Boron-Doped Anatase TiO2: Pure and Hybrid DFT Calculations - The

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Boron-Doped Anatase TiO2: Pure and Hybrid DFT Calculations Emanuele Finazzi, Cristiana Di Valentin, and Gianfranco Pacchioni* Dipartimento di Scienza dei Materiali, UniVersita` di Milano-Bicocca, Via R. Cozzi, 53, 20125, Milano, Italy ReceiVed: August 13, 2008; ReVised Manuscript ReceiVed: October 1, 2008

We report the results of density functional theory calculations on the electronic structure of boron-doped anatase TiO2. For the calculations we used both standard and hybrid exchange-correlation functionals. On the basis of a close comparison of computed and measured observable properties, in particular hyperfine coupling constants from electron paramagnetic resonance experiments and core level binding energies from X-ray photoelectron spectroscopy spectra, we propose the existence of both substitutional to oxygen and interstitial boron atoms in the bulk of anatase. Boron substitional to oxygen results in a paramagnetic defect, [BTi3]•, which introduces new states in the midgap of the material. The analysis of the stability of this center, however, shows that it should not be the dominant species and should convert into interstitial boron after annealing at high temperature. Various possible sites for interstitial boron have been considered where the dopant is coordinated to three, [BO3], or to four, [BO4], oxygen atoms. The electronic characteristics of interstitial boron are rather independent of the site where the atom is incorporated. Boron in interstitial positions behaves as a three-electron donor with formation of B3+ and reduction of Ti4+ to Ti3+. The possible copresence of substitutional and interstitial boron could also result in internal charge transfer leading to more complex situations. 1. Introduction Doping of titania with nonmetal atoms is attracting an increasing interest related to the search for more active photocatalysts able to allow the injection of electrons from the valence to the conduction band using visible sunlight.1 A great deal of attention has been devoted to nitrogen-doped TiO2, N-TiO2,2-11 but recently attention has been moved also toward boron-doped TiO2, or toward the effect of codoping with pairs of dopants, like B and N, B/N-TiO2.12-15 It has been suggested that B-TiO2 is a more active photocatalyst than pure titania,16-21 and that boron induces a band gap narrowing20,22 and helps in enhancing the lifetime of electron-hole pairs. Despite a significant number of studies, however, the local structure around the boron impurity and the electronic nature of the dopant are far from being understood. A number of experimental studies concluded that boron is incorporated in interstitial sites in the form of B3+. The evidence comes mainly from X-ray photoelectron spectroscopy (XPS) spectra. Often B-TiO2 exhibits a peak of the B 1s level around ≈192 eV,12,14,17-20,22 which increases in intensity as the level of doping is increased; the standard binding energy of B 1s in boron oxide, B2O3, or in boric acid, H3BO3, where boron forms three B-O bonds in a planar configuration, is ≈194 eV,22 while in TiB2 the level shifts to smaller binding energies, about 188 eV,22 due to the change in oxidation state. In some cases the ≈192 eV B 1s peak coexists with other peaks at higher binding energies, indicating the possible formation of B2O3 microaggregates into or at the surface of the titania structure.13,17 In this respect, the absence of the peak at 194 eV is a signature of the fact that B has entered into the structure as a diluted impurity, not in the form of B2O3 nanoaggregates.22 B 1s features at smaller binding energies, 190.6 eV, have also been reported.13 In et al.13 attributed the enhanced photocatalytic activity of B-TiO2 to a substitutional B occupying O sites, so * Corresponding author. E-mail: [email protected].

that boron forms direct bonds with Ti ions.13 According to other studies boron forms paramagnetic species, with typical signals in an electron paramagnetic resonance (EPR) experiment.23 This is more compatible with a substitutional boron impurity and, in any case, suggests the possible existence or coexistence of various B-related species, depending on the preparation method. From a theoretical point of view, B-TiO2 has been investigated at the density functional theory (DFT) level making use of the local density approximation (LDA)14,24 or of the generalized gradient approximation (GGA).22,25 Three possible structures have been considered, with the B atom substituting a Ti ion, and an O ion, or in an interstitial position. There is general consensus that boron substitutional to titanium is energetically less favorable.22,24 The reported DFT calculations have tried to provide an explanation for the observed modification of photocatalytic activity of B-TiO2. The results, however, do not point to a single explanation. Yang et al.25 and Gombac et al.14 suggested that B doping results in a blue shift of the absorption spectra due to a small increase of the band gap when boron is in interstitial positions, an observation which is supported by UV-visible absorption spectra of B-TiO2.18 A band gap narrowing was suggested for boron substitutional to oxygen,14,24 attributed to the presence of midgap states.24 It should be mentioned, however, that none of the calculations reported in the literature can be considered state-of-the-art. Pure DFT calculations in fact suffer from the well-known limitation of an incorrect description of the self-interaction contribution.26 This leads to band gaps that are too small and, as a consequence, to a general tendency to delocalize holes and electrons in insulators or wide gap semiconductors.27-30 The problem is well-known in particular in relation to the study of titania.31-33 The band structure of reduced titania exhibits a well-defined peak at about 0.8-0.9 eV below the conduction band attributed to the presence of Ti3+ ions.34,35 Standard DFT approaches fail in reproducing this important feature and place the corresponding level into the conduction band, so that the corresponding electronic state

