Bulk and Surface Polarons in Photoexcited Anatase TiO2 - The

LETTER pubs.acs.org/JPCL

Bulk and Surface Polarons in Photoexcited Anatase TiO2 Cristiana Di Valentin*,† and Annabella Selloni‡ † ‡

Dipartimento di Scienza dei Materiali, Universit
a di Milano-Bicocca,Via R. Cozzi 53, 20125 Milano, Italy Department of Chemistry, Princeton University, Princeton New Jersey 08544, United States

bS Supporting Information ABSTRACT: Using hybrid functional electronic structure calculations, we have investigated the structure and energetics of photogenerated electrons and holes in the bulk and at the (101) surface of anatase TiO2. Excitons formed upon UV irradiation are found to become self-trapped, consistent with the observation of temperature-dependent Urbach tails in the absorption spectrum and a large Stokes shift in the photoluminescence band of anatase. Electron and hole polarons are localized at Ti3+ and O
lattice sites, respectively. At the surface, the trapping sites generally correspond to undercoordinated Ti3+5c and O
2c surface atoms or to isolated OH species in the case of a hydroxylated surface. The polaron trapping energy is considerably larger at the surface than in the bulk, indicating that it is energetically favorable for the polarons to travel from the bulk to the surface. Computed oneelectron energy levels in the gap and hyperfine coupling constants compare favorably with oxidation potential and EPR measurements. SECTION: Energy Conversion and Storage

espite many years of research aimed at finding more efficient oxide semiconductors, titanium dioxide (TiO2) is still one of the best materials for photocatalysis and solar energy conversion.1
5 Rutile is the thermodynamically most stable TiO2 phase, whereas anatase is usually considered to be more important for photocatalytic and photovoltaic applications. Recently, transient photoconductance measurements have shown that the lifetimes of photoexcited carriers are longer in anatase than in rutile, which may explain the higher photocatalytic efficiency of the anatase polymorph.6 Charge carriers produced by UV photoexcitation of TiO2 form localized polaronic states at low temperature. These polarons can undergo different trapping or recombination processes or can travel through the bulk of the material and possibly reach the surface, where they can undergo charge transfer reactions to adsorbates. Photogenerated charges in TiO2 have been probed by electron paramagnetic resonance (EPR) spectroscopy,7
11 photoluminescence (PL),12
15 and O2 photodesorption.16 For instance, PL measurements show that under interband excitation (hν > 3.2 eV) anatase exhibits a broad luminescence band centered at ∼2.3 eV, which is attributed to radiative recombination of a self-trapped exciton. Many questions, however, are still open, especially concerning the fate of the carriers that have reached the TiO2 surface: do these charges directly react with adsorbates, or are they first trapped by surface species and then transferred to the reactants? Is charge trapping beneficial or does it facilitate recombination? For photogenerated holes, in particular, competing direct and indirect transfer mechanisms have been proposed, the former being more favorable for strongly bound adsorbates (excellent hole scavengers) and the latter in the case of weakly bound ones.17,18 Hydroxyl groups are often invoked19 as surface traps for electrons and holes (indicated as

D

r 2011 American Chemical Society

Ti3+
OH and Ti4+
•OH, respectively), but the role of surface hydroxyl radicals in photooxidation processes is still controversial. For instance, recent studies have proposed that the water photooxidation reaction is initiated by a nucleophilic attack of a water molecule to a surface-trapped hole rather than by the charge-transfer oxidation of a surface Ti
OH group.20 In this work, we present a novel theoretical study of photoexcited anatase TiO2 based on first-principles electronic structure calculations. We focus on the initial stages of a typical photoinduced process (Figure 1), notably the creation of a bulk exciton, followed by the separation of the electron and the hole and the formation of two self-trapped polarons at lattice sites (e
tr and h+tr), and the surface trapped polarons, which result from the diffusion of e
tr and h+tr from the bulk toward the surface. It was shown recently that to describe the polaronic distortion in TiO2 within density functional theory (DFT) exact exchange must be introduced to some extent in the exchange functional21 or an on-site Hubbard U term must be added.22,23 This is because the self-interaction error of standard DFT always favors electron delocalization. By means of a DFT+U approach, for example, Dupuis and coworkers evaluated the activation barrier for the hopping transport process of localized electron and hole polarons in bulk anatase, for which they obtained values of 0.0924 and 0.1625 eV, respectively. Here we characterize the structure and energetics of polarons in bulk anatase and on the clean and hydroxylated anatase (101) surfaces by performing spin-polarized B3LYP26 hybrid functional calculations on supercell models with no symmetry constraints. We describe the Received: July 19, 2011 Accepted: August 16, 2011 Published: August 16, 2011 2223

