Screening Doping Strategies To Mitigate Electron Trapping at Anatase TiO2 Surfaces.

Nanocrystalline anatase titanium dioxide is an efficient electron transport material for solar cells and photocatalysts. However, low-coordinated Ti cations at surfaces introduce low-lying Ti 3d states that can trap electrons, reducing charge mobility. Here, a number of dopants (V, Sb, Sn, Zr, and Hf) are examined to replace these low-coordinated Ti cations and reduce electron trapping in anatase crystals. V, Sb, and Sn dopants act as electron traps, while Zr and Hf dopants are found to prevent electron trapping. We also show that alkali metal dopants can be used to fill surface traps by donating electrons into the 3d states of low-coordinated Ti ions. These results provide practical guidance on the optimization of charge mobility in nanocrystalline TiO2 by doping.

Introduction

Titanium dioxide (TiO2) is an important and widely used semiconductor and photocatalyst,[1−7] which is extremely useful for a range of applications including dye-sensitized solar cells,[8,9] water splitting,[10−12] pollution abatement,[13,14] and CO2 reduction.[15−17] The inexpensiveness, abundance, and superior electron transport properties of TiO2 make it appealing for these applications.[18−20] There are a number of TiO2 polymorphs that have different electronic transport properties, while the rutile phase is the most thermodynamically stable phase, the anatase phase (a-TiO2) is the more catalytically active material and most studied.[21−24] In solar energy applications, a-TiO2 is used as a transport material where the electron mobility is critical to the performance of the device, whereas for water splitting, a-TiO2 is irradiated with light, generating electron–hole separated charge carriers.[2,25] The transport of electrons (e–) and holes (h+) for both applications is vital to the efficiency of a-TiO2 where facet-dependent migration from bulk a-TiO2 to the surfaces can occur.[26,27] Ideally for water splitting, separation of electrons and holes is required; however, charge recombination and annihilation can occur, which is detrimental to conductivity.[26,28−31] The charge carriers can also localize on native cation/anion lattice sites (self-trapping) at surfaces, defects, dislocations, interfaces, or indeed within the bulk material, affecting their mobility throughout TiO2, which greatly affects its performance as an electron transport material for energy applications.

The self-trapping of electron and hole charge carriers in anatase TiO2 affects electron transport, charge recombination rates, and overall device efficiency. Shallow traps lie close to the conduction or valence band edges and mediate transport in TiO2,[32] while deeper traps in the band gap promote carrier recombination.[33] Electrochemical and photoluminescence studies provide valuable insights into the nature of traps in metal oxide samples.[34−37] There is no direct evidence to suggest that electron trapping occurs in bulk a-TiO2, but electron trapping does occur at surfaces of anatase TiO2.[37−39] Surface-trapped electrons have first-order steady state kinetics with slow hopping from trap to trap.[36] The surface states associated with trapped electrons have a distinct Fermi level from that of the bulk material, which leads to a nonuniform Boltzmann distribution resulting in barriers to detrapping.[39] The nature of the electron traps on different exposed surfaces of nanocrystalline anatase TiO2 remains unclear where the trapping of the photogenerated electrons and their hole counterparts is facet-dependent with their spatial separation, distribution, and density of traps on specific facets playing a key role.[26,29,34−36] Indeed, the trapping of electrons at different surface facets is found to interact differently with adsorbates, such as O2 and H2O, facilitating different reaction mechanisms to suggest that the affinity to trap electrons influences the facet reactivity and charge transfer.[38−40]

