Dispelling the Myth of Passivated Codoping in TiO2

Modification of TiO2 to increase its visible light activity and promote higher performance photocatalytic ability has become a key research goal for materials scientists in the past 2 decades. One of the most popular approaches proposed this as “passivated codoping”, whereby an equal number of donor and acceptor dopants are introduced into the lattice, producing a charge neutral system with a reduced band gap. Using the archetypal codoping pairs of [Nb + N]- and [Ta + N]-doped anatase, we demonstrate using hybrid density functional theory that passivated codoping is not achievable in TiO2. Our results indicate that the natural defect chemistry of the host system (in this case n-type anatase TiO2) is dominant, and so concentration parity of dopant types is not achievable under any thermodynamic growth conditions. The implications of passivated codoping for band gap manipulation in general are discussed.


■ INTRODUCTION
TiO 2 , is an earth abundant, chemically stable wide band gap semiconductor that is used in a broad range of applications. In particular, titanium dioxide is used as a photocatalyst for the degradation of dyes and pollutants, 1,2 the antimicrobial destruction of Staphylococcus aureus and Escherichia coli 3−6 as well as the splitting of water into H 2(g) and O 2(g) 7−9 to name a few. TiO 2 is popular in industry due to the wide range of scalable synthesis techniques such as sol−gel and chemical vapor deposition (CVD) that can be used to produce it. 10 The main drawback, however, is its large band gap (anatase = 3.2 eV) meaning that solely UV light is absorbed accounting for only ∼1−2% of the total solar irradiation that reaches the earth's surface. 11 In addition to this constraint, efficient photocatalysis demands that the conduction band minimum (CBM) and valence band maximum (VBM) must straddle the redox potentials of the species to be reduced/oxidized (e.g., for water splitting ∼1.23 eV) with a suitable overpotential of ∼0.2−0.3eV thereby requiring a band gap of 1.7−2.2 eV for suitable visible light photocatalysis. 11 Although the CBM of TiO 2 is energetically favorable for the reduction of protons, 12 the VBM is very low in energy (due to the high ionization potentials (IP) typical of n-type wide band gap materials 13,14 dominated by deep lying O 2p states) producing highly localized holes states. 15 Within the scientific literature, efforts to increase the efficiency of photocatalysis in TiO 2 via band gap reduction have focused on "raising" the VBM through acceptor doping. 16−20 This is typically achieved through nonmetal doping, i.e., with B, 18,21−23 C, 19,24−26 N, 16,17,27,28 or P. 16,20,29 In particular, nitrogen has been the "go-to" dopant for enhanced photocatalysis in TiO 2 since the work of Asahi et al. in 2001. 16 The popularity of N-doping in anatase is also due to the reproducibility of these results through a range of solutionprocessed and deposition-based techniques, such as sol− gel, 30,31 CVD, 32−34 or sputtering. 35−37 When doping anatase with nitrogen, it is assumed that the N 2p states hybridize with the top of the valence band, lowering the band gap and ionization potential. However, despite over a decade of research, the exact nitrogen species that forms within the anatase lattice is still scrutinized. The position of N has been suggested to be either substitutional (N O or N Ti ), interstitial (N i ), or part of a complex species with the lattice ions or unintentional dopants, such as H (NH 4 − ). 38−43 Interestingly, although experimental thin films of anatase display a red shifting of the band gap when nitrogen doped, N-doped rutile thin films display a blue shift. This has been proposed to be due to the denser crystal structure of rutile forming a wider O 2p valence band, and upon nitrogen doping a reduction in Coulombic repulsion is observed. 42 In reality, however, the nitrogen states form highly localized hole states just above the VBM corroborated through theoretical studies on both substitutional and interstitial nitrogen species. 38,40−43 Within the density functional theory (DFT) literature, multiple groups have managed to show that interstitial N displaces from the perfect interstitial site toward a lattice oxygen to form an N−O dumbbell which has also been corroborated using electron paramagnetic resonance (EPR) measurements. 43 Unfortunately, these localized N states are a source of electron−hole recombination especially at the high concentrations typically required for "band gap reduction". 44,45 Theoretical studies have also proposed the inducement of oxygen vacancies due to nitrogen incorporation providing intrinsic compensation typical of the high ionization potential of TiO 2 polymorphs. 12,42 Reports of beneficial carbon doping also exist in the literature, albeit less explored than nitrogen-doped TiO 2 in both experiment and theory. Carbon possesses small ionic radii (∼0.15−0. 16 Å 46 ) and generally prefers to exist as a 4+ cation (CH 4 , CO 2 etc.) although it can also exist in the 4− oxidation state as in TiC. Experimental techniques, such as X-ray photoelectron spectroscopy, 47,48 suggest substitutional carbon (C O ) species or carbonate species (CO 3 2− ) adsorbed into the lattice. Two theory papers, in particular, one by Di Valentin et al. 48 (using the standard Perdew−Burke−Ernzerhof functional) and a more recent hybrid DFT paper (HSE06) by Zhang and co-workers 49 elucidate the possible locations and downsides to carbon doping in anatase. Both Di Valentin et al. and Zhang and co-workers recognize the existence of carbon replacing Ti in the lattice (C Ti ) as a dominant defect whereby it acts as an isovalent dopant neither adding or removing electrons but possibly reducing the band gap at higher doping concentrations. 