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Ab-initio calculations of synergistic chromium–nitrogen codoping effects on the electronic and optical properties of anatase TiO2
Vacuum 92 (2013) 32e38
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Ab-initio calculations of synergistic chromiumenitrogen codoping effects on the electronic and optical properties of anatase TiO2 Matiullah Khan a, b, Wenbin Cao a, *, Ning Chen a, Asadullah a, M. Zubair Iqbal c a
Department of Inorganic Nonmetallic Materials, School of Materials Science and Engineering, University of Science and Technology Beijing (USTB), Beijing 100083, China b Physics Department, University of Science and Technology Bannu, 28100 Bannu, Pakistan c Department of Physics, University of Science and Technology Beijing (USTB), Beijing 100083, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 April 2012 Received in revised form 16 November 2012 Accepted 23 November 2012
Electronic and optical properties of compensated and noncompensated (Cr, N) codoped TiO2 have been investigated using density functional theory with plane wave basis set and pseudopotential. To investigate the formation of defect pair in the codoped models, defect pair binding energy was calculated. Compensated codoped model has two Cr atoms doped at Ti sites, one N atom at O sites along with an oxygen vacancy that gave stable configuration, better electronic and optical properties. Defect pair binding energy of this model showed that, individual defects would bind each other leading to stable configuration compared to mono-doped models. Band structure results showed that compensated (Cr, N) codoping introduced substantially broaden intermediate states in the forbidden band along with narrowed band gap. Furthermore, the Fermi level was shifted from top of the valence band to middle of the forbidden band describing half metallic character. Cr doping changed the nature of N 2p states from unoccupied to occupied which will improve electronehole pair separation. Optical properties comparison showed that all doped models effectively shifted the absorption edge of TiO2 towards visible light. Compensated (Cr, N) codoped TiO2 has better optical properties and covered wide absorption band in the visible light region, attributed to the stable configuration, narrowed band gap and widely distributed states in the band gap. Our results provide reasonable explanation of the experimental findings. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: First principle Optical properties Absorption peak Photocatalytic activity
1. Introduction TiO2 photocatalyst has been considered to be one of the promising semiconductors because of its potential applications in various fields including catalysis, electronics, coatings and pigments. The excellent properties such as low cost, non-toxicity, long term stability, strong oxidation and moderate reduction potential make it a promising photocatalyst for the decomposition of organic pollutants in water and air [1e4]. However, its wide band gap limits its efficiency in most of the photocatalytic processes because only ultraviolet (UV) is utilized for the creation of photoexcited charge carriers. As UV light is only 4% of the solar spectrum, therefore it is highly desirable to tailor the band gap of TiO2 in such a way so that it can absorb light in the visible region which accounts about 45% of the solar energy [5,6]. Doping is considered to be one of the promising methods for engineering the band gap of TiO2 by introducing either donor or
* Corresponding author. Tel./fax: þ86 10 62332457. E-mail address: [email protected] (W. Cao). 0042-207X/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.vacuum.2012.11.016
acceptor impurity states in the forbidden region or involving the reduction of effective band gap [7e10]. Since the pioneering work of Asahi et al. [11], non-metal doping is of considerable interest for the band gap modification of TiO2 and several non-metals doping such as N [12e16], C [17,18], and B [19] were extensively studied. However, the introduced impurity states due to non-metal dopants gave low photocatalytic efficiency because the partially occupied impurity states acts as a recombination center for photoexcited carriers [12]. The photoexcited electrons from the conduction band (CB) meet with the holes in the valence band (VB) following the three basic recombination mechanisms [20] such as: (1) Band to band recombination occurs due to the direct movement of the electron from conduction band to valence band to meet with a hole. The rate of this mechanism mainly depends on the product of the concentrations of present electrons and holes and its second order in carrier concentration [20]. (2) Trap-assisted recombination happens as a result of combining electrons in the CB indirectly with a hole in the VB through “trap” state [20e22]. This recombination may result from the introduction of partially occupied impurity states in the band gap due to some impurities doping. (3) Auger recombination occurs as a result of combining photoexcited
M. Khan et al. / Vacuum 92 (2013) 32e38
electrons and holes using band to band transition mechanism and the obtained energy is transferred to other carriers [20]. Recent experimental work [21e24] and theoretical calculations [25e27] showed that transition metal and non-metal codoped TiO2 improved the visible light photocatalytic activity by decreasing the rate of electronehole pair recombination. Codoped models by substituting transition metals such as W at Ti sites and non-metals such as N at O sites were found effective in reducing the band gap of TiO2 [28]. Theoretical calculations revealed that Cr doping at Ti sites in TiO2 reduced the band gap of TiO2 by introducing localized level of t2g in the band gap which shifted its absorption edge towards visible light [29]. Zhu et al. [30] synthesized Cr3þ doped anatase TiO2 using combine solegel and hydrothermal method in which Cr3þ substitute Ti4þ ion in TiO2 lattice, and improved visible light absorption as well as visible light photocatalytic activity on the degradation of XRG. The improved visible light absorption and photocatalytic activity were attributed to the creation of impurity states due to Cr doping which effectively reduced the band gap of TiO2 [30]. Mesoporous Cr-doped TiO2 photocatalyst synthesized using evaporation-induced selfassembly method [31] enhanced photocatalytic activity for the doped sample compared to pure TiO2 [31]. Pan et al. [32] synthesized Cr and N-codoped TiO2 using solegel method which effectively shifted the absorption edge towards visible light and it was argued that Cr3þ or Cr4þ ion either substitute Ti4þ site or remain isolated on the surface of TiO2 [32]. Recently Kurtoglu et al. [33] performed theoretical calculations for CreN-codoped TiO2 and found that strong coupling exists in CreN pair which was attributed to the formation of bond with covalent character. It was argued that these strong CreN bonds might be important for the high photocatalytic activity of CreN codoped TiO2 [33]. To investigate the stability of defect pair in a codoped model, defect pair binding energy calculations were widely used [27,34,35]. Positive value of the defect pair binding energy indicates that individual defects will bind each other when both are present in the sample. For observing the stability of doped Cr and N in a (Cr, N) codoped TiO2, it is recommended to calculate the defect pair binding energy. Different compensated and noncompensated (Cr, N) codoped TiO2 models were simulated by CASTEEP code of Materials Studio 5.5 and then compared with each other. For compensated models, Cr atom at Ti sites and N atom at O sites were introduced, and then for charge compensation an oxygen vacancy was created. In the case of noncompensated systems, Cr and O atoms were added at Ti and O sites, respectively, to the 2 3 1 supercell, geometrically optimized, and then their electronic and optical properties were calculated. The present work was arranged as: computational details; gave briefly the methods which were applied in the calculations, results and discussion; describes the obtained results which were technically discussed, and finally, the conclusion section describes the main outcome of this research work. 2. Computational details Spin-polarized density functional theory (DFT) calculations were performed by the CASTEP code [36] based on the plane wave method. The PerdeweBurkeeErnzerhof (PBE) parameterization [37] of the generalized gradient approximation (GGA) [38] was utilized for the exchangeecorrelation potential. The electron wave function was expanded in plane waves up to a cutoff energy of 380 eV and the k space integration was done with a 2 2 2 kmesh [39]. For getting stable atomic configuration, pure and doped models were geometrically optimized [40]. The convergence threshold for self-consistent tolerance was set to 2.0 106 eV/ atom and atomic relaxations were carried out until the residual forces were below 0.01 eV/ A.
