Electronic and optical properties of C and Nb co-doped anatase TiO

Electronic and optical properties of C and Nb co-doped anatase TiO

₂

H.X. Zhu

^a,b

, J.-M. Liu

^a,⇑

aLaboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China

bCollege of Physical Science and Electronic Techniques, Yancheng Normal University, Yancheng 224002, China

a r t i c l e i n f o

Article history:

Received 23 September 2013

Received in revised form 22 November 2013 Accepted 22 December 2013

Available online 23 January 2014

Keywords:

Anatase TiO2

Electronic structure Optical absorption

a b s t r a c t

The electronic and optical properties of C, C–Nb and C–2Nb doped anatase TiO2are studied using the first principles calculations. For the C-doped TiO2, three subbands in the band gap are generated due to the C-2p states, which suppress the effective band gap for electron transfer, while the gap states are partially occupied and probably serve as the recombination centers for electrons and holes. Therefore, the C–2Nb co-doping is investigated for the charge compensation consideration. Two possible co-doping configura- tions are comprehensively studied and compared. The three subbands in the band gap of the C mono-doped TiO2become fully occupied because the two Nb atoms contribute sufficient electrons for compensation.

Furthermore, the optical properties of the co-doped TiO2and pure TiO2are calculated. It is found that the optical absorption of the C–2Nb co-doped TiO2extends its coverage over the visible light region.

Ó2013 Elsevier B.V. All rights reserved.

1. Introduction

In the family of semiconductor photocatalysts, titanium dioxide (TiO2) has been extensively studied because of its strong catalytic activity, a long lifetime of photon-generated carriers, high chemical and thermal stability, and low cost. It is an ideal catalytic material for environmental pollutants degradation as well as water splitting and purification, utilizing sunlight irradiation. TiO2has three basic crystalline phases: brookite (Pbca), anatase (I4₁/amd), and rutile (P42/mnm)[1]. Particularly, anatase TiO2has received an extensive attention for its higher catalytic activity [2]. However, a main drawback of anatase TiO2 is its intrinsic wide band gap (Eg= 3.2 eV), which means that TiO2can only be activated by ultra- violet radiation from sunlight. While an ideal photocatalyst should have wide visible light photoelectrochemical (PEC) activity, at the same time, the band edges must straddle the redox potentials of water. To improve the visible light catalytic absorption of TiO2a large amount of theoretical and experimental work has been car- ried out to tailor the band gap of TiO₂[3–6].

Doping with various impurities in TiO2is a common method to reduce the band gap. Usually, those non-metallic elements with thep-orbital energy higher than that of oxygen are preferred for the doping, since the valence band maximum (VBM) of TiO2mainly consists of oxygen 2pstates. This suggests that most favored non- metallic elements include N[4,7], C[8], B[9], and S[10]. Particu- larly, the C doping has received an extensive attention. Since it firstly found that C-doped TiO2promotes the photocatalytic activ- ity of TiO2 to some degree and exhibits two optical absorption

thresholds at 535 and 440 nm[11]. Soon after, more experimental studies confirmed that C-anion doping could induce different degrees of the redshift of the optical absorption edge of TiO2

[12–15]. Xu et al. found the optical band-gap decrease of 0.45 eV and 1.05 eV respectively in C-doped anatase TiO2 [16]. These experiments all indicate that substitutional C-anion doping can lead to several different optical absorption thresholds in TiO2. First-principles calculations are also extensively carried out to study the electronic and optical absorption properties of C-anion and C-cation doped TiO2[17]. With respect to the undoped TiO2, the band gap of C-anion doped TiO2 changes slightly but some impurity states are introduced in the band gap. Due to the isolated impurity states above the VBM, the doped TiO2shows remarkable improvement over undoped TiO2 in terms of the photocatalytic activity and optical absorption for visible light. Moreover intersti- tial C-doped TiO2has also been studied using first-principles calcu- lations [18,19]. It is found that the interstitial C dopants also introduce impurity states in the band gap and show the visible- light absorption in C-doped TiO_2. However, a vital issue for the mono-element doping is related to the fact that the doping leads to partial occupation of the localized mid-gap states[20], which unfortunately may create recombination centers. These centers certainly slow down the light-induced charge carrier migration to the surface during the photocatalysis[21,22], and thus reduce the catalysis efficiency.