10.1021/jp8072238 CCC: $40.75  2009 American Chemical Society Published on Web 12/15/2008

Boron-Doped Anatase TiO2 is fully delocalized.31-33 The problem can be eliminated or reduced by using the many-body GW approximation36 or using more “pragmatic” approaches, like hybrid functionals, where the “exact” Hartree-Fock exchange is partly mixed in with the DFT exchange,31 or the use of the DFT+U method which corrects some of the inadequacies connected with the DFT treatment of localized states.32 The problem of a more appropriate description of localized states in the gap of anatase is also related to another phenomenon. It has been shown recently both experimentally and theoretically that the inclusion of nitrogen atoms as dopants in the structure of TiO2 greatly facilitates the creation of oxygen vacancies in the material.11 This is due to an internal charge transfer from the states associated with an oxygen vacancy (Ti3+), which lie high in the gap, to the states associated with a N impurity, which are just above the valence band.10 This leads to an electron transfer from the Ti3+ to the N atom, with formal reoxidation of titanium and reduction of nitrogen, Ti3+ + Nb f Ti4+ + Nb- (b ) bulk).11 The energetics of the process and the nature of the states require the use of more sophisticated theoretical methods or at least a validation of the results obtained at the standard DFT level with more robust approaches. In this work we have considered the nature of B-doped TiO2 by performing both standard and hybrid DFT supercell calculations. We considered various possible interaction modes of B in the matrix of bulk anatase, and we try to carefully compare the results with experimental data, in particular hyperfine coupling constants with EPR data for the paramagnetic species and core level binding energies with XPS spectra. From this comparison a rather unambiguous assignment of the observed species is possible. 2. Computational Details The calculations have been performed including spin polarization using the generalized gradient approximation (GGA) with the PBE37 functional, and the hybrid B3LYP38,39 functional. The Kohn-Sham orbitals were expanded in Gaussian type orbitals (GTO), as implemented in the CRYSTAL06 code40 (the allelectron basis sets are Ti 86411(d41),41 O 8411(d1),42 and B 621(d1)43). For an improved description of the Ti3+ species, we have added a more diffuse d function with R exponent ) 0.13. The use of two different functionals is justified by the fact that they provide different estimates of the band gap and, consequently, of the position of impurity levels in the gap of the material. Furthermore, experience from our group shows that usually the hyperfine coupling constants (see below) are better evaluated with hybrid functionals. We considered a nearly cubic 22 × 22 × 1 supercell (96 atoms) to model B-doped bulk anatase. The optimized bulk lattice parameters were taken from previous PBE (a ) 3.786 Å and c ) 9.737 Å)44 and B3LYP (a ) 3.776 Å and c ) 9.866 Å) calculations.45 Full-geometry optimization was performed until the largest component of the ionic forces was less than 1 × 10-4 au (PBE) or 5 × 10-4 au (hybrid functionals). In order to identify the presence of both global and local minima, we have considered various starting points for the optimization by manually distorting the structure and then letting the system completely relax. The k-space sampling was restricted to the Γ-point. The CRYSTAL densities of states (DOS) have been obtained with a 36 k-points mesh. For the paramagnetic defects, the hyperfine interactions of the electron spin with the nuclear spin of the 11B and 47Ti nuclides have been determined. The hyperfine spin-Hamiltonian, Hhfc ) S•A•I, is given in terms of the hyperfine matrix A which

J. Phys. Chem. C, Vol. 113, No. 1, 2009 221 describes the coupling of the electron with the nuclear spin.46 The components of A can be represented as

[

] [

A1 0 0 B1 0 0 A ) 0 A2 0 ) aisoU + 0 B2 0 0 0 A3 0 0 B3

]

