxation.

set cutoff was 350 eV, and the k-space integration was done with a 3  3  3 k-mesh.37 The convergence threshold for selfconsistent iteration was set at 10
4 eV/atom, and the lattice parameters and all the atomic positions were fully optimized until all components of the residual forces were smaller than 0.025 eV/ Å. The optimized lattice parameters of anatase TiO2 are a = 3.800 Å and c = 9.581 Å (listed in Table 1), in good agreement with experimental results,38 indicating that our methodology is reasonable. Calculations were conducted for a 288-atom anatase supercell containing one, two, three, four, six, and nine P atoms in the substitutional site of Ti atoms, corresponding to the P concentrations (CP) of 0.3, 0.7, 1.0, 1.4, 2.1, and 3.1 atm. %, respectively. The density of states (DOS) for P-doped anatase with different concentrations of phosphorus were calculated by using the tetrahedron method with Bl€ochl corrections.

III. RESULTS AND DISCUSSION First of all, to reveal whether the doped phosphorus impurity prefers to occupy the site of O (anion-doped) or Ti (cationdoped) in the anatase TiO2 crystal, we calculated the formation energies (Ef) of the substitutionally doped systems according to Ef ¼ EðP-dopedÞ
½EðpureÞ þ nμP
nμTi  Ef ¼ EðP-dopedÞ
½EðpureÞ þ nμP
nμO  Here, E(P-doped) is the total energy of the supercell containing the P impurity; E(pure) is the total energy of the ideal cell; and μP, μO, and μTi represent the chemical potentials of the P, O, and Ti atoms, respectively. The symbol n is the number of substitutional phosphorus atoms. In practice, the formation energy depends on the growth condition, which can be Ti-rich and O-rich or anything in between.39 Under the Ti-rich condition, the Ti chemical potential = was assumed as the energy of one atom in bulk Ti (μTi = μmetal Ti
7.726 eV), whereas the O chemical potential was calculated by the relationship μTi þ 2μO = μ(TiO2).31 Under the O-rich growth condition, the O chemical potential was assumed to be in equilibrium with O2 gas, that is, μO = μ(O2)/2 =
4.901 eV, whereas the chemical potential of Ti was calculated by the above formula. For the P impurity, the chemical potential was calculated according to μP = (1/4)[μ(P4O10)
5μ(O2)]. Correspondingly, we carried out the energetics calculation under different circumstances, and the obtained results are listed in Table 2. It is found that the formation energies for P substituting O in anatase under Ti-rich and O-rich

Figure 2. Density of states (DOS) for (a) pure anatase and P-doped configurations with various doping levels at (b) 0.3, (c) 0.7, (d) 1.0, (e) 1.4, (f) 2.1, and (g) 3.1 atm. %. The dotted line represents the Fermi level, whereas the solid line represents the valence band maximum of undoped anatase TiO2.

conditions are 10.52 and 15.48 eV, respectively. However, for P substituting Ti in the same conditions, the formation energies are 11.26 and 1.32 eV, respectively. This indicates that it is relatively easier to incorporate P atoms into the anatase TiO2 lattice by replacing Ti sites under the richer O condition. Furthermore, we have also considered several possible cases of the interstitial sites and calculated their formation energies. It turned out that a specific interstitial site where the P atoms are surrounded by four nearest O atoms, similar to that of B dopant in anatase,40 has the minimum formation energy (4.13 eV). However, even this minimum formation energy is much larger than that (1.32 eV) of the substitution case, indicating the energetically unfavorable occupancy of P interstitial in anatase as compared with the substitutional sites. On the basis of the above calculation results, we simulated the P cationdoped TiO2 anatase system with 288 atoms by using the 4  3  2 repetition of the unit anatase, as shown in Figure 1. The P
O bond 8185

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Figure 3. Electron transition energy for the configurations of (a) pure anatase and various P doping levels at (b) 0.3, (c) 0.7, (d) 1.0, (e) 1.4, (f) 2.1, and (g) 3.1 atm. %. The inset is the transition energy curve dependent on the P doping level.