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TiO2 mainly exists in three polymorphs, namely: anatase (space group I4/amd and Z ¼ 4), rutile (space group P42/mnm and Z ¼ 2) and brookite (space group Pbca and Z ¼ 8). Anatase phase is more active in the photocatalytic processes and therefore it is widely investigated. Anatase phase has body centered tetragonal Bravais lattice having 12 atoms in two primitive cells. Its structure can be explained by three crystallographic parameters a, c and oxygen fractional coordinate u. The values of a, c and u obtained at 300 K from X-ray and neutron diffraction data were found to be 3.782 Å, 9.502 A, and 0.208 Å, respectively. Anatase TiO2 unitcell has two primitive cells having Ti and O atoms positioned at (0, 0, 0), (0, ½, ), (0, ½, u þ 1/4), (0, ½, ½ u), respectively. ¼) and (0, 0, u), (0, 0, u Thus each Ti4þ is coordinated to six oxygen anions (O2) and each O2 is being coordinated to three Ti4þ forming an OTi3 pattern. The obtained structure can be described by chain of distorted TiO6 octahedra having two long and four short TieO bonds [41e43]. To simulate noncompensated (Cr, N) codoped TiO2, supercell with 2 3 1 replication of the anatase TiO2 unitcell was constructed which has 72 atoms. Single Cr and N doping in anatase TiO2 were performed by replacing Ti and O atoms, respectively. Substitutional Cr and N doping at Ti and O sites, respectively, were selected because recent theoretical calculations showed [23] that it was stable and energetically favorable compared to other substitutional/interstitial doped models. Cr-doped TiO2 (CreTiO2), N-doped TiO2 (NeTiO2), and noncompensated Cr and N-codoped TiO2 had doping concentrations of 1.38%, 1.38%, and 2.78%, respectively. For the noncompensated codoped system, three different codoping configurations with respect to the locations of individual dopants with each other were introduced. Cr and N atoms at Ti and O sites were doped at a distance of 1.67 Å, 4.16 A, and 8.94 A represented by noncompensated model A, noncompensated model B and noncompensated model C, respectively. To simulate compensated (Cr, N) codoped TiO2, supercell of 2 2 1 repetition of anatase TiO2 was used. Cr and N atoms were doped adjacent to each other at Ti and O sites, respectively, along with an oxygen vacancy gave compensated model A. In compensated model B, along with an oxygen vacancy, Cr and Ti were doped a distance of 3.80 A in 2 2 1 supercell of anatase TiO2. Compensated model C has an oxygen vacancy and two Cr atoms at Ti sites with a distance of 3.18 A and N atom at O sites located a distance of 3.80 A and 5.62 A from the two Cr atoms. All doped models were geometrically optimized for getting stable atomic positions, and then the electronic and optical properties were evaluated. 3. Results and discussion Our calculated lattice parameters of the relaxed cell for pure A and c ¼ 9.677 A, found in agreement anatase TiO2 are; a ¼ 3.806 with the theoretical [44] as well as experimental results [45] indicating that our calculation methods were reasonable. Single Cr and N doping in the anatase TiO2 supercell were achieved by replacing the lattice Ti and O atoms by Cr and N, respectively. Theoretical calculations [25e27] revealed that Ti and O sites were preferentially substituted by transition metals and non-metal, respectively. To observe change in the bond lengths due to codoped models, the averaged bond lengths of noncompensated and compensated codoped models were calculated and summarized in Table 1. For noncompensated model A, we found that the CreN bond length of 1.664 A compared to the TieN bond length of 2.026 A was in close agreement with the recent calculations [33]. However for compensated case, the compensated model A had the CreN bond length of 1.936 A as compared to the 1.826 A for TieN. This shows that the TieN bond length is smaller compared to the CreN bond length for charge compensated models.
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M. Khan et al. / Vacuum 92 (2013) 32e38
Table 1 Averaged bond lengths of pure TiO2 along with Noncompensated and compensated A). codoped TiO2 in the unit of angstrom ( TieO OeO CreO TieN NeO TieTi TieCr CreN Pure TiO2 1.967 2.704 Noncompensated Model A 1.948 2.702 1.973 2.026 2.730 Noncompensated Model B 1.952 2.951 1.869 1.903 2.713 Noncompensated Model C 1.952 2.732 1.875 1.892 2.846 Compensated Model A 1.947 2.741 1.960 1.826 2.653 Compensated Model B 1.950 2.732 1.909 1.880 2.756 Compensated Model C 1.951 2.733 1.870 1.881 2.719
2.913 1.664 2.956 2.958 2.954 2.942 1.936 2.935 2.910 2.926 2.969
For codoped models, defect pair binding energy is widely used to investigate the stability of codoped pair. It describes that weather the codoped systems is stable/unstable compared to mono-doped systems [27,34,35]. So, for investigating the formation of defect pairs in the noncompensated and compensated codoped models, the binding energies (Eb) of the defect pair in anatase TiO2 supercell was calculated. For noncompensated codoped models, the defect pair binding energy was calculated using Eq. (1).
Eb ¼ ET ðTi23 CrO48 Þ þ ET ðTi24 O47 NÞ ET ðTi23 CrO47 NÞ ET ðTiO2 Þ
(1)
where ET(Ti23CrO48), ET(Ti24O47N), ET(Ti23CrO47N) and ET(TiO2) represent the total energies (calculated with the same supercell model) of Cr-doped TiO2, N-doped TiO2, noncompensated (Cr, N) codoped TiO2 and pure anatase TiO2, respectively. For compensated codoped models A and B, the defect pair binding was calculated using Eq. (2)
Eb ¼ ET ðTi15 CrO31 Þ þ ET ðTi16 O31 NÞ ET ðTi15 CrO30 NÞ EðTiO2 Þ (2) where ET(Ti15CrO31), ET(Ti16O31N), ET(Ti15CrO30N) and E(TiO2) are the total energies of Cr-doped at Ti sites with an oxygen vacancy, Ndoped TiO2, compensated model A or B and pure TiO2, respectively. For compensated model C, the following formula was used to calculate the defect pair binding energy.
Eb ¼ ET ðTi14 Cr2 O31 Þ þ ET ðTi16 O31 NÞ ET ðTi14 Cr2 O30 NÞ ET ðTiO2 Þ
(3)
here ET(Ti14Cr2O31) and ET(Ti14Cr2O30N) represent the total energies of two Cr-doped at Ti sites with an oxygen vacancy model and compensated model C, respectively. The binding energies of the defect pair in noncompensated and compensated models are summarized in Table 2. Positive value of the defect pair binding energy shows that the individual defects will bind each other in the codoped system to form stable configuration as compared to monodoped models. In noncompensated codoped models, noncompensated model A provided maximum defect pair binding energy describing the adjacent locations of Cr and N as the most stable configuration, this was found in agreement with literature
Table 2 Binding energies of the defect pairs in the codoped models. (Cr, N) codoped TiO2 model
Defect pair binding energy (eV)
Noncompensated Model A Noncompensated Model B Noncompensated Model C Compensated Model A Compensated Model B Compensated Model C
2.17 1.14 1.20 2.24 3.00 5.72
[33]. However, in compensated mode, compensated model C has the maximum defect pair binding energy. The compensated model C has a defect pair binding energy of 5.72 eV, found maximum among all codoped models. Thus, compensated model C is considered to be the most stable configuration of CreN-codoped TiO2. In this case, the individual defects will bind each other and will provide stable configuration compared to mono-doped systems. Among all noncompensated models, noncompensated model B gave the reduced band gap and better optical properties. Similarly, comparison of the compensated models showed that compensated model C had stable configuration and better optical absorption in the visible light. For further comparing the electronic and optical properties of codoped models with NeTiO2, CreTiO2 and pure TiO2, noncompensated model B was selected from the noncompensated models and compensated model C was selected from the compensated models. So, hereafter, noncompensated model B should be named as noncompensated (Cr, N)eTiO2 and compensated model C should be named as compensated (Cr, N)eTiO2. For understanding variations in the band gap due to different mono-doped and codoped models, the band structure of the undoped and doped models was calculated, as shown in Fig. 1. The calculated band gap for pure anatase TiO2 is 2.13 eV (Fig. 1 (a)) found consistent with recent theoretical results [46]; however, underestimated as compare to the experimental value, due to the well-known shortcoming of DFT calculations. Cr doping introduced impurity states in middle of the forbidden region, as shown in Fig. 1 (b). This impurity states will shift the photoexcited carriers to the conduction band which could be further used in the oxidation/ reduction process. Furthermore, the Fermi level was shifted from top of the valence band to middle of the forbidden region describing the half metallic character (Fig. 1 (b)). Fig. 1 (b) showed that compared to un-doped TiO2, the valence band maximum (VBM) and conduction band minimum (CBM) came closer to each other and the distance between them reduced to 2.0 eV as compared to 2.13 eV for un-doped TiO2. Reduction in the band gap and the creation of impurity states in middle of the forbidden region may be beneficial for shifting the absorption edge of TiO2 towards visible region. Compared to pure TiO2, the substitution of N at O sites (Fig. 1 (c)) declined the CBM by about 0.33 eV which effectively reduced electrons transition energy. Moreover, N doping introduced isolated states in the band gap located at about 0.72 eV above top of the valence band. The creation of isolated impurity states and reduction of the effective band gap may help in reducing electron transition energy from valence to conduction band leading to the absorption in the visible region. The band structure of noncompensated (Cr, N)eTiO2 is depicted in Fig. 1 (d). The distance between VBM and CBM was reduced to 1.86 eV compared to 2.13 eV for pure TiO2. Due to Cr and N codoping, widely distributed impurity states were introduced in the band gap. Some states due to Cr doping are located at the Fermi level while some are located above it. The isolated impurity state due to N doping is located at about 0.49 eV below the Fermi level. In case of compensated (Cr, N)eTiO2, the CBM is located about 2.0 eV above the VBM, as shown in Fig. 1 (e). Along with widely distributed states, the Fermi level is shifted up in the forbidden region. The magnitude of impurity states is increased which is due to the increase amount of Cr doping concentration. The widely distributed impurity states in the band gap will allow a range of visible light photons for absorption. The (Cr, N) codoping in TiO2 gives the hybridization of Cr and N electronic states resulting in substantially broaden impurity levels, and led to the formation of intermediate bands which is in agreement with recent experimental findings [23]. Due to the reduced band gap and widely distributed impurity states in the band gap, the electron transition energy will be reduced which will improve the visible light absorption.