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Table 1. Singlet
Triplet Excitation Energy, HOMO-LUMO Gap, and Trapping Energy for Electrons, Holes, and Excitons in the Bulk and at Bare and Hydroxylated Anatase (101) Surfacesa S0 f T1

HOMO
LUMO

ΔEtrap (e
)

ΔEtrap (h+)

ΔEtrap (e

h+)

bulk

3.50

3.9

0.23

0.74

0.58

bare (101) surface

3.25

4.3

0.62

1.45

OH (101) surface

3.15

4.4

ANATASE

0.95

split pair a

Figure 1. Schematic representation of the initial stages of a photoinduced process in anatase TiO2: creation of a bulk exciton upon light irradiation, formation of self-trapped polarons at bulk lattice sites, and polarons trapped at surface sites. The surface may be hydroxylated.

ground and (photo)excited states as the lowest energy close-shell singlet (S0) and open-shell triplet (T1) spin configurations, respectively. The triplet exciton state is the lowest excited state and has a longer lifetime than the higher energy singlet exciton (S1) in many insulators and large gap semiconductors, including TiO2 anatase.13,27 Moreover, the singlet close-shell and the triplet configurations are the lowest energy states for the corresponding spin multiplicities and therefore can be correctly calculated by DFT. Through structural relaxation, the electron and hole in the triplet configuration28,29 become localized, allowing the evaluation of the polaronic distortion and self-trapping energy. The triplet excited state calculations started from the singlet ground state geometry, and no recourse to techniques guiding the initial guess of the electron and hole localization sites was made. Electrons, Holes, and e
h Pairs in Bulk Anatase TiO2. For simplicity, we first consider the addition of a single excess electron (e
) and a single hole (h+) separately in a supercell of bulk anatase. A compensating uniform background of charge is introduced to re-establish the neutrality of the supercell. As initial structure, we take the geometry of the neutral TiO2 ground state and then allow it to fully relax, keeping the cell size fixed. For the excess electron, the state in the conduction band (CB) is initially delocalized over several lattice Ti sites; after structural relaxation, the e
becomes self-trapped at a Ti lattice site (Ti4+), which then becomes formally Ti3+, with an energy gain (trapping energy) associated with the polaronic distortion ΔEtrap = 0.23 eV (Table 1 and Figure S1a in the Supporting Information). We denote such a localized species e
tr; the fraction of the localized electron density at the Ti3+ site is ∼80%. The equatorial Ti3+
O bonds are elongated from 1.942 Å (bulk value) to 2.005
2.009 Å, whereas the variation of the axial Ti3+
O bonds is smaller from 2.014 to 2.040 Å. (See Table S1 in the Supporting Information.) This nicely correlates with the fact that the extra electron is localized in a dxy state, as the Ti-derived states at the bottom of the TiO2 CB indeed have dxy character.30 In the case of a hole in the valence band (VB), the self-trapping energy is 0.74 eV (Table 1). A much smaller value for the hole self-trapping energy, 0.2 eV, has been recently reported by Zawadzki et al.,31 who used, however, a simplified Δ-SCF procedure to reduce the DFT self-interaction error. The self-trapped hole is highly localized (∼85%) on a single lattice oxygen (O2
) that then becomes formally O
, with a polaronic distortion involving all three O
Ti

All energies are in electronvolts.