The focus of this paper is to build on previous work examining electron trapping at the anatase surfaces and identify suitable dopants that can either remove or nullify electron traps on nanocrystalline a-TiO2. Experimental studies investigating electron trapping have alluded surface traps being present on nanocrystalline anatase TiO2 from two sources: oxygen vacancy formation and/or low-coordinated Ti cations on the surface.[37,41,42] Our recent work using hybrid density functional theory (DFT) calculations has shown that electron trapping does not occur in the bulk of anatase TiO2,[43] and further calculations showed that there were no electron-trapping surface states on the defect-free, pristine low-index surfaces;[44] however, using the a-TiO2(103) stepped surface as an example, we showed that low-coordinated Ti cations contributed to electron trapping. Our work is in agreement with DFT calculations using a Hubbard +U (DFT+U) correction, which have modeled the behavior of excess electrons in TiO2 showing that a carrier-free description of electrons occupying conduction band states (i.e., no electron trapping) is accurate[45] but in contrast to other previous DFT+U work.[46−50] Our calculations challenge the convention that low-index pristine surfaces contain electron trap states on facets of a-TiO2 and suggest that undercoordinated Ti cations from surface defects are a stronger contributing factor than point defects for electron trapping. These low-coordinated Ti cations introduce defect states lying at the bottom of the conduction band that can trap excess electrons but do not generate any additional electrons in the system,[44,51−54] whereas point defects such as oxygen vacancies introduce filled defective states that cannot trap additional electrons.[50,55−58]

In the present study, hybrid DFT calculations are used to investigate substitutional doping of the low-coordinated Ti cations on a-TiO2 and show that they can remove the surface states at the bottom of the conduction band associated with electron trapping. In our previous work, electron trapping occurs on the (103) surface, and this is used as a model to demonstrate that doping can remove electron traps. Typically, doping in a-TiO2 is carried out to improve the TiO2 as a photocatalyst with various chemical modifications to change the electronic structure for TiO2 to adsorb in the visible light spectrum. Some examples of improving the photoconductivity of TiO2 in such a way include nitrogen,[59−63] a transition metal,[64,65] sulfur,[66−68] carbon,[69,70] boron,[71] lanthanide,[72] zirconium,[73−75] and flourine.[76] Although many doping studies in the literature are focused on altering the band gap of TiO2 for photocatalysis, there have been few that specifically examine the influence dopants have on electron traps in anatase TiO2 nanocrystals. Our focus therefore is to go beyond the conventional thinking of doping TiO2 by this approach and examine candidates on the (103) surface that will remove electron traps. We find that dopants such as V, Sb, and Sn trap additional electrons similar to Ti, while Zr and Hf species do not trap excess electrons, and we show why these species are suitable candidates to remove electron traps. We also demonstrate that electron-donating alkali metals (Li, Na, K, Rb, and Cs) can fill the surface traps and are another approach to remove electron traps from a-TiO2.

Computational Methodology

Hybrid density functional theory (DFT) calculations using the generalized gradient approximation (GGA) were carried out using the CP2K simulation package.[77] Exact Hartree–Fock (HF) exchange is mixed into the exchange-correlation functional (hybrid-DFT) to overcome the issue of the self-interaction error (SIE) that is well known in DFT. We use a truncated PBE0 hybrid-DFT exchange-correlation functional that includes long-range corrections to the interaction potential (PBE0-TR-LRC) with a global dependence. This defines a range of separations in the electron integrals to implement the HF exact exchange, and standard PBE is used outside of this defined range. The truncation radius (Rc) must be smaller than half the distance of the lattice vectors to ensure that there is no interaction between neighboring cells, and we set our radius to 6.00 Å as shown previously to give converged structural and electrical properties.[43] The percentage of HF exact exchange to include in these calculations was parameterized by satisfying the Koopmans’ condition to within 0.05 eV for electron and hole polarons in bulk TiO2 anatase (yielding α = 10.5%), which gives a band gap within 3% of the experimental value.[43] Triple ζ basis sets were used for both titanium and oxygen for accurate calculations[78,79] and the Goedecker–Teter–Hutter (GTH) pseudopotentials for both species available within CP2K.[80−82] A multigrid approach for mapping products of Gaussians onto a real-space integration grid is used in CP2K where the wide and smooth Gaussian functions are mapped onto a coarser grid, and the electron density is mapped onto the finest grid. The plane wave energy cutoff, a reference grid that controls the Gaussian mapping onto the multigrid, is set to 60 Ry. Five multigrids are used, and the plane wave cutoff is sufficiently converged at 600 Ry for the finest level of the multigrid. The electronic properties of the electron trapped in each surface will be detailed by spin density, partial (decomposed l quantum number) electronic density of states (PEDOS). The number of electrons for each species is determined using the Bader’s atoms in molecules (AIM) approach,[83] implemented by Henkelman et al.[84−87] All structural images and spin density plots are visualized using the VESTA software.[88,89] Further details on our computational method and setup are detailed in the Supporting Information.

