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Band Structure Engineering: Insights from Defects, Band Gap, and Electron Mobility, from Study of Magnesium Tantalate Taifeng Liu,†,§ Michel Dupuis,‡,∥ and Can Li*,† †

State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, and Dalian National Laboratory for Clean Energy, Dalian 116023, China ‡ Department of Chemical and Biological Engineering and Computation and Data-Enabled Science and Engineering Program, University at Buffalo, State University of New York, Buffalo, New York 14260, United States S Supporting Information *

ABSTRACT: Anion doping of semiconductors with nitrogen is a strategy often adopted to narrow the band gap of semiconductors and increase the range of light absorption. However, the influence of nitrogen doping on the electron mobility in the semiconductor is not fully understood and characterized. In this work, we used magnesium tantalate MgTa2O6 as a model system and hybrid density-functional theory calculations to characterize the mobility of electrons using the small polaron model in the presence of nitrogen-doping defects as well as oxygen-vacancy defects. We found that electron mobility is not significantly affected when MgTa2O6 is doped with a molar ratio N/O of ∼2%. However, in the presence of oxygen vacancies combined with nitrogen doping with the same molar ratio N/O of ∼2%, the barrier to electron hopping in the vicinity of the defects is much lower than that in pristine MgTa2O6 and in MgTa2O6 with oxygen-vacancy defects only. These results suggest that nitrogen doping combined with anion vacancy not only narrows band gap but also enhances electron mobility, a finding that may lead to new strategies toward synthesizing more efficient photocatalysts.

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INTRODUCTION Solar-driven water splitting with semiconductor-based photocatalysts is one of the most ideal routes to convert solar energy into chemical fuel.1−3 An ideal photocatalyst for water splitting should have a suitable band gap to harvest the solar energy in the visible region of the solar spectrum, as well as appropriate band edge positions to meet the thermodynamic criteria for water splitting. In addition to these energy-based requirements, the mobility of the photogenerated charge carriers should be large.4 Materials like TiO2, SrTiO3, and NaTaO35−16 are not able to show photocatalytic activity under visible light due to their large band gap. These observations have led to growing interest in band gap engineering to enable visible light absorption, and in particular doping of materials is a widely used approach to manipulate band gaps.17−20 Doping a metal oxide semiconductor is known as one effective strategy to extend the material optical absorption edges and develop photocatalysts for visible light-driven water splitting.21 Anion doping by nitrogen has been the subject of many theoretical and experimental studies. Recently, nitrogendoped strontium tantalite Sr5Ta4O15 and magnesium tantalate MgTa2O6 have been synthesized and significant improvements in the photocatalytic activity have been observed, with enhanced visible light absorption with band edges favorably positioned for solar water splitting.22,23 In these studies, it was demonstrated that the enhanced visible light absorption is due to the presence of nitrogen-induced localized mid-gap states that reduce the effective band gap.24,25 However, these states are considered detrimental to photocatalytic activity as they © XXXX American Chemical Society

may act as electron−hole recombination centers and thus reduce the photoconversion efficiency.26 In parallel, defects like oxygen vacancies are known to form spontaneously in N-doped oxide materials to compensate for the charge imbalance arising from nitrogen doping of the oxide semiconductor. These defects are believed to trap photogenerated electron−hole pairs and accelerate their recombination.27 Although nitrogen-doped semiconductors have been extensively studied for photocatalytic purposes, most of the studies have focused on narrowing the band gap to increase light absorbance. Little focus has been given to the effect of doping on polaron transfer and mobility. In this paper, we report an the investigation of both electron mobility and band gap changes in a nitrogen-doped semiconductor, namely, nitrogen-doped MgTa2O6. The paper is organized as follows: first, we outline the computational approach and the technical details; second, we present and discuss the results for pristine material, then for a material with oxygen vacancies (Vo), one nitrogen (1Ns) atom, and two nitrogen (2Ns) atoms substitution defects, and last, for a material with both (2Ns) substitutions and oxygen vacancies together. We find that single oxygen vacancy alone is not thermodynamically stable, nor are 1Ns-substitution defects. For defects involving 2Ns substitutions, we find that the system easily relaxes to highly stable N2 defects with a covalent N−N bond. In the presence of an oxygen vacancy (Vo) nearby, the Received: December 16, 2015 Revised: February 22, 2016

A

DOI: 10.1021/acs.jpcc.5b12314 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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assisted by vibrations). The energy barrier ΔG is then calculated as ΔG = ER0.5 − ER1. With use of Einstein’s formula, the electron mobility along that direction can be estimated approximately by

excess electrons from the Vo make the 2Ns-substitution defects stable (with no formation of N2 clusters). Electron polaron hopping processes in the vicinity of (2Ns + Vo) defects have a much lower activation energy.

