Band gap engineering of compensated (N, H) and (C, 2H) codoped anatase TiO2: A first-principles calculation

Chemical Physics Letters 539–540 (2012) 175–179

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Band gap engineering of compensated (N, H) and (C, 2H) codoped anatase TiO2: A first-principles calculation Min Li a, Junying Zhang a,⇑, Dong Guo b, Yue Zhang c a

Key Laboratory of Micro-nano Measurement, Manipulation and Physics (Ministry of Education), Department of Physics, Beihang University, Beijing 100191, PR China Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, PR China c School of Materials Science and Engineering, Beihang University, Beijing 100191, PR China b

a r t i c l e

i n f o

Article history: Received 25 March 2012 In final form 27 April 2012 Available online 8 May 2012

a b s t r a c t The electronic structures and optical properties of non-compensated (C, H)-, compensated (N, H)- and (C, 2H)-doped anatase TiO2 have been investigated using spin-polarized density functional theory. The calculated results indicated that compensated (N, H) codoped TiO2 exhibited the enhanced optical absorption under visible-light irradiation in comparison with N doped TiO2 and pure TiO2. Compensated (C, 2H) codoped TiO2 may also be a good candidate for visible-light photocatalyst materials due to the band gap narrowing significantly and the elimination of some local states. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Titania (TiO2) is a promising material for application as photocatalyst for environmental cleaning, and water splitting, and also in solar cells due to its low cost, nontoxic, long-term stability and high oxidative power [1,2]. However, the photoreaction efficiency of TiO2 is to some extent constrained by its wide intrinsic band gap, which requires ultraviolet portion of the solar spectrum [3,4]. Because ultraviolet light accounts for only a small fraction (5%) of the sun’s energy as compared to visible light (45%), the shift in optical response of TiO2 from the ultraviolet light to the visible spectral range will have a profound positive effect on the practical applications of the material. It is well known that to enhance the solar energy conversion efficiency, the desirable photocatalyst should have an optimal band gap [4,5]. Consequently, band gap engineering has been an important issue for optimizing the performance of TiO2. A common approach to band gap reduction has been focussed on doping various impurities in TiO2 [6–16]. Compared to the metal doping, nonmetal doping, especially N [15,17– 19] and C [8,20–24] doping, has been extensively investigated to account for the visible light activity both theoretically and experimentally. In 2001, Asahi et al. [4] have reported that anatase TiO2 doped with N can remarkably improve the photocatalytic activity under visible-light irradiation. This was attributed to the mixing of N 2p with O 2p states. Further theoretical and experimental research found that the N-doping did not cause the narrowing of the band gap of the anatase TiO2 [25–28]. Instead, the formation of localized midgap states above the valence band maximum by N-doping is responsible for the visible photoactivity. In addition, ⇑ Corresponding author. Fax: +86 10 82315351. E-mail address: [email protected] (J. Zhang). 0009-2614/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2012.04.057

recent experimental and theoretical studies also indicated that Cdoping induced several localized occupied states in the band gap which could effectively extend the optical absorption of TiO2 to the visible region [8,20–24]. However, these localized midgap states may create recombination centers inside TiO2, which mitigate the light-induced charge carriers’ migration to the surface for photocatalysis [25,6]. It has been recognized that compensated codoping in TiO2 can reduce the recombination centers which can effectively improve the charge carriers’ migration efficiency and enhance the photocatalytic activity [13–16]. Hydrogen is a very active atom, which can represent qualitatively different behavior depending on the host. Recently, Chen et al. [29] found that the photocatalytic activity of TiO2 could be greatly enhanced by introducing hydrogenation. Recent reports have proposed and demonstrated the use of the N/H [30,31] codoping to improve visiblelight photocatalytic efficiency due to band gap narrowing. Li et al. [32] have suggested that the visible-light response in C/H codoped TiO2 may be due to two isolated energy states in the band gap. Considering that substitutional N or C yields unpaired electrons in the doped system, the down-spin states can be different from spin-up states. Therefore, spin polarized density functional theory (DFT) should be employed in the calculation. Furthermore, the photocatalytic activity of the compensated (C, 2H) codoped TiO2 has not been reported up to now. Therefore, the nonmetals (N or C) and H compensated codoping effect on the electronic structure and optical properties of TiO2 by spin polarized DFT are worthy of attention, which might eventually help to understand the photocatalytic activity of doped TiO2 and design high-efficient photocatalyst. In the present work, we focus on the investigation of the electronic structures and optical properties of compensated (N, H) and (C, 2H) codoped TiO2. We find that compensated (N, H)