(1)

where U is the unit matrix. The isotropic part, aiso, of each coupling constant is related to the spin density at the nucleus (the Fermi contact term)

aiso ) (2µo/3)gNβNgeβe < Fs >

(2)

where µo is the permeability of free space, gN is the nuclear g-factor, ge is the electronic g-factor for the site under consideration, βN and βe are the nuclear and Bohr magnetons, and < Fs > is the expectation value at the nucleus of the spindensity operator. In one-electron systems, < Fs > ) |Ψs(0)|2. The anisotropic traceless tensor B results from the dipolar interaction. X-ray photoemission spectroscopy (XPS) is a powerful technique for studying the nature of a boron dopant. The interpretation of these spectra is not always straightforward as the final core level shift is the result of several contributions, often of opposite sign.47 The simplest and most immediate interpretation of a core level binding energy (CLBE) shift is that an increase corresponds to an “oxidized” species, since a reduced electronic charge results in a weaker Coulombic repulsion which acts to stabilize the core levels of the system. We have determined the CLBEs of the B 1s levels in various configurations using the Kohn-Sham eigenvalues, -εi. In this way final state effects are not included. This is not a severe approximation as we use the same approach to determine “internal” reference values, like the B 1s CLBE in H3BO3 (185.8 eV). This CLBE has been determined for the free H3BO3 molecule using exactly the same method and basis set used for the calculations on pure and doped anatase (CRYSTAL option Molecule). More than absolute values, we are interested in relative shifts, and these should be much less dependent on final state effects.47 3. Results 3.a. Boron Substitutional to Oxygen. The first system considered is a B atom that replaces a three-coordinated O atom in the anatase lattice, Figure 1a and 1b. The B atom is bound to three Ti ions with two short and one long distances, r(B-Ti1) ) 2.11-2.12 Å and r(B-Ti2) ) 2.38 Å, respectively; see Figure 1b. In this structure the B atom is coplanar with the neighboring Ti atoms. Boron has an odd number of valence electrons, and the corresponding neutral defect is by necessity paramagnetic. We considered a doublet state. The unpaired electron is shared between the B and the single Ti ion below it (long B-Ti distance), as clearly shown by the spin-density plot, Figure 1c (PBE) and 1d (B3LYP). Notice that the spin distribution is rather similar in the two approaches, indicating a similar level of localization. The electron occupies a hybrid B 2p-Ti2 3d orbital; the population analysis shows that 0.59 (PBE) and 0.67 (B3LYP) electrons reside on B, and 0.21 electrons are on the vicinal Ti atom (both PBE and B3LYP). This singly occupied level with mixed B-Ti character and the other doubly occupied B 2p-Ti 3d level give rise to localized states in the gap of TiO2, Figure 1e and 1f. An empty, almost pure 2p level is also present on the B atom. In PBE, Figure 1e, the occupied states are rather high in the gap, about 1.7-1.9 eV above the top of the valence band and only 0.6-0.4 eV below the bottom of the conduction band; in B3LYP, Figure 1f, the states are deeper in the gap, at

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Figure 1. Properties of a boron atom substituting an oxygen atom in the lattice of anatase. (a) Optimal geometry. B, black sphere; Ti, small gray spheres; O, large white spheres. (b) Optimal distances around the boron atom: r(B-Ti1) ) 2.38 Å (PBE and B3LYP); r(B-Ti2) ) 2.12 Å (PBE) and 2.11 Å (B3LYP). (c) and (d) Spin-density plots determined at the PBE and B3LYP levels, respectively. (e) and (f) PDOS curves determined at the PBE and B3LYP levels, respectively. (g) Schematic representation of the position of the energy levels induced by substitutional boron. ∆E1 ) 0.35 eV (PBE) and 1.73 eV (B3LYP) is the distance of the singly occupied level from the bottom of the conduction band; ∆E2 ) 0.56 eV (PBE) and 2.10 eV (B3LYP) is the distance of the doubly occupied B 2p level from the bottom of the conduction band; ∆E3 ) 1.65 eV (PBE) and 1.78 eV (B3LYP) is the distance of the doubly occupied 2p level on boron from the top of the valence band; Eg ) 2.21 eV (PBE) and 3.88 eV (B3LYP) is the energy gap.

about 1.7 eV from the conduction band edge. The position of the impurity states with respect to the top of the valence band is thus similar while the distance from the bottom of the conduction band is much larger in B3LYP, Figure 1g. This reflects the different values of the band gap of pure anatase in PBE and B3LYP, 2.2 and 3.9 eV, respectively, computed at the Γ point. Anatase TiO2, however, has an indirect gap between ∼X and Γ,48 and these values are slightly overestimated compared to the real gap. The formation energy of a substitutional B impurity can be estimated from the following equation:

TiO2 + B f TiO2-Bs+ (1/2)O2

(3)

In this process an oxygen atom is removed from the lattice and replaced by a B atom; it is assumed that oxygen leaves the material in the form of an oxygen molecule. The computed ∆E for this reaction at the B3LYP level is +3.6 eV, indicating a cost for the process. This means that the Ti-B bonds are weaker than the Ti-O ones, and that the formation of this defect is not particularly favorable from a thermodynamic point of view. At this point we consider the observable properties of this defect center, starting from the core level binding energies. The B 1s level in substitutional boron, [BTi3]•, is computed at 181.7 eV. As an internal reference we take boric acid, H3BO3, where B is in a +3 oxidation state and the 1s level is calculated at 185.8 eV. Thus, [BTi3]• has a core level shift with respect to H3BO3 of -4.8 eV, fully consistent with the fact that the atom is not oxidized and that it formally keeps its valence electrons (neutral or partially reduced). This assignment is reinforced by the analysis of the experimental binding energies of B 1s level in H3BO3 (≈193.0 eV) and TiB2 (≈188 eV).18,22 The shift going from the oxidized to the neutral form is of ≈-5 eV, not far from that computed in our case.