To overcome this negative effect, one strategy is to find the way to further occupy those unoccupied localized mid-gap states, i.e.

the so-called compensated doping. Indeed, recently it has been widely recognized that compensated doping in TiO2using transi- tion elements (Nb, Cr, Mo, Ta, etc.)[23–25]or non-transition ele- ment Sb[4,26], with the above mentioned non-metallic doping 0927-0256/$ - see front matterÓ2013 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.commatsci.2013.12.048

⇑Corresponding author. Tel.: +86 2583596595; fax: +86 2583595535.

E-mail address:shyzhhx13@163.com(J.-M. Liu).

Contents lists available atScienceDirect

Computational Materials Science

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m m a t s c i

element N, C, B, S, etc. The strategy may be called the compensated co-doping. For the compensated model, anion is bonded to cation, it is noted that the full charge compensation only occurs when the doped anion and cation are bonded together, and the configuration generally possesses the lowest total energy[7,27,28], which is rea- sonable because the doped anion and cation can form a strong bond by a direct charge transfer. In which these transition metal impurities act as electron donors to occupy the unoccupied local- ized mid-gap states. Therefore, the recombination centers as gen- erated in the mono-doped TiO₂ can be effectively annihilated, and thus the migration efficiency of electrons and holes can be im- proved and the photocatalytic activity can be enhanced[29]. Any- how, so far researches have comprehended our understanding of the photocatalytic mechanisms in doped and co-doped TiO2which benefits to the design of high-efficient photocatalyst materials with visible light radiation. The donor–acceptor co-doping is the most common and effective design scheme[3,7,8]. Along this line, the compensated co-doping using non metallic elements C and H, i.e. (C, 2H) co-doped TiO2, was reported to narrow markedly the band-gap of TiO₂ [30]. Compared with those non-compensated and mono-doping approaches, some of the local states in the (C, 2H) co-doped TiO2 seems to be eliminated to some extent, due to the strong mixing of the C-2p and O-2p states, which is either unfavorable for application purpose.

Nevertheless, the photocatalyst efficiency of TiO2is not yet satis- fied for applications. Additional roadmaps to modify the band gap are still required to absorb the visible light. An important design principle is that the band edges of doped system must straddle the redox potentials of water. According to the above analysis, the Nb and C co-doping may be a good scheme. Some works[25,26]have been carried out about Nb and C co-doped TiO2, However, related comprehensive theoretical studies on the electronic structures of the C–2Nb compensated co-doped anatase TiO₂are still lacking. In particular, specific calculations on the optical properties of the C–2Nb compensated co-doped anatase TiO2are still non-available.

In this paper, we investigate the electronic structures and opti- cal properties of the C and Nb co-doped anatase TiO2from the den- sity functional theory. For comparison, we study the electronic and optical properties of the C, C–Nb and C–2Nb doped anatase TiO₂in detail, at the same time, for the C–2Nb co-doped TiO2, the two pos- sible doped configurations is also comprehensively studied and compared.

2. Models and computation details

We perform the first-principles calculations based on the den- sity functional theory (DFT) with the Viennaab initio simulation package (VASP5.2) code [31,32]. The exchange and correlation potentials are described using the generalized gradient approxima- tion (GGA) Perdew–Becke–Erzenhof (PBE) function[33]. The pro- jector augmented wave (PAW) pseudopotential [34] is utilized for the interaction of valence electrons with ionic core. It is known that with respect to the standard DFT scheme, the DFT +Uscheme and the hybrid (HSE) scheme may be more accurate in obtaining the electronic structure in materials with big band gap[35–37].

However, the standard DFT is still capable of reliably calculating various properties of the electronic structure except underestimat- ing the band gap[3,30], despite of the disadvantages of underesti- mating the band gap, the standard DFT calculations is still capable of many properties calculation and has been widely used all the time and have received good results such as[3,38,39]. For absorp- tion spectra, which are calculated by GGA and the scissor approx- imation correction. Furthermore, in Section 3.5, we calculated some data by using the GGA +Uin order to test the effect of Hub- bardU.