bonds: the axial bond elongates from 2.014 to 2.260 Å, and the equatorial bonds elongate from 1.942 to 2.050 Å. (See Table S1 in the Supporting Information.) To represent photoexcited bulk anatase TiO2, we compute the lowest triplet spin solution using the atomic geometry of the singlet ground state. We find that such vertical S0 fT1 transition costs 4.08 eV, and the two unpaired electrons are in delocalized states at the top of the VB and at the bottom of the CB, respectively. As a comparison, our B3LYP calculations give a HOMO
LUMO gap of 3.9 eV for the singlet ground state, in good agreement with the results of recent GW32
34 and hybrid B3LYP functional studies,35 which obtained indirect band gaps values in the range of 3.6 to 3.9 and 3.98 eV, respectively. When the geometry of the excited triplet state is allowed to relax fully to its minimum energy, the gain due to the self-trapping of the chargecarriers is 0.58 eV. This is less than the sum of the trapping energies of isolated (e
tr) and (h+tr) species, indicating that some interaction occurs between the two polarons. As a result, the total energy difference between singlet and triplet spin configurations in their respective minima is 3.5 eV. The self-trapped excited electron is largely (78%) localized on a lattice Ti3+ ion, whereas the hole is 85% localized on the lattice O
center, in axial position with respect to the Ti3+ (Figure S1c in the Supporting Information). The two charges are close to one the other, suggesting that they can recombine quite easily. The Ti3+
O
bond distance in the exciton is elongated to 2.074 Å with respect to the bulk Ti
O value of 2.014 Å. The occupied one-electron state associated with the hole is inside the VB, as indicated by the projected DOS on the O
species (Figure S1c in the Supporting Information), whereas the unoccupied component (hole) is 1.83 eV above the VB top. The one-electron state of the excited electron at the Ti3+ site lies 0.73 eV below the bottom of the CB. Experimentally, the existence of self-trapped excitons in bulk anatase is evidenced by the large Stokes shift in the PL band13 and by the exponential temperature dependence of the Urbach tail in the absorption spectra.36 The one-photon excitation of the selftrapped exciton PL (vertical S0 f S1 transition) is peaked at ∼3.3 eV,13 and the optical gap has been estimated to be ∼3.4 eV.36 Electrons, Holes, and e
h Pairs at the Bare Anatase (101) Surface. The same series of calculations described above for the bulk were performed for the anatase (101) surface (Figure 2). These show that an extra CB electron becomes trapped at a fivefold coordinated Ti5c3+ site with an energy gain of 0.62 eV. (See Table 1.) The spin is almost fully localized on this ion (90%, see Figure 2a), leading to elongated Ti3+-O bonds on the surface (1.93 to 2.07 Å against 1.84 to 1.99 Å for the perfect surface; see Table S1 in the Supporting Information). Previous DFT+U studies of an excess electron on rutile (110) found that surface 2224

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Figure 2. Spin density contours and total and projected density of states for: (a) one extra electron, (b) one extra hole, and (c) an electron
hole pair on the anatase TiO2(101) surface. Projection is onto the trapping atomic species (Ti5/6c3+ and/or O2c
). Black and gray spheres represent Ti and O atoms, respectively.

Ti5c3+ and subsurface Ti6c3+ sites are very close in energy.22 For anatase (101), we also found a solution with the extra electron localized on a subsurface Ti6c3+, but this is less stable than the one with the electron at Ti5c3+ by 0.24 eV. For an extra hole in the VB, 94% of the density becomes trapped at a bridging oxygen O2c (Figure 2b), leading to strongly elongated Ti
O2c

Ti bonds (2.05 against 1.84 Å for the perfect surface; see Table S1 in the Supporting Information). The energy gain associated with the hole surface self-trapping is very large: 1.45 eV. Therefore, our calculations predict that the undercoordinated Ti5c and O2c surface sites are better traps for the photoexcited charge carriers than the bulk lattice sites, indicating that it is energetically favorable for the bulk self-trapped polarons to travel to the surface. For our model of the anatase (101) surface, the total energy difference between the fully relaxed singlet and triplet states is

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Figure 3. Spin density contours and total and projected density of states of one extra hole on the hydroxylated anatase TiO2(101) surface: (a) intrapair and (b,c) splitpair. Projection is onto the trapping atomic species (O2c
or •OHt). Black and gray spheres represent Ti and O atoms, respectively. Small spheres represent H atoms.