Results

The optimized (103) surface is shown in Figure . The (103) surface is terminated with four coordinated Ti cations (Tisurf) and two coordinated O anions, while the subsurface layers have six coordinated Ti cations (Tisub) and three coordinated O anions similar to bulk anatase TiO2. Surface Tisurf cations and O anions have bond lengths ranging from 1.69 to 1.98 Å. The Ti cations in the bulk region of the slab (Tibulk) have similar bond lengths (<1% deviation) to the optimized anatase TiO2 bulk and can be used as a reliable reference for calculating electron-trapping energies. The partial decomposed (species and angular momentum) electronic density of states (PEDOS) plots for Ti cations in different environments in the surface slab are also shown in Figure . The band gap for both the surface and bulk regions is 3.12 eV and in good agreement (<3%) with the experimental band gap (3.2 eV). The most noticeable difference between the Tisurf and Tibulk cations is the large Ti 3d peak at the bottom of the conduction band (CBM) associated with the Tisurf cations that is absent for Tibulk cations. The presence of states associated with the Tisurf cations at the CBM will have implications for electron trapping in the (103) surface of anatase TiO2. The calculated Bader charge for the Tisurf ions is 9.8 electrons (e–) or a charge of +2.2 since our Ti potential contains 12 valence electrons. For Tisub and Tibulk, the Bader charge is 9.7 e– (+2.3), and the O surface anions have a charge of 7.2 e– or −1.2 since there are six valence electrons in the potential. Both Ti cations and O anions have a spin of 0.0 μβ.

Figure 1

(a) (103) Surface slab and calculated PEDOS for different Ti cations and (b) local geometry of an electron trapped at a surface Ti atom and the associated PEDOS. The blue and red spheres are the lattice sites for the Ti cations and O anions, while the green and red lines are the Ti 3d and O 2p projected DOS. The black dashed line shows the position of the Fermi Level.

As shown from our previous work,[44] the only site capable of trapping an excess electron is the Tisurf cation, as shown in Figure b, while all other sites in the subsurface and bulk regions prefer delocalized electronic solutions similar to bulk a-TiO2.[43] The electron trapped at this site reduces Ti4+ to Ti3+ as we see a decrease in the Tisurf charge from +2.2 to +2.0 with some further charge spread across neighboring ions. The presence of the trapped electron increases the spin on the Ti cation from 0.0 to 0.74 μβ. The geometric structure around the reduced Ti cation becomes distorted with surface bond lengths increasing by 0.1–0.15 Å. The calculated trapping energy is +0.07 eV with respect to the delocalized solution in the bulk of the slab implying that electrons would prefer to be delocalized in the bulk crystal than trapped at low-coordinated surface Ti atoms. The trapping of electrons at these sites can be considered to be kinetically trapped, as observed by experiment,[36] but thermodynamically unfavorable. The PEDOS shows that the electron trap is a shallow donor where the occupied Ti 3d defect peak is 0.45 eV below the CBM. This peak was previously seen at the conduction band edge (Figure a), and the trapped electron fills this state.

The dopants we initially consider to passivate the Tisurf electron trap are V, Sb, Sn, Zr, and Hf (that all have a stable +4 oxidation state). Zr and Hf are of particular interest as these species are known to be polaronic materials in their parent MO2 oxides.[90−93] These materials have contrasting polaronic behavior, and only hole trapping is seen in ZrO2, while both electron and hole trapping is observed in HfO2. This will allow a comparison between each dopant and other dopant species for examining their behavior and effect on electron trapping in TiO2. The dopants can replace the low-coordinated Ti cations on the surface where the rationale is to remove the states at the CBM associated with electron trapping (Figure ). The distribution of dopants was examined in different layers of the slab from the surface (1) to the bulk region (4) as shown in Figure where the calculated relative energies for each layer are given in Table . We find that there is a difference of approximately 0.2 eV between the different surface and subsurface sites, suggesting that the dopants could potentially replace either the four or six coordinated Ti cations. In the bulk region of the slab, Sn, Zr, and Hf have more favored energies compared to the surface region; however, although the thermodynamics may suggest that they are more stable, there would be a large experimental kinetic barrier to drive these dopants into a bulk region to replace Ti cations in TiO2 nanocrystals, and thus the dopants would be expected to be in the surface region. For the interest of this study, we will focus on replacing the Tisurf cations.