48,49,50 Due to the typical coordinations of carbon, it was found that C Ti defects prefer a four-coordinate configuration adding strain to the system due to the sixcoordinate environment of Ti (where Ti can hybridize 3d orbitals). Due to the small ionic radii, interstitial carbon possesses relatively low formation energies under both Tipoor/O-rich and Ti-rich/O-poor conditions where it acts as a donor. C O is only expected to form toward highly O-poor regimes where it induces the formation of oxygen vacancies thereby compensation occurs as with nitrogen defects. The defects that are expected to give states in the band gap suitable for visible light excitation are the C O related species which do not form as readily as substitutional nitrogen species. 49 Transition metals can also act as acceptor dopants in particular Ni, 51−53 Fe, 54−57 Co, 58−60 Cr, 61−64 and Cu, 65−68 for example. It has been proposed that transition metal dopants provide an additional service by acting as an electron (or hole) trap enhancing the efficiency. 69−72 Whether this increases or decreases electron−hole separation is still in debate with certain metal cations increasing the recombination rate (i.e., chromium) and others decreasing (i.e., copper and iron). 45, 73 Beneficial effects are not just limited to acceptor doping as donors such as Nb, 10,74 Ta, 75−77 Sb, 78,79 or W 80,81 also displays an enhancement of the photoactivity of anatase despite no band gap reduction or states within the band gap. The enhanced effects could likely be due to the increased electron concentration and mobility realized through donor doping and thus an increase in reducing electrons or even an enhanced surface segregation as seen with Sb and Ta. 82,83 To rectify the recombination issues encountered from doping with nonmetals, an approach to fully passivate the dopant states while retaining the reduced band gap was proposed by Wei and co-workers. 44 Within this formalism, the additional incorporation of a donor to the anatase lattice should have the effect of annihilating the additional holes brought about by acceptor doping and is shown schematically in Figure 1. Thus, the beneficial band gap narrowing exhibited by N-doped TiO 2 can be retained while alleviating the recombination centers. Due to the location of the anatase CBM relative to the reduction potential, 12 a preferable resonant donor is required so that no downward shift of the CBM occurs. This makes Nb, Ta, Mo, and W ideal donors for this effect. 44 showing promising results such as the 7-fold increase in photocatalytic degradation of methylene blue or the 4-fold increase in decomposition of methyl orange with [Cr + C] codoped anatase. 88,93 The term "full passivation" is used in this context to describe the concentration parity of acceptor and donor dopants.
Numerous computational studies have been carried out on codoped systems for band gap engineering, 44  Carbon codoped systems were suggested to reduce the band gap too much, which combined with the problems associated with doping with C mean that reproducibility will be an issue in this context, despite a few promising results. 93, 95 Within the codoping literature, there exists a lack of distinction between the increased photoactivity seen due to passivated codoping and that seen from individually doping with either nonmetal or metal aliovalent ions. Claims are also made about the increase in photocatalytic activity such as with the 7-fold increase and 4-fold increase of [Nb + N] and [Mo + C] systems of which the degradations of methylene blue and methyl orange rely just as much on reduction processes favouring an increased mobility and concentration of conduction band electrons. 88,93 Methylene blue and methyl orange photocatalytic tests also rely on multistage degradation which can proceed via adsorption, therefore, making the difference between photocatalytic electron/hole transfer indistinguishable from other processes. Bartlett also remarked that stoichiometric pairing or full passivation of Nb + N was not achieved, even providing a follow up study on the composition dependence of Nb and N. 89 This work concluded that in fact a larger incorporation of Nb both decreased the optical band gap and increased the photoactivity and is echoed by Chadwick et al. 86,89 Zhang et al. also noted that although [Mo + C] showed an increase in the rate of methylene blue degradation compared to the undoped and carbon-doped TiO 2 systems, they also found that C incorporates preferentially on the Ti site and thus cannot be deemed to provide full passivation. 95 An analysis of the ionic radii of dopants in TiO 2 shows that for Nb, Ta, W, Cr, Mo, and W, a range of 0.59− 0.64 Å is observed (compared to 0.60 Å, for Ti) making these highly soluble dopants, therefore low formation energies would be expected. 46 In this work, we demonstrate through theoretical calculations of the [Nb + N] and [Ta + N] codoped systems that charge compensation is simply not possible in anatase TiO 2 under thermodynamic equilibrium due to its inherent n-type nature.

