First-principle study of electronic structures and optical properties of chromium and carbon co-doped anatase TiO

(1)

First-principle study of electronic structures and optical properties of chromium and carbon co-doped anatase TiO

2

H.X. Zhu

^a,b

, J. – M. Liu

^b,c,n

aCollege of New Energy and Electronic Engineering, Yancheng Teachers University, Yancheng 224002, China

bLaboratory of Solid State Microstructures and Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

cInstitute for Advanced Materials, Hubei Normal University, Huangshi 435002, China

a r t i c l e i n f o

Article history:

Received 19 April 2016 Received in revised form 23 May 2016

Accepted 30 May 2016 Available online 2 June 2016 Keywords:

Anatase TiO2

Cr-C codoping Electronic structure Optical properties

a b s t r a c t

The band structure, density of states, electron density difference, and optical properties of Cr and C co- doped anatase TiO2are studied usingfirst principles calculations under the framework of the density functional theory. We mainly discuss three possible Cr–C adjacent co-doped configurations, where one Cr atom and one C atom substitute for one Ti atom and O atom respectively. The band structures show that the sub-bands induced mainly by C-2pstate and Cr-3dstate narrow the effective band gap down to 0.86 eV and 1.19 eV for different doped configurations. Doped Cr and C ion have different degree polarization, which will promote the electrons and holes separating. The calculated optical absorption spectrum exhibits shifts of the absorption edges of the three Cr–C co-doped TiO2samples towards the visible light region.

1. Introduction

Metal oxide semiconductors, such as ZnO, In2O3, Cu2O, TiO2, and so on, have beenﬂourished in various semiconductor applications including spintronics [1], photovoltaics [2] and photocatalysis [3] etc. In developing those novel materials, chemical substitution or “doping” into those semiconductors by a foreign species has been one of the most powerful methods for tuning or altering the basic electronic band structures of the intrinsic semiconductors [4,5]. Among the family of metal-oxide semiconductors, titanium dioxide (TiO2) is one of the most promising photocatalysis for solar light utilization because of its high chemical and thermal stability, strong catalytic activity, and non- toxicity etc. It has been the most widely studied and may be used to split water, clean up environment such as purifying water and air, degrade environmental pollutants, and convert photo-electrochemical energy under solar light irradiation[6–9].

However, the intrinsic band gap of anatase TiO2is3.2 eV[10], which means that anatase TiO2can only be activated by ultraviolet light irradiation. That is to say, the photo-electrochemical energy conversion efﬁciency of TiO2for using solar light energy is rather low because the ultraviolet light only accounts for four percent of the solar energy. In order to improve the efﬁciency of harvesting the solar energy, the best ideal band gap value should be2.0 eV,

which can realize the visible light absorption of TiO2. Narrowing the band gap of TiO2has been acknowledged as the main avenue for enhancing the performance of its photo-electrochemical energy conversion. So far, many experimental and theoretical works have been carried out to modify the band gap of titanium dioxide [11–15], and shift its absorption edge toward the visible light region.

Doping TiO2with different foreign elements is one of the most effective and direct ways to tailor the band edges[16,17]. Those different foreign elements may be non-metallic elements or transition metals. For non-metallic elements, those with thep- orbital energy higher than that of oxygen, such as, C, N, B, and S etc are chosen usually [18] For transition metals, those with the d-orbital energy lower than that of titanium, such as Nb, Mo, Cr, and V etc are chosen. What is more, some latest researches showed that transition metal and non-metal co-doped TiO2may have narrow effective bandgap and enhanced the visible light photocatalytic activity [19–22]. So far, many experimental and theoretical attempts have been made to extend the absorption edge of TiO2 to the visible light region by co-doping non-metal elements and transition metals. Long et al. found that substituting transition metal W at Ti site and non-metal N at O site could reduce the effective band gap[23]. Pan et al. synthesized the Cr–N co-doped TiO₂ using sol-gel method which effectively shifts the absorption edge towards visible light[24]. Zhu et al. performed theoretical calculations on Nb–C、Mo–C co-doped TiO2and found that the co-doping is conducive to create visible light photocatalysis[20,25]. There are many other kinds co-doping trials such Contents lists available atScienceDirect

journal homepage:www.elsevier.com/locate/ceramint

Ceramics International

http://dx.doi.org/10.1016/j.ceramint.2016.05.200

nCorresponding author.

E-mail addresses:shyzhhx13@qq.com,liujm@nju.edu.cn(J.–M. Liu).