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COMPUTATIONAL DETAILS We carried out spin-polarized density-functional theory (DFT) calculations using the Vienna Ab-Initio Simulation Package (VASP) code.28,29 For structure determination we adopted the Perdew-Burke-Ernzerh (PBE) parametrization30 of the exchange and correlation potential in the generalized gradient approximation (GGA).31 The electron wave function was expanded in plane waves up to an energy cutoff of 400 eV. Selfconsistent DFT energies were converged to 10−4 eV, and geometry optimization were deemed converged when the residual forces on the atoms were less than 0.01 eV/Å. The Γcentered k-point mesh of the Brillouin zone sampling for the primitive cells was set at 9 × 9 × 4 based on the Monkhorst− Pack scheme.32 The primitive cell contains two formula units MgTa2O6, and we used 3 × 3 × 1 supercells for a total of 162 atoms and the Brillouin zones were sampled using 2 × 2 × 2 meshes. All the electronic property calculations (beyond geometry) used the Heyd-Scuseria-Ernzerhof (HSE) hybrid density functional,33 for which the exchanges and correlation energy is given by

( ) ΔG

eD μ= = kBT

e(1 − c)a 2ν0 exp − k T B

kBT

(2)

where (1 − c) is the probability that a neighboring site is available for hopping, ΔG is the energy barrier, v0 is the longitudinal optical phonon frequency, kB is Boltzmann’s constant, T is temperature, and a is the transfer distance. We took (1 − c) ≈ 1, T = 300 K, and v0 = 1013 Hz. Nearest neighbor Ta atoms were selected as final states of hopping processes.

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RESULTS AND DISCUSSION 1. Pristine MgTa2O6. The MgTa2O6 (MTO) crystal is in the space group P42/mnm.41 As shown in Figure 1a, the crystal

HSE E XC = αE XSR (μ′) + (1 − α)E XPBE,SR (μ′) + E XPBE,LR (μ′)

+ ECPBE

(1)

where α and μ′ define the mixing coefficient and the screening parameter, respectively. We used α = 25% mixing for the exchange and μ′ = 0.3 Å−1 for the screening parameter, which yielded the band gap of MgTa2O6 being very close to the experimental value (see results below). We characterized the electron transport in the bulk stoichiometric MgTa2O6 and nitrogen-doped MgTa2O6 using the small polaron model as formulated in Marcus/Holstein theory.34,35 To model an electron polaron, one extra electron was added to Ta 5d and the DFT+U approach was used to enable electron localization.36−38 In the DFT+U approach, the on-site Coulomb interaction U and exchange parameter J are the determining factors for the magnitude of the on-site correction.39 Here, we used a fixed J value of 1.0 eV and varied the U value to find an appropriate parameter Ueff = U − J. Several Ueff values were tested and we found Ueff = 5 eV to yield electron polarons with localized character. To model an electron polaron transfer process, three relevant states are involved: the initial, final, and transition states. In the initial state, the electron is localized on one particular Tantalum atom site. When the polaron hops to an adjacent site (another Tantalum atom), the final state is formed. In a periodic crystal, the initial and final states are identical as the Tantalum atoms have the same chemical environment. With the electron localized on equivalent initial and final sites, we can use a linear interpolation scheme to describe the polaron transfer pathway.40 R1 and R2 are defined as vectors of the threedimensional coordinates of all atoms in the initial and final polaron states, respectively. Then the coordinates of all atoms along the hopping pathway can be approximated as Rx = xR1 + (1 − x)R2, where x varies from 0.0 to 1.0. The value x = 0.5 corresponds to the midpoint that happens to be the transition state due to translation or symmetry equivalence of the final and initial states and assuming an adiabatic process (thermally

Figure 1. (a) MgTa2O6 (MTO) unit cell, ball and stick model, O, Mg, and Ta atoms are marked. (b) Total and projected density of states for the MTO unit cell; the Fermi level is set at 0 eV.