■ COMPUTATIONAL METHODOLOGY
Density functional theory (DFT) calculations using the periodic code, VASP (Vienna Ab-initio Simulation Package), 110−113 and the hybrid HSE06 (Heyd−Scuseria−Ernzerhof) 114 functional were performed on the bulk geometric and electronic relaxations as well as all studied intrinsic and extrinsic defects of anatase TiO 2 . The intrinsic defects and dopants (Ta, Nb, N) were simulated using 3 × 3 × 2 supercell expansions (∼108 atoms) of the geometrically relaxed conventional cell of anatase TiO 2 . The HSE06 hybrid functional 115,116 provides excellent descriptions of the electronic and structural properties of all of the known polymorphs of TiO 2 , 10,12,117−123 and hybrid functionals are, in general, a marked improvement on local or semilocal DFT functionals as they better deal with the self-interaction error. 124 The projector augmented wave 125  An initial geometry optimization of the bulk conventional cell was carried out minimizing the volume, lattice parameters, cell angles, and the ions within the cell until the forces acting on all of the atoms were less than 10 meV Å −1 . A 700 eV planewave energy cutoff and a Γ-centered 7 × 7 × 5 k-point mesh were sufficient to calculate the electronic and structural properties. The bulk electronic properties can be found in ref 123. From this, a 3 × 3 × 2 supercell containing 108 atoms was formed to evaluate the defect properties of the material. Geometry optimizations of each defective supercell and its respective charge states involved calculating the relaxation of only the ions within the cell, keeping the cell volume, lattice parameters, and angles fixed. A plane wave energy cutoff of 450 eV, Γ-centered 2 × 2 × 2 k-point mesh, and spin polarization were used to relax the supercells to the same force convergence as for the conventional bulk. The anatase lattice and dopant states are restricted by the formation of limiting phases (as discussed in the Supporting Information, SI) and are tabulated in Table 1. Table 1 also displays the k-point meshes used in the geometry optimizations (force convergence criterion: <10 meV Å −1 ) and the calculated enthalpies of formation (ΔH f ). These enthalpies of formation are in good agreement with the standard temperature and pressure experimental results, with differences expected due to the difference in temperature (DFT formation energies are calculated at 0 K) and may be due to the choice of the HSE06 functional for these limits.
Defect Formalism. Equation 1 defines the enthalpy of formation for a defect (D) in charge state, q. Where IC CORR BF E D,q is the total energy of the defective supercell in charge state q and E H is the total energy of the host supercell. E i and μ i refer to the elemental reference energy and chemical potentials of species "i" (Ti (s) , O (g) , Ta (s) , Nb (s) , and N (g) ), respectively. n i is either negative or positive depending on whether the species is added to or removed from the system. The Fermi energy (E F ) ranges from the valence band maximum (VBM) to the conduction band minimum (CBM). The band gap (E g ) of anatase has been determined to be 3.41 eV from our primitive cell calculations consistent with other ab initio works. 12,127−132 ϵ VBM H refers to the eigenvalue of the VBM from the host supercell calculation, and ΔE POT is a potential alignment term to account between the difference between electrostatic The calculated enthalpies of formation ΔH f for the relaxed structures are also tabulated with experimental values 126 in parentheses.