(2)

as, Mo–N, C–W, Cr–C, Fe–N, and so on[26–29]. It was reported that the Cr doped TiO2 can effectively enhance the visible light photocatalytic activity because the introduced localized gap states by the Cr-3d electrons reduce the band gap of TiO2 [26]. Using the combined sol-gel and hydrothermal method, Zhu et al. synthesized the Cr doped anatase TiO2in which Cr atoms substitute Ti atoms, and which enhanced the visible light absorption as well as the visible light photocatalytic activity on the degradation of XRG [30]. In addition, both experimental and theoretical studies have shown that the C-doped TiO2can signiﬁcantly improve the visible light absorption of TiO2 [31,32]. Khan et al. synthesized the C-doped TiO2, and found that it promotes the visible light photocatalytic activity and exhibits two optical absorption peaks at 535 and440 nm[33]. Theoretical calculations on the C doped TiO2predict that three isolated impurity states introduced by the C-2p orbital above the VBM, reducing the effective band gap of TiO₂. This improves the optical absorption for visible light [34].

Thus, according to the above analysis, it may be expected that the Cr– and C– co-incorporation into TiO2 can cause some unusual optical transitions and the remarkable improvement of the optical absorption in the visible region. Although this work[34]also involved some study on the Cr–C co-doped TiO2, systematic theoretical studies of the Cr–C co-doped anatase TiO2is still lacking. In particular, to the best of our knowledge, there are still no works involving specific calculations on electronic structures of different configurations and the optical properties of the Cr–C co-doped TiO2. In this paper, we mainly investigate the electronic structures and optical properties of the Cr and C co-doped anatase TiO2using the density functional theory (DFT). We mainly discuss three nonequivalent Cr–C adjacent co-doped configurations. Furthermore, the optical properties of the three Cr–C adjacent co-doped TiO2

conﬁgurations and pure TiO2are calculated. The microscopic me- chanism for band gap narrowing and the origin of the enhanced visible light photocatalytic activity are also discussed in details.

2. Models and computation details

All calculations based on the density functional theory (DFT) are performed using the Vienna ab initio simulation package (VASP5.2) code [35,36]. The projector augmented wave (PAW) method [37] is utilized for treating the interaction of valence electrons with ionic core. The conﬁgurations of O-2s²2p⁴, C-2s²2p², Ti-3d²4p², and Cr-3d⁵4s¹are treated as the valence electrons. The exchange and correlation potential are modeled using the generalized gradient approximation (GGA) Perdew-Becke-Erzenhof (PBE) function[38]. The plane-wave basis sets are generated using a cutoff energy of 450 eV. Thek-point grid is set to 555 for the Brillouin Zone[39]. The energy convergence threshold is set to 1.010⁶eV/atom. For the structure optimization, both the pure and doped systems are fully relaxed until the Hellmann-Feynman force acting on each atom is reduced down to 1.0 meV/Å. The standard DFT often signiﬁcantly underestimates the band-gap of transition-metal oxides[40,41], due to its inaccuracy in dealing with the exchange correlation function of d electrons of transition- metal[42–44]. The GGAþU approach is an effective and simple method to describe the strongly correlated interaction. So, we also calculate the electronic and optical properties by using the GGAþU scheme in order to test the effect of Hubbard U on the electronic structure of doped anatase TiO2. We choose the U¼5.8 eV for the Ti-3delectrons and 2.8 eV for the Cr-3d electrons in our calculation, as used in earlier work[45].

The optical properties are essentially calculated by the frequency dependent complex dielectric function as

ε

⁽

ω

⁾¼

ε

1(

ω

⁾þ i

ε

2(

ω

). From calculating the momentum matrix elements between the occupied and unoccupied wave functions, we can obtain the

imaginary part

ε

²⁽

ω

^),The calculation formula are shown as fol- low:

(

^ω

)

^π

∑ ( )

Ω ψ ψ δ ω

ϵ ℏ = ϵ

^ − − ℏ

( )

e ur E E

2 ,

1

c v k k

c k

v

k k

2

2 0 , ,

2

wherevandcrepresent the valence band and conduction band, respectively,kis the vector of reciprocal lattice,uis the vector of polarization electricﬁeld, and

ω

is the photon frequency. The real part

ε

1(

ω

⁾can be calculated from the imaginary part

ε

2(

ω

^{) using}

the Kramer–Kronig relationship [46]. As the optical absorption spectrum can provide comparative information on the optical properties of materials[47], here, we will calculate the absorption spectrum of doped anatase TiO2. The optical absorption spectra can be calculated from the real and imaginary parts of the dielectric function using[48]:

α ω( ) = ε ( ) +ω ε ( ) −ω ε ω( )

( )

⎡⎣⎢ ⎡

⎣⎢ ⎤

⎦⎥⎤

2 ⎦⎥ ,

12 2

22 1

1 2

As the GGA method often underestimates the band gap, in order to obtain the accurate optical absorption spectra, the scissor approximation correction [49] of 1.16 eV is used to correct the optical results, and make the results compatible with experimental data. Moreover, in order to test the effect of Hubbard U on the optical properties, we calculated the optical absorption spectrum using the GGAþU for comparison.