3.25 eV, to be compared with the surface HOMO
LUMO gap of 4.3 eV. (See Table 1.) We were unable to find a converged solution for the vertical triplet excited state using the groundstate geometry, which prevents us from determining the trapping energy for the surface exciton. However, the results for the isolated (e
tr) and (h+tr) indicate that this should be larger than for the bulk. After relaxation, the hole is localized on a bridging oxygen (94%), resulting in two elongated Ti
O2c
Ti bond lengths: from 1.84 Å in the ground state to 2.04
2.11 Å (Figure 2c and Table S1 in the Supporting Information). Differently from what found in the bulk, the electron localizes on a subsurface Ti3+ (81%), not directly connected to the surface bridging oxygen (Figure 2c). The single-particle eigenvalue associated with the Ti3+ polaron and the unoccupied spin down component of the O
polaron are both in the band gap, at ∼1 eV 2225

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Figure 4. One-electron Kohn
Sham eigenvalues (in eV) of electron and hole polaron states in the bulk and on the anatase TiO2 (101) surface. Top panel: triplet spin configuration; middle panel: one extra hole; lower panel: one extra electron.

below the CB bottom and 2.3 eV above the VB top, respectively (Figure 2c). Electrons, Holes, and e
h Pairs at the Hydroxylated Anatase (101) Surface. Our finding of hole trapping at a surface oxygen site is consistent with a previous suggestion by Nakamura and Nakato in the context of water photooxidation.20,37 Several studies, however, have considered terminal hydroxyl groups (OHt) as “the” surface hole traps19 Ti
OHt þ hþ f Ti
• OHt Interestingly, Ti ions bound to hydroxyls have also been proposed to be potential electron traps19 Ti4þ
OHt þ e
f Ti3þ
OHt To investigate the role played by surface hydroxyls, we have considered a dissociated water molecule adsorbed on the anatase (101) surface model, corresponding to one water molecule every six surface Ti5c ions (0.17 ML coverage). Because water adsorbs preferentially in molecular form on anatase (101),38 the underlying assumption is that dissociation took place somewhere else, for example, at a step, and that the fragments diffuse on the surface. The heterolytic water dissociation produces two hydroxyl groups, a terminal OHt group and a bridging hydroxyl (OHbr) TiO2 þ H2 O f Ti5c
OHt þ Ti6c
OHbr
Ti5c The hydroxyls can be either next-neighbors sharing the same Ti5c (intrapair configuration) or further apart (split-pair configuration) on the surface. (See Figure 3.) In the former case, there is hydrogen bonding interaction between the proton of the OHbr and the oxygen of the OHt. In the split-pair configuration, no interaction is present between the two hydroxyls. The total energies of these two configurations differ by 0.05 eV in favor of the intrapair.

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We investigated the possibility of trapping an isolated hole at an OHt group. For the intrapair case, the hole actually localizes on a bare surface bridging oxygen away from the hydroxyls (Figure 3a). By contrast, in the case of the split-pair configuration, localization of the hole on the oxygen of the Ti
OHt group is preferred to localization on a surface O2c by 0.20 eV (Figure 3b vs Figure 3c). The hole trapping energy is 0.95 eV. The lowest unoccupied spin-down state (hole) is fully localized on the oxygen of OHt and lies high in the gap, 2.26 eV above the VB edge (Figure 4), whereas the spin-up component is a state deep in the oxygen 2p valence band, as shown by the DOS projected onto the O of OHt in Figure 3b. This is the first computational evidence of the capability by an isolated OHt to trap a photoinduced hole. In the case of an isolated electron, we find that the titanium ion in the Ti
OHt group, which is now six-coordinated, is not a preferred trapping site; instead, the electron localizes on a subsurface Ti ion. Calculations of the triplet excited state for both the intrapair and split-pair configurations give similar singlet
triplet energy differences: 3.18 vs 3.14 eV. These values are about 0.1 eV lower than the one obtained for the clean surface. For the intrapair case, the hole is again localized on a bare surface bridging oxygen while the electron is on the neighboring Ti6c. By contrast, in the case of the split-pair configuration, the electron and the hole are localized on the titanium and the oxygen of the Ti
OHt group, thus forming a strongly bound exciton trapped at Ti
OHt Ti
OHt þ hν f Ti3þ
• OHt This finding suggests that isolated hydroxyl groups, if present, can trap photoexcited electron
hole pairs, whereas the presence of a nearby interacting OHbr group (intrapair configuration) hinders charge trapping, possibly because of the positive charge of the OHbr proton (see below). The one-electron energy level associated with the Ti3+ ion is 1.24 eV below the CB edge and thus 0.2 eV lower in energy than for the clean surface, whereas the unoccupied (hole) state associated with the •OH radical lies very high in the gap (2.67 eV above the VB top, Figure 4). In summary, our results indicate that photoexcited electrons and holes in anatase TiO2 become self-trapped at Ti3+ and O
lattice sites, respectively. At the surface, the trapping sites generally correspond to undercoordinated Ti3+5c and O
2c surface atoms or to isolated OH species in the case of a hydroxylated surface. The lattice relaxation energy associated with the trapping is considerably larger at the surface than in the bulk because of the possibility for the surface structure to relax with fewer constraints. This suggests that it is energetically favorable for the photogenerated charges to travel from the bulk to the surface. Given the relatively low energy barrier estimated for polaron hopping through the material,24 it is expected that at RT the photogenerated electrons and holes will primarily populate surface sites. To support these findings, we computed the EPR hyperfine coupling constants of an unpaired electron associated with a photogenerated hole on the 17O nucleus. These quantities have been experimentally determined for an aqueous suspension of anatase TiO2 powder by isotopic exchange with H217O.10 For the trapped hole on a surface bridging oxygen (Ti
O2c