structure is described by a unit cell which is triple that of the conventional rutile unit cell along the tetragonal c-axis. The cations, which occupy half of the octahedral available sites, are surrounded by O2− organized in a hexagonal closed-packed arrangement. This yields a chemically ordered network of interpenetrating edge and corner-sharing slightly distorted octahedrals. Successive Mg−O planes (at z = 0 and 0.5) are separated by two Ta−O planes (z ∼ 1/6 and z ∼ 1/3).42 The oxygen atoms in the Mg−O planes marked as O1 are different from that in the Ta−O planes marked as O2. The two types of oxygen atoms differ in their proximity to Mg atoms, O1 being closer and O2 farther. The lattice constant of the MTO is calculated to be a = b = 4.688 Å, c = 9.267 Å, which is in good agreement with the experimental (a = b = 4.718 Å, c = 9.212 Å)43 and literature values.44 The calculated total density of states (DOS) and projected density of states (PDOS) of MTO are plotted in Figure 1b. The computed band gap of MTO is 4.32 eV, close to the experimental value 4.34 eV.23 The PDOS shows that the valence band maximum (VBM) is majority O 2p in character and the conduction band minimum (CBM) is mainly composed of Ta 5d. 2. One Nitrogen Atom (1Ns)-Doped MTO and One Oxygen Vacancy (Vo)-Doped MTO. Initially, we investigated substitutions of one oxygen atom by one nitrogen atom (1Ns) B

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more stable 1Ns structure is the one shown in Figure 2b with the N atom at the O2 position. The total DOS and PDOS for this 1Ns defect are plotted in Figure 3a with the inset focusing

at various oxygen positions. We then considered single oxygen vacancies (Vo) at the same oxygen positions. These two cases correspond to doping concentration with a molar ratio N/O or Vo/O of ∼1% given the size of our supercell. 2.1. 1Ns-Doping MTO. As shown in the Figure 1a, there are two kinds of oxygen atoms in the unit cell of MTO marked as O1 and O2. We considered single N atom substitution at either O position. The optimized structures are shown in Figure 2a,b.

Figure 3. Total and projected density of states for (a) 1Ns-doped MTO and (b) Vo-doped MTO; the Fermi level is set at 0 eV. Inserts give close-up views of the defect states.

Figure 2. Optimized structures of (a), (b) 1Ns-doped MTO, blue represents the N atom, and (c), (d) oxygen vacancy (Vo)-doped MTO.

To characterize the stability of the doped MTO, we calculated the defect formation energy (Ef) using the following relation Ef = Edoped − MTO + mμO − EMTO − nμ N

on the N-induced states. Two states appear in the band gap, one slightly above the VBM around the Fermi level (EF) and the other is approximately at mid gap. The insert indicates that the gap state is composed of N 2p and O 2p states, with the majority contribution from the N 2p state. Note that the DOS was obtained with hybrid functional DFT at the GGA structure. N is a trivalent atom bonded to two Ta atoms, resulting in a dangling electron of majority spin. The spin polarization of the DFT wave function exhibits an upward shift of states from the valence band (VB) (near VB state) and a corresponding downward shift of states from the conduction band (CB) (midgap state). The energy gap of the CB edge and the near VB state is now 4.24 eV. The energy gap between the N-induced states (the occupied near VB state and the empty mid-gap state) is ∼2.75 eV, still too large for visible light absorption. Furthermore, the concentration of these states is small as they arise from low defect concentration. Overall, the defect-induced band gap changes for 1Ns-doped MTO are small and do not achieve visible light absorption. Lastly, we note that the introduction of N substitution induces an imbalance in spin states, a half-filled dangling electron state, and an empty gap state that likely act as electron−hole recombination centers and thus reduce the photogenerated current24 and the photocatalytic activity of the semiconductor. Later, we report on the interaction of 1Ns defects with other defects, such as other N substitutions and also oxygen vacancies. 2.2. Vo-Doped MTO. Just like for 1Ns doping, we considered oxygen vacancies at the O1 and O2 positions. The optimized structures are shown in Figure 2c,d. The formation energies of O1 and O2 vacancies were found to be 0.756 and 0.627 eV, implying that oxygen vacancies in MTO are not thermochemically stable. As for 1Ns defects, a vacancy at the O2 site requires