The plane-wave basis sets are generated using a kinetic cutoff energy of 450 eV (the convergence of the energy with cut-off shown inFig. S1). The integrations in reciprocal space is done by using the Monkhorst–Pack mesh for the Brillouin Zone[40]. The kpoint grid is set to be 555 for the 221 supercell, and 353 for the 231 supercell. For the structure optimiza- tion, we fully relax the doped lattice, including the lattice constants and atomic position, until the Hellmann–Feynman force acting on each atom is reduced down to less than 1.0 meV/Å.

We simulate the C mono-doped and C–Nb co-doped anatase TiO2using a 221 TiO2supercell containing 48 atoms. For the C mono-doping, one O is replaced by one C atom, denoted as TiO2@C. Similarly, for the C–Nb co-doping, one O atom and one Ti atom is replaced by one C atom and one Nb atom respectively, de- noted as TiO2@C–Nb. The atomic doping concentration is 4.16 at%, and the Nb doped concentrations about 2.1 at%. Schematics of TiO2@C and TiO2@C–Nb are shown inFig. S2. Moreover, for the C–2Nb compensated co-doped anatase TiO2, in order to get the same atomic doping concentration for compare, we use a 321 TiO₂supercell containing 72 atoms, and one O atom and two Ti atoms are replaced by one C atom and two Nb atoms respec- tively on the (0 1 0) planes, as shown inFig. 1and the Nb doped con- centrations about 2.1 at%. As we know that experimental material of Nb doped TiO2is generally Nb0.07Ti0.93O2(with atomic ratio of Nb to Ti at 7:93)[41,42], and the Nb doped concentration is about 2.3 at%. So, our C–2Nb co-doped TiO2choose 321 supercells with 72 atoms, having two doped Nb and one C atoms, and the Nb doped concentration is also about 2.1 at%. That is to say, our Nb doped concentration is close to experimental doped concentra- tion. Here, compensated co-doping system is our main focus, so the doped atom ratio of Nb to C should be at 2:1. Moreover, at low car- bon concentrations, carbon substitutional to oxygen is favored[18].

All those will ensure our doped concentrations and positions are reasonable. For compensated model, anion is bonded to cation. It is noted that the full charge compensation only occurs when the doped anion and cation are bonded together, and the configuration generally possesses the lowest total energy[27,28]. Therefore, there only are two non-equivalent compensated co-doping configurations: (i) one C–Nb bonding is along the [1 0 0] direction, and the other bonding is along the [0 0 1] direction, denoted as TiO2@C–2Nb–I, and (ii) both C–Nb bonds are along the [1 0 0] direc- tion, denoted as TiO2@C–2Nb–II. For our 321 supercell with 72 atoms, to investigate the size effect, we compare inFig. S3the band structures of anatase TiO2 with C–2Nb doped in 321 and 331 supercells. We find the finite size effects for 321 supercell may be ignored.

3. Results and discussion 3.1. Optimized geometry structure

The optimized structural parameters of pure, TiO2@C, TiO2@C–Nb, TiO2@C–2NbI and TiO2@C–2NbII are shown inTable 1.

The lattice parameters of the optimized cell for pure anatase TiO2

are: a=b= 3.804 Å and c= 9.663 Å, agreement with the earlier experimental [43] as well as theoretical[7–8,44]reports, which indicated that our structural optimization method is reasonable.

As shown inTable 1, the lattice constant changed slightly with dif- ferent doping system. For TiO2@C and TiO2@C–Nb, the changes of the lattice parameters relative to pure system are less than 0.05 Å, so the non-compensated doping has a very small influence on the lattice parameters. For TiO2@C–2NbI and TiO2@C–2NbII, the lattice parameterahas a growth about 0.05 Å,and the lattice parametersb andaare increased by about 0.1 Å and 0.3 Å. Obviously, compen- sated co-doping has some influence on the lattice parameters b

anda, which must be an average effect of internal atomic position adjustment of doping system. So, in order to further observe the changes of internal atomic position due to compensated co-doping, we calculated the bond lengths of TiO2@C–2NbI and TiO2@C–2NbII and summarized in data. At the same time, the optimized atomic positions on the (0 1 0) plane and the bonds are plotted inFig. 2, and the bond lengths are marked out with numbers in the diagram.

