Tailoring the electronic and optical properties of anatase TiO2 by (S, Nb) co-doping from a DFT plus U calculation

Solid State Communications 223 (2015) 54–59

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Tailoring the electronic and optical properties of anatase TiO2 by (S, Nb) co-doping from a DFT plus U calculation Dahua Ren a, Huiran Li a, Xinlu Cheng a,b,n a b

Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, PR China Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610064, PR China

art ic l e i nf o

a b s t r a c t

Article history: Received 24 June 2015 Received in revised form 4 September 2015 Accepted 18 September 2015 Accepting editor: M. Grynberg Available online 3 October 2015

The geometrical structure, defect formation, electronic and optical properties of S-doped, Nb-doped, and (S, Nb)-codoped anatase TiO2 were successfully calculated by the first-principles plane-wave ultrasoft pseudopotential method based on the density functional theory with plus U method. Firstly, the geometrical structure demonstrates that the (S, Nb) co-doping can effectively induce lattice distortion and reduce the recombination of electron–hole pairs. Note that the (S, Nb)-codoped system further reduces the band gap compared with pure and mono-doped TiO2 due to the mixture of S 2p and Nb 4d states appears in the gap, which results in an obvious red-shift in the optical absorption spectra and improves the photocatalytic activity. Moreover, the (S, Nb) co-doping should be grown under Ti-rich conditions while S or Nb mono-doping is expected to be easier under O-rich conditions. The above results would be beneficial to further developing for titanium dioxide photocatalyst. & 2015 Elsevier Ltd. All rights reserved.

Keywords: A. Codoping anatase TiO2 D. Electronic structure D. Optical properties E. Density functional theory

1. Introduction Titanium dioxide (TiO2) has been extensively studied as one of the most promising semiconductor photocatalysts because of its excellent properties such as high photocatalytic activity, good chemical and thermal stability, low cost etc. [1–4]. Therefore, anatase TiO2 plays a very important role in ideal catalytic materials for water splitting and purification as well as environmental pollutants degradation through sunlight irradiation. Nevertheless, anatase TiO2 has just been limited in ultraviolet light range due to its wide band gap (
3.20 eV), which leads to quite low solar energy usage [5,6]. Therefore, it is the construction of efficient and sustainable photocatalysts working well under visible light that becomes a major challenge in the photocatalyst field [7]. Doping TiO2 with all kinds of impurities is a common approach to tailor the band gap. Thus, many efforts have been made to modify the electronic structure of TiO2 in order to extend the optical absorption edge into visible-light range and increase the photocatalytic efficiency through doping TiO2 with non-metals (N [8], C [9], B [10], I [11,12], S [13,14] etc.), transition metals [15,16], nonmetal–non-metal codopants [17,18] and metal–non-metal codopants [19–25]. Experimental and theoretical doping with sulfur n Corresponding author at: Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, PR China. Tel.: þ 86 28854 05526; fax: þ 86 28854 05515. E-mail addresses: [email protected] (D. Ren), [email protected] (H. Li), [email protected] (X. Cheng).

http://dx.doi.org/10.1016/j.ssc.2015.09.011 0038-1098/& 2015 Elsevier Ltd. All rights reserved.

(cation, anion) into TiO2 have succeeded in narrowing its band gap [14,26]. For example, Li et al. [27] prepared S-doped TiO2 which showed strong absorbance under visible light. Tian et al. [28] pointed out substitutional S-anion doped anatase TiO2 leaded to the red-shift of absorption edge because an impurity state S 3p located above the valence band. In addition, recent researches demonstrated that the red-shift of the absorption edge increased and the band gap decreased gradually with the sulfur concentration increasing [29,30]. However, as the impure S-doping states occurs upon the valence band top, the recombination center formation of electrons and holes would be induced and thus the photocatalytic activity would be decreased. Furthermore, Nb-doped anatase TiO2 based on first-principle method has been reported. Osorio-Guillén et al. [31] calculated the formation energy of Nb-doped TiO2 with the generalizedgradient-approximation (GGA) Perdew–Burke–Ernzerhof (PBE) functional. Liu et al. [32] studied the electronic structure and optical properties using the local density approximation (LDA). Both of them focused on the substitutional Nb dopant for Ti sites and the reduced band gap. However, the mono-element Nb doping forms partial occupation of the localized mid-gap states [33], which may form recombination centers to degrade the photocatalysis efficiency [34,35]. Fortunately, recent researches have proved that metal–nonmetal doping TiO2 can decrease the recombination of electron–hole pairs as the metal ions play a role in mediators for charge transfer. Indeed, it was shown that (N, Fe)-codoped TiO2 noticeably increased the photocatalytic activity under visible-light irradiation [4]. Therefore, the