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codoped TiO2 forms the continuum states above the top of the valence band, and thus limits the formation of electron–hole recombination centers. The compensated (C, 2H) codoping system gives rise to much more effective band gap narrowing than either noncompensated doping or monodoping systems. The narrowing of the band gap and reduction of recombination centers could serve to contribute to the improvement of photocatalytic activity. Consequently, the compensated (N, H) and (C, 2H) codoped TiO2 are very promising photocatalytic materials. 2. Computational details The calculations were carried out using the CASTEP code [33], based on spin-polarized DFT within the generalized gradient approximation (GGA) by Perdew and Wang (PW91 – GGA) for exchange correction. The valence electrons of all atoms used in these calculations are defined by ultrasoft pseudopotentials. It is well known that the DFT + U or DFT hybrid methods [34,35], as the improvement of standard DFT, can overcome underestimation of band gap in a standard DFT calculation. However, the DFT is still sufficiently satisfying to investigate the relative changes of band gap due to doping. The cutoff energy for the plane wave expansion was 340 eV and the Monkhorst–Pack k-point mesh for the Brillouin-zone integration was generated with a 3  7  3. Structural relaxations were performed until all the residual forces on atoms were less than 5 meV/Å. 3. Results and discussion 3.1. Optimized structure and formation energy The lattice parameters of a relaxed cell for pure anatase TiO2 are found to be a = 3.80 Å and c = 9.79 Å, in good agreement with other theoretical results [36]. However, a small difference exists between experimental values (a = 3.78 and c = 9.51) [37] and our calculated results. For doping cases, a 2  2  1 anatase TiO2 supercell containing 48 atoms is used. The codoping system is created by substitution of one O atom by one N or C atom at the center of the supercell, where H is bonded to the N or C atom. For N/H and C/H doping models, we consider two possible types of H atom on the N (C) site. First, H atom is perpendicular to the Ti–O–Ti plane. Secondly, H atom is parallel to the Ti–O–Ti plane. Our calculated results indicate that the hydrogen atom is stable to be perpendicular to the Ti–O–Ti plane. For compensated (C, 2H) codoped TiO2, we also consider two possible types. It is found that two H atoms perpendicular and parallel to the Ti–O–Ti plane, respectively, are more stable than two H atoms both perpendicular to the Ti–O–Ti plane. Thus, we plot the stable compensated codoping models (N, H) and (C, 2H) in Figure 1. To modify the structure of TiO2 through doping, we first consider the effect of different doping on lattice constants. Table 1 shows the change of lattice constants of anatase TiO2 by various doping approaches. The monodoping and codoping systems do not cause significant change to the lattice constant, which could be the results of optimized size match. As shown in Table 1, the Ti–N bond lengths are slightly larger than pure Ti–O ones. However, the structure changes for replacing one O with one C atom are more noticeable than those for substituting one O with one N atom. The optimized N–H bond length is 1.040 Å. The optimized C–H bond lengths are 1.107 and 1.095 Å in the (C, 2H) codoping model. To examine the relative difficulty of incorporating different ions into the lattice, we calculate the dopant formation energy according to the equation below,

EðTi16 O31 NÞform ¼ EðdopedÞ  EðpureÞ  lN þ lO ;

ð1Þ

Figure 1. 2  2  1 Supercell used for (a) compensated (N, H)-codoped anatase TiO2; (b) compensated (C, 2H)-codoped anatase TiO2. The gray and red spheres represent the Ti and O atoms, respectively, and the blue, dark and white spheres represent the N, C and H atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)

EðTi16 O31 CÞform ¼ EðdopedÞ  EðpureÞ  lC þ lO ;

ð2Þ

EðTi16 O31 NHÞform ¼ EðdopedÞ  EðpureÞ  lN  lH þ lO ; EðTi16 O31 CHÞform ¼ EðdopedÞ  EðpureÞ  lC  lH þ lO ;

ð3Þ ð4Þ

EðTi16 O31 CH2 Þform ¼ EðdopedÞ  EðpureÞ  lC  2lH þ lO ;