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Fig. 1. Band structure of: (a) pure anatase TiO2, (b) Cr-doped TiO2, (c) N-doped TiO2, (d) noncompensated (Cr, N)eTiO2, and (e) compensated (Cr, N)eTiO2. The EF represents the Fermi level.
For further understanding the modification in the band gap and the creation of impurity states, the density of states (DOS) and projected density of states (PDOS) of the un-doped and doped models were evaluated. The DOS for pure TiO2 and different doped models are depicted in Fig. 2. For N-doped TiO2 (Fig. 2 (b)), only slight variation in the VBM was found while the CBM was shifted to lower energy values compared to un-doped TiO2 (Fig. 2 (a)). Fig. 2 (c) shows that Cr doping shifted the Fermi level to the middle of the forbidden region, describing the half metallic character of a semiconductor. Noncompensated (Cr, N)eTiO2 also described half metallic character and it was found that codoping narrowed the band gap effectively, as shown in Fig. 2 (d). The DOS of compensated (Cr, N)eTiO2 is shown in Fig. 2 (e). Widely distributed impurity states are located throughout the band gap which may helps in improving visible light absorption. To understand the nature of impurity states in the band gap, the PDOS of pure and
doped models were calculated, as shown in Fig. 3. Fig. 3 (a) shows that the valence band of TiO2 is mostly composed of O 2p states while the conduction band comes from Ti 3d states. Due to N doping (Fig. 3 (b)), N 2p states were introduced in the band gap which is responsible for shifting the photoexcited carriers to the conduction band. Major part of the N 2p states lies in the valence band while some parts appeared in the form of localized states located at about 0.72 eV above the valence band maximum (Fig. 3 (b)), found consistent with literature [15]. Cr doping narrowed the band gap by 0.13 eV compared to pure TiO2. Moreover, Cr 3d states (Fig. 3 (c)) are partially located in the conduction band while its major part appeared in the form of localized states located in middle of the forbidden region which may provide step for transferring photoexcited electrons to the conduction band. PDOS of the noncompensated (Cr, N)eTiO2 is shown in Fig. 3 (d). Cr 3d and N 2p states were simultaneously introduced and partially located in the
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M. Khan et al. / Vacuum 92 (2013) 32e38
Fig. 2. Total density of states (DOS): (a) pure TiO2, (b) N-doped TiO2, (c) Cr-doped TiO2, (d) Noncompensated (Cr, N) codoped TiO2, and (e) compensated (Cr, N) codoped TiO2.
valence and conduction band while some parts appeared in the form of widely distributed states in middle of the forbidden region. These states may be responsible for absorbing visible light photons. The PDOS of compensated (Cr, N)eTiO2 (Fig. 3 (e)) showed that Cr 3d states are widely distributed in the forbidden region. The compensated codoping changed the nature of N 2p states from unoccupied to occupied states. Changing the nature of N 2p states will be important for improving the visible light photocatalytic activity of codoped sample. Spin-polarized calculations showed that N doping at O sites induced antiferromagnetism (AFM) in TiO2. N dopant introduced magnetic moment of 1.45 mB per N atom in the anatase TiO2 supercell which is found close to the reported value [47]. Cr doping at Ti sites induced ferromagnetism (FM) in TiO2, contributing magnetic moment of 2.61 mB per Cr atom, found
Fig. 3. Projected density of states (PDOS) of: (a) pure TiO2, (b) N-doped TiO2, (c) Crdoped TiO2, (d) noncompensated (Cr, N) codoped TiO2, and (d) compensated (Cr, N) codoped TiO2. The vertical line at energy equal to zero represents the Fermi level.
increased compared to the theoretical value [48]. Furthermore, codoped model also showed ferromagnetic behavior. Interaction of photons with the electrons in a system describes optical properties which gives detail information about the electronic band structure of a semiconductor. Optical photons interaction with the electrons in a particular system can be described in terms of time-dependent perturbations of the ground-state electronic states. Absorption of photon will lead to the electron transitions between occupied and unoccupied states which can be described as a joint density of states between valence and conduction band. CASTEP calculates the optical properties from the dielectric function which consists of real and imaginary parts (3 ¼ 3 1þi3 2). Within proper selection rules, the imaginary part of the dielectric function 3 2(u) can be calculated from the momentum matrix elements between the occupied and unoccupied wave functions. The real part 3 1(u) is related to the electronic polarizability of the material and it can be evaluated from the imaginary part using KramerseKronig transform [49,50]. Optical properties such absorption coefficient, reflectivity, refractive index and energy loss function can be calculated from the real and imaginary parts of the dielectric function. As our calculated band gap was underestimated compared to experimental value, therefore scissor approximation was used [51] to make our results compatible with experimental values. Scissor operator shifts the unoccupied conduction band states with respect to occupied valence band states. Scissor operator of 1.07 eV was applied for adjusting the results with experimentally observed values. The optical properties including imaginary part of the dielectric function, absorption coefficient, reflectivity, refractive index and loss function are shown in Fig. 4. For any material, the imaginary part of the dielectric function is the pandect of optical properties. For comparing the optical properties of un-doped and doped models, the imaginary part of the dielectric function was calculated, as shown in Fig. 4 (a). Fig. 4 (a) shows that un-doped TiO2 can only respond to UV light having no absorption peak in the visible region. The main peak for un-doped TiO2 was obtained at 4.60 eV, assigned to the excitation from the O 2p states in the valence band to the Ti 3d states in the conduction band. All doped models showed enhance visible as well as UV light absorption compared to un-doped TiO2, attributed to the narrowed band gap due to the creation of impurity states. N doping in TiO2 improved its optical properties by giving absorption in the visible and UV light range with the absorption edge at about 1.33 eV in the visible region and strong absorption peak in the UV region at 4.66 eV. The visible light absorption may originate from the electron transition from O 2p states to Ti 3d states through N 2p states while the peak at 4.66 eV is attributed to the direct transition of electrons from O 2p to Ti 3d states. These results were found consistent with experimental [52] and theoretical findings [3,6]. Cr doping concentration of 1.38% exhibited strong absorption in the visible and UV light range with absorption peaks at 1.15 and 4.71 eV, respectively. The absorption peak at 1.15 eV may come from step wise shifting of the electrons from the valence to conduction band though Cr 3d states while absorption in the UV region may originate from excitation between the valence and conduction band of TiO2. These findings were found in close agreement with the experimental results which showed that Cr doping effectively shifted the absorption edge of TiO2 towards visible light [32]. Noncompensated (Cr, N)eTiO2 showed broad absorption in the visible range along with enhanced absorption in the UV region compared to un-doped TiO2. The absorption edge for noncompensated codoped model is at 0.5 eV along with main absorption peak at 4.62 eV. Absorption in the visible region may come from excitation through the narrowed band gap due to codoping. Compensated (Cr, N)eTiO2 has better visible as well as UV light absorption due to the reduced band gap and the existence
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Fig. 4. Optical properties of pure anatase TiO2 and different doped models: (a) imaginary part of the dielectric function, (b) absorption coefficient, (c) reflectivity, (d) refractive index, and (e) loss function.