Ti), the computed isotropic or Fermi contact term, aiso, is
37 G, to be compared with the experimental value of (22 G; this difference may be partially attributed to the fact that our calculations do not include a flexible basis set for the s core levels, as 2226

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The Journal of Physical Chemistry Letters required for an accurate determination of aiso.39 The calculated dipolar tensor, B = [45, 45,
90] G, is in very good agreement with the experiment, B = [41, 41,
82] G. Thus, the B3LYP functional yields a degree of spin localization for the photogenerated hole that is consistent with direct experimental measurements. Notice that this is not necessarily always the case: in other oxides, for example SiO2, higher portions of exact exchange are needed to provide the correct hole localization on O sites.40 When the hole is localized on a surface OHt group, the computed hyperfine coupling constants with 17O are similar (aiso =
38 G, B = [48, 48,
96] G); however, we observe also a large coupling with the proton (aiso =
23 G, B = [30,
23,
8] G), which has not been reported in the literature. This may be due to a very short lifetime of the Ti
•OHt species in aqueous solution or to the absence of isolated Ti
OHt species. Finally, we compare the one-electron energy levels of photoexcited electrons and holes, Figure 4, with the corresponding levels for n- and p-typed doped anatase. Although Kohn
Sham eigenvalues are just a crude approximation of the position of the defect states in the gap and of the ionization potential, electron affinity, or redox potential of the system, such an analysis is justified because we are more interested in a comparison than in the absolute values of the level positions. We previously found that n-type dopants such as F or Nb introduce states at 0.82
0.78 eV below the CB,41 whereas the results of this work show that the photogenerated electron in the bulk is at 0.73 eV below CB. Therefore, Ti3+ species generated by n-type dopants are very similar to Ti3+ species produced by photoexcitation, in full agreement with EPR measurements.7,42 On the contrary, computed trapped hole states in nitrogen-doped TiO2, N-TiO2, are at 2.67 eV above the VB,43 that is, much higher in the gap than self-trapped holes in bulk anatase, which are 1.90 eV above VB. (See Figure 4.) This appears to be in line with the observed lower photooxidation properties of N-doped TiO2.44 We also notice that at the surface the computed energy levels of the self-trapped carriers are deeper in the gap with respect to the corresponding bulk levels, confirming that there is a driving force for electrons and holes to travel from the bulk toward the surface. However, an increased stability of the trap states also means a lower redox potential of the trapped carriers. Experimentally, oxidation potentials for holes during photocatalytic one-electron oxidation reactions are found to be reduced by about 1.3 to 1.4 V upon trapping,45 indicating that the one electron energy levels in Figure 4 overestimate the position of the hole states in the gap. Nonetheless, if a better acceptor (a scavenger), such as O2 for electrons or CH3OH for holes, is adsorbed on the surface, then the carriers should be preferentially transferred to the adsorbate rather than remain trapped at surface sites. This mechanism, which is the basis of the TiO2 photoreactivity, needs to be further investigated, but the detailed understanding of the formation of bulk and surface polarons discussed here is the necessary prerequisite for more specific analyses of photoreactivity.