lengths in phosphorus cation-doped anatase TiO2 are 1.727 and 1.779 Å, which are significantly contracted as compared with the undoped anatase (1.940 and 2.001 Å). This is reasonable because the P5þ radius (0.35 Å) is shorter than that of Ti4þ (0.68 Å), leading to the contraction of the bond lengths and the compression of the lattice. To investigate the electronic properties of P-doped anatase TiO2, we have calculated the DOSs of anatase TiO2 for various levels of phosphorus doping, and the obtained results are plotted in Figure 2. Our calculated energy gap of pure anatase TiO2 is about 2.3 eV. The band-gap underestimation compared with the experimental value (3.2 eV for anatase) is due to the well-known shortcoming in DFT.29 From Figure 2b,c, it is seen that, under lower doping concentrations (CP e 0.7 atm. %), doping with phosphorus in anatase does not result in significant variation of the conduction band, while there is a slight rise of the valence band maximum compared to the pristine anatase. With increasing of the phosphorus doping levels, the variation of the valence band maximum is more obvious (see Figure 2d
g). Particularly, at the doping concentration of 3.1 atm. %, a photoreactive state is formed on the top of the valence band (Figure 2g), making the valence band edge upshift by about 0.28 eV with respect to pure anatase. Meanwhile, the position of the conduction band is hardly shifted by the change of doping values. Thus, the band gap of TiO2 can be modified by a change of P doping levels. A phosphorus dopant atom has three unpaired electrons with strong P 3p character, similar to its neighboring O 2p states, leading to the strong hybridization between P and its neighboring O atoms. The full overlap of P 3p and O 2p then elevates the donor level to be above the valence band. Moreover, it is worthwhile to note that the DOSs of oxygen atoms far from the substituted P center and Ti atoms in the TiO2 lattice have little change compared with those of pure anatase. Consequently, the origin of the change of the optical energy gap mainly arises from the interaction of the neighboring atoms rather than an average effect from the whole lattice. It should be mentioned that our calculations were carried out starting from a common knowledge that the

solubility of nonmetallic dopants in TiO2 is quite low, generally not higher than 5%. This is in contrast with some of the previous studies,20,32 which were focused on P-doped TiO2 with the nominal concentrations of the dopants and neglected the fact that not all the dopant atoms were substituted at the Ti sites in the host lattice. To evaluate the optical absorption of a photocatalyst, the decisive parameter is the transition energy defined as the energy difference between the valence band maximum and the lowest unoccupied level (i.e., the Fermi level), not simply the band-gap energy. Figure 3 displays the optical energy gap for different doping levels extracted from our band structure calculation. It should be noted that, for compatibility with the experimental result, we modified the calculated band gaps of various configurations with reference to that of pure TiO2 (3.2 eV), as approved by previous studies.41 In Figure 3, the yellow
purple areas represent variations in the valence band maximum and the red dotted line is the location of the Fermi level. At the low doping concentrations of 0.4 and 0.7 atm. %, the transition energies are 2.96 and 2.90 eV, respectively, smaller than the band-gap energy of anatase TiO2. At higher levels of P doping, it is found that the position of the Fermi level lies above the conduction band minimum and upshifts gradually with the increase of the dopant concentration. Correspondingly, the transition energies are 3.01, 3.10, 3.38, and 3.45 eV for the P doping levels of 1.0, 1.4, 2.1, and 3.1 atm. %, respectively. To show the relationship between the optical transition energy and impurity doping level more explicitly, we plot in the inset of Figure 3 the dependence of the transition energy on the P doping concentrations. Clearly, there exits a minimum point of the optical transition energy at the P concentration of about 0.7 atm. %. Furthermore, the optical transition energy becomes larger than the intrinsic band gap of TiO2 (3.2 eV) when the P concentration approaches about 1.6 atm. % or higher. These results suggest that the impurity doping content plays a significant role in mediating the photoabsorption of anatase TiO2. To clarify the origin of the impurity concentration-dependent optical absorption, we explore the variation of the Fermi level 8186