of widely distributed impurity states in the band gap. This model showed two main peaks, at 2.12 eV and at 4.90 eV, located in the visible and UV regions, respectively. The visible light absorption may come from the excitation between valence and conduction band through the impurity states in the band gap while the UV light absorption will come from the direct transition between O 2p and Ti 3d states. In doped models, the absorption in low energy region may originate from the electronic intraband transitions between Cr 3d to Ti 3d states and/or N 2p to Cr 3d or Ti 3d states. Compensated (Cr, N)eTiO2 has broad absorption range in the visible light region due to the widely distributed impurity states in the band gap, while Cr-doped TiO2 has good absorption properties in the visible range in the form of strong peak at 1.15 eV due to the creation of Cr 3d states in the forbidden region. Fig. 4 (b) describes absorption coefficient spectrum of the pure TiO2 and different doped models. Un-doped TiO2 has no absorption peak in the visible region while all doped models provided some sort of absorption in the visible region describing that doping narrowed the band gap of TiO2. Doped models have absorption in the visible region but still the main absorption peaks occurred in UV range due to the intrinsic band gap nature of anatase TiO2. Compensated codoped model has good absorption in the form of broad absorption region due to the
narrowed band gap and the existence of widely distributed impurity states in the band gap. Experimental result showed that (Cr, N) codoping effectively improved the visible light absorption of TiO2 compared to single Cr or N-doped TiO2 [32]. It is argued that doped models may provide good visible light photocatalytic activity compared to un-doped TiO2. Pan et al. [32] synthesized Cr/TiO2, TiO2-xNx, and Cr/TiO2xNx, and found that (Cr, N) codoping effectively improved the visible light absorption compared to Cr/TiO2 and TiO2xNx; however it had poor photocatalytic activity compared to mono-doped samples using the photodegredation of methylene blue, attributed to the extra imperfections introduced during codoping process [32]. Recent experimental [33] results showed that Cr-doped TiO2 films did not induce any visible light photocatalytic activity; however N-doped TiO2 and (Cr, N) codoped TiO2 films are active in the visible region providing similar activity. Moreover, (Cr, N) codoped TiO2 was found more active among the doped samples in the UV region having same activity as un-doped films [33]. This controversy may due to the different doping concentrations because Pan and Wu [32] doped Cr in the TiO2 with the molar ratio of 0.32% and then it was thermally treated in pure ammonia atmosphere at 550 C, while Kurtoglu et al. [33] synthesized their films composed of Ti1xCrxO2yNy
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(0.04 < x < 0.06 and 0.25 < y < 0.30). Zhu et al. [30] synthesized Cr3þ doped anatase TiO2 with the help of solegel and hydrothermal process and found that Cr3þ substitutes Ti4þ which showed that Cr doping effectively improved the photocatalytic activity of TiO2 under both UV and visible light irradiation with an optimal doping concentration of 0.15% and 0.2%, respectively [30]. Fan et al. [31] synthesized mesoporous Cr-doped TiO2 and found that Cr doping extended the photoresponse of TiO2 towards visible region along with the enhanced visible light photocatalytic activity compare to pure mesoporous TiO2 and nonporous Cr-doped TiO2 [31]. Reflectivity, refractive index and loss function for the un-doped and doped models are provided in Fig. 4 (c)e(e), respectively. Doping impurity atoms improved the reflectivity of TiO2, as evident from Fig. 4 (c). Fig. 4 (c) showed that Cr-doped TiO2 has higher reflectivity in the region 0e1 eV. Further increase in the energy axis, Cr-doped TiO2 exhibited abrupt reduction in its reflectivity value and became equal to that of un-doped TiO2, while in high energy regions, it gave strong peaks at 6.75 and at 8.75 eV. N-doped TiO2 and Noncompensated (Cr, N)eTiO2 have smooth increase in the reflectivity in low and high energy region while it gave same reflectivity as un-doped TiO2 in the region 3.25e4.50 eV. Compensated (Cr, N)eTiO2 has higher reflectivity from 0 to 3.0 eV and from 7.4 to 12 eV. As a whole, compensated (Cr, N)eTiO2 provided better reflectivity among pure and all doped models. The refractive indexes for the un-doped and doped models are depicted in Fig. 4d. Cr doping in anatase TiO2 produced abrupt variation in the refractive index value of TiO2. N-doped and noncompensated codoped model have smooth increase in the refractive index values in low energy region (0e2.67 eV) and smooth decrease in the high energy region (8.33e14 eV); however, in the rest of the region they have nearly same value like un-doped TiO2. Among all models, compensated codoped model has higher refractive index values in the low energy region. Loss function describes the energy loss to a fast moving electron during its passage through a materials medium. Peaks in the loss function spectra relate with trailing edges in the reflection spectra and gives variation in the reflectivity. Un-doped TiO2 has loss function peak at 7.20 eV (Fig. 4 (e)) which described abrupt reduction in the reflectivity as evident from the reflectivity curve in Fig. 4 (c). In case of Cr-doped TiO2, the peaks occur at 1.50, 7.50, and at 9.0 eV describing abrupt decrease in the reflectivity’s in that particular energy values. N-doped and noncompensated (Cr, N)eTiO2 have peaks at 7.50 eV and at about 8.50e8.80 eV, attributed to the corresponding reduction in the reflectivity’s values. Compensated (Cr, N)eTiO2 has strong loss function peak at 9.90 eV which describes the abrupt change in the reflectivity values in this region, as verified from Fig. 4 (c). 4. Conclusions Using density functional theory calculations, the electronic and optical properties of Cr-doped TiO2, N-doped TiO2, noncompensated, and compensated (Cr, N) codoped TiO2 were investigated. Cr doping at Ti sites introduced Cr 3d states in middle of the band gap and N doping at O sites created N 2p states located at about 0.72 eV above the valence band maximum. In compensated (Cr, N) codoped TiO2, Cr doping changed the character of N 2p states from unoccupied to occupied states which will help in improving photocatalytic activity of the codoped system. Compensated (Cr, N) codoped TiO2 has reduced band gap along with widely distributed Cr 3d and N 2p states in the band gap. Defect pair binding energy showed that individual defects in compensated codoped models will bind each other leading to the geometrically stable state, compared to monodoped models. All doped models have absorption in the visible range compared to pure TiO2 attributed to the creation of impurity
states in the band gap and narrowed band gap. Compensated (Cr, N) codoped TiO2 has better absorption in the visible and UV range attributed to the stable configuration, reduced band gap and widely distributed impurity states in the band gap. Our results provide reasonable explanation for the experimental findings. Acknowledgements This work has been financially supported by National Natural Science Foundation of China under the grant number of 51072019, National High-tech Research and Development Program under the grant number of 2012AA030302 and the Opening Project of State Key Laboratory of High Performance Ceramics and Superfine Microstructure under the grant SKL201112SIC. References [1] Iwaszuk A, Nolan M. J Phys Chem C 2011;115:12995. [2] He J, Liu Q, Sun Z, Yan W, Zhang G, Qi Z, et al. J Phys Chem C 2010;114:6035. [3] Spadavecchia F, Cappelletti G, Ardizzone S, Ceotto M, Falciola L. J Phys Chem C 2011;115:6381. [4] Long R, English NJ. Chem Mater 2010;22:1616. [5] Peng Y, He J, Liu Q, Sun Z, Yan W, Pan Z, et al. J Phys Chem C 2011;115:8184. [6] Han X, Shao G. J Phys Chem C 2011;115:8274. [7] Zhu J, Chen F, Zhang J, Chen H, Anpo M. J Photochem Photobiol A 2006;180:196. [8] Adan C, Bahamonde A, Fernández-Garcia M, Martínez-Arias A. Appl Catal B 2007;72:11. [9] Zhou M, Yu J, Cheng B. J Hazard Mater 2006;137:1838. [10] Liu B, Wang X, Cai G, Wen L, Song Y, Zhao X. J Hazard Mater 2009;169:1112. [11] Asahi R, Morikawa T, Ohwaki T, Aoki K, Taga Y. Science 2001;293:269. [12] Irie H, Watanabe Y, Hashimoto K. J Phys Chem B 2003;107:5483. [13] Di Valentin C, Pacchioni G, Selloni A. Phys Rev B 2004;70:085116. [14] Yang K, Dai Y, Huang B. J Phys Chem C 2007;111:18985. [15] Yang K, Dai Y, Huang B, Han S. J Phys Chem B 2006;110:24011. [16] Finazzi E, Di Valentin C, Selloni A, Pacchioni G. J Phys Chem C 2007;111:9275. [17] Khan SUM, Al-Shahry M, Ingler WB. Science 2002;297:2243. [18] Di Valentin C, Pacchioni G, Selloni A. Chem Mater 2005;17:6656. [19] Yang K, Dai Y, Huang B. Phys Rev B 2007;76:195201. [20] Yu PY, Cardona M. Fundamentals of semiconductors: physics and materials properties. New York: Springer; 2005. [21] Gu DE, Yang BC, Hu Y-D. Catal Commun 2008;9:1472. [22] Liu J, Han R, Zhao Y, Wang H, Lu W, Yu T, et al. J Phys Chem C 2011;115:4507. [23] Zhu W, Qiu X, Iancu V, Chen XQ, Pan H, Wang W, et al. Phys Rev Lett 2009; 103:226401. [24] Huang Y, Ho W, Ai Z, Song X, Zhang L, Lee S. Appl Catal B 2009;89:398. [25] Gai Y, Li J, Li SS, Xia JB, Wei SH. Phys Rev Lett 2009;102:036402. [26] Zhao Z, Liu Q. Catal Lett 2008;124:111. [27] Yin WJ, Tang H, Wei SH, Al-Jassim MM, Turner J, Yan Y. Phys Rev B 2010;82: 045106. [28] Long R, English NJ. Appl Phy Lett 2009;94:132102. [29] Umebayashi T, Yamaki T, Itoh H, Asai K. J Phys Chem Solids 2002;63:1909. [30] Zhu J, Deng Z, Chen F, Zhang J, Chen H, Anpo M, et al. Appl Catal B 2006;62:329. [31] Fan X, Chen X, Zhu S, Li Z, Yu T, Ye J, et al. Catal A: Chem 2008;284:155. [32] Pan CC, Wu JCS. Mater Chem Phys 2006;100:102. [33] Kurtoglu ME, Longenbach T, Sohlberg K, Gogotsi Y. J Phys Chem C 2011;115: 17392. [34] Ma X, Wu Y, Lu Y, Xu J, Wang Y, Zhu Y. J Phys Chem C 2011;115:16963. [35] Wang D. Appl Phys Lett 2009;95:012106. [36] Clark SJ, Segall MD, Pickard CJ, Hasnip PJ, Probert MIJ, Refson K, Payne MC. Z. Kristallogr. 2005;220:567. [37] Perdew JP, Bruke K, Ernzerhof M. Phys Rev Lett 1996;77:3865. [38] Perdew JP, Chevary JA, Vosko SH, Jackson KA, Pederson MR, Singh DJ, et al. Phys Rev B 1992;46:6671. [39] Long R, English NJ. J Phys Chem C 2010;114:11984. [40] Pfrommer BG, Côté M, Louie SG, Cohen ML. J Comput Phys 1997;131:233. [41] Wu X, Holbig E, Neumann GS. J Phys Condens Matter 2010;22:295501. [42] Muscat J, Swamy V, Harrison NM. Phys Rev B 2002;65:224112. [43] Labat F, Baranek P, Domain C, Minot C, Adamo C. J Chem Phys 2007;126: 154703. [44] Long R, English NJ. Chem Phys Lett 2009;478:175. [45] Burdett JK, Hughbanks T, Miller GJ, Richardson JW, Smith JV. J Am Chem Soc 1987;109:3639. [46] Zhou Z, Li M, Guo L. J Phys Chem Solids 2010;71:1707. [47] Bai Y, Chen Q. Solid State Commun 2008;147:169. [48] Peng H, Li J, Li S, Xia J. J Phys Condens Matter 2008;20:125207. [49] Sun J, Wang HT, He J, Tian Y. Phys Rev B 2005;71:125132. [50] Shao G. J Phys Chem C 2009;113:6800. [51] Yu X, Li C, Ling Y, Tang TA, Wu Q, Kong J. J Alloys Compd 2010;507:33. [52] Livraghi S, Chierotti MR, Giamello E, Magnacca G, Paganini MC, Cappelletti G, et al. J Phys Chem C 2008;112:17244.