(3)

where EMTO and Edoped−MTO are the total energies of bulk MTO and doped MTO. The quantities μO and μN represent the chemical potential for O and N atoms and n and m define the number of N or O atoms introduced or replaced. Defect formation energies vary with synthesis conditions (i.e., O-rich and Ta-rich). In the case of MTO, the chemical potential of the constituent elements must satisfy the relationship μMg + 2μTa + 6μO = μMTO

(4)

where μX denotes the chemical potential of the species X. Under the environment of O-rich conditions, μO was calculated from the energy of an oxygen molecule (μO = 1 /2μO2) and μTa was derived from eq 4. In the case of Ta-rich conditions, μTa was obtained from the energy of Ta in pure Ta bulk crystal and μO was determined from eq 4. μN was calculated as the energy of the nitrogen atom in the homonuclear diatomic molecules in the gas phase, that is, μN = 1/2μN2. μMg was obtained from the energy of the Mg in Mg bulk crystal. The chemical potential μMTO was taken as the DFT energy per chemical unit in bulk MTO. The formation energies of one nitrogen atom substitution at O1 or O2 atom site were calculated to be −0.466 and −0.511 eV, respectively. Here, the lower the formation energy, the more stable the structure. Thus, 1Ns substitution of O2 is only slightly more stable (by ∼0.055 eV) than 1Ns substitution of O1. This finding is consistent with the stronger electrostatic interaction between O1 and Mg than between O2 and Mg. The C

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Figure 4. Optimized structures and total and projected density of states for (a), (b) 2Ns-doped MTO and (c),(d) N2-doped MTO. The Fermi level is set at 0 eV. Inserts give close-up views of the defect states.

stable. The formation energy of the 2Ns defect with N substitutions at two O1 sites is larger than the energy of all other cases, meaning this 2Ns substitution would be hardest. This finding is consistent with the ealier result that 1Ns substitution would not be easiest at an O1 site. Only the most stable structure was considered further and is shown in Figure 4a. In this structure, the distance between the two N atoms is 2.767 Å, indicative of no chemical bond existing between the two N atoms. The DOS of this structure is shown in Figure 4b, with the inset focusing on the defect-induced states. Consistent with the 1Ns-defect description above, the DOS and PDOS show three states in the band gap that are composed of the N 2p, O 2p, and Ta 5d states, with the majority contribution from the N 2p state. This time, the majority spin-dangling electron states appear slightly above the VB, and two empty spin-polarized minority spin states appear in the gap. This situation is similar to the 1Ns-defect description. As discussed above, the energy gap is decreased by a small amount only that does not achieve visible light absorption. Starting from the 2Ns-defect structure shown in Figure 4a, a small distortion was introduced by shortening the N−N distance between the N atoms and then the structure allowed to relax. After optimization, we obtained a new totally different structure shown in Figure 4c that exhibits a significantly shorter N−N distance, indicative of the formation of an N−N covalent bond. Indeed, in this new structure, the length of the N−N bond is 1.423 Å, which is very close to the N−N single-bond distance of 1.450 Å in hydrazine N2H4. We refer to this defect structure as an N−N cluster defect and label it as N2-doped MTO. The formation of N−N cluster structures has already been reported in other N-doped systems.49,50 The formation energy of this new N2-doped structure is ca. −1.254 eV, indicative of N2-doped MTO being thermochemically stable and the N2 cluster forming spontaneously in MTO. It is much more stable than the 2Ns-doped structure of Figure 4a. The DOS and PDOS of the N2-doped structure are shown in Figure 4d. There are now three states in the gap below the