We extend the primitive cell of anatase TiO2to a 221 supercell containing 48 atoms, which is generally the size used for doping[48,50], and use the supercell to simulate C, Cr and Cr–C doped systems. For the Cr doped TiO2, one Cr atom substitutes for one Ti, and denoted such systems as TiO₂@Cr. Similarly, for the C doping, one C atom substitutes for one O atom, which is denoted as TiO2@C. For the Cr–Cr adjacent co-doped anatese TiO2, it has three nonequivalent co-doped configurations denoted as TiO2@Cr– CI, TiO2@Cr–CII and TiO2@Cr–CIII. The three cases are schemati- cally shown inFig. 1(a)–(c) respectively. For those Cr–C non-adjacent doped configurations, the total energy is always higher than the adjacent models, i.e. the adjacent co-doping have the lowest total energy, as to say, Cr–C adjacent co-doped configurations is the most stable.

3. Results and discussion 3.1. Local structure distortions

The optimized lattice constants of different doped system anatase TiO2are evluated. The lattice parameters of pure system are a¼3.803 Å, b¼3.803 Å and c¼9.663 Å, in agreement with calculated and measured data[51,52], conﬁrming the reasonability of our optimization method. It is found that the lattice constants change little upon the different doped lattices, which is not strange considering that the atomic size of Cr is very close to Ti and that of C to O. In order to further observe the variations of internal bond lengths due to adjacent Cr–O co-doping, the atomic positions and the bonds on the (100) plane are presented inFig. 2, and the corresponding bond length is marked out in digit. It is observed that the internal structure of TiO2@Cr–C I and TiO2@ Cr–C II changes in similar way. Here we mainly compare the internal structural variations of two typical compensated adjacent co- doping conﬁgurations: TiO2@Cr–C I and TiO2@Cr–C III. At the same time, the corresponding bond lengths of pure TiO2are also plotted inFig. 2(a) as a reference for comparison. It is seen that the local structure of TiO2@Cr–C I shown inFig. 2(b) is seriously distorted with respect to pure TiO2 lattice. In particular, the C–Cr bond length (1.623 Å) of TiO2@Cr–CI is0.323 Å shorter than the Ti–O

(3)

ones (1.946 Å) of pure TiO2, and the Cr–O bond length (2.228 Å) along the [010] direction is longer than the Ti–O ones (1.946 Å) of pure TiO2. Furthermore, the Cr atom slightly moves upward along the [001] direction. For the TiO2@Cr–C III, as shown inFig. 2(c), the local structure is also slightly distorted. The Cr–O bond length (1.860 Å) along the [010] direction is shorter than the Ti–O ones

(1.946 Å) of pure TiO2by upward shift along the [001] direction for 0.35 Å. All those local structure distortions will damage the crystalfield of oxygen octahedron on several levels, and it is worth mentioning that the Jahn-Teller distortion will play an important role in a further splitting between thet2g(dxy, dxz, dyz) andeg(dz², dx²-dy²) states of d orbit of chromium, which will affect the Fig. 1.Schematic of configurations of 221 supercell of anatase TiO2doped by one C atom and one Cr atoms, (a)–(c) are three kinds of Cr–C adjacent co-doped configurations respectively.

Fig. 2. Optimized (100) plane lattice structures of pure (a), TiO2@Cr–C I (b), and TiO2@Cr–C III (c).

(4)

electronic structure and optical properties of TiO2system, and the relevant discussion will be further discussed in the following.

3.2. Electronic structures

To understand the variations of electronic structure due to the various co-doped conﬁgurations, the band structures of pure TiO2

and doped TiO2are calculated, and the results are plotted inFig. 3.

It is seen that the band gap of pure anatase TiO2 is 2.04 eV,

consistent with previous theoretical results[53,54]. Yet, it is still underestimated with respect to experimental value of 3.2 eV [55], due to the well-known shortcoming of the GGA. For Cr doped TiO2, the Cr-induced bands appear in the forbidden region, as shown inFig. 3(b). The Fermi level (the red dash line) is shifted from the top of the valence band maximum (VBM) to the middle of the impurity states, exhibiting the half metallic character. At the same time, these impurity states will shift the photo-excited car- riers to the conduction band, which may be further involved in the Fig. 3.The calculated band structures of pure system (a), TiO2@Cr–C I (b), TiO2@Cr–C II (c), and TiO2@Cr–C III (d). The red dashed lines represent the Fermi level. (For interpretation of the references to color in thisﬁgure legend, the reader is referred to the web version of this article.)

(5)

oxidation reduction process. The band structure of TiO2@Cr–C I and TiO₂@MCr–C II are similar to each other, as shown in theFig. 3 (c) and (d), respectively. The Fermi energy (EF) is above the VBM, showing the semiconducting character. The VBM in these co- doped TiO2 mainly consists of the C-2pstates coupled with the adjacent Cr-3dstates. Because of the Jahn-Teller effect, thet2g(dxy, dxz, dyz) andeg(dz², dx²–dy²) states ofdorbit of chromium further splitt, thet2gstates further splits into Cr-dxy, Cr-dxz, Cr-dyzstates.