D. Ren et al. / Solid State Communications 223 (2015) 54–59

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synergistic effect of codoping with the above mentioned nonmetal (C, N, B, I, S etc.) and transition metal ions (Nb, Cr, Mo, Ta, Fe etc.) into TiO2 can successfully extend the absorption edge into visible light range and significantly improve the efficiency of photocatalysis [4, 36–39]. According to the above analysis, the (S, Nb)-codoping may be a good scheme and has not been studied even though a few works have been carried out about Nb–M (M ¼C, N, Ta) [36,40] and S–X (X ¼I, N) [17,41] codoped TiO2. So it is very necessary to investigate the electronic structures and optical properties of the (S, Nb)codoped anatase TiO2. In this work, we calculate the electronic structures and optical properties of the (S, Nb)-codoped anatase TiO2 based on the density functional theory (DFT). For comparison, we also study the electronic and optical properties of the S-, and Nb-doped anatase TiO2 in detail.

It is well known that the GGA method underestimates the band gap of TiO2 in comparison with the experimental results (2.11 eV vs. 3.20 eV), which is consistent with the calculated band gap [46]. However, DFTþ U approach introduces an on-site correction to well describe systems with localized d electrons, which can produce better band gaps compared with experimental results. The values of parameter U¼ 7.5 eV for the Ti-3d electrons [45] and 4.0 eV for the Nb-4d electrons [47] will be used in the following GGA þU calculations to test the Hubbard effect on the electronic structure of doping anatase TiO2. Accordingly, the calculated band gap of pure anatase TiO2 was 3.06 eV, which agrees well with the experimental value of 3.20 eV [48]. For optical properties the complex dielectric function is ε ¼ ε1 þiε2. Commonly, the imaginary part of the dielectric function, ε2, can be calculated from the momentum matrix elements described by the formula [49]:

2. Models and computational methods

ε2 ðℏωÞ ¼

The bulk unit cell of anatase TiO2 (Ti4O8) has a symmetry of space group D19 4h I 41 =amd. A relaxed (2  2  1) 48-atom anatase supercell is consisted of the doped systems, as shown in Fig. 1. In S- or Nb-doped TiO2 model, an O atom is substitutional for a S atom or a Ti atom is substituted by a Nb atom. Similarly, for (S, Nb)-codoped TiO2, an O atom is replaced by a S atom, and one of its adjacent Ti atoms is replaced by a Nb atom in the supercell. Therefore, after substituting a Nb atom at the Ti site, the Nbdoping concentration is 6.25%(Ti1  xO2Nbx), which could be comparable with the experimental results [42]. The electronic and optical properties of S-, Nb-doped and (S, Nb)-codoped anatase TiO2 with first-principles calculations based on DFT were performed as implemented in the VASP code [43]. The ultrasoft pseudopotential with 2s22p4(O), 3s23p4(S), 4d45s1 (Nb) and 3p63d34s2(Ti) was applied to describe the interaction between electrons and ionic core. The electronic exchangecorrelation energy was the generalized gradient approximation (GGA) with Perdew–Burke–Ernzerhof (PBE) [44]. The energy cutoff was set to be 380 eV [45] for all calculations to ensure the accurate results and Brillouin zone integrations were approximated by using the special k-point sampling of Monklorst–Pack mesh size of 5  5  5. In the optimization, the convergence threshold for selfconsistent tolerance and maximum force tolerance was set as 10  5 eV/atom and 0.03 eV/Å, respectively.

where Ω, C, V, k, ω, û are the volume of cell, conduction band, valence band, k point, frequency of incident light, external field vector respectively, while ψ Ck and ψ Vk represent the eigenstates. The real part of the dielectric function, ε1, can be evaluated from ε2 by the Kramer–Kronig relationship [50]. Subsequently, the corresponding absorption coefficient was obtained using the following equation:

2e2 π X

Ωε0

k;V ;C

  j ψ Ck j u^ U rj ψ Vk j 2 δ½ECk  ECk  ℏω

½ε2 ðωÞ þ ε22 ðωÞ1=2  ε1 ðωÞ αðωÞ ¼ 2ω 1 2

ð1Þ

!1=2 ð2Þ

3. Results and discussions 3.1. Geometry structure and formation energy The optimized structural parameters of pure, S-, Nb-doped and (S, Nb)-codoped TiO2 are listed in Table 1. After geometrical optimization, the calculated lattice parameters of pure TiO2 are obtained a ¼b ¼3.806 Å and c¼ 9.679 Å, which accord well with the experiment values [51] and theoretical values [4,52], respectively. The calculated result indicates that the structural optimization method is reasonable and authentic.