less energy than a vacancy at the O1 site, consistent with stronger electrostatic interaction of O1 with Mg. The total DOS and PDOS of this more stable structure were calculated and are plotted in Figure 3b with the inset focusing on the Voinduced states. The description of the states arising from Vo remains a challenge to theory as a different theoretical model gives rise to different models with two antiferromagnetically coupled localized electron states, or one localized electron state (with the other electron delocalized), or zero localized states and the two electrons delocalized.45−48 In spite of intense attempts, the present calculations exhibited a single localized electron state, with the second electron being delocalized over all Ta atoms in the supercell. The insert of DOS and PDOS shows clearly the Ta 5d nature of the state lying near the bottom of CB; thus, the band gap is not significantly affected by Vo defect. So far, the MTO doping through one nitrogen substitution (1Ns) or through one oxygen vacancy (Vo) were investigated. It is found that both cases have drawbacks, so these two cases may contribute very little to photocatalysis activity. In what follows, doping via two nitrogen substitutions 2Ns doping and two nitrogen substitutions combined with one oxygen vacancy (2Ns + Vo) doping were discussed. The aim is to assess if these combined defects can lead to narrowed band gap and compensation of the trap states. 3. 2Ns-Doped MTO and N2-Doped MTO. We considered a double nitrogen atom substitution 2Ns of different oxygen atom sites. Such defect corresponds to a molar ratio N/O of ∼2%, similar to the molar ratio observed in X-ray photoelectron spectroscopy experiment.23 Several situations were considered: 2Ns substitutions at the two O1 sites; 2Ns substitutions at one O1 site and one O2 site; and finally 2Ns substitutions at the two O2 sites. Nearest neighbor and next nearest neighbor sites were considered, giving rise to a total of 36 structures displayed in Figure S1 and S2 in the Supporting Information. The formation energies of these defects were calculated and are listed in Table S1 in the Supporting Information. The formation energies are all positive, meaning that 2Ns defects are not thermochemically D

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The Journal of Physical Chemistry C Fermi level, one near the VB edge with O character and two occupied N−N induced gaps states. The results are consistent with the description of Yin et al.,50 the double-hole mediated dopant−dopant coupling giving rise to two N-induced gap states that are fully occupied. The N−N bond gives rise also to a doubly occupied state of σ-bond character deep in the VB and an unoccupied state of antibonding σ* character high in the CB. The DOS shows that the energy gap of N2-doped MTO is 2.62 eV, which may be in the range of visible light absorption. The PDOS shows that the VBM is composed of the N 2p and O 2p hybridized states, with the majority contribution from the N 2p state. This is evidence that N atom doping in the form of N2 clusters would induce visible light absorption. The spin balance of the states in the gap suggest that they would have no role as electron−hole recombination centers and therefore no detrimental effects on charge mobility. Compared to the 1Ns and 2Ns substitution cases discussed above (Figure 3a or Figure 4b), it can be said that the localized impurity states in 1Ns and 2Ns doping were passivated by the formation of the N−N cluster. 4. (2Ns + Vo)-Doped MTO. Earlier, we saw that 1Ns-defect and 2Ns-defect states give rise to N-induced spin-unbalanced hole states in the gap that have the potential to act as recombination centers and to be detrimental to photocatalytic activity. When two 1Ns substitutions occur on nearby centers, each carrying a hole state, we found that such a structure reorganizes to form covalent N−N clusters. We discuss now the case of 2Ns defects (molar ratio N/O was ∼2%) in the presence of a nearby oxygen vacancy (with a molar ratio Vo/O was about 1%). We label this defect as (2Ns + Vo). The excess electrons resulting from the oxygen vacancy are anticipated to pair up with the dangling electrons of the N atoms resulting in charge compensation. Earlier, we showed that 1Ns substitutions at O2 sites are the most stable substitutions. Also, oxygen vacancies at O2 sites are easiest if not thermochemically stable. To investigate the combined effect of oxygen vacancy and N atom substitutions, we first selected an oxygen vacancy at an O2 site, and then we selected a first 1Ns substitution at a nearby O2 site followed by a second 1Ns substitution at another O2 site. Only nearest neighbor and next nearest neighbor sites were considered for a total of 17 structures that were optimized as shown in Figure S3 in the Supporting Information. The defect formation energies were calculated and are listed in Table S2 in the Supporting Information. The formation energies of (2Ns + Vo)-doped MTO are all negative, a finding consistent with oxygen vacancies forming easily in 1Ns-doped MTO.27 It is interesting to note that the formation energies of 2Ns defects and Vo defects separately were positive, while the formation energy of a (2Ns + Vo) defect is negative. In the 2Ns system, each nitrogen atom is a hole state with minority spin-polarized states in the band gap. In Vo defect partially occupied localized states near the CB appear. When considered together, the gap states resulting from the combined doping/defect are now all fully occupied due to charge compensation. This observation rationalizes the finding that the formation energies of these defect structures are negative and that these structures are now stable. Only the most stable configuration is shown in Figure 5a and considered further. The DOS and PDOS of this (2Ns + Vo) structure are shown in Figure 5b with the inset focusing on the N-induced defect states. The DOS shows the presence of two gap states just above the VB edge with an energy gap to the CB of 3.47 eV,