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The Journal of Physical Chemistry C with the P doping concentration on the basis of a degenerate semiconductor model.42 From Figure 3, we note that the Fermi level increases monotonically with the impurity levels. The upshift of the Fermi level is caused by the excessive electrons donated by the P cation dopants, which serve as an n-type of impurity in TiO2.43 For n-type semiconductors, the Fermi level is related to the donor concentration according to the following equation44   ND EF ¼ EC þ k0 T ln NC Here, EC represents the conduction band minimum, ND is the donor concentration, and NC is the effective density of states in the conduction band. From our calculations, when the phosphorus concentration is 0.7 atm. %, which corresponds to the donor concentration (ND) of 1020 cm
3, the Fermi level is located at nearby the bottom of the conduction band. With more phosphorus atoms doping in anatase (g1.0 atm. %), the position of the Fermi level is lifted to be above the conduction band minimum (see Figure 3), and then P
TiO2 becomes a neardegenerate or degenerate semiconductor. We note that the critical concentration for P-doped TiO2 being a degenerate semiconductor is close to those of P-doped Si and Ge (4  1019 and 8  1019 cm
3 for P
Si and P
Ge, respectively).42 For a degenerate semiconductor, as the Fermi level is below the bottom of the conduction band, like in the case of 0.7 atm. % P doping in TiO2, the transition energy is about 0.30 eV smaller than the intrinsic band gap of anatase. Thus, the optical absorption edge for lightly P-doped TiO2 is red shifted to 430 nm, providing an explanation for some experimental observations that the optical absorption and photocatalytic activity of P-doped anatase TiO2 in the visible light region (400
550 nm) are enhanced.18,28 However, upon further increasing the dopant concentrations, the Fermi surface is mediated deep inside the conduction band, and the absorption edge of TiO2 is shifted to higher energies. Consequently, this leads to an increase of the photon excitation energy and induces a significant blue shift of the absorption edge, as discovered in many experimental studies.17,19 Considering the effect of doping concentration on the Fermi level and the band structures, we come to the conclusion that there exists a critical phosphorus concentration with a minimum transition energy for P cation-doped anatase TiO2 systems. The enhancement of visible light absorption of TiO2 is critical for its further applications in solar energy conversion. Although many experimental studies reported that visible light absorption could be improved via doping of various impurities in TiO2, such as S,14 P,18,28 and transition-metal elements,10 at present, our knowledge on the relationship of doping concentration and absorption improvement is still somewhat insufficient. In some cases,17,20,28 it was found that high doping levels in TiO2 do not necessarily result in high absorption. This indicates that the enhancement of optical absorption of TiO2 is not linear with the impurity concentration. Usually, the impurity dopant atoms incorporated into the TiO2 lattice are substituted on the host atom sites (Ti or O sites). Like phosphorus dopants in P-doped TiO2, the doped anion and cation elements act as donors or acceptors, introducing new photoreactivity states to narrow the optical energy gap. Because the donor or acceptor elements can mediate the Fermi level into the conduction band or valence band depending on the

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impurity doping concentration, the optical absorption for these doped TiO2 cases is likely to have a critical point. Therefore, the theoretical intuition we discovered in TiO2 is possibly applicable to other n- or p-type semiconductor systems and explains numerous experimental controversies of optical absorption in doped TiO2. It should be pointed out that the critical doping concentration might not be the same for different impurity doping systems, and case-by-case studies are needed. This is easy to understand, because different impurity elements contribute diverse amounts of charge carriers to the semiconductor host and/or have a distinct ability to hybridize with the host bands.41 The implication of our calculation results is that they address the necessity of considering the influence of impurity concentration when one intends to modify the optical absorption of TiO2 for photocatalysis purposes via the doping approach. The effect of oxygen vacancies (VO's) cannot be ignored in the visible light sensitivity and the photocatalytic activity because VO's are a common defect in TiO2.45,46 Many studies of N-doped TiO2 have also discussed the role of the oxygen vacancies in the visible light absorption and in the photocatalytic activity.47 However, the common defect is rarely to be considered in P cation-doped TiO2 because the P dopant is liable to form a donor level at the valence band edge and the Coulomb repulsion between excess electrons and oxygen vacancies prevents the oxygen vacancies from forming. In addition, the formation energy of oxygen vacancies in P cation-doped TiO2 is very large, indicating the impossibility of forming oxygen vacancies in P-doped TiO2. In addition, there is an important issue worth mentioning. Generalized gradient approximation (GGA) is a common theoretical method for standard density functional theory (DFT), but the method has a self-interaction defect. GGA þ U and hybrid functionals are used to correct some of the inadequacies. Because the object of our calculation is the bulk form of the substitutional site model, there are few differences for the calculation of structural parameters and P-doped placeholders from the approaches of GGA and GGA þ U.48 Although strengthening the Coulomb repulsion through GGA þ U makes the band gap widen, thus affecting the DOS results, the overall trend remains. Consequently, it still can be used as a reference for experimental work.