TABLE 1: Hyperfine Coupling Constants (in G) for Boron Substitutional to Oxygen in Bulk Anatase, [B-Ti3]•, B3LYP Results nucleus 47

Ti B 11 B 11

theory theory exptl23

spin pop.

aiso

B1

B2

B3

0.21 0.67 s

14.0 33.6 36.3

1.8 -8.9 -1.3

2.8 -11.1 -11.3

-4.6 20.0 12.6

The second observable property considered is the hyperfine coupling of the unpaired electron with the 10B and 11B nuclides, Table 1. We concentrate on the 11B species, which has a natural abundance of 80.1%; the corresponding values of 10B are simply determined by the respective nuclear magnetic moments and can be obtained as Ai(10B)/Ai(11B) ) 0.335. The calculations show that the hyperfine constant is largely anisotropic, a sign of the fact that the electron occupies an orbital with p or d character. The aiso value is 33.6 G, Table 1. This value is intermediate between those of two classical paramagnetic B centers, the boron electron center, )B• (aiso(exptl) ) 108 G49), and the boron-oxygen hole center, )B-O• (aiso(exptl) ) 12.5 G,50 aiso(theory) ) 11.3 G,51), where the interaction with boron is of the superhyperfine type since the electron is largely localized on the O atom. The value of 33.6 G computed here for the [BTi3]• center is thus consistent with a defect where the unpaired electron is shared between B and the neighboring Ti atom. The analysis of the dipolar part shows that the system is nearly axial, with B1 ≈ B2 ) - (1/2)B3, Table 1, consistent with the fact that the singly occupied orbital has B 2pz-Ti 3dz2 character. The spin density is mainly distributed on the Ti below the B impurity, as shown also by the hyperfine coupling constants, Table 1. These theoretical results can be compared with a recent EPR experiment on B-TiO2.23 It was found that many paramagnetic species are present in B-TiO2; only one of these species is relevant in this context and clearly shows a coupling of the

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Figure 2. Optimal structure of an interstitial boron atom in bulk anatase. (a) Three-coordinated boron in the basal plane of the cavity, [BO3] (structure a). (b) Three-coordinated boron in the plane normal to the basal plane of the cavity, [BO3] (structure b). (c) Four-coordinated boron, [BO4] (structure c).

unpaired electron with the boron nucleus. The measured aiso ) 36.3 G23 is in surprisingly good agreement with that calculated here for a substitutional boron atom, Table 1. At a first look, the agreement is much lower for the dipolar part, which in the experiment does not take the typical form of an electron in a p orbital (-B, -B, 2B). In fact, the three components observed experimentally are B1 ) -1.3, B2 ) -11.3, and B3 ) 12.6 G, Table 1. As described in ref 23, this anisotropic part, however, can be divided into two matrices based on two dipolar interactions along two different directions, i.e., (-B, -B, 2B) + (2B′, -B′, -B′), with B ) 8 G and B′ ) 3.3 G. This decomposition suggests that the spin density is delocalized over two boron p orbitals, instead of one as found in the calculations. Apart from this aspect, which may have various origins, the analysis of the hyperfine interactions in theory and experiment shows a very close similarity. On this basis, it is possible to conclude that the substitutional boron species [BTi3]• shown in Figure 1 is an excellent candidate for one of the boron defects present in B-TiO2. 3.b. Interstitial Boron. Several authors have pointed out that boron assumes interstitial positions in the lattice of anatase or rutile, forming B-O bonds instead of B-Ti bonds.12,14,17-22 There are at least three positions in the bulk of anatase where a boron atom can be placed in interstitial sites and we cannot exclude that other structures exist. In two of these sites boron assumes a nearly trigonal planar coordination, Figure 2a and 2b. The two situations are locally similar as both correspond to a [BO3] complex, but differ in terms of second neighbors and relative orientation. In structure a, Figure 2a, the [BO3] unit lies in the basal plane of the intestitial cavity, while in structure b, Figure 2b, boron lies in a plane that is normal to the basal plane. The two sites are interconnected as moving the B atom upward form site a leads to structure b. The two structures correspond to local minima on the potential energy surface and are separated by an energy barrier, not investigated here. If the boron atom is further displaced upward along the z-direction, it moves into a pseudotetrahedral cavity where it is coordinated to four oxygen atoms, forming a [BO4] unit, structure c, Figure 2c.