Moreover, for comparison, the corresponding parts of the perfect system are also presented inFig. 2(a) as a reference, it is seen that the local lattice of TiO2@C–2NbI shown inFig. 2(b) is seriously dis- torted. The Nb–C bond lengths (1.938 Å) of TiO₂@C–2NbI are short- er than the Ti–O ones (1.946 Å) of pure system along the [1 0 0]

direction, while, the Nb–C bond length (2.001 Å) is longer than the Ti–O ones (1.999 Å) of pure along the [0 0 1] direction. For the TiO2@C–2NbII, the local lattice is also distorted as shown in Fig. 2(c). The local structural distortions will also affect the changes of other Ti–O bond length within the doped system. So, we also ob- serve the changes of the interior Ti–O bond length along the [0 1 0]

direction (here not display in diagram). It is found the interior Ti–O bond length changes from 1.946 Å to 1.878 Å for TiO2@C–2NbI, and changes from 1.946 Å to 1.885 for TiO₂@C–2NbII, which is consis- tent with the lattice parameters data fromTable 1.

For non compensated model, C–2Nb doped TiO2 have many doped configurations, we choose some configurations to calculate the total energy and compare with compensated model. The related configuration diagram also is put inSupplementary Information Fig. S4, and the total energy of non-compensated configurations compare with compensated model of TiO2@C–NbI shown in Fig. S5. The total energy of compensated model of TiO₂@C–NbI is set to be zero point as reference. We found the energy of non com- pensated configurations is all larger than compensated model, which confirms that compensated co-doping configuration gener- ally possesses the lowest total energy[27,28].

3.2. Defect formation energy

Furthermore, in order to explore the relative difficulty of doping under different growth conditions, we calculated the doping for- mation energy of different doping system. The doping formation energy for TiO2@C, TiO2@C–Nb, and TiO2@C–2Nb can be calculated by the following relational expression respectively:

EðTiO2@CÞ_form¼EðTiO2@CÞ EðpureÞ þ

l

_O

l

_C ð1Þ

EðTiO2@CNbÞ_form¼EðTiO2@CNbÞ EðpureÞ þ

l

_Oþ

l

_Ti

l

_C

l

_Nb ð2Þ

EðTiO2@C2NbÞ_form¼EðTiO2@C2NbÞ EðpureÞ þ

l

_O

þ2

l

_Ti

l

_C2

l

_Nb ð3Þ whereE(TiO2@C),E(TiO2@C–Nb),E(TiO2@C–2Nb) are the total en- ergy of the corresponding doped system respectively, andE(pure) is the total energy of the pure host system,

l

Tiand

l

Oare the chem- ical potentials for Ti and O respectively in compound TiO2regarding the Ti–O phase diagram, satisfying expression

l

Ti+ 2

l

O=

l

[TiO2], with

l

[TiO2] being the chemical potential of compound TiO2, if the synthesis circumstance is O rich, then

l

O=

l

O[O2/2] and

l

Ti=

l

[TiO2]–2

l

O[O2/2],

l

O[O2/2] is the chemical potential of O ele- ment which equals to half of the total energy of an oxygen molecule.

However, if the synthesis circumstance is Ti rich, one has

l

Ti=

l

Ti[Bulk] and then

l

O= (

l

[TiO2]–

l

Ti[Bulk])/2,

l

Ti[Bulk] is the Fig. 1.Schematic of two kinds configurations of 231 anatase TiO2supercell codoped by one C atom and two Nb atoms, (a) TiO2@C–2NbI, and (b) TiO2@C–2NbII. The red (small solid), blue (big grey), brown (small solid), green (big dark) balls are the O, Ti, C, Nb ions, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 1

The optimized structural parameters (Å) of pure, TiO2@C, TiO2@C–Nb, TiO2@C–2NbI, and TiO2@C–2NbII.

a(Å) b(Å) c(Å)

Pure 3.804 3.804 9.663

3.806^a 3.806^a 9.677^a

3.845^b 3.845^b 9.537^b

3.782^c 3.782^c 9.502^c

TiO2@C 3.842 3.788 9.664

TiO2@C–Nb 3.848 3.801 9.708

TiO2@C–2NbI 3.851 3.693 9.948

TiO2@C–2NbII 3.845 3.694 9.960

aSee Ref.[7].

b See Ref.[8].

c See Ref.[43].