Figure 5. (a) Optimized structures of (2Ns + Vo)-doped MTO. (b) Total and projected density of states for (2Ns + Vo)-doped MTO; the Fermi level is set at 0 eV. Inserts give close-up views of the defect states.

substantially smaller than the band gap of bulk MTO, albeit still far from visible light absorption. The PDOS shows that these near edge states consist predominantly of N 2p and O 2p states, with the majority contribution from the N 2p states. The spin unbalance of the 1Ns substitution impurity states seen in Figure 3a have disappeared. This finding is consistent with the N 2p states accepting the excess electrons originating from the oxygen vacancy and changing their state from N2− to a N3− valence state. Although the new energy gap does not reach into the visible region in the (2Ns + Vo)-doped MTO system, this system shows increased light-harvesting range. 5. Stability of Different Nitrogen Species in MTO. In the above section, we used formation energies as indicative of most stable structures, for example, among the many configurations of 1Ns-doped MTO. This approach was used for example in ref 20 to compare the stability of different nitrogen-doped structures in TiO2. The relative stability of these diverse species varies as a function of the oxygen chemical potential (μO), which is a parameter that characterizes the oxygen environment during synthesis. Oxygen-poor conditions correspond to a low value of μO, and conversely, oxygen-rich conditions correspond to a high value of μO. By referencing μO to the energy of an O atom in the O 2 molecule 1 ( μO = 2 μ(O2 ) + μ′O), we take −5 ≤ μ′O ≤ 0, where the value μ′O = 0 corresponds to the oxygen-rich limit at which oxygen condensation will occur, where μ′O = −5 eV is approximately one-sixth of the enthalpy of formation of MgTa2O6. In Figure 6 we report the energies of formation of the most stable nitrogen-doped structure discussed in the earlier sections as a function of μ′O, according to the formula 1 1 Ef = Edoped − MTO − [EMTO + nμ N − mμO] (5) n n .

For all species, Eform increases as μO increases (positive slope), indicating that oxygen-poor conditions are more favorable for implanting substitutional nitrogen. In the 1Ns-, 2Ns-, and N2-doped cases, the N2-doped MTO is the most stable defect, whether in oxygen-poor or -rich conditions. This shows forming N−N cluster in nitrogen-doped systems lowers E

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Table 2. Activation Energies ΔGe and Directional Electron Mobility μe in MTO, and Hopping Activation Energies ΔGe in Vo-Doped MTO and (2Ns + Vo)-Doped MTO

Figure 6. Formation energies (Eform, in eV) as a function of the oxygen chemical potential (μO) for different nitrogen species in MTO.

the energy of the systems and increases their stability. The formation energy of (2Ns + Vo)-doped MTO is the highest in the oxygen-rich conditions and is the lowest in the oxygen-poor case, which means (2Ns + Vo)-doped MTO is only stable in oxygen-poor conditions. 6. Electron Mobility. We characterized the energetics associated with electron polaron transfer processes in the N2doped and (2Ns + Vo)-doped structures considering hopping processes in the vicinity of the defect. To model an electron polaron, we carried out calculations that included one excess electron. The excess electron was localized at a Ta atom and formed a small polaron. Several Ta atoms were selected in N2doped and (2Ns + Vo)-doped MTO, marked with labels A, B, ..., H or 1, 2, ..., 3 shown in Figure S4a,b of the Supporting Information. The notation A−B or 1−2 is used to indicate electron hopping from Tantalum atom A (or 1) to Tantalum atom B (or 2). We calculated the activation energies for the various hopping processes using an approach similar to the one followed for the stoichiometric system, but for the Ta atoms in the vicinity of the N2 defects. To facilitate comparison, activation energies of polaron hopping in Vo-doped MTO and bulk MTO were also calculated using the same Ta atoms in identical supercells. The spin density of one extra electron in bulk, Vo-doped, N2-doped, and (2Ns + Vo)-doped MTO are shown in Figure S5 of the Supporting Information. It can be seen clearly that the excess electron is localized on one Ta atom in these structures and that these polarons have Ta 5d states character. The calculated activation energies and electron mobility for MTO and activation energies for Vo-doped, N2doped, and (2Ns + Vo)-doped MTO for these specific hopping steps are listed in Tables 1 and 2. The activation energies are