The conduction band minimum (CBM) has additional band mainly consisting of the Cr-3dyzstates. The effective band gap of the co- doped TiO2falls down to 1.18 eV, suppressing the band gap of pure TiO2 for 0.86 eV. This effect is highly favored since the visible light absorption activity is remarkably enhanced.

Fig. 3(e) shows the band structure of TiO2@Cr–C III and one finds that the EF is still above the VBM but the band structure characteristics are significantly different from those of the TiO2@Cr–C I and TiO2@Cr–C II. The Cr-3d and C-2p states also contribute to the deep gap state in addition to the bands at the edges of pure TiO2. The deep gap states are mainly contributed by the Cr-3dxy and Cr-3dyz. It is also found that the crystal field of oxygen octahedra of the TiO2@Cr–C III is most severely modulated, having stronger Jahn-Teller effect than TiO2@Cr–C I and TiO2@Cr–C II, lowering the state degeneration and thus additional energy level splitting. The further Cr-3dstate splitting induces the deep gap state in the gap. Moreover, the deep gap state can reduce the energy for transferring electron from the VBM to the CBM, improving the visible light absorption activity of TiO2.

To illustrate the general features of electronic structures of the doped TiO2, the orbital-decomposed band structures are calculated and we choose the TiO2@Cr–C III as an example to present in Fig. 4. The VBM is primarily from the hybridization of the C 2p

orbitals and Cr 3dorbitals, whereas the CBM mainly comes from the hybridization of the 3d orbitals of Ti and Cr. The gap state below the CBM mainly comes from the Cr 3dorbitals. We plot the projected DOS (PDOS) of TiO2@Cr–C I and TiO2@Cr–C III in the energy interval between 1.0 eV and 6.0 eV and the data are plotted inFig. 5, which conﬁrms again that the bottom of the conduction band primarily comes from the hybridization between the Ti-3d and Cr-3dorbitals in the anti-bonding states, and the top of the valence band features the hybridization of the C-2p and Cr-3d orbitals in the bonding states.

In order to further illustrate the electronic structures of the adjacent co-doped TiO2, the electron density and charge density difference are calculated, as plotted inFig. 6. The charge density difference features of TiO2@Cr–C I and TiO2@Cr–C II are similar to each other, we choose to show the case of TiO2@Cr–C I inFig. 6. In Fig. 6(a) and (b) are plotted the electron density proﬁles of TiO2@Cr–C I and TiO2@Cr–C III, respectively. It is found that the electron density in the region between Cr and C is larger than that between Ti and O, which shows that the covalent bonding in the C–Cr group is stronger than that in O–Ti group. The electron density in the region between Cr and the top adjacent O is larger than that of Ti–O of pure TiO2, and the electron density between Cr and the right adjacent O is smaller than that of Ti–O of pure TiO2. For TiO2@Cr–C III, as shown inFig. 6(c), the electron density between Cr and the left or right adjacent O is also larger than that of Ti–O of pure TiO2.Fig. 6(d) to (f) show the charge density difference diagrams of pure TiO2, TiO2@Cr–CI and TiO2@Cr–CII respectively. The electron density in the C atom region near the Cr is larger than that in O region of pure system, which implies that C accepted more electrons in the Cr–C co-doping system. The electron density difference in the Cr atom region near C reduces

Fig. 4.The calculated orbital-decomposed band structures of TiO2@Cr–C I : (a) the 3d orbital of Ti, (b) the 2p orbital of O, (c) the 3d orbital of Cr and (d) the 2p orbital of C.

The red dashed lines represent the Fermi level. (For interpretation of the references to color in thisﬁgure legend, the reader is referred to the web version of this article.)

(6)

largely, which also conﬁrms that the Cr atom of TiO2@Cr–C system donated more electrons than the Ti atom. Furthermore, due to the difference in the valence of C anion and O anion and the internal structure distortion, Chromium cation along Cr–C direction have a certain polarization, which is in agreement with the literature [24,56]. Moreover, other ions around the Cr and C ion also have different degree polarization. It maybe form an effective polar- izationﬁeld in the interior of TiO2@Cr–C system, which will promote the electrons and holes separating and improving the visible catalytic activity the Cr–C co-doped system[57].