Fig. 2.Optimized (0 1 0) plane atomic structures of pure (a), TiO2@C–2NbI (b), and TiO2@C–2NbII (c). The atomic bond lengths are numerically labeled.

chemical potential of Ti element which is calculated from thehcp bulk metal Ti structure, i.e.

l

Ti[Bulk] =

l

Ti[metal]. As we know the formation enthalpyDHTiO₂for anatase TiO2may calculate by the for- mula: DHTiO2¼ ð

l

_Ti

l

_Ti½BulkÞ þ2ð

l

_O½O2=2Þ, and the calculated formation enthalpy is10.32 eV under the Ti rich condition, which is close to measured value reported in literature[45]and theoretical value in literature[25].

l

Cis the chemical potentials for C, which is calculated from the graphite, i.e.

l

C=

l

[graphite]/4;

l

Nbis the chem- ical potentials for Nb, which is calculated from thehcpbulk metal Nb structure, i.e.

l

Nb=

l

Nb[metal]. Obviously, for different synthesis cir- cumstance, the doping formation energy are different. Here we cal- culated doped formation energy under two extreme conditions. The calculated doping formation energies for TiO2@C, TiO2@C–Nb, TiO2@C–2NbI and TiO2@C–2NbII under Ti-rich and O-rich conditions respectively are displayed inTable 2. It is found that the formation energies for TiO2@C are 3.83 eV and 9.01 eV under Ti-rich and O-rich conditions respectively, which are in agreement with the value re- ported in literature[25]. This showed that C mono-doping (p-type doping) is difficult due to the low VBM and strong self-compensation [46,47]. For co-doped systems, the formation energies under Ti-rich condition are larger than those under O-rich condition, that is to say, TiO2@C–2Nb is easy to be formed under O-rich condition, which is constant with the previous theoretical study[25,26].

3.3. Electronic structures

The calculated band structures of pure TiO2 are plotted in Fig. 3(a). It is found that the pure anatase TiO2 is a direct band gap semiconductor, with the calculated band gap of 2.11 eV, which is similar to previous theoretical work[8,48]. But our result is still underestimated compared to the experimental band gap of 3.2 eV [49], due to the well-known limitation of the generalized gradient approximation (GGA).Fig. 3(b) is the band diagram of TiO2@C, we find the bands originating from C-2p states (shown inFig. 4(a)) mainly appear in the band gap, Here, the three gap states are lo- cated just about VBM of anatase TiO2, and the gap (Eg= 2.04 eV) be- tween the lowest Ti-3d band and the highest O-2p band is close to that (Eg= 2.11 eV) in the pure TiO2, showing that C-doped system cannot narrow the band gap, which verify again that the improved visible light photo-activity for C-doped TiO2is induced by the exis- tence of the isolated midgap levels rather than the band gap nar- rowing [8,26]. Moreover, TiO2@C have partially occupied localized midgap states, which is easy to create recombination cen- ters for electrons and holes inside TiO2[50], and may reduce the light-induced charge carrier migration to the surface for photoca- talysis [51]. When the supercell is doped with one C atom and one Nb atom, the three isolated midgap levels move a little to the valence band maximum (VBM), as shown inFig. 3(c). Although Nb provides an electron for compensation, partially occupied local- ized midgap states still existed. The calculated band structure of TiO2@C–2NbI and TiO2@C–2NbII are plotted in Fig. 3(d and e) respectively. Now, the two Nb provide two electrons as donor en- ough to occupy unoccupied localized gap states, and all gap states are fully occupied by electrons. At the same time, these gap states suppress obviously the effective band gap and thus improve visible light photo-activity. Compared the band structures of the two

Table 2

Calculated formation energies for TiO2@C, TiO2@C–Nb, TiO2@C–2NbI, and TiO2@C–2NbII.