’ COMPUTATIONAL DETAILS We use the CRYSTAL0646 package where the Kohn
Sham orbitals are expanded in Gaussian-type orbitals. (The all-electron 47 basis sets are O 8
411(d1), Ti 86
411 (d41), √ and H√311(p1).) The TiO2 anatase bulk was modeled by a 2 2  2 2  1 bulk supercell with 96 atoms. To describe the surface, we used a slab of three triatomic layers with 108 atoms and 1  3 periodicity along the [101] and [010] directions; no periodic boundary condition

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was imposed in the direction perpendicular to the surface. The optimized lattice parameters were taken from previous studies.48 These supercell models should be sufficiently large because the electron and hole polarons turn out to be well-localized on a single atomic species. The k-space sampling for the bulk (surface) geometry optimizations included eight (four) k points. Densities of states (DOSs) were computed using a 36 k-point mesh. To analyze the electronic structure, we also computed projected DOS (PDOS) onto the trapping atomic species (Ti3+ or O
or OH). The zero energy for all DOS is set at the vacuum level, corresponding to an electron at an infinite distance from the surface. This level is straightforward to define for neutral slabs, and the computed CB edge position, at ∼4 eV below the vacuum level (
0.5 V versus NHE), is in good agreement with that obtained from flat-band potential measurements.1 For charged slabs and for the bulk, the Ti 1s core states were aligned to the Ti 1s core states of the reference neutral slab.

’ ASSOCIATED CONTENT

bS

Supporting Information. Structural parameters for selftrapped electron and hole polarons. Spin density contours and total and projected density of states for electron and hole polarons in bulk anatase. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT We are pleased to thank G. Pacchioni for useful discussions. C.D.V. acknowledges the CARIPLO Foundation for financial support through an Advanced Materials Grant 2009. Regione Lombardia and CILEA Consortium are gratefully acknowledged for the computational resources. A.S. acknowledges the U.S. Department of Energy (grant DE-FG02-05ER15702) for financial support. ’ REFERENCES (1) Gr€atzel, M. Photoelectrochemical Cells. Nature 2001, 414, 338–344. (2) Henderson, M. A. A Surface Science Perspective on TiO2 Photocatalysis. Surf. Sci. Rep. 2011, 66, 185–297. (3) Thompson, T. L.; Yater, J. T., Jr. Surface Science Studies of the Photoactivation of TiO2-New Photochemical Processes. Chem. Rev. 2006, 106, 4428–4453. (4) Fujishima, A.; Zhang, X.; Tryk, D. A. TiO2 Photocatalysis and Related Surface Phenomena. Surf. Sci. Rep. 2008, 63, 515–582. (5) Chen, X.; Mao, S. S. Titanium Dioxide Nanomaterials: Synthesis, Properties,. Modifications and Applications. Chem. Rev. 2007, 107, 2891–2959. (6) Xu, M.; Gao, Y.; Moreno, E. M.; Kunst, M.; Muhler, M.; Wang, Y.; Idriss, H.; W€oll, C. Photocatalytic Activity of Bulk TiO2 Anatase and Rutile Single Crystals Using Infrared Absorption Spectroscopy. Phys. Rev. Lett. 2011, 106, 138302–4. (7) Nakaoka, Y.; Nosaka, Y. ESR Investigation into the Effects of Heat Treatment and Crystal Structure on Radicals Produced over Irradiated TiO2 Powder. J. Photochem. Photobiol., A 1997, 110, 299–307. (8) Dimitrijevic, N. M.; Saponjic, Z. V.; Rabatic, B. M.; Poluektov, O. G.; Rajh, T. Effect of Size and Shape of Nanocrystalline TiO2 on Photogenerated Charges. An EPR Study. J. Phys. Chem. C 2007, 111, 14597–14601. 2227

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