Chemistry of Materials
Article potentials between the defective and host supercells. To account for the finite size of the supercell, two corrections are applied; E CORR IC and E CORR BF . The former correction is an imagecharge correction which is necessary due to the long-ranged nature of the Coulomb interaction, 133,134 thus correcting for the interaction of the defect with its periodic images. The scheme used herein utilizes the formalism by Hine and Murphy 135 based on the Lany and Zunger correction. 136 The latter correction, E CORR BF , corresponds to a band filling correction 136,137 associated with the relatively high defect concentrations that give rise to an unphysical band gap renormalization present for the finite-sized supercell calculation.
Thermodynamic Limits. To determine the enthalpies of formation for a given defect over a chemical potential range relating to the equilibrium growth conditions of the host material (TiO 2 ), competing phases must be calculated to create upper and lower bounds on the phase space.
The chemical potential bounds placed on the host can be calculated through the enthalpies of the formation of anatase TiO 2 Typically, the O-poor limit is determined by the formation of a secondary phase, Ti 2 O 3 , however, in practice, this is difficult to reach under general deposition temperatures and oxygen partial pressures in experiment. The O-poor limit is thus rationalized to be in the region of μ O = −2 eV, 138,139 which is what we will use as our Ti-rich/O-poor limit in this study. The Ti-poor/O-rich boundary is limited via the formation of oxygen gas (O 2(g) ); thus, the chemical potential ranges for Ti and O are Ti-rich/O-poor The thermodynamic transition levels ( Figure 2) display the thermal equilibrium transition from charge state q to q′ at a specific Fermi level and can be calculated using the equation Such transitions may be seen using experimental techniques such as deep level transient spectroscopy. 140 Equilibrium Concentrations. The equilibrium defect and carrier concentrations were determined through calculation of the self-consistent Fermi energy, as implemented in the code SC-FERMI. 141,142 The concentration of defect D in charge state q, [D,q] is given by where N D is the density of sites on which the defect in question can form, g D,q is the degeneracy of the defect state, k is Boltzmann's constant, and T is the temperature. Electron (n 0 ) and hole (p 0 ) concentrations are determined using the equations where ρ(E) is the density of states (DOS), E g is the band gap, ■ RESULTS Defect Thermodynamics. To understand the thermodynamic defect chemistry of codoped anatase TiO 2 , density functional theory using the hybrid functional, HSE06 114 was utilized. HSE06 has previously been shown to accurately reproduce the electronic and geometric structures of TiO 2 polymorphs relative to experiment. 10  To assess the ability of fully passivated codoping in TiO 2 , the defect thermodynamics of the TiO 2 :[Nb + N] and TiO 2 : [Ta + N] systems were analyzed and compared. These systems were chosen due to their abundance in the literature and from previous theory calculations identifying them as ideal candidates for water splitting. 44,[84][85][86][87][88][89][90][91]100,156,157 Both Nb and Ta have been shown to easily dope into TiO 2 10,74−77,158 and success has been seen in N-doped TiO 2 . 16,17,27,28 The calculations of these defects were carried out alongside the possible codoped clusters in TiO 2 using the hybrid HSE06 115,116 functional.
Mono Doping of Anatase with N, Nb, and Ta. All mono-doped anatase TiO 2 systems were analyzed to determine the thermodynamic viability of the chosen defects and any points of unintentional compensation. Figure 2