Figure 2

Different lattice positions in the surface slab examined for the dopant distribution.

Table 1

The Calculated Energies Relative to the Surface Site for the Distribution of Dopants in the (103) Slab as Shown in Figure

bond	1 (eV)	2 (eV)	3 (eV)	4 (eV)
V	0.00	+0.11	+0.32	+0.32
Sb	0.00	+0.21	+0.55	+0.55
Sn	0.00	–0.09	–0.54	–0.46
Zr	0.00	–0.11	–0.49	–0.29
Hf	0.00	–0.19	–0.44	–0.34

After relaxation, all the dopants maintain the same geometry and coordination of the Ti cation site with changes to the bond lengths. The calculated metal–oxygen bond lengths in the surface layer (M-Osurf) and the subsurface layer (M-Osub) are given in Table . All dopants have longer bond lengths than those of Ti–O with the largest change seen for the bonds oriented toward the subsurface layer where Sb and Zr show the greatest increase. The dopants distort the local geometry on the surface with changes in Ti–O bond lengths being observed on the next nearest-neighbor positions.

Table 2

The Calculated Bond Lengths for the Ti–O Surface Bonds and the Dopant–O Bonds

bond	M-Osurf (Å)	M-Osub (Å)
Ti–O	1.98 (×2)	1.83, 1.69
V–O	2.01 (×2)	1.82, 1.61
Sb–O	2.15 (×2)	1.99, 1.89
Sn–O	2.05 (×2)	1.98, 1.89
Zr–O	2.10 (×2)	1.96, 1.84
Hf–O	2.06 (×2)	1.92, 1.83

The calculated partial density of states (PDOS) for each of the doped surfaces is shown in Figure . There are significant differences in the electronic structure for the V and Sb dopants when replacing a Tisurf ion. The V dopant has a +4 oxidation state with one unpaired electron as shown by the occupied V 3d peak approximately 1 eV above the VBM and has a spin of 0.97 μβ. Sb can adopt a +4 oxidation state in one phase of its parent oxides,[94] and the Sb dopant has a +4 oxidation state when replacing the Ti cation with an unoccupied Sb 5p state approximately 1 eV above the VBM (Figure c) and a spin of 0.36 μβ, thus behaving in a similar manner to that of Sb doping of SnO2.[95,96] The potentials for V and Sb have 13 and 5 electrons, respectively, so using the calculated Bader values for the V and Sb dopants, their charges are +2 and +3.8, respectively. The Sb dopant has a larger charge than either Ti or V. Further inspection of the Bader charges and volumes shows that, due to the larger ionic radius of Sb, some of the charge on Sb is incorrectly assigned to the surrounding oxygen atoms. Accounting for this fact, the real Sb Bader charge is found to be around +2.2. The Sn, Zr, and Hf dopants have a +4 oxidation state similar to that of the Ti+4 cation and do not introduce any defect states in the band gap (Figure c,e,f) where their absence shows that these dopants are isoelectronic to Ti. The charges for Sn, Zr, and Hf dopants are +4.0, +2.5, and +2.6. Similar to Sb, the Bader charge on the Sn ion is misleading due to its large ionic radius. Accounting for the charge on the surrounding oxygen atoms, the Sn dopant has a charge of +2.4. All dopants have a spin of 0.0 μβ.

Figure 3

(a) Local structure of the (103) surface and the calculated PEDOS plots for (b) V-, (c) Sn-, (d) Sb-, (e) Zr-, and (f) Hf-doped surfaces. The blue and red spheres are the Ti and O ions, while the red and green lines are the p and d states. The black dashed line shows the position of the Fermi Level.