Ti rich (eV) O-rich (eV)

TiO2@C 3.83 9.01

TiO2@C–Nb 2.99 2.19

TiO2@C–2NbI 5.02 10.53

TiO2@C–2NbII 5.09 10.46

(a) (b)

(c) (d)

(e)

Fig. 3.The calculated band structures along the high symmetry lines of the Brillouin zone for a supercell of pure system (a), TiO2@C (b), TiO2@C–Nb (c), TiO2@C–2NbI (d) and TiO2@C–2NbII (e). The red dashed lines represent the Fermi level. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

(a)

(b)

(c)

(d)

Fig. 4.Calculated TDOS and PDOS for the TiO2 a supercell of TiO2@C (a), TiO2@C–Nb (b), TiO2@C–2NbI (c), and TiO2@C–2NbII (d). The VBM of pure anatase TiO2is chosen as the Fermi level and set as energy zero. The dashed lines represent the highest occupied levels in the doped TiO2.

kinds doping configurations of TiO2@C–2Nb, the main difference is that there are significant differences in energy interval of gap states, which may also have some affect on optical properties of doping system. Further validation will be discussed in Section3.4.

The calculated total density of states (TDOS) and projected den- sity of states (PDOS) of TiO2@C, TiO2@C–Nb, TiO2@C–2NbI and TiO₂@C–2NbII are shown inFig. 4. In the case of TiO₂@C, the C dop- ant introduce three isolated midgap levels above the VBM and slightly affect the VB and CB edges. However, these gap states are all partially occupied because a carbon atom has two less 2p electrons than that of an oxygen atom. Moreover, such p-type dop- ing is difficult to form due to the relatively large formation energy, and easy to produce oxygen vacancies and form recombination centers for electrons and holes. In the case of TiO2@C–Nb, shown in Fig. 4(b). The C-2p states coupled with the Nb-4d state, and the partially occupied states still exist because the single donor of- fered by one Nb only could partially compensate the double accep- tor C. To further compensate, two Nb doping is necessary,Fig. 4(c and d) displayed the DOS of TiO2@C–2NbI and TiO2@C–2NbII, we find that the conduction band edge of co-doping system slightly are affected, which will keep the reduction potential potentials of pure TiO2. Moreover, the band gap states become entirely occupied because two single donors provided by two Nb atoms could totally compensate the double acceptor C. The C-2p states coupled with the adjacent O-2p, Nb-4d, Ti-4d state. Detailed information can be found inFig. 5(Fig. 5displayed the calculated partial charge density distributions of three isolated gap states for TiO2@C–2NbI and TiO2@C–2NbII, respectively), we found that the C-2p orbit split into C-2px, C-2py, C-2pzorbits, it is clear that the orbital character of the three isolated gap state is mostly attributed to the orbits of C-2px, C-2py, C-2pzcoupled with the adjacent O-2p, Nb-4d, Ti-4d orbits. ComparedFig. 4(c) withFig. 4(d), it is found that the dis- tance between the two lower gap states of TiO₂@C–2NbI is larger than that of TiO2@C–2NbII.

In order to further understand the electronic structure of the two configurations of TiO₂@C–2NbI and TiO₂@C–2NbII, the calcu- lated electron density and charge density difference are plotted inFig. 6. Comparison ofFig. 5(a–c), we find that the electron den- sity in the region between the C and Nb is larger than that between the O and Ti of pure system, which means that the covalent bond- ing in C–Nb group is stronger than that in O–Ti group. SeeFig. 5(b), the electron density in the region of C–Nb along the [0 0 1] direc- tion is smaller than that of C–Nb along the [1 0 0] direction. This implies that the overlapping of C and Nb along the [0 0 1] direction

is smaller than that along the [1 0 0] direction, while inFig. 5(c), be- cause the two C–Nb group are completely symmetrical in the geo- metric position, the electron density in the region of two C–Nb groups are the same to each other. SeeFig. 5(d–f), the charge den- sity difference of pure TiO2, TiO2@C–2NbI and TiO2@C–2NbII, it is found that the electron density difference in C region is larger than that in O region of undoped system, which means that electron numbers accepted by C in the C–2Nb co-doped system are larger than those accepted by O in the pure system. That also implies that the Nb in co-doping system donated more electrons than the Ti in the pure system. Moreover, the Nb ions are polarized along the C–Nb direction because of the repulsion of C ions, it is consistent with literature[52], and, other ions around the dopants also have different degree polarization. All of these are possible to produce an effective polarization field in the doped system, which may im- prove the catalytic performance of the system due to promote the separation of photoexcited electrons and holes[53,54].