3.3. The effect of Hubbard U

In order to illustrate the Hubbard effect on the electronic structure, we also study the electronic structure the pure and co- doped anatase TiO2system using GGAþU, and the TDOS, the PDOS and band structure are all calculated using the GGAþU. The TDOS calculated using GGA and GGAþU are shown in Fig. 7(a) and

(b) respectively. The band gap of pure anatase TiO2 obtained by GGAþU is 3.0 eV, only 0.2 eV less than the experimental value of 3.2 eV, which proves that GGAþU method can get more accurate band gap value compared to GGA. Comparing TDOS obtained from GGA and GGAþU, weﬁnd that the doping system band gap be- comes wider mainly by elevating the CBM because of the incorporation of Hubbard U. The gap state below CBM mainly caused by Cr-3dorbital become deep gap state, which is obvious because the position of the CBM mainly consisted of the Ti-4d states shift towards the higher energy and Cr-3d electron become more localized. At the same time, because of the stronger Jahn-Teller effect, Cr-3dorbital further split. The three doping conﬁguration of TiO₂@Cr–C all have deep gap state by GGAþU. The gap state can reduce the energy for transferring electron from the VBM to the CBM, further improving the visible light absorption activity of TiO2.

3.4. Optical properties

The optical absorption spectra of pure TiO2, TiO2@Cr–C I, TiO2@Cr–C II and TiO2@Cr–C III are calculated using GGAþ the scissor approximation correction and GGAþU respectively.Fig. 8 (a) is optical absorption spectra diagram obtained by GGAþ the scissor approximation correction, and the energy region of the visible light is about from 1.64 eV to 3.19 eV. We ﬁnd that the absorption edge of pure TiO2mainly locate in the ultraviolet light region, which is in agreement with the theoretical and experimental result of the band gap[58,59]. For the pure TiO2, the optical excitation mainly proceeded from electrons transiting from the O-2pto Ti-3dstates, and the optical absorption edge of pure TiO2is ﬁt for its band gap of 3.2 eV. The Optical absorption edge of Cr–C co-doped anatase TiO2 has shifted into visible light range compared with pure system, which means that co-doping TiO2

achieved the expectant absorption edge redshift. Due to the states of doping foreign atom in the band gap, electrons shifting from doping foreign states to CBM need less energy excitation, which means more visible light absorption. However, the shifting the optical absorption edge depends on the band nature of atom doping conﬁgurations, the absorption edges of TiO2@Cr–C I and TiO2@Cr–C II are similar to each other because of the similar band structure nature. Moreover, the absorption coefﬁcient of TiO2@Cr– C III is larger than that of TiO2@Cr–C I and TiO2@Cr–C II in the Fig. 5.Calculated PDOS of TiO2@Cr–C I (a) and TiO2@Cr–C II (b). The dashed lines

represent the Fermi level.

Fig. 6.Calculated electron density for pure (a), TiO2@Cr–C I (b) and TiO2@Cr–C III (c); the electron density difference for pure (d), TiO2@Cr–C I (e), and TiO2@Cr–C III (f).

Contours show the values in a slice of the (100) plane. The units are electrons Å³. In panels (a), (b) and (c), Color from blue to red represent electron density changes from low to high. In panels (d), (e) and (f), Color red (blue) represent the electron density increased (decreased). (For interpretation of the references to color in thisﬁgure legend, the reader is referred to the web version of this article.)

(7)

visible light region. It means that co-doping configuration III is most effective to improve the visible light absorbing of doping system. These the differences in optical absorption efficiency arise from the different electronic structure of different configuration.

Fig. 8(b) is optical absorption spectra diagram obtained by GGAþU method, we found that the optical absorption spectra calculated by GGAþU is similar to each other compared with the result obtained by GGAþ the scissor approximation as a whole. For example, the optical absorption spectra of co-doped system all show the visible light absorbing. That is to say, C and Cr co-doped anatase TiO2 realizes the expected visible light absorption both by using GGAþ the scissor approximation and GGAþU methods.

However, the absorption spectrum obtained by two the different methods still has a little difference in the details. From theﬁgure, the absorption spectrum of TiO2@Cr–C I is similar to each other by two the different methods, difference mainly exist in TiO2@Cr–C II and TiO2@Cr–C III, and the absorption spectrum of TiO2@Cr–C II and TiO2@Cr–C III have a obvious peak at 2.88 eV and 0.668 eV respectively, at the same time, the absorption coefﬁcient of TiO2@Cr–C II is increased in visible region compared to GGA method. These differences in details may be the minute variations of the electronic structure caused by Hubbard U. However, the results of the two methods on the whole have shown that Cr–C co- doped TiO2 can enhance the absorption of visible light, and it Fig. 7.Calculated TDOS of pure TiO2and Cr–C co-doped TiO2using GGA (a) and GGAþU (b).

Fig. 8.Calculated optical absorption spectrum of pure TiO2, and Cr–C co-doped TiO2using GGAþthe scissor approximation correction (a) and using GGAþU (b).

(8)

improves the ability of converting photoelectrochemical energy under sunlight irradiation.