In order to examine the electron trapping behavior of these dopants, an additional electron is added in the presence of a precursor polaronic distortion around the Tisurf site, and this was optimized self-consistently. The lowest energy configurations of the excess electron for each dopant species are shown in Figure . The addition of an electron to the V-doped surface leads to reduction of the V dopant (V4+ to V3+). The added electron becomes spin-paired with the previous unpaired electron on the V ion. There is a decrease in the charge of the V ion from +2.0 to +1.7 resulting in a spin of −0.03 μβ. The reduction of the V ion is 0.13 eV more favorable than the delocalized solution in the bulk and 0.22 eV more favorable than trapping at other Tisurf cations. A similar behavior is seen for the Sn-doped surface when an electron is added. The electron preferentially traps itself on the Sn dopant in the a-TiO2(103) surface over the Tisurf cations as shown by the spin density plot in Figure b with a calculated trapping energy of −0.01 eV compared to the delocalized solution in the bulk and 0.01 eV more favored than an electron trapped on a nearby Tisurf cation. There is a decrease in the charge of the Sn dopant from +2.4 to +1.7 and an increase in spin to 0.6 μβ indicating a reduction of Sn+4 to Sn+3. For the Sb-doped surface, the addition of an electron fills the unoccupied Sb 5p state on the Sb dopant. Reduction of surface Ti cations near the Sb dopant was not energetically feasible, and the electron always favored migrating to fill the unoccupied Sb 5p state on the Sb dopant. The charge decreases from +2.2 to +1.4, and the spin decreases to 0.0 μβ confirming the reduction of the Sb dopant. The calculated energy to fill the unoccupied defect state is −0.001 eV compared to the delocalized solution in the bulk indicating that the excess electron has no preference between the Sb dopant and bulk. When an excess electron is trapped at the Tisurf cation beside a dopant species, it will migrate under surface relaxation onto a dopant cation indicating that electrons are more likely to be present on the dopant than on the Tisurf cation suggesting that these dopants act as stronger trapping sites than surface Tisurf cations.

Figure 4

Local geometry, spin density plot for electron trapping in (a) V-, (b) Sn-, (c) Sb-, (d) Zr-, and (e) Hf-doped (103) surface slabs. The blue and red spheres are the lattice sites for the Ti cations and O anions, while the green isosurface shows the location of the excess electron (0.004 electrons/Å3).

A different electron-trapping behavior is observed for the Zr- and Hf- doped (103) a-TiO2 surfaces. An additional electron will not localize on the the Zr or Hf dopant as seen for V, Sn, and Sb, and the electron preferentially migrates to reduce another Tisurf cation as shown in Figure d,e. This occurs on next nearest-neighbor sites for the Zr-doped surface, while for Hf-doped TiO2, the electron will migrate to the next chain of Tisurf cations. The reduced Ti cation has a decrease in charge from +2.2 to +1.9. It was still energetically unfavorable to localize an electron on the dopant using 25% HF exchange, and the electron migrated to a low-coordinated surface Ti, suggesting that electron trapping will never occur on the Zr and Hf dopants. Trapping the electron on the doped Zr and Hf surfaces costs an energy of +0.17 and +0.10 eV, respectively, relative to a delocalized electron in the anatase bulk indicating that the presence of the dopant makes it less favorable for the electron to be present at the surface. These dopant species do not trap electrons as there are no low-energy peaks at the CBM capable of accommodating extra electrons as shown by the PEDOS plots.

The calculated PEDOS plots given in Figure provide further evidence to the electron trapping nature of the V, Sn, and Sb dopants, while showing that no trapping occurs on Zr and Hf dopants. The reduction of V and Sn dopants by trapping an excess electron is shown by the defect levels in the band gaps (Figure a,b) where the excess electron on V pairs with the previous unpaired electron (Figure b) having a deep defect level approximately 1 eV below the CBM, while for Sn, the extra electron occupies a Sn 5p defect level of 0.25 eV above the VBM. The presence of a Sn 5p defect level at the CBM suggests that further electron trapping is likely on the Sn dopant. The absence of a defect peak in the band gap for the Sb-doped surface supports the filling of the unoccupied defect state by the excess electron. For the Zn and Hf dopants, the shallow defect Ti 3d level approximately 0.45 eV below the CBM is an indication of electron trapping on the Tisurf cations. Trapping does not occur on the dopants as their d band states lie deep in the CB and a wider number of states near the CBM is similar to bulk TiO2 suggesting that no electron trapping can occur.