3.4. Optical properties

The optical properties are essentially calculated by the dielec- tric function, which consist of two parts of the real and imaginary parts. The frequency dependent complex dielectric function can be expressed as

e

(x) =

e

1(x) +i

e

2(x). This is mainly related with the electronic structure of the materials. The imaginary part

e

2(x) can be calculated from the momentum matrix elements between the occupied and unoccupied wave functions. The real part of the dielectric function

e

1(x) can be calculated from the imaginary part of dielectric function

e

2(x) by the Kramer–Kronig relationship[55].

As the optical absorption spectrum can provide a comparative information on the optical properties of materials, which has been usually applied in previous studies[26,30], therefore, in this paper, we will study the optical characteristics of the doped system through the calculation of absorption spectrum. The corresponding absorption spectra were evaluated using the following expression [26]:

a

ð

x

Þ ¼ 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

e

²₁ð

x

Þ þ

e

²₂ð

x

Þ q

e

1ð

x

Þ

¹₂

ð4Þ

where

a

(x) is the absorption coefficient,

e

1(x) and

e

2(x) are the real part and the imaginary part of the dielectric function, respec- tively. In the most general case, the absorption coefficient is a ten- sor with six components because of the optical anisotropy of the

Fig. 5.Calculated partial charge density distributions of three isolated gap states of TiO2@C–2NbIa(1)a(3) and TiO2@C–2NbIIb(1)b(3).

crystal. In this paper, we analyze the absorption spectrum along the Xaxis to discuss the effect of the doping, which is a method widely adopted in the literature[56]. In addition, the calculated band gap was underestimated compared to experimental value, therefore, in order to make our optical absorption results compatible with experimental values, the scissor approximation[7,57]was used to correct the calculated optical results. The so-called scissors operator is to shift directly the unoccupied conduction band states relative to occupied valence band states. Our calculated band gap is 2.11 eV, while experimental gap value is 3.2 eV. So we select scissor opera- tor of 1.09 eV, and it is used to adjust our results to achieve exper- imentally observed values. At last, the calculated optical absorption coefficient curves as the function of photon energy for undoped TiO2, TiO2@C–2NbI and TiO2@C–2NbII are shown inFig. 7. In gen- eral, the wavelength region of visible light is 390–760 nm, and the energy region is about 1.64–3.19 eV marked out in Fig. 7 using green oblique lines. SeeFig. 7, we found that the absorption edge of pure TiO2is out of the region of visible light and locate in the range of ultraviolet light. In comparison, both the absorption edges of TiO2@C–2NbI and TiO2@C–2NbII extend up to the visible light re- gion. That is to say, co-doping achieved the expected absorption edge redshift[41]. Compensated co-doped anatese TiO₂has good

absorption in the form of broad absorption region due to the exis- tence of widely distributed impurity states in the band gap. More- over, the absorption coefficient of TiO2@C–2NbII (the red line in the graph) is larger than that of TiO2@C–2NbI (the dark blue line in the graph) in the range of visible light on the whole. It indicated that C–2Nb co-doped TiO2in configuration II is more conducive to improving the absorption of visible light, which may be due to the slight differences in the electronic structure of the two kinds configurations. Our calculated absorption spectra further confirm that the compensated C–2Nb co-doped TiO2is a feasible method to improve visible light catalytic absorption.

3.5. The effect of Hubbard U

We have demonstrated that the GGA functional provides a good overall description of the electronic and optical properties of co- doped anatase TiO2. To improve the accuracy of band structure and energy gap, the non-local effect needs to be incorporated in the XC functionals[58,59]. Indeed, it is well known that the DFT of- ten underestimates the band-gap values of transition-metal oxides significantly[60,61], due to its inaccuracy in dealing with the XC functionals of d electrons. In order to account for strongly corre- lated interactions of the d electrons, the GGA +Umethod was used to calculate the electronic properties, and HubbardUparameters, introduced by Dudarev et al.[62]are applied to Ti-3d and Nb-3d electrons. As a simple and effective method, the on-site effective Ucorrection has been extensively used to take into consideration due to the Coulomb interaction in some transition-metal oxides structures. TheU= 5.8 eV for the Ti-3d electrons[63]and 4.0 eV for the Nb-4d electrons[64]will be used in the following GGA +U calculations to test the Hubbard effect on the electronic structure of doped anatase TiO2.