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Ab-initio calculations of synergistic chromiumenitrogen codoping effects on the electronic and optical properties of anatase TiO2 Matiullah Khan a, b, Wenbin Cao a, *, Ning Chen a, Asadullah a, M. Zubair Iqbal c a
Department of Inorganic Nonmetallic Materials, School of Materials Science and Engineering, University of Science and Technology Beijing (USTB), Beijing 100083, China b Physics Department, University of Science and Technology Bannu, 28100 Bannu, Pakistan c Department of Physics, University of Science and Technology Beijing (USTB), Beijing 100083, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 April 2012 Received in revised form 16 November 2012 Accepted 23 November 2012
Electronic and optical properties of compensated and noncompensated (Cr, N) codoped TiO2 have been investigated using density functional theory with plane wave basis set and pseudopotential. To investigate the formation of defect pair in the codoped models, defect pair binding energy was calculated. Compensated codoped model has two Cr atoms doped at Ti sites, one N atom at O sites along with an oxygen vacancy that gave stable configuration, better electronic and optical properties. Defect pair binding energy of this model showed that, individual defects would bind each other leading to stable configuration compared to mono-doped models. Band structure results showed that compensated (Cr, N) codoping introduced substantially broaden intermediate states in the forbidden band along with narrowed band gap. Furthermore, the Fermi level was shifted from top of the valence band to middle of the forbidden band describing half metallic character. Cr doping changed the nature of N 2p states from unoccupied to occupied which will improve electronehole pair separation. Optical properties comparison showed that all doped models effectively shifted the absorption edge of TiO2 towards visible light. Compensated (Cr, N) codoped TiO2 has better optical properties and covered wide absorption band in the visible light region, attributed to the stable configuration, narrowed band gap and widely distributed states in the band gap. Our results provide reasonable explanation of the experimental findings. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: First principle Optical properties Absorption peak Photocatalytic activity
1. Introduction TiO2 photocatalyst has been considered to be one of the promising semiconductors because of its potential applications in various fields including catalysis, electronics, coatings and pigments. The excellent properties such as low cost, non-toxicity, long term stability, strong oxidation and moderate reduction potential make it a promising photocatalyst for the decomposition of organic pollutants in water and air [1e4]. However, its wide band gap limits its efficiency in most of the photocatalytic processes because only ultraviolet (UV) is utilized for the creation of photoexcited charge carriers. As UV light is only 4% of the solar spectrum, therefore it is highly desirable to tailor the band gap of TiO2 in such a way so that it can absorb light in the visible region which accounts about 45% of the solar energy [5,6]. Doping is considered to be one of the promising methods for engineering the band gap of TiO2 by introducing either donor or
* Corresponding author. Tel./fax: þ86 10 62332457. E-mail address: [email protected] (W. Cao). 0042-207X/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.vacuum.2012.11.016
acceptor impurity states in the forbidden region or involving the reduction of effective band gap [7e10]. Since the pioneering work of Asahi et al. [11], non-metal doping is of considerable interest for the band gap modification of TiO2 and several non-metals doping such as N [12e16], C [17,18], and B [19] were extensively studied. However, the introduced impurity states due to non-metal dopants gave low photocatalytic efficiency because the partially occupied impurity states acts as a recombination center for photoexcited carriers [12]. The photoexcited electrons from the conduction band (CB) meet with the holes in the valence band (VB) following the three basic recombination mechanisms [20] such as: (1) Band to band recombination occurs due to the direct movement of the electron from conduction band to valence band to meet with a hole. The rate of this mechanism mainly depends on the product of the concentrations of present electrons and holes and its second order in carrier concentration [20]. (2) Trap-assisted recombination happens as a result of combining electrons in the CB indirectly with a hole in the VB through “trap” state [20e22]. This recombination may result from the introduction of partially occupied impurity states in the band gap due to some impurities doping. (3) Auger recombination occurs as a result of combining photoexcited
M. Khan et al. / Vacuum 92 (2013) 32e38
electrons and holes using band to band transition mechanism and the obtained energy is transferred to other carriers [20]. Recent experimental work [21e24] and theoretical calculations [25e27] showed that transition metal and non-metal codoped TiO2 improved the visible light photocatalytic activity by decreasing the rate of electronehole pair recombination. Codoped models by substituting transition metals such as W at Ti sites and non-metals such as N at O sites were found effective in reducing the band gap of TiO2 [28]. Theoretical calculations revealed that Cr doping at Ti sites in TiO2 reduced the band gap of TiO2 by introducing localized level of t2g in the band gap which shifted its absorption edge towards visible light [29]. Zhu et al. [30] synthesized Cr3þ doped anatase TiO2 using combine solegel and hydrothermal method in which Cr3þ substitute Ti4þ ion in TiO2 lattice, and improved visible light absorption as well as visible light photocatalytic activity on the degradation of XRG. The improved visible light absorption and photocatalytic activity were attributed to the creation of impurity states due to Cr doping which effectively reduced the band gap of TiO2 [30]. Mesoporous Cr-doped TiO2 photocatalyst synthesized using evaporation-induced selfassembly method [31] enhanced photocatalytic activity for the doped sample compared to pure TiO2 [31]. Pan et al. [32] synthesized Cr and N-codoped TiO2 using solegel method which effectively shifted the absorption edge towards visible light and it was argued that Cr3þ or Cr4þ ion either substitute Ti4þ site or remain isolated on the surface of TiO2 [32]. Recently Kurtoglu et al. [33] performed theoretical calculations for CreN-codoped TiO2 and found that strong coupling exists in CreN pair which was attributed to the formation of bond with covalent character. It was argued that these strong CreN bonds might be important for the high photocatalytic activity of CreN codoped TiO2 [33]. To investigate the stability of defect pair in a codoped model, defect pair binding energy calculations were widely used [27,34,35]. Positive value of the defect pair binding energy indicates that individual defects will bind each other when both are present in the sample. For observing the stability of doped Cr and N in a (Cr, N) codoped TiO2, it is recommended to calculate the defect pair binding energy. Different compensated and noncompensated (Cr, N) codoped TiO2 models were simulated by CASTEEP code of Materials Studio 5.5 and then compared with each other. For compensated models, Cr atom at Ti sites and N atom at O sites were introduced, and then for charge compensation an oxygen vacancy was created. In the case of noncompensated systems, Cr and O atoms were added at Ti and O sites, respectively, to the 2 3 1 supercell, geometrically optimized, and then their electronic and optical properties were calculated. The present work was arranged as: computational details; gave briefly the methods which were applied in the calculations, results and discussion; describes the obtained results which were technically discussed, and finally, the conclusion section describes the main outcome of this research work. 2. Computational details Spin-polarized density functional theory (DFT) calculations were performed by the CASTEP code [36] based on the plane wave method. The PerdeweBurkeeErnzerhof (PBE) parameterization [37] of the generalized gradient approximation (GGA) [38] was utilized for the exchangeecorrelation potential. The electron wave function was expanded in plane waves up to a cutoff energy of 380 eV and the k space integration was done with a 2 2 2 kmesh [39]. For getting stable atomic configuration, pure and doped models were geometrically optimized [40]. The convergence threshold for self-consistent tolerance was set to 2.0 106 eV/ atom and atomic relaxations were carried out until the residual forces were below 0.01 eV/ A.