Chemistry of Materials
Article respectively. This is likely due to the similar ionic radii of Nb and Ta (∼64 pm) to Ti (∼61 pm) 46 causing minimal strain to the anatase lattice upon incorporation of these dopants (the six surrounding O atoms move ∼1−1.5% away from the dopant center). Both substitutional Nb and Ta act as resonant donors donating one electron to the conduction band with the 1+/0 transition levels occurring above the CBM. The electron density is, therefore, delocalized over the Ti 3d orbitals that make up the CBM (Figure 3c). These results are indicative of the high conductivities seen in experiment TiO 2 10,158 and is reproduced in the theoretical literature. 119 Binding energies (E BE ) for the clusters were calculated using the equations  are the enthalpies of formation of the cluster and substitutional Nb(Ta) and N, respectively. p, m, and n refer to the charge states of each defect state and E F is the Fermi energy. As E F occurs around the CBM, the last term in this case is equal to 0 as p = 0, m = +1, and n = −1, respectively. For each case, positive binding energies indicate the favorable formation of the defect clusters. The binding energies for [Nb Ti + N O ] and [Ta Ti + N O ] are 0.17 and 0.08 eV, respectively, indicating a small preference for complex formation, however, the formation energy difference between N O and the substitutional n-type defects is likely to significantly negate this effect such that no 1:1 compensation will occur. For [Nb Ti + (NO) O ], a similarly small binding energy of 0.07 eV exists; however for [Ta Ti + (NO) O ], the binding energy is −0.04 eV indicating that the complex formation is unfavorable.

Chemistry of Materials
Defect and Carrier Concentrations. The calculated equilibrium defect and carrier concentrations as a function of temperature (T) are shown in Figure 5 for the cases of Nb and N codoping (left panel) and Ta and N codoping (right panel). As can be seen from Figure 2, Nb Ti and Ta Ti have very similar formation energies, as do the complexes involving the different metal dopants with N impurities. As a consequence, the concentrations for both cases are quite similar, although the Ta Ti have slightly higher concentrations at each T than the Nb Ti due to their lower formation energy (by 0.16 eV). From Figure 5, we see that in each case, the Nb Ti or Ta Ti impurities dominate, as expected from their low formation energies. Under O-poor conditions, the dopants are compensated predominantly by electron carriers, resulting in a strongly ntype system, with E F close to the conduction band minimum (see the insets).  Figure 5). The system is, therefore, insulating under these conditions.
The most notable feature from Figure 5 is the lack of significant concentrations of N impurities across all values of T, which is a consequence of the relatively high formation energies of the related defects. This can, in part, be related back to equation 1 and the chemical potential limits imposed on the defects by TiO 2 . For the nitrogen-related defects, the cost of N−N bond breaking is high, thus the change in μ N within the chemical potential limits of TiO 2 is low compared to μ Ta or μ Nb . Concentrations above 10 17 cm −3 are only observed for T > 1200 K, and we predict that many of those N atoms will be incorporated as complexes, but with significantly smaller concentrations than isolated Nb or Ta dopants, which act as shallow n-type donors. Note that in this analysis, we assume all defects are at the dilute limit, and we, therefore, do not include defect−defect interactions, but considering the low binding energies we calculate for the complexes, we expect that such interactions will have a minor effect on the computed concentrations. The key point is the relatively high formation energies of N-related defects, whether they be isolated or in complexes. Our results clearly demonstrate that Nb or Ta dopants will dominate, which results in an n-type system under O-poor conditions or an insulating system under O-rich conditions, due to the compensation by V Ti . Assuming defect formation occurs under thermodynamic equilibrium, the N dopants will only play a minor role in the defect chemistry.