IV. CONCLUSIONS Using the density functional theory calculations, we have investigated the dopant concentration dependence of electronic and photoabsorption properties of the P-doped TiO2 system. An interesting finding regarding the photoabsorption of P-doped TiO2 is presented; that is, there exists a critical phosphorus doping concentration (0.7%) for achieving the maximum absorption of solar light. At low doping concentration (1.6%), the optical energy gap of photoexcitation is blue shifted as a result of the upshift of the Fermi level that is located deep inside the conduction band. This theoretical picture provides some insights into understanding many controversial experimental observations in the nonmetallic element-modified TiO2 and may also be applicable to other cation-doped oxide systems. 8187

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’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (Grant Nos. 10725522, 10979044, 10979041, and 11079004) and Knowledge Innovative Program of The Chinese Academy of Sciences (KJCX2-YW-N40). ’ REFERENCES (1) Fujishima, A.; Honda, K. Nature 1972, 238, 37. (2) Bard, A. J.; Fox, M. A. Acc. Chem. Res. 1995, 28, 141. (3) Hadjiivanov, K. I.; Klissurski, D. G. Chem. Soc. Rev. 1996, 25, 61. (4) Fox, M. A.; Dulay, M. T. Chem. Rev. 1993, 93, 341. (5) Hoffmann, M. R.; Martin, S. T.; Choi, W.; Bahnemann, D. W. Chem. Rev. 1995, 95, 69. (6) Chen, X.; Mao, S. S. Chem. Rev. 2007, 107, 2891. (7) Heller, A. Acc. Chem. Res. 1995, 28, 503. (8) Choi, W.; Termin, A.; Hoffmann, M. R. J. Phys. Chem. C 1994, 98, 13669. (9) Matsumoto, Y.; Murakami, M.; Shono, T.; Hasegawa, T.; Fukumura, T.; Kawasaki, M.; Ahmet, P.; Chikyow, T.; Koshihara, S.y.; Koinuma, H. Science 2001, 291, 854. (10) Ikeda, T.; Nomoto, T.; Eda, K.; Mizutani, Y.; Kato, H.; Kudo, A.; Onishi, H. J. Phys. Chem. C 2008, 112, 1167. (11) Bechstein, R.; Kitta, M.; Sch€utte, J.; K€uhnle, A.; Onishi, H. J. Phys. Chem. C 2009, 113, 3277. (12) Asahi, R.; Morikawa, T.; Ohwaki, T.; Aoki, K.; Taga, Y. Science 2001, 293, 269. (13) Khan, S. U. M.; Al-Shahry, M.; Ingler, W. B. Science 2002, 297, 2243. (14) Umebayashi, T.; Yamaki, T.; Itoh, H.; Asai, K. Appl. Phys. Lett. 2002, 81, 454. (15) Yu, J. C.; Zhang, L.; Zheng, Z.; Zhao, J. Chem. Mater. 2003, 15, 2280. (16) He, J.; Liu, Q.; Sun, Z.; Yan, W.; Zhang, G.; Qi, Z.; Xu, P.; Wu, Z.; Wei, S. J. Phys. Chem. C 2010, 114, 6035. (17) K€or€osi, L.; Papp, S.; Bertoti, I.; Dekany, I. Chem. Mater. 2007, 19, 4811. (18) Lin, L.; Lin, W.; Zhu, Y. X.; Zhao, B. Y.; Xie, Y. C. Chem. Lett. 2005, 34, 284. (19) Korosi, L.; Dekany, I. Colloids Surf., A 2006, 280, 146. (20) Li, F.; Jiang, Y.; Xia, M.; Sun, M.; Xue, B.; Liu, D.; Zhang, X. J. Phys. Chem. C 2009, 113, 18134. (21) Zhao, W.; Ma, W.; Chen, C.; Zhao, J.; Shuai, Z. J. Am. Chem. Soc. 2004, 126, 4782. (22) Raj, K. J. A.; Ramaswamy, A. V.; Viswanathan, B. J. Phys. Chem. C 2009, 113, 13750. (23) Long, R.; English, N. J. J. Phys. Chem. C 2009, 113, 9423. (24) Randeniya, L. K.; Bendavid, A.; Martin, P. J.; Preston, E. W. J. Phys. Chem. C 2007, 111, 18334. (25) In, S.; Orlov, A.; Berg, R.; García, F.; Pedrosa-Jimenez, S.; Tikhov, M. S.; Wright, D. S.; Lambert, R. M. J. Am. Chem. Soc. 2007, 129, 13790. (26) Li, D.; Haneda, H.; Hishita, S.; Ohashi, N. Chem. Mater. 2005, 17, 2588. (27) Lin, L.; Zheng, R. Y.; Xie, J. L.; Zhu, Y. X.; Xie, Y. C. Appl. Catal., B 2007, 76, 196. (28) Zheng, R.; Lin, L.; Xie, J.; Zhu, Y.; Xie, Y. J. Phys. Chem. C 2008, 112, 15502. (29) Di Valentin, C.; Pacchioni, G.; Selloni, A. Phys. Rev. B 2004, 70, 085116. (30) Yang, K.; Dai, Y.; Huang, B. J. Phys. Chem. C 2007, 111, 12086.

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