33
TiO2 mainly exists in three polymorphs, namely: anatase (space group I4/amd and Z ¼ 4), rutile (space group P42/mnm and Z ¼ 2) and brookite (space group Pbca and Z ¼ 8). Anatase phase is more active in the photocatalytic processes and therefore it is widely investigated. Anatase phase has body centered tetragonal Bravais lattice having 12 atoms in two primitive cells. Its structure can be explained by three crystallographic parameters a, c and oxygen fractional coordinate u. The values of a, c and u obtained at 300 K from X-ray and neutron diffraction data were found to be 3.782 Å, 9.502 A, and 0.208 Å, respectively. Anatase TiO2 unitcell has two primitive cells having Ti and O atoms positioned at (0, 0, 0), (0, ½, ), (0, ½, u þ 1/4), (0, ½, ½ u), respectively. ¼) and (0, 0, u), (0, 0, u Thus each Ti4þ is coordinated to six oxygen anions (O2) and each O2 is being coordinated to three Ti4þ forming an OTi3 pattern. The obtained structure can be described by chain of distorted TiO6 octahedra having two long and four short TieO bonds [41e43]. To simulate noncompensated (Cr, N) codoped TiO2, supercell with 2 3 1 replication of the anatase TiO2 unitcell was constructed which has 72 atoms. Single Cr and N doping in anatase TiO2 were performed by replacing Ti and O atoms, respectively. Substitutional Cr and N doping at Ti and O sites, respectively, were selected because recent theoretical calculations showed [23] that it was stable and energetically favorable compared to other substitutional/interstitial doped models. Cr-doped TiO2 (CreTiO2), N-doped TiO2 (NeTiO2), and noncompensated Cr and N-codoped TiO2 had doping concentrations of 1.38%, 1.38%, and 2.78%, respectively. For the noncompensated codoped system, three different codoping configurations with respect to the locations of individual dopants with each other were introduced. Cr and N atoms at Ti and O sites were doped at a distance of 1.67 Å, 4.16 A, and 8.94 A represented by noncompensated model A, noncompensated model B and noncompensated model C, respectively. To simulate compensated (Cr, N) codoped TiO2, supercell of 2 2 1 repetition of anatase TiO2 was used. Cr and N atoms were doped adjacent to each other at Ti and O sites, respectively, along with an oxygen vacancy gave compensated model A. In compensated model B, along with an oxygen vacancy, Cr and Ti were doped a distance of 3.80 A in 2 2 1 supercell of anatase TiO2. Compensated model C has an oxygen vacancy and two Cr atoms at Ti sites with a distance of 3.18 A and N atom at O sites located a distance of 3.80 A and 5.62 A from the two Cr atoms. All doped models were geometrically optimized for getting stable atomic positions, and then the electronic and optical properties were evaluated. 3. Results and discussion Our calculated lattice parameters of the relaxed cell for pure A and c ¼ 9.677 A, found in agreement anatase TiO2 are; a ¼ 3.806 with the theoretical [44] as well as experimental results [45] indicating that our calculation methods were reasonable. Single Cr and N doping in the anatase TiO2 supercell were achieved by replacing the lattice Ti and O atoms by Cr and N, respectively. Theoretical calculations [25e27] revealed that Ti and O sites were preferentially substituted by transition metals and non-metal, respectively. To observe change in the bond lengths due to codoped models, the averaged bond lengths of noncompensated and compensated codoped models were calculated and summarized in Table 1. For noncompensated model A, we found that the CreN bond length of 1.664 A compared to the TieN bond length of 2.026 A was in close agreement with the recent calculations [33]. However for compensated case, the compensated model A had the CreN bond length of 1.936 A as compared to the 1.826 A for TieN. This shows that the TieN bond length is smaller compared to the CreN bond length for charge compensated models.
34
M. Khan et al. / Vacuum 92 (2013) 32e38
Table 1 Averaged bond lengths of pure TiO2 along with Noncompensated and compensated A). codoped TiO2 in the unit of angstrom ( TieO OeO CreO TieN NeO TieTi TieCr CreN Pure TiO2 1.967 2.704 Noncompensated Model A 1.948 2.702 1.973 2.026 2.730 Noncompensated Model B 1.952 2.951 1.869 1.903 2.713 Noncompensated Model C 1.952 2.732 1.875 1.892 2.846 Compensated Model A 1.947 2.741 1.960 1.826 2.653 Compensated Model B 1.950 2.732 1.909 1.880 2.756 Compensated Model C 1.951 2.733 1.870 1.881 2.719
2.913 1.664 2.956 2.958 2.954 2.942 1.936 2.935 2.910 2.926 2.969
For codoped models, defect pair binding energy is widely used to investigate the stability of codoped pair. It describes that weather the codoped systems is stable/unstable compared to mono-doped systems [27,34,35]. So, for investigating the formation of defect pairs in the noncompensated and compensated codoped models, the binding energies (Eb) of the defect pair in anatase TiO2 supercell was calculated. For noncompensated codoped models, the defect pair binding energy was calculated using Eq. (1).
Eb ¼ ET ðTi23 CrO48 Þ þ ET ðTi24 O47 NÞ ET ðTi23 CrO47 NÞ ET ðTiO2 Þ
(1)
where ET(Ti23CrO48), ET(Ti24O47N), ET(Ti23CrO47N) and ET(TiO2) represent the total energies (calculated with the same supercell model) of Cr-doped TiO2, N-doped TiO2, noncompensated (Cr, N) codoped TiO2 and pure anatase TiO2, respectively. For compensated codoped models A and B, the defect pair binding was calculated using Eq. (2)
Eb ¼ ET ðTi15 CrO31 Þ þ ET ðTi16 O31 NÞ ET ðTi15 CrO30 NÞ EðTiO2 Þ (2) where ET(Ti15CrO31), ET(Ti16O31N), ET(Ti15CrO30N) and E(TiO2) are the total energies of Cr-doped at Ti sites with an oxygen vacancy, Ndoped TiO2, compensated model A or B and pure TiO2, respectively. For compensated model C, the following formula was used to calculate the defect pair binding energy.