Figure 5

Calculated PEDOS plot for electron trapping in (a) V-, (b) Sn-, (c) Sb-, (d) Zr-, and (e) Hf-doped (103) surface slabs. The red and green lines are the p and d states. The black dashed line shows the position of the Fermi Level.

Another approach to reduce electron trapping in anatase TiO2 is the introduction of electron-donating species to fill the electron surface traps. In order to examine this, we introduced alkali metal (Li, Na, K, Rb, and Cs) interstitials into the anatase (103) surface. Alkali metal-doped TiO2 is well studied, especially Li-doped TiO2 where many experimental studies have shown that alkali metal can easily be incorporated into TiO2 and show improvements in conductivity over undoped TiO2.[97−100] Their effect, however, on electron traps in TiO2 has not been considered and is an interesting approach to consider nullifying the electron traps that exist on anatase TiO2 crystals. In order to find the most energetically favored interstitial position, the metal ions were relaxed in various sites in the surface and subsurface layers with the relaxed geometry for the lowest energy position of each species shown in Figure . There appears to be an ionic radius size effect on the lowest energy configuration. The smaller Li and Na ions reside in the subsurface layers, while the larger K, Rb, and Cs ions prefer to move from the subsurface layers and sit on the (103) surface. Rb and Cs interstitials are large enough to form additional Rb/Cs–O bonds with the O anions in the step pulling them away from the coordinated Ti cations, resulting in the Ti cation becoming three-coordinated. The calculated bond lengths for the alkali interstitials in the (103) surface are given in Table where the increase in bond lengths with increasing ionic radii can be seen. The bond lengths for the large cations become too large for the surface to accommodate the interstitial position, so K/Rb/Cs migrate to the surface edge in order to relieve any surface strains.

Figure 6

Local geometry of the alkali metal interstitials in the (103) surface slab for (a) Li, (b) Na, (c) K, (d) Rb, and (e) Cs. The blue and red spheres are the lattice sites for the Ti cations and O anions, while the green, purple, magenta, pink, and turquoise spheres are the Li, Na, K, Rb, and Cs interstitials. The position of the excess electron is shown by the green spin density plot (0.004 electrons/Å3).

Table 3

The Calculated Bond Lengths for the Metal–Oxygen Surface Bonds of the Interstitial Ions along the a and c Directions

bond	a direction (Å)	c direction (Å)
Li–O	1.90 (×2)	2.12, 1.95
Na–O	2.18 (×2)	2.22, 2.14 (×2)
K–O	2.62 (×2), 2.79 (×2)	3.10
Rb–O	3.00	2.90 (×4)
Cs–O	3.06	3.10 (×4)

The spin density plots in Figure show that the neighboring Tisurf cation contains excess electron density donated from the presence of the alkali metal interstitial ion. The alkali metal donates the electron to fill the electron trap state that resides at the bottom of the CBM, reducing the Ti+4 to Ti+3. This electron-donating process is supported by the calculated PEDOS plots for Li and Na incorporation in TiO2 as shown in Figure where only the plots for Li and Na interstitials are shown since the PEDOS plots for the other alkali metals have similar characteristics. There are negligible Li/Na 1/2s states in the VB suggesting that a small amount of electrons resides on the alkali metal, while the occupation of the electron trap is seen with the presence of the defect peak approximately 1 eV from the CBM on the Ti PEDOS. The reduction process for each surface is also supported by the decrease in the Tisurf cation charge from +2.2 to +1.9 and an increase in the spin on the reduced Ti cation from 0.0 to 0.88 μβ.

Figure 7

Calculated PEDOS plots for (a) Li- and (b) Na-doped TiO2. The blue, red, and green lines are the s, p, and d states where the black dashed line shows the position of the Fermi level. The top of the valence band is aligned to 0 eV.