TABLE 2: Properties of Interstitial Boron Atom in Bulk Anatase method spin [BO3] Figure 2a PBE B3LYP [BO3] Figure 2b PBE B3LYP [BO4] Figure 2c PBE B3LYP

3/2 3/2 3/2 3/2 3/2 3/2

∆E,a eV 6.75 (6.66)b 5.42 6.21 (6.05)b 4.85 6.49 (6.35)b 5.00

r(B-O) r(B-O) -ε(B 1s),c (1), Å (2), Å eV 1.405 1.395 1.378 1.370 1.511 1.508

1.388 1.380 1.417 1.407 s s

s 184.3 s 184.2 s 185.0

a Formation energy calculated as ∆E ) E(B) + E(TiO2) E(B-TiO2) b In parentheses are given the values for the state with spin S ) 1/2. c As internal reference for the calculations of CLBE shifts, we use the B 1s level in H3BO3, 185.8 eV.

The geometric and electronic structure of an interstitial boron impurity in bulk anatase are intimately connected and must be discussed together. Boron is a three-valent atom which, once added to the anatase lattice, can act as a three-electron donor. The ground state can be high-spin quartet (S ) 3/2) or lowspin doublet (S ) 1/2). We have considered both possibilities at the PBE level. We always found that the high-spin state (S ) 3/2) is favorable, no matter where the boron atom sits. The energy difference, however, is small, of the order of 0.1-0.2 eV, and the question of the exact nature of the ground state, quartet or doublet, is not relevant, for reasons that will be clarified below. Therefore, the calculations at the B3LYP level have been performed only for S ) 3/2. The addition of a boron atom to each of the three interstitial positions results in a large energy gain, Table 2. At the PBE level the formation energy of the defect with respect to a gasphase B atom is 6.2-6.8 eV, depending on the site where B is incorporated; at the B3LYP level this energy is significantly lower, from 4.9 to 5.4 eV, but still very large. This means that each B-O bond has a strength of about 2 eV in the [BO3] structures, and a bit lower when B is bound to four oxygens as in [BO4]. Both methods, PBE and B3LYP, indicate the [BO3] structure a as most stable, followed by the tetrahedral site, [BO4], and by the other trigonal planar conformation [BO3] (b). The energy differences are of the order of 0.3-0.6 eV, Table 2.

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Figure 3. Spin density plots and PDOS for an interstitial boron atom, [BO3], structure (a), Figure 2a. Top, PBE results; bottom, B3LYP results.

It is interesting at this point to analyze the origin of the highspin ground state and the corresponding spin distribution. We restrict the analysis to the [BO3] structure a, as the general features are very similar for the other two interstitial sites. An inspection of the spin-density plots reveals that there is no residual spin associated with the boron atom, Figure 3; the spin in fact is clearly distributed over the neighboring Ti ions. This feature is common to both PBE and B3LYP results and does not depend on the method used. The absence of spin density on the interstitial boron is further confirmed by the hyperfine coupling constants computed for 11B which, at variance with the case described in section 3.a, are numerically zero. This result clearly indicates that boron has donated its three valence electrons to the lattice, becoming formally B3+. This is further supported by the analysis of the projected density of states, PDOS, Figure 3. No states are present in the gap at the PBE level, and boron contributes to a number of states below the O 2p valence band. The excess electrons are delocalized over several Ti atoms, and the corresponding energy levels have conduction band character. This is the typical situation found in reduced titania when calculations are performed with pure DFT functionals. In reality, as we mentioned in the Introduction, the presence of Ti3+ ions in reduced TiO2 gives rise to new states in the gap at about 0.8 eV below the conduction band.34,35 These states are usually reproduced by hybrid DFT functionals which provide a more localized description of the excess electrons.31 However, even hybrid functionals tend sometimes to provide partially delocalized pictures of the Ti3+ states.33 The localization in fact is largely connected to a pronounced polaronic distortion of the lattice around the Ti3+ ion where the electron is localized. In absence of this distortion, the state becomes partly delocalized.31 This is what we found here for B-doped TiO2 at the B3LYP level when we consider interstitial B atoms, Figure 3. The PDOS shows some occupied states just

below the conduction band edge due to partly delocalized Ti 3d states. Probably, by inducing a specific distortion around Ti, it could be possible to obtain a fully localized solution. This, however, is not relevant for the nature of the boron defect, as it simply concerns the formation of reduced Ti ions by electron transfer from the boron dopant. This discussion also clarifies why the question of the spin multiplicity of the ground state is not relevant: the energy difference between high (S ) 3/2) and low (S ) 1/2) spin configurations is small because we are dealing with the spin coupling of electrons delocalized over Ti 3d states, and not localized on B 2p orbitals. In case of full localization, however, one would expect the S ) 3/2 solution to be considerably more stable than the S ) 1/2 since pairing up two electrons in a localized Ti 3d has a considerable cost, as previously shown for the oxygen vacancy triplet and singlet solutions.31 To summarize, we have clear theoretical evidence that the process accompanying the addition of boron atoms in interstitial sites is the following:

B + 3Ti4+ f Bi3++ 3Ti3+

(4)

This is similar to what happens when C atoms are incorporated in interstitial sites (carbonate species) in C-doped TiO2.52 This is also what it has been suggested experimentally by some authors.14,53 Boron acts as a reducing agent and transfers its three valence electrons to Ti ions. The cost of the ionization is compensated by the formation of strong bonds between the B atom and the neighboring oxygens, which in fact relax significantly from their lattice positions toward the interstitial B impurity. The B-O distances are about 1.4 Å in [BO3] and slightly longer, 1.5 Å, in [BO4], Table 2. The inward relaxation of the oxygen atoms to “screen” the positively charged boron atom is clearly visible in Figure 2. The picture of a charge transfer from B to Ti is further supported by the population

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Figure 4. Spin-density plot and PDOS for a [BO4]-VO pair of defects, obtained by displacement of a substitutional to oxygen boron atom into a tetrahedral interstitial site. B3LYP results.

analysis, which indicates a net charge of 0.87 e on B, and, most important, by the core level binding energies. The B 1s level in structure a [BO3] is found at 184.3 eV (and at similar energies in [BO3] (b) (184.2 eV) and in [BO4] (185.0 eV), Table 2). The shift with respect to the H3BO3 internal reference, 185.8 eV, is 1.5 eV only and is fully consistent with the presence of a partly oxidized boron atom. Notice that in the experiment the XPS peak associated with a diluted boron impurity is found around ≈192 eV, with a shift of about 1 eV with respect to the H3BO3 reference, 193 eV, in nice agreement with the calculations. Assuming that substitutional boron [BTi3]• (B 1s 181.7 eV) and interstitial boron [BO3] (B 1s 184.3 eV) are simultaneously present in the material, the corresponding B 1s peaks should be separated by 2.6 eV according to the calculations. 3.c. Relative Stability of Substitutional and Interstitial Boron. The previous discussion shows that both substitutional and interstitial boron species are likely to be observed experimentally, depending on the preparation conditions. In order to verify the stability of a substitutional B atom, [BTi3]•, compared to an interstitial one, [BOn], we have considered a supercell where the B atom is initially in a substitutional to oxygen position, Figure 1, and we have moved it into a tetrahedral site where it is coordinated to four O atoms, Figure 2c. Since the boron atom was replacing an oxygen in the lattice, this is equivalent to adding B in an interstitial position and removing an oxygen from a lattice site, i.e., forming an oxygen vacancy. We denote this pair of defects [BO4]-VO, where VO indicates an oxygen vacancy. The formation energy of an oxygen vacancy in bulk anatase, computed with respect to (1/2)O2, is 4.2-4.8 eV, depending on the method used.30,33 This means that the displacement of the B atom from the substitutional to the interstitial position has a net cost associated with the formation of an oxygen vacancy and a gain associated with the addition of boron to the lattice. The calculations performed at both PBE and B3LYP levels show that the [BO4]-VO structure is 3.5 eV (PBE) and 3.0 eV (B3LYP), respectively, more stable than that with a B atom substituting a lattice oxygen, [BTi3]•. Since the two supercells contain the same number of atoms, one can safely conclude that the energy gain associated with an interstitial boron atom largely compensates the cost of creating an oxygen vacancy. This is not too surprising if we consider that boron forms very strong bonds with oxygen: the cost to break the boric acid, H3BO3, into a B atom and three OH• radicals is 5.80 eV per B-O bond, computed at the B3LYP level. This result clearly

shows that interstitial boron is preferred with respect to substitutional boron and that the latter is a metastable structure which may convert into interstitial boron and an oxygen vacancy at temperatures sufficiently high to overcome the energy barrier separating the two minima. The comparison with the C- and N-doped systems is interesting. The Ci-VO system is more stable than the Cs one by 0.4 eV only,52 while the Ni-VO system is less stable than the Ns one.54 These results indicate a specific trend along the row: going from B to C to N the reducing power of the element decreases as expected, and B is the most easily oxidized element. It is interesting to further analyze the relative stability of the three different B species in bulk anatase as a function of the oxygen chemical potential, µO, a parameter characterizing the oxygen environment during the synthesis. The environment acts as a reservoir, which can give or take any amount of oxygen without changing its temperature and pressure.55,56 A low/high value of the oxygen chemical potential corresponds to oxygenpoor/-rich conditions. By referring µO to the energy of an oxygen atom in the O2 molecule, µO ) (1/2)µ(O2) + µO′, we take -4 eV e µO′ e 0, where the value µO′ ) 0 corresponds to the O-rich limit at which oxygen condensation will occur.55,56 In Figure 5 we report the energies of formation of the three B-doped models considered in this work as a function of µO′, according to the formula