Eb ¼ ET ðTi14 Cr2 O31 Þ þ ET ðTi16 O31 NÞ ET ðTi14 Cr2 O30 NÞ ET ðTiO2 Þ
(3)
here ET(Ti14Cr2O31) and ET(Ti14Cr2O30N) represent the total energies of two Cr-doped at Ti sites with an oxygen vacancy model and compensated model C, respectively. The binding energies of the defect pair in noncompensated and compensated models are summarized in Table 2. Positive value of the defect pair binding energy shows that the individual defects will bind each other in the codoped system to form stable configuration as compared to monodoped models. In noncompensated codoped models, noncompensated model A provided maximum defect pair binding energy describing the adjacent locations of Cr and N as the most stable configuration, this was found in agreement with literature
Table 2 Binding energies of the defect pairs in the codoped models. (Cr, N) codoped TiO2 model
Defect pair binding energy (eV)
Noncompensated Model A Noncompensated Model B Noncompensated Model C Compensated Model A Compensated Model B Compensated Model C
2.17 1.14 1.20 2.24 3.00 5.72
[33]. However, in compensated mode, compensated model C has the maximum defect pair binding energy. The compensated model C has a defect pair binding energy of 5.72 eV, found maximum among all codoped models. Thus, compensated model C is considered to be the most stable configuration of CreN-codoped TiO2. In this case, the individual defects will bind each other and will provide stable configuration compared to mono-doped systems. Among all noncompensated models, noncompensated model B gave the reduced band gap and better optical properties. Similarly, comparison of the compensated models showed that compensated model C had stable configuration and better optical absorption in the visible light. For further comparing the electronic and optical properties of codoped models with NeTiO2, CreTiO2 and pure TiO2, noncompensated model B was selected from the noncompensated models and compensated model C was selected from the compensated models. So, hereafter, noncompensated model B should be named as noncompensated (Cr, N)eTiO2 and compensated model C should be named as compensated (Cr, N)eTiO2. For understanding variations in the band gap due to different mono-doped and codoped models, the band structure of the undoped and doped models was calculated, as shown in Fig. 1. The calculated band gap for pure anatase TiO2 is 2.13 eV (Fig. 1 (a)) found consistent with recent theoretical results [46]; however, underestimated as compare to the experimental value, due to the well-known shortcoming of DFT calculations. Cr doping introduced impurity states in middle of the forbidden region, as shown in Fig. 1 (b). This impurity states will shift the photoexcited carriers to the conduction band which could be further used in the oxidation/ reduction process. Furthermore, the Fermi level was shifted from top of the valence band to middle of the forbidden region describing the half metallic character (Fig. 1 (b)). Fig. 1 (b) showed that compared to un-doped TiO2, the valence band maximum (VBM) and conduction band minimum (CBM) came closer to each other and the distance between them reduced to 2.0 eV as compared to 2.13 eV for un-doped TiO2. Reduction in the band gap and the creation of impurity states in middle of the forbidden region may be beneficial for shifting the absorption edge of TiO2 towards visible region. Compared to pure TiO2, the substitution of N at O sites (Fig. 1 (c)) declined the CBM by about 0.33 eV which effectively reduced electrons transition energy. Moreover, N doping introduced isolated states in the band gap located at about 0.72 eV above top of the valence band. The creation of isolated impurity states and reduction of the effective band gap may help in reducing electron transition energy from valence to conduction band leading to the absorption in the visible region. The band structure of noncompensated (Cr, N)eTiO2 is depicted in Fig. 1 (d). The distance between VBM and CBM was reduced to 1.86 eV compared to 2.13 eV for pure TiO2. Due to Cr and N codoping, widely distributed impurity states were introduced in the band gap. Some states due to Cr doping are located at the Fermi level while some are located above it. The isolated impurity state due to N doping is located at about 0.49 eV below the Fermi level. In case of compensated (Cr, N)eTiO2, the CBM is located about 2.0 eV above the VBM, as shown in Fig. 1 (e). Along with widely distributed states, the Fermi level is shifted up in the forbidden region. The magnitude of impurity states is increased which is due to the increase amount of Cr doping concentration. The widely distributed impurity states in the band gap will allow a range of visible light photons for absorption. The (Cr, N) codoping in TiO2 gives the hybridization of Cr and N electronic states resulting in substantially broaden impurity levels, and led to the formation of intermediate bands which is in agreement with recent experimental findings [23]. Due to the reduced band gap and widely distributed impurity states in the band gap, the electron transition energy will be reduced which will improve the visible light absorption.
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35
Fig. 1. Band structure of: (a) pure anatase TiO2, (b) Cr-doped TiO2, (c) N-doped TiO2, (d) noncompensated (Cr, N)eTiO2, and (e) compensated (Cr, N)eTiO2. The EF represents the Fermi level.
For further understanding the modification in the band gap and the creation of impurity states, the density of states (DOS) and projected density of states (PDOS) of the un-doped and doped models were evaluated. The DOS for pure TiO2 and different doped models are depicted in Fig. 2. For N-doped TiO2 (Fig. 2 (b)), only slight variation in the VBM was found while the CBM was shifted to lower energy values compared to un-doped TiO2 (Fig. 2 (a)). Fig. 2 (c) shows that Cr doping shifted the Fermi level to the middle of the forbidden region, describing the half metallic character of a semiconductor. Noncompensated (Cr, N)eTiO2 also described half metallic character and it was found that codoping narrowed the band gap effectively, as shown in Fig. 2 (d). The DOS of compensated (Cr, N)eTiO2 is shown in Fig. 2 (e). Widely distributed impurity states are located throughout the band gap which may helps in improving visible light absorption. To understand the nature of impurity states in the band gap, the PDOS of pure and
doped models were calculated, as shown in Fig. 3. Fig. 3 (a) shows that the valence band of TiO2 is mostly composed of O 2p states while the conduction band comes from Ti 3d states. Due to N doping (Fig. 3 (b)), N 2p states were introduced in the band gap which is responsible for shifting the photoexcited carriers to the conduction band. Major part of the N 2p states lies in the valence band while some parts appeared in the form of localized states located at about 0.72 eV above the valence band maximum (Fig. 3 (b)), found consistent with literature [15]. Cr doping narrowed the band gap by 0.13 eV compared to pure TiO2. Moreover, Cr 3d states (Fig. 3 (c)) are partially located in the conduction band while its major part appeared in the form of localized states located in middle of the forbidden region which may provide step for transferring photoexcited electrons to the conduction band. PDOS of the noncompensated (Cr, N)eTiO2 is shown in Fig. 3 (d). Cr 3d and N 2p states were simultaneously introduced and partially located in the
36
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Fig. 2. Total density of states (DOS): (a) pure TiO2, (b) N-doped TiO2, (c) Cr-doped TiO2, (d) Noncompensated (Cr, N) codoped TiO2, and (e) compensated (Cr, N) codoped TiO2.
valence and conduction band while some parts appeared in the form of widely distributed states in middle of the forbidden region. These states may be responsible for absorbing visible light photons. The PDOS of compensated (Cr, N)eTiO2 (Fig. 3 (e)) showed that Cr 3d states are widely distributed in the forbidden region. The compensated codoping changed the nature of N 2p states from unoccupied to occupied states. Changing the nature of N 2p states will be important for improving the visible light photocatalytic activity of codoped sample. Spin-polarized calculations showed that N doping at O sites induced antiferromagnetism (AFM) in TiO2. N dopant introduced magnetic moment of 1.45 mB per N atom in the anatase TiO2 supercell which is found close to the reported value [47]. Cr doping at Ti sites induced ferromagnetism (FM) in TiO2, contributing magnetic moment of 2.61 mB per Cr atom, found
Fig. 3. Projected density of states (PDOS) of: (a) pure TiO2, (b) N-doped TiO2, (c) Crdoped TiO2, (d) noncompensated (Cr, N) codoped TiO2, and (d) compensated (Cr, N) codoped TiO2. The vertical line at energy equal to zero represents the Fermi level.