First, let us examine the effect of HubbardUcorrection on the doped configurations, using TiO2@C–2Nb as examples, where U= 5.8 eV and 4.0 eV are applied to the Ti-3d and Nb-3d electrons respectively. The TDOS calculated using the GGA +Uare shown in Fig. 8(b and d). ComparingFig. 8(a–d), it is apparent that the incor- poration of HubbardUopens up the energy gap by elevating the CBM about 0.7 eV, and the VBM shows ignorable difference be- tween the GGA and GGA +Ucalculations. This is mainly attributed Fig. 6.Calculated electron density of pure (a), TiO2@C–2NbI (b) and TiO2@C–2NbII (c), and the electron density difference of pure (d), TiO2@C–2NbI (e) and TiO2@C–2NbII (f).

Contours show the values in a slice of the (0 1 0) plane. The units are electrons ų. In panels (a–c), color from blue to red represent electron density changes from low to high.

In panels (d–f), color red (blue) represent the electron density increased (decreased) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

Fig. 7.Calculated optical absorption spectrum of pure TiO2, TiO2@C–2NbI and TiO2@C–2NbII.

to the fact that the VBM of the doped TiO2is mainly composed of the O-2p states and the CBM is mainly composed of the Ti-4d states. Other than that, we find that the characteristics of TDOS have almost no change from the GGA +U and GGA calculations.

Such as, the shape of three gap states induced by doping atoms is also similar to each other.

Second, we recalculate the optical properties of TiO2@C–2NbI and TiO2@C–2NbII using GGA +U. the calculated optical absorption coefficient curves as the function of photon energy for undoped TiO2, TiO2@C–2NbI and TiO2@C–2NbII are shown inFig. 9. We find that the absorption edge of pure TiO2is out of the region of visible light and locate in the range of ultraviolet light. In visible light re- gion, absorption spectrum for TiO2@C–2NbI (the dark blue line in Fig. 9) exhibits two optical absorption peaks at 2.56 eV and 3.00 eV, and absorption spectrum for TiO2@C–2NbI (the red line inFig. 9) exhibits one optical absorption peaks at 2.46 eV, which

shows that the co-doped models provide good visible light photo- catalytic activity compared to experimental results of mono-doped system[12,13]. ComparingFigs. 9 and 7(The optical absorption spectrum shown inFig. 7 is calculated by GGA and the scissor approximation correction), we find that both the absorption edges by two different methods extend up to the visible light region. That is to say, co-doped TiO₂ achieve the expected absorption edge redshift both using GGA and GGA +U methods. Moreover, the TiO2@C–2Nb systems exhibit stronger visible light absorption using GGA +U.

4. Conclusion

In summary, we have carefully calculated the electronic struc- tures and optical properties of TiO2@C, TiO2@C–Nb, TiO2@C–2NbI and TiO2@C–2NbII using the first-principles density functional cal- culations. Our results indicate that the mono-doping of C is diffi- cult to form due to the large positive formation energy, and that the gap states are partially occupied are also easy to form the recombination centers for electrons and holes. For TiO₂@C–2Nb, the co-doping structures become easy to form because the com- pensated co-doping effect results in a larger negative formation en- ergy under O rich condition. The gap states not only become fully occupied by electrons but also suppress obviously the effective band gap, and the optical absorption edges extend up to the visible light region. Moreover, the configurations of TiO2@C–2NbII is more conducive to improving the absorption of visible light.

Acknowledgements

This work was supported by the National 973 Projects of China (Grant Nos. 2011CB922101 and 2009CB623303), the Natural Sci- ence Foundation of China (Grant Nos. 11234005 and 11074113), and the Priority Academic Program Development of Jiangsu Higher Education Institutions, China.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.commat- sci.2013.1 2.048.

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