Discussion

Electron self-trapping is harmful to the performance of TiO2 as an electron transport layer in solar cell devices since the excess electrons from an external bias will trap themselves at Ti cation lattice sites reducing its efficiency. Reducing or removing these traps from TiO2 nanocomposites is of critical importance to ensure that electrons are allowed to flow through the medium without hindrance. We examined two approaches to reduce the contribution of low-coordinated surface Ti cations toward electron trapping in nanocrystals of anatase TiO2: (1) substitutional doping to remove the Ti 3d states associated with electron traps and (2) introduction of electron-donating interstitials to fill the associated Ti 3d electron trap states. The examined dopants with stable variable oxidation states such as V and Sb were found not to relieve electron trapping at the (103) surface. V introduced more electron traps to the system as low-lying V d states were introduced at the CBM and could be further reduced from V+4 to V+3. It is also more energetically favored to carry out this reduction than having electrons delocalized in the bulk system. The Sb dopant is also not a good candidate to reduce electron trapping in the (103) surface as this dopant introduces unoccupied defect states into the surface. These states act as electron traps in addition to the low-coordinated Ti cations. We also found that using Sn as a dopant to reduce electron trapping was not viable as it was more favored to reduce the Sn dopant compared with the Ti cations. Sn is more electronegative than Ti and will have a tendency to attract electrons, while the lower-lying Sn 5p states in the conduction band are more easily accessed than the Ti 3d states. From our predictions, it is therefore not advisable to use V, Sn, or Sb as a chemical modification in a-TiO2 for solar cell applications as these species further contribute to electron trapping. The migration of Sn ions into a-TiO2 when examining a SnO2/TiO2 composite[101,102] can greatly affect the electron transport efficiency since Sn will trap electrons, thus preventing Sn incorporation in a-TiO2 is desirable to maintain the photocatalytic activity and electron transport properties.

Both Zr and Hf were found to be useful candidates to remove electron traps from the (103) surface of anatase TiO2. These dopants removed the trapping states at the CBM associated with electron trapping as the Zr 4d and Hf 5d states are higher in energy. The additional electrons could not localize on the Zr/Hf because of this, and it was more energetically favorable to move to and reduce the low-coordinated Ti cations. Increasing the concentration of these dopants could eliminate more of the Tisurf electron traps leading to improved mobility in a-TiO2. Using nonreducible dopants such as Zr is beneficial to reduce electron trapping in anatase TiO2 since this species removes low-lying electron trapping states at the CBM. Experimental studies have eluded Zr doping in improving photocatalytic properties of a-TiO2, and doping with Zr to remove electron traps is perhaps a contributing factor to this improvement.[73,103−105]

The use of alkali metal candidates is also useful for removing electron traps from anatase TiO2. These species donated electrons into the low-coordinated Ti cations and filled the electron trap states at the CBM. Any additional electrons into the anatase crystals would therefore not get trapped since the states are now filled. Using electron-donating species is beneficial to reduce electron trapping in anatase TiO2.

Conclusions

In summary, hybrid density functional theory was used to examine approaches to reduce electron trapping in nanocrystals of TiO2. Low-coordinated Ti cations on surfaces of anatase TiO2 were found to greatly contribute to electron trapping since these species introduce low-lying Ti 3d states at the bottom of the conduction band. These states can then be filled with additional electrons in the nanocrystal, and the electrons become trapped at these surface artifacts. A number of dopants were examined to replace these low-coordinated Ti cations and reduce electron trapping in anatase TiO2. Dopants such as V and Sb that can achieve stable variable oxidation states were found to enhance electron trapping through the introduction of additional defect states in the band gap or the bottom of the conduction band. This is expected to reduce electron mobility in anatase TiO2 as these dopants would act as electron traps in addition to the low-coordinated surface Ti cations. We found that Zr and Hf will improve electron mobility in anatase TiO2 as these species do not introduce additional defect peaks or further d state peak traps at the bottom of the conduction band, reducing the number of electron traps present in samples. Alkali metals are also expected to improve electron transport in TiO2. These species can donate extra electrons into the low-lying Ti 3d states at the bottom of the conduction band associated with electron trapping. If the traps are already filled by these alkali earth metal interstitials, then additional electrons into nanocrystals of anatase TiO2 are expected not to trap themselves, thus reducing electron trapping.