Fig. 1. (Color online) Supercell model for (a) pure, (b) (S, Nb)-codoped anatase TiO2 in the present work. The gray, red, yellow and blue spheres represent the Ti, O, S and Nb atoms, respectively.

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D. Ren et al. / Solid State Communications 223 (2015) 54–59

As listed in Table 1, the changes of lattice constants of anatase TiO2 are significant for mono- and co-doping TiO2. Both Ti–S and Nb–O bond lengths for S- and Nb-doped anatase TiO2 are longer than the Ti–O ones of the pure anatase TiO2. Thus the distortion of the crystal lattice around S anion is just appeared. For the (S, Nb)codoped TiO2, the Nb–S and Nb–O bond lengths are shorter than the Ti–S and Ti–O ones as the radius of S and Nb atoms are larger than that of O and Ti atoms. The results demonstrate that the (S, Nb)-codoping leads to a large lattice distortion which would

Table 1 The calculated equilibrium lattice parameters (Å), average bond lengths (Å) and defect formation energies Ef (eV) of the pure and doping anatase TiO2.

Pure TiO2

S-doped

Nb-doped

(S, Nb)codoped

a(Å)

b(Å)

c(Å)

Ti(Nb)–O or Ti(Nb)–S (Å)

Ef in eV (Ti rich)

Ef in eV(O rich)

3.806 3.782a 3.818b 3.804c 3.877 –

3.806 3.782a 3.818b 3.804c 3.989 –

9.679 9.502a 9.480b 9.663c 9.906 –

1.976 1.956a 1.976b

– – –

– – –

1.53 –

13.26 –

3.938 3.796e 3.876f 3.884

3.924 3.796e 3.876f 4.006

9.895 9.559e 9.758f 9.966

2.001, 2.287 2.004d, 2.276d 2.042, 2.005 – 2.023f 2.069(1.995), 2.355(2.239)

 1.90 – – 2.95

5.92 – –  0.96

a

Ref. [51] Ref. [4] Ref. [52] d Ref. [14] e Ref. [53] f Ref. [46] b

EðTi16 O31 SÞf orm ¼ EðdopedÞ  EðpureÞ  μS þ μO

ð3Þ

EðTi15 O32 NbÞf orm ¼ EðdopedÞ  EðpureÞ  μNb þ μTi

ð4Þ

EðTi15 O31 NbSÞf orm ¼ EðdopedÞ  EðpureÞ  μNb  μS þ μTi þ μO

ð5Þ

where E(doped) and E(pure) are the total energies of the doping and pure systems, respectively; μS is the chemical potential of S, which is determined from the sulfur dioxide (μS ¼ μSO2  2μO ); μNb is the chemical potential of Nb, which is calculated from the bulk (μNb ¼ μmetal Nb ); μO and μTi are the chemical potentials of O and Ti, respectively. For TiO2, the chemical potentials of O and Ti always satisfy the relationships μTi þ 2μO ¼ μTiO2 , and μO r μO2 =2, μTi r μmetal . Notably, the formation energy is different for O- or TiTi rich growth conditions. Under Ti-rich growth condition, μTi can be achieved from the bulk Ti (μTi ¼ μmetal ) and then μO ¼(μ(TiO2) Ti  μTi)/2. Otherwise, under O-rich growth conditions, the chemical potential μO can be determined from the ground state energy of the O2 molecule (μO ¼ μ(O2)/2) and then μTi ¼ μ(TiO2)  2μO. The calculated formation energies for S-, Nb-doped, (S, Nb)-codoped anatase TiO2 under Ti- and O-rich conditions are summarized in Table 1. The smaller the doping formation energy Ef is, the easier impurity ions are incorporated into TiO2. It is observed that the formation energies of S-, Nb-doped anatase TiO2 under O-rich condition are less than those under Ti-rich condition except for (S, Nb)-codoped anatase TiO2. It means that the mono-doped systems can be formed easily under O-rich conditions, on the contrary the

4

4

3

3

2

2

1

1

Energy(eV)

Energy(eV)

c

influence the dipole moments and reduce the formation of recombination centers. In order to understand the relative difficulty of doping under different growth conditions, the formation energies of different doping systems are calculated and then the doping formation energies Ef are given by

0 -1 -2

0 -1 -2 -3

-3

-4 -4 -5

G

F

Q

Z

G

4

4

3

3

2

2

1

1

Energy(eV)

Energy(eV)

-5

0 -1 -2

-4

-5

-5 -6

Q

Z

G

Z

G

G

F

Q

Z

G

-2 -3

F

Q

0

-4

G

F

-1

-3

-6

G

Fig. 2. The calculated band structures of (a) pure TiO2, (b) S-doped TiO2, (c) Nb-doped anatase TiO2 and (d) (S, Nb)-codoped TiO2.