ΔGe (eV)

ΔGe (eV)

μe (10−6) (cm2/(V s))

A−B C−E F−G G−H D−F

0.318 0.122 0.349 0.189 0.379

0.318 0.178 0.354 0.178 0.369

2.38 380 0.970 380 0.556

direction

ΔGe (eV)

ΔGe (eV)

ΔGe (eV)

μe (10−6) (cm2/(V s))

1−2 1−3 1−4 2−3 3−4

0.143 0.152 0.090 0.116 0.111

0.348 0.347 0.170 0.381 0.401

0.369 0.354 0.178 0.384 0.369

0.556 0.970 380 0.626 0.556

MTO

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CONCLUSIONS In this work, we investigated N doping of MTO with regard to band gap and electron mobility, employing the formalism of hybrid DFT. Our results show that (1) one single nitrogen atom (with a molar ratio N/O of ∼1%) substitution does not result in band gap narrowing, while it induces localized impurity states that likely facilitate charge carrier recombination and hinder transport. (2) Two nitrogen atoms (molar ratio N/O of ∼2%) doped MTO give rise to N−N clusters within the solid that narrow the band gap substantially, but electron transport is not affected by N−N clusters. (3) Two nitrogen atoms doped MTO with oxygen vacancy can be easily formed. These defects can narrow the band gap slightly, but may enhance significantly the mobility of electrons while eliminating charge carrier recombination centers. From band gap and charge mobility perspectives, this work suggests a path forward to increasing photocatalysis efficiency, by combining and controlling N doping with O vacancies. Future mesoscale simulation will focus on the relation between mobility and doping concentration at the mesoscale level.

MTO

direction

Vo-doped MTO

conclusions emerge from Table 2. First, for the same hopping directions, the activation barrier for electron polaron hopping in Vo-doped MTO is almost the same as that in MTO. Second and interestingly, for several directions, the hopping activation energies in (2Ns + Vo)-doped MTO are significantly smaller than those in MTO, including notably in the 2−3 direction, where the activation barrier in (2Ns + Vo)-doped MTO is ∼0.3 eV smaller, corresponding to a hopping rate larger by over 4 orders of magnitude at room temperature. To recapitulate, in the case of N2 defects, it was found that the energetics for hopping processes in the vicinity of N2 clusters are not significantly altered by the presence of the N−N cluster, while in the vicinity of (2Ns + Vo) defects, electron polarons are significantly more mobile. These observations are valid in the assumption of small doping concentration. The effect of small doping concentration on transport over the meso- and macroscale would need to be addressed with kinetic models that capture the collective dynamics of many polarons at the larger scales.

Table 1. Activation Energies ΔGe and Directional Electron Mobility μe in MTO, and Hopping Activation Energies ΔGe in N2-Doped MTO N2-doped MTO

(2Ns + Vo)-doped MTO

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b12314. Optimized structures of 2Ns-doped and (2Ns + Vo)doped MTO, formation energy of 2Ns-doped and (2Ns + Vo)-doped MTO, selected Ta atoms for electron polaron in N2-doped and (2Ns + Vo)-doped MTO, and spin

essentially unchanged for N2-doped MTO compared to those of bulk MTO, suggesting that two nitrogen atoms doping forming N−N cluster in MTO does not significantly alter electron polaron transport near the defect. Furthermore, lowlying empty state exists in the gap that could act as an electron polaron trap. In (2Ns + Vo)-doped MTO, the following F

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The Journal of Physical Chemistry C

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density in bulk, Vo-doped, N2-doped, and (2Ns + Vo)doped MTO (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 86-411-84379070. Fax: 86-41184694447. Present Addresses §

University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049, China (T.L.). ∥ State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, and Dalian National Laboratory for Clean Energy, Dalian 116023, China (M.D.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by the National Natural Science Foundation of China (No. 21373209) and the National Basic Research Program of China (973 Program, Grant No. 2014CB239400). The authors acknowledge Dr. X. Zhou, Prof. H. X. Han, Prof. F. X. Zhang, Dr. S. S. Chen, Ms. Y. Qi, and Ms. J. Y. Cui for valuable discussions.

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