4. Conclusion

In summary, we have carefully investigated the electronic structures and optical property of pure TiO₂, Cr-doped TiO₂ and Cr–C co-doped TiO2systems using GGA. Cr mono-doping reduce the band gap of TiO2little. Then, we mainly discuss three possible Cr–C adjacent co-doped configurations because of adjacent co- doping having the lowest total energy. Because of the doping of foreign atoms Cr and C into the TiO2system, the local structure distortions will damage the crystalfield of oxygen octahedron on several levels, due to the Jahn-Teller effect, thet2gandegstates ofd orbit of chromium will split further. The band structures of adjacent co-doping show that the gap states induced mainly by C-2p state and Cr-3dstate reduce the effective band gap about 0.86 eV and 1.19 eV respectively for different co-doped configuration, and the deep gap states mainly induced by splitting states Cr-3dyz, all those above will improve the ability of converting photoelectrochemical energy of TiO₂under sunlight irradiation. At the same time, chromium cation along Cr–C direction have a certain polarization, moreover, other ions around the Cr and C ion also have different degree polarization, which can form an effective polar- izationfield in the interior of TiO2@Cr–C system. The interior po- larizationfield in TiO2@Cr–C system will promote the electrons and holes separating and improving the visible catalytic activity of the Cr–C co-doped system. Furthermore, the calculated optical absorption spectrum also shows that the absorption edges of Cr–C co-doped TiO2 systems extend up to the visible light region.

Moreover, we also calculate some electronic structures and optical property of co-doping system using GGAþU, and the result also conﬁrmed that Cr–C co-doped TiO2 can improve the ability of converting photoelectrochemical energy of TiO2 under sunlight irradiation.

Acknowledgements

This work was supported by the National Key Research Pro- gramme of China (Grant no. 2016YFA0300100 ), the National Natural Science Foundation of China (Grants no. 11234005 and no.

51431006).

References

[1]S.J. Pearton, W.H. Heo, M. Ivill, D.P. Norton, T. Steiner, Dilute magnetic semiconducting oxides, Semicond. Sci. Technol. 19 (2004) R59.

[2]X.J. Feng, K. Shankar, O.K. Varghese, M. Paulose, T.J. Latempa, C.A. Grimes, Vertically aligned single crystal TiO2nanowire arrays grown directly on transparent conducting oxide coated glass: synthesis details and applications, Nano Lett. 8 (2008) 3781.

[3]Y.W. Heo, D.P. Norton, L.C. Tien, Y. Kwon, B.S. Kang, F. Ren, S.J. Pearton, J.

R. LaRoche, ZnO nanowire growth and devices, Mater. Sci. Eng. R 47 (2004) 1.

[4]H. Irie, Y. Watanabe, K. Hashimoto, Nitrogen-concentration dependence on photocatalytic activity of TiO2-xNxpowders, Chem. Lett. 32 (2003) 772.

[5]X. Chen, S.S. Mao, Titanium dioxide nanomaterials: synthesis, properties, modiﬁcations, and applications, Chem. Rev. 107 (2007) 2891.

[6]A. Fujishima, K. Honda, Electrochemical Photolysis of Water at a Semi- conductor Electrode, Nature 238 (1972) 37.

[7]J.H. Carey, J. Lawrence, H.M. Tosine, Photodechlorination of PCB’s in the pre- sence of titanium dioxide in aqueous suspensions, Bull. Environ. Contam.

Toxicol. 16 (1976) 697.

[8]S.N. Frank, A.J. Bard, Heterogeneous photocatalytic oxidation of cyanide and sulﬁte in aqueous solutions at semiconductor powders, J. Phys. Chem. 81 (1977) 1484.

[9]B. Regan, M. Grätzel, A low-cost, high-efﬁciency solar cell based on dye-sen- sitized colloidal TiO2ﬁlms, Nature 353 (1991) 737.

[10]R. Asahi, T. Morikawa, T. Ohwaki, K. Aoki, Y. Taga, Visible-light photocatalysis

in nitrogen-doped titanium oxides, Science 293 (2001) 269.

[11] X.B. Chen, L. Liu, P.Y. Yu, S.S. Mao, Increasing Solar Absorption for Photo- catalysis with Black Hydrogenated Titanium Dioxide Nanocrystals, Science 331 (2011) 746.

[12]G.M. Wang, H.Y. Wang, Y.C. Ling, Y.C. Tang, X.Y. Yang, R.C. Fitzmorris, C.

C. Wang, J.Z. Zhang, Y. Li, Hydrogen-treated TiO2nanowire arrays for photoelectrochemical water splitting, Nano Lett. 11 (2011) 3026.

[13]W. Choi, A. Termin, M.R. Hoffmann, The role of metal ion dopants in quantum- sized TiO2: correlation between photoreactivity and charge carrier re- combination dynamics, J. Phys. Chem. 98 (1994) 13669.

[14]S. Kohtani, A. Kudo, T. Sakata, Spectral sensitization of a TiO2 semiconductor electrode by CdS microcrystals and its photoelectrochemical properties, Chem.

Phys. Lett. 206 (1993) 166.