ð5Þ

where E(doped) is the total energy of TiO2 with dopant, and E(pure) is the total energy of the supercell of pure TiO2. lN is the chemical potential of N, which is determined by the energy of the N2 molecule (lN = l(N2)/2). lH represents the calculated chemical potentials of free molecule H2 (lH = l(H2)/2). lC is calculated from the formulas [8], lC = l(CO2)l(O2). The growth of an engineered TiO2 will not be an equilibrium process but a kinetic process, which can be either Ti-rich, O-rich, or anything in between. Under Ti-rich conditions, the lTi chemical potential is assumed to be the energy of bulk Ti while the lO chemical potential is calculated by the growth condition,

2lO þ lTi ¼ lðTiO2 Þ:

ð6Þ

Under O-rich conditions, the lO chemical potential is calculated from the ground-state energy of the O2 molecule (lO = l(O2)/2), while the chemical potential of Ti is obtained by growth condition (6). The calculated formation energies are summarized in Table 1. For N and C-monodoped TiO2 systems, our calculated results are in good agreement with the previous theoretical values [8,14–16]. The calculated formation energies of C-monodoped TiO2 are larger than that of N-monodoped TiO2 under both Ti-rich and O-rich conditions, which indicate that C monodoping is relatively more difficult than N monodoping. The compensated (N, H) codoped TiO2 is more energetically favorable in comparison with N monodoping system under the Ti-rich growth conditions due to the smallest formation energy. Moreover, the formation energies of compensated (C, 2H) codoped TiO2 are much smaller than those of C monodoping and (C, H) codoping systems under both Ti-rich and O-rich growth conditions. Especially, the compensated (C, 2H) codoped TiO2 can be formed easily under Ti-rich growth conditions considering its formation energies. 3.2. Electronic structures To compare the modifications to electronic structures by various doping approaches, we consider the total density of states (TDOS) and partial density of states (PDOS) of pure anatase TiO2, N-, (N, H)-doped TiO2, as shown in Figure 2. For N-monodoped TiO2, it is clear from Figure 2b that the isolated bands are formed

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M. Li et al. / Chemical Physics Letters 539–540 (2012) 175–179 Table 1 The lattice constants (Å) and the formation energies Eform (eV) of different kinds of TiO2. Structure Pure

Eform (Ti-rich) –

Eform (O-rich)

a

b

c

Ti–O (N, C)

N(C)–H

–

3.80

3.80

9.79

1.947 2.011 1.973 2.079 2.023 2.220 2.013 2.078 2.054 2.328 2.084 2.160

–

N-doped

0.12

4.79

3.81

3.79

9.79

C-doped

7.99

12.90

3.82

3.79

9.81

(N, H)-doped

2.10

2.81

3.81

3.79

9.80

(C, H)-doped

6.50

11.42

3.80

3.81

9.84

(C, 2H)-doped

4.72

9.63

3.85

3.79

9.76

– – 1.040 1.098 1.095 1.107

Ef moves to higher energy with respect to pure TiO2. The valence band top states mainly consist of the spin up and down N 2p states, which is different from N monodoping system. The acceptor N 2p states are mixed with O 2p states and the continuum mixed states shift the valence band edge upward. Moreover, the conduction band edge shows no change, and thus does not affect the reducing powers of TiO2. The band gap is reduced by 0.29 eV, as compared to the case of pure TiO2. Although the band gap of compensated (N, H) codoped TiO2 is slightly larger than that of N-doped TiO2, the local trapping is eliminated which can enhance the lifetimes of photoexcited carriers. Therefore, compensated (N, H) codoping system could serve as a better visible-light photocatalyst than monodoping system. In order to understand the effect of C and H doping system on electronic structure, we calculate the total density of states (TDOS) and partial density of states (PDOS) of pure anatase TiO2, C-, (C, H)and compensated (C, 2H)-doped TiO2, as shown in Figure 3. For Cmonodoped TiO2, three band gap states of C 2p orbital character emerge in both the spin-up bands and spin-down bands, respectively. The calculated band gap is decreased by about 0.21 eV with respect to the pure TiO2. For (C, H) codoped TiO2, it is clear from Figure 3c that the (C, H) codoping system introduces two localized states as deep acceptors in the spin-up bands. In addition, one localized state exists in the spin-down bands. The localized states, composed of C 2p, Ti 3d, and a few O 2p states, are not vanished completely from the band gap. The calculated band gap is about 2.07 eV, smaller by 0.12 eV than pure TiO2. For compensated (C, 2H)-doped TiO2, the continuum states above the valence band edge are formed due to strong mixing of C 2p and O 2p states, and some localized states are eliminated to some extent. Moreover, the band gap reduction for compensated (C, 2H) codoping system is 0.33 eV, which is larger than those of non-compensated doping and monodoping systems. 3.3. Optical properties Figure 2. TDOS and PDOS plots for (a) pure TiO2; (b) N-doped TiO2; (c) compensated (N, H)-codoped TiO2. The highest occupied level is chosen as the Fermi level Ef with dotted line and the Fermi level of pure TiO2 is taken as the reference level which is set at zero.