D. Ren et al. / Solid State Communications 223 (2015) 54–59

co-doped system will be favorably formed under Ti-rich conditions. Under O- and Ti-rich growth conditions, the formation energy of S-doped anatase TiO2 is much larger than that of Nbdoped.

means of electronic orbits of impurity atoms, resulting in the decrease of the band gap for the co-doping. Specifically, the band gaps for S-doped, Nb-doped and (S, Nb)-codoped systems decrease 0.73, 0.81 and 0.91 eV, respectively. For S-doped anatase TiO2, the bottom of conduction band moves toward Fermi level, the impure state is located in the valence band, thus electrons in the valence band can be excited to impure energy levels and finally to the conduction band. In the case of Nb-doped anatase TiO2, one isolated impurity energy level is just located below the conduction band bottom and another impurity energy level is situated around Fermi level. Therefore, the above impure states are located in the band gap and the band gap of anatase TiO2 is narrowed after S or Nb doping. For (S, Nb)-codoped anatase TiO2, the splitting of the energy levels becomes more apparent compared with the monodoping because of the more impurity energy levels formed in the band gap. In short, (S, Nb) co-doping can efficiently modify the band structure of anatase TiO2, and introduce impure energy levels

3.2. Electronic structure

Pure TiO2

50 45

30 15 0 45 30 15 0 45 30 15 0

Nb-doped TiO2

(S,Nb)-codoped TiO2

35 30 25 20 15 10 5 0

-5

-4

-3

-2

-1 0 Energy(eV)

1

2

3

-6

4

-5

-4

-3

-2

-1

0

1

2

3

4

3

4

Energy(eV)

50

50

O_2p Ti_3d S_3p

45 40

O_2p Ti_3d Nb_4d

45

PDOS(electrons/eV)

PDOS(electrons/eV)

O_2p Ti_3d

40

S-doped TiO2

PDOS(electrons/eV)

TDOS(electrons/eV)

The calculated band structures of pure TiO2 and S-, Nb-doped, (S, Nb)-codoped anatase TiO2 are plotted in Fig. 2. It is observed that new impurity energy levels appear in the forbidden gap and the band gap decreases because of the decreasing degree of crystal symmetry after doping as well as the destructions of periodic potential field. Moreover, the decreasing grade of conduction band bottom is a bit smaller than that of valence band top, thus the band gap has become a little narrower after doping especially for the co-doping. At the same time, three new defect energy levels are introduced between valence band and conduction band by

60 45 30 15 0 45

57

35 30 25 20 15

40 35 30 25 20 15

10

10

5

5

0

0 -6

-5

-4

-3

-2

-1

0

1

2

3

4

-6

-5

-4

-3

Energy(eV)

-2

-1

0

1

2

Energy(eV)

50

O_2p Ti_3d S_3p Nb_4d

PDOS(electrons/eV)

45 40 35 30 25 20 15 10 5 0 -6

-5

-4

-3

-2

-1

0

1

2

3

4

Energy(eV)

Fig. 3. (a) The calculated total density of states(TDOS) of pure and doping anatase TiO2; calculated partial density of states(PDOS) of, (b) pure anatase TiO2, (c) S-doped anatase TiO2, (d) Nb-doped anatase TiO2 and (e) (S, Nb)-codoped anatase TiO2.

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D. Ren et al. / Solid State Communications 223 (2015) 54–59

3.3. Optical properties

Absorption coefficient(cm )

60000 50000

Pure S-doped Nb-doped (S,Nb)-codoped

40000 Visible light

30000 20000 10000 0 1.0

1.5

2.0

2.5

3.0

3.5

4.0

Energy(eV) Fig. 4. Optical absorption spectra of pure and doped TiO2 models.