[15]K. Hiehata, A. Sasaharal, H. Onishi, Local work function analysis of Pt/TiO2

photocatalyst by a Kelvin probe force microscope, Nanotechnology 18 (2007) 84.

[16]K.E. Karakitsou, X.E. Verykios, Effects of altervalent cation doping of TiO2on its performance as a photocatalyst for water cleavage, J. Phys. Chem. 97 (1993) 1184.

[17] W. Zhu, X.F. Qiu, V. Iancu, X.-Q. Chen, H. Pan, W. Wang, N.M. Dimitrijevic, T. Rajh, H.M. Meyer, M.P. Oaranthaman, G.M. Stocks, H.H. Weitering, B.H. Gu, G. Eres, Z.Y. Zheng, Band gap narrowing of titanium oxide semiconductors by noncompensated anion-cation codoping for enhanced visible-light photoactivity, Phys. Rev. Lett. 103 (2009) 226401.

[18]R.H. Zhang, Q. Wang, Q. Li, J.F. Dai, D.H. Huang, First-principle calculations on optical properties of C–N-doped and C–N-codoped anatase TiO2, Physica B 406 (2011) 3417.

[19]J. Zhang, J.H. Xi, Z.G. Ji, MoþN codoped TiO2sheets with dominant {001} facets for enhancing visible-light photocatalytic activity, J. Mater. Chem. 22 (2012) 17700.

[20] H.X. Zhu, J.-M. Liu, Electronic and optical properties of C and Nb co-doped anatase TiO2, Comput. Mater. Sci. 85 (2014) 164.

[21]R. Long, N.J. English, Synergistic effects of Bi/S codoping on visible light-activated anatase TiO2photocatalysts fromﬁrst principles, J. Phys. Chem. C 113 (2009) 8373.

[22] C.P. Cheney, P. Vilmercati, E.W. Martin, M. Chiodi, L. Gavioli, M. Regmi, G. Eres, T.A. Callcott, H.H. Weitering, N. Mannella, Origins of electronic band gap reduction in Cr/N codoped TiO2, Phys. Rev. Lett. 112 (2014) 036404.

[23] R. Long, N.J. English, First-principles calculation of nitrogen-tungsten codoping effects on the band structure of anatase-titania, Appl. Phys. Lett. 94 (2009) 132102.

[24] C.C. Pan, J.C.S. Wu, Visible-light response Cr-doped TiO2XNXphotocatalysts, Mater. Chem. Phys. 100 (2006) 102.

[25] H.X. Zhu, J.-M. Liu, First principles calculations of electronic and optical properties of Mo and C co-doped anatase TiO2, Appl. Phys. A 117 (2014) 831.

[26] Y.Q. Gai, J.B. Li, S.S. Li, J.B. Xia, S.H. Wei, Design of narrow-gap TiO2: a passi- vated codoping approach for enhanced photoelectrochemical activity, Phys.

Rev. Lett. 102 (2009) 036402.

[27] C.C. Yen, D.Y. Wang, L.S. Chang, H.C. Shi, Characterization and photocatalytic activity of Fe-and N-co-deposited TiO2andﬁrst-principles study for electronic structure, J. Solid State Chem. 184 (2011) 2053.

[28] R.H. Zhang, Q. Wang, J. Liang, Q. Li, J.F. Dai, W.X. Li, Optical properties of N and transition metal R(R¼V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) codoped anatase TiO2, Physica B 407 (2012) 2709.

[29] Q. Wang, J.F. Liang, R.H. Zhang, Q. Li, J.F. Dai, First-principle study on optical properties of N La-codoped anatase TiO, Chin. Phys. B 22 (2013) 057801.

[30] J. Zhu, Z. Deng, F. Chen, J. Zhang, H. Chen, M. Anpo, J. Huang, L. Zhang, Hy- drothermal doping method for preparation of Cr^3þ-TiO2photocatalysts with concentration gradient distribution of Cr^3þ, Appl. Catal. B: Environ. 62 (2006) 329.

[31]J.G. Yu, G.P. Dai, Q.J. Xiang, M. Jaroniec, Fabrication and enhanced visible-light photocatalytic activity of carbon self-doped TiO2sheets with exposed {001}

facets, J. Mater. Chem. 21 (2011) 1049.

[32] K.S. Yang, Y. Dai, B.B. Huang, M.H. Whangbo, Density functional characterization of the visible-light absorption in substitutional C-anion-and C-cation- doped TiO2, J. Phys. Chem. C 113 (2009) 2624.

[33] S.U.M. Khan, M. Al-Shahry, W.B. Ingler Jr, Efﬁcient photochemical water splitting by a chemically modiﬁedn-TiO2, Science 297 (2002) 2243.

[34] K. Yang, Y. Dai, B. Huang, M.-H. Whangbo, Density functional characterization of the visible-light absorption in substitutional C-anion-and C-cation-doped TiO2, J. Phys. Chem. C 113 (2009) 2624.