within the bandgap, which are determined by spin down electron states. The localized states are composed of N 2p, Ti 3d, and a few O 2p states and the topmost part of the valence band mainly consists of the spin down N 2p states. The incorporation of N with greater atomic p orbital energies than that of O results in the valence band maximum (VBM) shifting to increased energy. Moreover, the conduction band minimum (CBM) is shifted down in energy, and hence the band gap is reduced by 0.48 eV. For compensated (N, H) codoped TiO2, our calculated results demonstrate that no isolated energy states appear in the band gap and the Fermi level

Optical properties are determined by the frequency dependent dielectric function e(x) = e1(x) + ie2(x), which is mainly a function of electronic structure. The imaginary part of the dielectric function, e2(x), can be calculated from the momentum matrix elements between the occupied and unoccupied wave function. The real part e1(x) can be evaluated from the imaginary part e2(x) by the famous Kramer–Kronig relationship. The corresponding absorption spectrum was estimated using the following equation:

IðxÞ ¼ 21=2 xf½e21 ðxÞ þ ie22 ðxÞ1=2  e1 ðxÞg1=2 :

ð7Þ

The scissors operation of 1.02 eV for anatase TiO2 has been carried out in optical absorption, in which the scissor operation is the difference between the calculated band gap and the experimental value. The calculated optical absorption spectra for (N, H) and (C,

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calculated results show clearly that pure anatase TiO2 will absorb mainly UV light with only weak absorption in the visible-light region. However, after introduction of dopants into TiO2, the absorption edges are shifted to the visible-light region. The optical absorption of compensated (C, 2H) codoped TiO2 is substantially red-shifted to the visible-light region as compared to the non-compensated (C, H) codoped, C monodoped and pure TiO2. In addition, the compensated (C, 2H) codoped TiO2 also exhibits much more favorable visible-light absorption than compensated (N, H) codoping system. Therefore, the compensated (C, 2H) codoping system may be a good choice for improving the absorption of visible-light. The enhancement of optical absorption under the visible-light region may promote the utilization of the solar light, which will consequently enhance the visible-light photocatalytic efficiency of TiO2. 4. Conclusion In summary, we calculated the electronic structures and optical properties of N-, C-, non-compensated (C, H)-, compensated (N, H)and (C, 2H)- doped anatase TiO2 on the basis of spin-polarized density functional theory. The results show that the formation energies of the compensated (N, H) and (C, 2H) codoping models are much smaller than that of monodoping and noncompensated codoping systems. The compensated codoping systems reduce the band gap effectively and shift the absorption edge to the visible-light region, which can enhance photocatalytic activity of TiO2. Compared to the compensated (N, H) doped TiO2, we predicted that (C, 2H) codoping system may be a better candidate for engineering TiO2 to narrow band gap and red-shift optical absorption. Acknowledgements Figure 3. Calculated TDOS and PDOS for (a) pure TiO2; (b) C-doped TiO2; (c) (C, H)codoped TiO2; (d) compensated (C, 2H)-codoped TiO2. The highest occupied level is chosen as the Fermi level Ef with dotted line and the Fermi level of pure TiO2 is taken as the reference level which is set at zero.

This work was supported by the National High Technology Research and Development Program of China (863 Program, Grant No. 2009AA03Z428), the National Natural Science Foundation of China (Grant No. 50872005) and the Innovation Foundation of BUAA for Ph.D. Graduates (Grant No. YWF-12-RBYJ-027). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]

Figure 4. Optical absorption curves calculated for different kinds of TiO2. The inset in figure shows the enlarged optical absorption spectrum with the wavelength ranging from 340 to 440 nm.

2H) codoped TiO2, are compared with individual N-, C-doped, noncompensated (C, H) codoped and pure anatase TiO2 (Figure 4). The

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