in the band gap. Hence, after co-doping the band gap of system effectively decreases, the separation of electron–hole pairs catches favorable, the absorption edge extends into visible light region and the photocatalytic activity makes improvement. It is found that pure anatase TiO2 is a direct band gap semiconductor in Fig. 2(a). The calculated band gap is 3.06 eV, which coincides very well with the theoretical values (3.08 eV) [4] by GGA þU method. Although the calculated value is a bit smaller than the experimental value of 3.20 eV, it shows a significant improvement compared with GGA method. As shown in Fig. 2(b), the calculated band gap for S-doped TiO2 is about 2.33 eV, indicating that the S doping induces a band gap narrowing with regard to the pure TiO2 and improves visible light photocatalytic activity. As depicted in Fig. 2(c), the calculated band gap of the Nb-doped TiO2 is only about 2.25 eV, which is lower than that of pure and Sdoped TiO2. Compared with the pure TiO2, a decline of the CBM and a slight increase of the VBM are found for Nb-doped TiO2. For (S, Nb)-codoped TiO2, the calculated band gap is just about 2.15 eV in Fig. 2(d). Compared with pure TiO2, its CBM is significantly reduced, and its VBM remains almost unchanged. The above results show that (S, Nb)-codoping can effectively reduce the band gap of anatase TiO2, and enhance the visible-light absorption. For further understanding the electronic structure of pure and S-, Nb-, (S, Nb)-doped TiO2, the total density of states (TDOS) and projected density of states (PDOS) are calculated and displayed in Fig. 3. The TDOS and PDOS of pure TiO2 are depicted in Fig. 3(a) and (b), respectively. It is found that the hybridizations of O 2p and Ti 3d states are consisted of the valence bands of pure TiO2. Moreover, the VBM is occupied by O 2p states, and the CBM is dominated by Ti 3d states. It means that the electron transition from O-2p to Ti-3d states is responsible for the optical absorption which is consistent with the results [14,19]. In Fig. 3(c) for S-doped TiO2, an impurity state of S 3p above the valence band is situated, in good agreement with the result [28]. It is also shown in Fig. 3(d) that Nb 4d states can induce a deep donor level inside the gap of TiO2, which is the reason that the Nb atom is commonly chose as an donor [36]. In the case of (S, Nb)codoped TiO2 in Fig. 3(e), the S 2p states stay in the valence band and the Nb 4d states are mainly located in the conduction band. As shown in Fig. 3(e), the narrowing band gap of the (S, Nb)-codoped TiO2 is caused by the synergistic effects of the S 2p and Nb 4d states, where both the CBM and VBM has a large shift down. As the impure energy levels are induced in the band gap, the electrons in the valence band can be firstly excited to them and subsequently excited to the conduction band under visible-light irradiation. Therefore, the absorption edge extends to visible-light region due to these impure energy levels appear in the gap.

Due to the optical anisotropy of the crystal, the absorption spectra along the Z axis between 1.0 and 4.0 eV are achieved to analyze the doping effect, as shown in Fig. 4. In order to compare the band gaps for different doped cases with the available experiment values, the calculated optical properties are corrected here by applying scissor operator (0.14 eV). It is recognized that incorporating impure atoms into TiO2 produces obvious red-shift effects. For S-doped system, the narrowing of band gap is responsible for the red-shift of optical absorption edge compared with pure anatase TiO2. For Nb-doped system, the band gap has a decline about 0.81 eV, thus it can also cause the red-shift in the optical absorption spectrum. Even though the mono-doping systems can extend the absorption edge to visible-light region, the absorption efficiency is not ideal. For (S, Nb)-codoped anatase TiO2, it has a larger absorption coefficient in visible-light region compared with the pure and S-, Nb-doped anatase TiO2, which is due to the obviously narrowed band gap and the appearance of the mixture of S 2p and Nb 4d impurities in the forbidden gap. These results may be responsible for improving the outstanding visiblelight photocatalytic activity and the red-shift of optical absorption edge in (S, Nb)-codoped TiO2.

4. Conclusions We have investigated the electronic and optical absorption properties of pure, S-doped, Nb-doped, and (S, Nb)-codoped anatase TiO2 by DFTþU method. The results show that the band gap for S doping system decreases about 0.73 eV and the band gap of Nb doping system reduces 0.81 eV. The synergistic effect of the S and Nb leads to lattice distortion, obviously narrowing band gap, and easy separation of photo-generated electron–hole pairs after co-doping. Furthermore, the (S, Nb)-codoped system should be grown under Ti-rich conditions while S or Nb mono-doping is expected to be easier under O-rich conditions. Moreover, the optical absorption spectra show that the (S, Nb)-codoped system exhibits a significant red-shift of absorption edge, and improves photocatalytic activity. It suggests that the (S, Nb)-codoped TiO2 has a high photocatalyst activity for developing efficient visiblelight photocatalysis.

Acknowledgments We thank the financial support from the National Natural Science Foundation of China (NSAF) about Grant no. 11374217 and NSFC. Grant no. 11176020).

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