Eform)Etot(B-doped TiO2) - [Etot(TiO2) + µB - mµO] (5) where m is the number of oxygen atoms removed from the system. For boron, we use a fixed value of the chemical potential µB ) (1/2)µ(B2H6) - (3/2)µ(H2). The range of µO′ was also translated in a more usual measure of oxygen concentration, the oxygen partial pressure at a fixed temperature of 700 K (top x-axis). It must be noted that values of oxygen chemical potential below 2 eV correspond to oxygen partial pressures which cannot be reached experimentally. The resulting graph shows that the interstitial B is the most stable species at any value of the oxygen chemical potential. The introduction of an oxygen vacancy (VO) in the system causes a dependency of the energy of formation of the defect with the oxygen concentration. The resulting [BO4]-VO defect is more stable than the substitutional B species at any value of the oxygen chemical potential. It is relevant to analyze the electronic structure of the [BO4]-VO defect. As we have seen above, interstitial boron donates three electrons to the Ti4+ ions of bulk anatase. The

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Figure 5. Formation energies (Eform, in eV) obtained at the B3LYP level as a function of the oxygen chemical potential (in eV) or of the oxygen partial pressure at fixed T ) 700 K (top x-axis), for different B species in anatase TiO2.

formation of an oxygen vacancy also leads to two excess electrons,31 for a total of five unpaired electrons. We have been able to converge the calculation on such high-spin solution (S ) 5/2), Figure 4 (B3LYP results). The excess electrons occupy the Ti 3d states with different levels of localization. The three electrons donated by the boron impurity are largely delocalized over several Ti ions, as discussed above, while the two electrons associated with the vacancy are essentially localized on the undercoordinated Ti ions adjacent to the vacancy, Figure 4a. As a consequence, these undecoordinated Ti3+ ions give rise to localized states at about 1-1.5 eV below the conduction band, Figure 4b, in agreement with experimental observations and previous calculations performed at the same level of theory.31 4. Discussion and Conclusions In this study we have considered the electronic structure of boron-doped anatase. Different from previous theoretical studies, we have applied two different methods, a pure DFT-GGA approach based on the PBE exchange-correlation functional and a popular form of hybrid functional where the exact Hartree-Fock exchange is partly mixed in with the DFT exchange (B3LYP). The usefulness of investigating defects in titania with more than a single method has been recently pointed out.30,31,33 Due to the different treatment of the self-interaction problem and of the different values of the band gap, these methods can result in different descriptions of the same defect in terms of localization of electrons or holes. The inclusion of the dopant in B-TiO2 has important consequences on the electronic structure of the material. The fact that these features are described in a similar way by both theoretical methods makes us confident of the validity of the results. We have found, in agreement with the existing literature, that boron in the bulk of anatase can assume different positions and give rise to very different situations. The first case analyzed is that of a boron atom replacing an oxygen atom in the lattice. When this occurs, the corresponding defect is paramagnetic and

Finazzi et al. can be detected by EPR.23 The unpaired electron is shared between B and the neighboring Ti atom, and occupies an orbital with B 2p- Ti 3d character. The computed hyperfine coupling constants are in nice agreement with those reported recently for the same system23 (the small deviation in the dipolar part can be due to local asymmetries in the chemical environment of the real system or to the existence of different variants of the same defect superposed in the EPR spectrum). Also the core level binding energy shifts clearly identify this defect as a “neutral or partly reduced” boron bound to Ti atoms. The defect can thus be rather unambiguously identified as a [BTi3]• center. This defect introduces new states in the gap of anatase. A precise positioning of the states is not easy as this is rather dependent on the method used. However, both PBE and B3LYP methods place the level quite high in the gap, well separated from the top of the valence band. The analysis of the energetics, however, shows that [BTi3]• is likely to be a metastable defect and that thermal annealing at high temperatures can destroy the defect leaving behind an interstitial boron atom and an oxygen vacancy. In fact, the calculations show that moving the B atom from the O-substitutional to an O-interstitial position leads to a net energy gain, despite the fact that the structure now contains undercoordinated Ti atoms (due to the presence of an oxygen vacancy). Clearly, interstitial boron is preferred. Therefore, while [BTi3]• can be formed under special conditions, it is not expected to be the dominant species in B-TiO2. Interstitial boron species have been investigated in detail considering various possible locations of the boron impurity. This can be either in a trigonal planar coordination, [BO3], or in a pseudotetrahedral site, [BO4]. In all cases the driving force for boron to occupy interstitial positions is the formation of rather strong bonds with oxygen. The most stable structure corresponds to a [BO3] unit, but the energy differences between the various sites are of the order of 0.3-0.6 eV, and it is not excluded that in a real system a statistical distribution of boron in a variety of sites is present. This is not relevant for the changes in electronic structure of the material as all the B-interstitials behave in the same way and introduce the same kind of defect states. In fact, the calculations clearly show that when boron is incorporated in interstitial positions it loses its three valence electrons, which are donated to the 3d states of lattice Ti ions, according to the following process: B + 3Ti4+ f Bi3+ + 3Ti3+.14,53 In our PBE and B3LYP calculations the resulting Ti3+ states are largely delocalized. This is the normal solution in PBE, while in the hybrid B3LYP approach this is probably due to the fact that we did not look for the proper polaronic distortion which favors localization of the excess electrons. This aspect, however, is not important here since the result shows that the inclusion of boron in interstitial positions leads to the same kind of defects produced by other procedures: reduction of titania under mild thermal treatment, addition of dopants like hydrogen57 or alkali metals,58 inclusion of fluorine,59 etc. All these methods lead to the formation of six-coordinated lattice Ti3+ ions (interstitial Ti ions are formed under other conditions, such as, for instance, surface sputtering or annealing at high temperatures).60 The boron atom in interstitial sites becomes fully oxidized, a fact which is well demonstrated by the B 1s core level binding energy which is shifted by +2.6 eV compared to [BTi3]• and by -1.6 eV with respect to the internal reference H3BO3. These computed shifts are broadly consistent with those measured experimentally. In this respect, it should be mentioned that the presence of substitutional boron in B-TiO2 has been suggested based on the presence of a shoulder at 190.6 eV in a broad XPS spectrum with a shift of 2.7 eV