[35] G. Kresse, J. Hafner, Efﬁciency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Phys. Rev. B 47 (1993) R558.

[36] G. Kresse, J. Furthmüller, Efﬁcient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 11169.

[37]P.E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50 (1994) 17953.

[38] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865.

[39] H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations, Phys.

Rev. B 13 (1976) 5188.

[40] G. Pacchioni, Modeling doped and defective oxides in catalysis with density functional theory methods: Room for improvements, J. Chem. Phys. 128 (2008) 182505.

[41]P. Mori-Sánchez, A.J. Cohen, W.T. Yang, Localization and delocalization errors in density functional theory and implications for band-gap prediction, Phys.

Rev. Lett. 100 (2008) 146401.

(9)

[42]V.I. Anisimov, F. Aryasetiawan, A.I. Lichtenstein, First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDAþ U method, J. Phys. Condens. Matter 9 (1997) 767.

[43]V.I. Anisimov, J. Zaanen, O.K. Andersen, Band theory and Mott insulators:

Hubbard U instead of Stoner I, Phys. Rev. B 44 (1991) 943.

[44]M.A. Korotin, V.I. Anisimov, D.I. Khomskii, G.A. Sawatzky, CrO2: a self-doped double exchange ferromagnet, Phys. Rev. Lett. 80 (1998) 4305.

[45]R. Long, N.J. English, First-principles calculation of electronic structure of V-doped anatase TiO2, ChemPhysChem 11 (2010) 2606.

[46]D.B. Melrose, R.J. Stoneham, Generalised Kramers-Kronig Formula for spatially dispersive Media, J. Phys. A Math. Gen. 10 (1977) L17.

[47]G. Shao, Red shift in manganese-and iron-doped TiO2: a DFTþU analysis, J.

Phys. Chem. C 113 (2009) 6800.

[48]Y. Fang, D.J. Cheng, M. Niu, Y.J. Yi, W. Wu, Tailoring the electronic and optical properties of rutile TiO2by (NbþSb, C) codoping from DFTþU calculations, Chem. Phys. Lett. 567 (2013) 34.

[49]T. Umebayashi, T. Yamaki, S. Yamamoto, A. Miyashita, S. Tanaka, Sulfur-doping of rutile-titanium dioxide by ion implantation: photocurrent spectroscopy and ﬁrst-principles band calculation studies, J. Appl. Phys. 93 (2003) 5156.

[50]X.G. Ma, Y. Wu, Y.H. Lu, J. Xu, Y.J. Wang, Y.F. Zhu, Effect of compensated co- doping on the photoelectrochemical properties of anatase TiO2photocatalyst, J. Phys. Chem. C 115 (2011) 16963.

[51]J.Y. Lee, J. Park, J.H. Cho, Electronic properties of N-and C-doped TiO2, Appl.

Phys. Lett. 87 (2005) 011904.

[52]J.K. Burdett, T. Hughbanks, G.J. Miller, J.W. Richardson, J.V. Smith, Structural- electronic relationships in inorganic solids: powder neutron diffraction studies of the rutile and anatase polymorphs of titanium dioxide at 15 and 295 K, J. Am. Chem. Soc. 109 (1987) 3639.

[53]R. Asahi, Y. Taga, W. Mannstadt, A.J. Freeman, Electronic and optical properties of anatase TiO2, Phys. Rev. B 61 (2000) 7459.

[54]K. Yang, Y. Dai, B. Huang, Origin of the photoactivity in boron-doped anatase and rutile TiO2calculated fromﬁrst principles, Phys. Rev. B 76 (2007) 195201.

[55]H. Tang, H. Berger, P.E. Schmid, F. Levy, G. Burri, The Electronic Struc-ture of SrTiO3and Some Simple Related Oxides (MgO, A12O3, SrO, TiOz), Solid State Commun. 23 (1977) 161.

[56]W.J. Shi, S.J. Xiong,Ab initiostudy on band-gap narrowing in SrTiO3with Nb- C-Nb codoping, Phys. Rev. B 84 (2011) 205210.

[57]J. Sato, H. Kobayashi, Y. Inoue, Photocatalytic activity for water decomposition of indates with octahedrally coordinated d10 conﬁguration. II. Roles of geo- metric and electronic structures, J. Phys. Chem. B 107 (2003) 7970.

[58]Z. Zhou, M. Li, L. Guo, Aﬁrst-principles theoretical simulation on the electronic structures and optical absorption properties for O vacancy and Ni impurity in TiO2photocatalysts, J. Phys. Chem. Solids 71 (2010) 1707.

[59]W.J. Yin, H.W. Tang, S.H. Wei, M.M. Al-Jassim, J. Turner, Y.F. Yan, Band structure engineering of semiconductors for enhanced photoelectrochemical water splitting: the case of TiO2, Phys. Rev. B 82 (2010) 045106.