■ DISCUSSION
The realization of fully passivated codoping in [Nb + N] of [Ta + N] codoped TiO 2 , however, is certainly unobtainable due to the inherent preference for n-type defects and dopants in anatase TiO 2 . As seen in Figures 2 and 5, under both growth regimes, substitutional Nb(Ta) are the dominant defects and are far lower in energy than any of the nitrogen or cluster species. The implication of this work is that although it is possible for the codoped clusters to form within the lattice (as shown by the binding energies), there will always be a higher concentration of n-type dopant and thus there will be no possibility to produce a fully passivated system. The lack of quantitative data on dopant concentrations in the previous experimental literature makes it impossible to ascertain whether full compensation has occurred. 87 86 These results open up a further question: is compensated codoping of TiO 2 possible at all? In terms of the other potential co-dopant pairs, [W + C] and [Mo + C], we consider that in both of these cases, the formation energy of the donor dopant will be much lower than that of any acceptor-based Crelated defect in anatase TiO 2 . Indeed, previous theoretical results have indicated that carbon interstitials are the dominant C-related defect under most growth conditions, and hence C will act as a donor and not as an acceptor in a compensated codoping pair which would raise the VBM of TiO 2 . These insights beg the question of whether passivated codoping as a band gap modification strategy in any material is achievable?

Chemistry of Materials
The answer to this question perhaps lies most simply in an analysis of the absolute band alignments of the band edges of the host system to be doped, relative to the vacuum level, Figure 6. TiO 2 is a natively n-type semiconductor, with a large electron affinity and a large ionization potential (IP). Systems that share this type of band alignment are almost always n-type in nature, such as SnO 2 , ZnO, In 2 O 3 , etc. It has been demonstrated repeatedly by both theory and experiment that p-type doping in these systems is not achievable. 13,14,162,163 It follows that efforts to produce passivated codoping in these and similar systems would be fighting against thermodynamics, as the n-type dopant will always be dominant over the p-type dopant.
Materials with a lower IP display a higher probability of effective incorporation of acceptor type defects, as is seen for natively p-type materials, such as Cu 2 O, CuAlO 2 , and SnO. 171−175 These type of systems often possess large band gaps, however, which means that although VBM positions are perhaps more ideal relative to the redox potential for water splitting, the same problems of weak light absorption exist as in n-type TiO 2 , and effective passivated codoping to lower the CBM while retaining the VBM position would face the inverse of the problems that we run into for codoping of TiO 2 i.e. p-type defects will dominate over n-type defects. It is, therefore, likely that in practice only a truly bipolar material, which can be successfully doped both n-type and p-type, could approach full passivation. An additional benefit of bipolar materials is that they generally possess band gaps that are already within the visible light active range, and so passivated codoping is not likely to be necessary. Therefore, the future for passivated codoping is quite unclear.

■ CONCLUSIONS
Using hybrid density functional theory, an analysis of the thermodynamic properties of two archetypal systems: [Ta + N] and [Nb + N] codoped anatase TiO 2 , has been undertaken demonstrating that passivated codoping of anatase TiO 2 is not possible. Analyzing the defect chemistry of these systems demonstrates that a severe doping asymmetry arises due to the inherent n-type nature of anatase. This asymmetry always favors incorporation of a higher concentration of the electron donating dopant, meaning that full passivation is not achievable for a system grown at thermodynamic equilibrium.

■ ACKNOWLEDGMENTS
This work made use of the ARCHER U.K. National Supercomputing Service (http://www.archer.ac.uk) via our membership of the U.K.'s HEC Materials Chemistry Consortium, which is also funded by the EPSRC (EP/ L000202). B.A.D.W. would like to acknowledge the use of the "bapt" python-package by A. Ganose (https://github.com/utf/ bapt) to plot the band alignment in Figure 6. The UCL Legion and Grace HPC Facilities (Legion@UCL and Grace@UCL) were also used in the completion of this work. D.O.S, C.J.C., and I.P.P. would like to acknowledge support from the EPSRC (EP/N01572X/1). D.O.S. acknowledges support from the European Research Council, ERC, (grant no. 758345). We are grateful to the U.K. Materials and Molecular Modelling Hub for computational resources, which is partially funded by EPSRC (EP/P020194/1). Figure 6. Band alignment of anatase TiO 2 164 compared to a selection of n-type and p-type semiconductors: ZnO, 165 169 SnO. 170 The ionization potentials for each compound are displayed relative to the vacuum level (0 eV).

Chemistry of Materials
Article