Boron-Doped Anatase TiO2

J. Phys. Chem. C, Vol. 113, No. 1, 2009 227

with respect to the main peak attributed to inclusions of B2O3.13 According to our calculations, the levels of substitutional boron should be considerably more shifted (by about 4.8 eV) compared to a B in the +III oxidation state. Different from other theoretical studies,22,25 we will not attempt an explanation of the increased photoactivity of B-TiO2 based on these results. The reasons are the following. It is certainly tempting to assign the origin of the increased activity to [BTi3]• centers, as these introduce new states in the gap which should lead to a red shift in the absorption of the material. Apart from the fact that the theoretical determination of the exact position of the level in the gap is not easy, there are two reasons that make this explanation not fully convincing. First of all, we have shown that this center is not the most stable one, and in fact its presence is still under discussion and has been reported only in a minority of studies.23 Most of the experimental works indicate the presence of oxidized boron, i.e., boron in interstitial sites.12,14,17-22 The second reason is that if we assume that both [BTi3]• and [BO3] species are simultaneously present in the sample, one could expect the occurrence of other internal charge transfer mechanisms. In particular, the Ti3+ states induced by [BO3] or associated with oxygen vacancies naturally present in the system, lying high in the gap, could transfer one electron into the unoccupied B 2p level of [BTi3]• according to the process

[BTi3]• + Ti3+ f [BTi3]-+Ti4+

(6)

This phenomenon has been suggested recently for B-TiO215 and is very similar to what occurs in N-doped titania where most of the active nitrogen species are in a diamagnetic form, Nb-, since they trap one electron from the Ti3+ states associated with the presence of oxygen vacancies.11 In order to study the possible occurrence of this internal charge transfer, we have considered a supercell where a substitutional B and an oxygen vacancy are simultaneously present. The vacancy generates two Ti3+ ions, and one of these ions transfers spontaneously one electron into the empty 2p orbital of the Bs impurity, which now has two singly occupied levels (triplet state) and can be classified as Bs-. This shows that the presence of dopants like B and N in the material may have more complicated consequences which are at the basis of the observed photoactivity. More work, both theoretical and experimental, is needed in order to clarify this aspect. It has also been suggested that interstitial boron induces a small opening of the band gap and a blue shift of the absorption spectrum.25 We have shown that interstitial boron leads to reduced Ti3+ ions with electronic states near the conduction band edge. This is hardly compatible with a band gap opening. Furthermore, the presence of these extra states makes a clear identification of the conduction band edge very delicate, and probably beyond the accuracy of the methods used. To summarize, we have shown rather unambiguously that boron can exist in at least two major forms as a dopant in bulk anatase, and we have proposed two structures, one paramagnetic where boron is “neutral”, [BTi3]•, and one diamagnetic where boron is oxidized, [BO3]. The paramagnetic [BTi3]• could easily trap electrons from other defect states (e.g., Ti3+ ions) and convert into the EPR-silent [BTi3]- species. Oxidized boron should be observed in association with Ti3+ states, provided that these centers do not transfer charge to other defects in the system. The two B centers are characterized by different XPS signals, although the concentration of the less stable [BTi3]• susbtitutional centers could be too low to provide a clear peak. We hope that the results of this work can help to shed light

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