increased compared to the theoretical value [48]. Furthermore, codoped model also showed ferromagnetic behavior. Interaction of photons with the electrons in a system describes optical properties which gives detail information about the electronic band structure of a semiconductor. Optical photons interaction with the electrons in a particular system can be described in terms of time-dependent perturbations of the ground-state electronic states. Absorption of photon will lead to the electron transitions between occupied and unoccupied states which can be described as a joint density of states between valence and conduction band. CASTEP calculates the optical properties from the dielectric function which consists of real and imaginary parts (3 ¼ 3 1þi3 2). Within proper selection rules, the imaginary part of the dielectric function 3 2(u) can be calculated from the momentum matrix elements between the occupied and unoccupied wave functions. The real part 3 1(u) is related to the electronic polarizability of the material and it can be evaluated from the imaginary part using KramerseKronig transform [49,50]. Optical properties such absorption coefficient, reflectivity, refractive index and energy loss function can be calculated from the real and imaginary parts of the dielectric function. As our calculated band gap was underestimated compared to experimental value, therefore scissor approximation was used [51] to make our results compatible with experimental values. Scissor operator shifts the unoccupied conduction band states with respect to occupied valence band states. Scissor operator of 1.07 eV was applied for adjusting the results with experimentally observed values. The optical properties including imaginary part of the dielectric function, absorption coefficient, reflectivity, refractive index and loss function are shown in Fig. 4. For any material, the imaginary part of the dielectric function is the pandect of optical properties. For comparing the optical properties of un-doped and doped models, the imaginary part of the dielectric function was calculated, as shown in Fig. 4 (a). Fig. 4 (a) shows that un-doped TiO2 can only respond to UV light having no absorption peak in the visible region. The main peak for un-doped TiO2 was obtained at 4.60 eV, assigned to the excitation from the O 2p states in the valence band to the Ti 3d states in the conduction band. All doped models showed enhance visible as well as UV light absorption compared to un-doped TiO2, attributed to the narrowed band gap due to the creation of impurity states. N doping in TiO2 improved its optical properties by giving absorption in the visible and UV light range with the absorption edge at about 1.33 eV in the visible region and strong absorption peak in the UV region at 4.66 eV. The visible light absorption may originate from the electron transition from O 2p states to Ti 3d states through N 2p states while the peak at 4.66 eV is attributed to the direct transition of electrons from O 2p to Ti 3d states. These results were found consistent with experimental [52] and theoretical findings [3,6]. Cr doping concentration of 1.38% exhibited strong absorption in the visible and UV light range with absorption peaks at 1.15 and 4.71 eV, respectively. The absorption peak at 1.15 eV may come from step wise shifting of the electrons from the valence to conduction band though Cr 3d states while absorption in the UV region may originate from excitation between the valence and conduction band of TiO2. These findings were found in close agreement with the experimental results which showed that Cr doping effectively shifted the absorption edge of TiO2 towards visible light [32]. Noncompensated (Cr, N)eTiO2 showed broad absorption in the visible range along with enhanced absorption in the UV region compared to un-doped TiO2. The absorption edge for noncompensated codoped model is at 0.5 eV along with main absorption peak at 4.62 eV. Absorption in the visible region may come from excitation through the narrowed band gap due to codoping. Compensated (Cr, N)eTiO2 has better visible as well as UV light absorption due to the reduced band gap and the existence
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Fig. 4. Optical properties of pure anatase TiO2 and different doped models: (a) imaginary part of the dielectric function, (b) absorption coefficient, (c) reflectivity, (d) refractive index, and (e) loss function.
of widely distributed impurity states in the band gap. This model showed two main peaks, at 2.12 eV and at 4.90 eV, located in the visible and UV regions, respectively. The visible light absorption may come from the excitation between valence and conduction band through the impurity states in the band gap while the UV light absorption will come from the direct transition between O 2p and Ti 3d states. In doped models, the absorption in low energy region may originate from the electronic intraband transitions between Cr 3d to Ti 3d states and/or N 2p to Cr 3d or Ti 3d states. Compensated (Cr, N)eTiO2 has broad absorption range in the visible light region due to the widely distributed impurity states in the band gap, while Cr-doped TiO2 has good absorption properties in the visible range in the form of strong peak at 1.15 eV due to the creation of Cr 3d states in the forbidden region. Fig. 4 (b) describes absorption coefficient spectrum of the pure TiO2 and different doped models. Un-doped TiO2 has no absorption peak in the visible region while all doped models provided some sort of absorption in the visible region describing that doping narrowed the band gap of TiO2. Doped models have absorption in the visible region but still the main absorption peaks occurred in UV range due to the intrinsic band gap nature of anatase TiO2. Compensated codoped model has good absorption in the form of broad absorption region due to the
narrowed band gap and the existence of widely distributed impurity states in the band gap. Experimental result showed that (Cr, N) codoping effectively improved the visible light absorption of TiO2 compared to single Cr or N-doped TiO2 [32]. It is argued that doped models may provide good visible light photocatalytic activity compared to un-doped TiO2. Pan et al. [32] synthesized Cr/TiO2, TiO2-xNx, and Cr/TiO2xNx, and found that (Cr, N) codoping effectively improved the visible light absorption compared to Cr/TiO2 and TiO2xNx; however it had poor photocatalytic activity compared to mono-doped samples using the photodegredation of methylene blue, attributed to the extra imperfections introduced during codoping process [32]. Recent experimental [33] results showed that Cr-doped TiO2 films did not induce any visible light photocatalytic activity; however N-doped TiO2 and (Cr, N) codoped TiO2 films are active in the visible region providing similar activity. Moreover, (Cr, N) codoped TiO2 was found more active among the doped samples in the UV region having same activity as un-doped films [33]. This controversy may due to the different doping concentrations because Pan and Wu [32] doped Cr in the TiO2 with the molar ratio of 0.32% and then it was thermally treated in pure ammonia atmosphere at 550 C, while Kurtoglu et al. [33] synthesized their films composed of Ti1xCrxO2yNy
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(0.04 < x < 0.06 and 0.25 < y < 0.30). Zhu et al. [30] synthesized Cr3þ doped anatase TiO2 with the help of solegel and hydrothermal process and found that Cr3þ substitutes Ti4þ which showed that Cr doping effectively improved the photocatalytic activity of TiO2 under both UV and visible light irradiation with an optimal doping concentration of 0.15% and 0.2%, respectively [30]. Fan et al. [31] synthesized mesoporous Cr-doped TiO2 and found that Cr doping extended the photoresponse of TiO2 towards visible region along with the enhanced visible light photocatalytic activity compare to pure mesoporous TiO2 and nonporous Cr-doped TiO2 [31]. Reflectivity, refractive index and loss function for the un-doped and doped models are provided in Fig. 4 (c)e(e), respectively. Doping impurity atoms improved the reflectivity of TiO2, as evident from Fig. 4 (c). Fig. 4 (c) showed that Cr-doped TiO2 has higher reflectivity in the region 0e1 eV. Further increase in the energy axis, Cr-doped TiO2 exhibited abrupt reduction in its reflectivity value and became equal to that of un-doped TiO2, while in high energy regions, it gave strong peaks at 6.75 and at 8.75 eV. N-doped TiO2 and Noncompensated (Cr, N)eTiO2 have smooth increase in the reflectivity in low and high energy region while it gave same reflectivity as un-doped TiO2 in the region 3.25e4.50 eV. Compensated (Cr, N)eTiO2 has higher reflectivity from 0 to 3.0 eV and from 7.4 to 12 eV. As a whole, compensated (Cr, N)eTiO2 provided better reflectivity among pure and all doped models. The refractive indexes for the un-doped and doped models are depicted in Fig. 4d. Cr doping in anatase TiO2 produced abrupt variation in the refractive index value of TiO2. N-doped and noncompensated codoped model have smooth increase in the refractive index values in low energy region (0e2.67 eV) and smooth decrease in the high energy region (8.33e14 eV); however, in the rest of the region they have nearly same value like un-doped TiO2. Among all models, compensated codoped model has higher refractive index values in the low energy region. Loss function describes the energy loss to a fast moving electron during its passage through a materials medium. Peaks in the loss function spectra relate with trailing edges in the reflection spectra and gives variation in the reflectivity. Un-doped TiO2 has loss function peak at 7.20 eV (Fig. 4 (e)) which described abrupt reduction in the reflectivity as evident from the reflectivity curve in Fig. 4 (c). In case of Cr-doped TiO2, the peaks occur at 1.50, 7.50, and at 9.0 eV describing abrupt decrease in the reflectivity’s in that particular energy values. N-doped and noncompensated (Cr, N)eTiO2 have peaks at 7.50 eV and at about 8.50e8.80 eV, attributed to the corresponding reduction in the reflectivity’s values. Compensated (Cr, N)eTiO2 has strong loss function peak at 9.90 eV which describes the abrupt change in the reflectivity values in this region, as verified from Fig. 4 (c). 4. Conclusions Using density functional theory calculations, the electronic and optical properties of Cr-doped TiO2, N-doped TiO2, noncompensated, and compensated (Cr, N) codoped TiO2 were investigated. Cr doping at Ti sites introduced Cr 3d states in middle of the band gap and N doping at O sites created N 2p states located at about 0.72 eV above the valence band maximum. In compensated (Cr, N) codoped TiO2, Cr doping changed the character of N 2p states from unoccupied to occupied states which will help in improving photocatalytic activity of the codoped system. Compensated (Cr, N) codoped TiO2 has reduced band gap along with widely distributed Cr 3d and N 2p states in the band gap. Defect pair binding energy showed that individual defects in compensated codoped models will bind each other leading to the geometrically stable state, compared to monodoped models. All doped models have absorption in the visible range compared to pure TiO2 attributed to the creation of impurity
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