Modeling Electronic Trap States at Interfaces between Anatase

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Modeling Electronic Trap States at Interfaces between Anatase Nanoparticles Nam Q. Le, and Igor V Schweigert J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b04322 • Publication Date (Web): 14 Jun 2017 Downloaded from http://pubs.acs.org on June 20, 2017

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The Journal of Physical Chemistry

Modeling Electronic Trap States at Interfaces between Anatase Nanoparticles Nam Q. Le∗,† and Igor V. Schweigert∗,‡ †NRC Postdoctoral Associate, U.S. Naval Research Laboratory, Washington DC 20375 ‡Code 6189, U.S. Naval Research Laboratory, Washington DC 20375 E-mail: [email protected]; [email protected]

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Abstract Interfaces between crystallites in nanocrystalline anatase can give rise to localized electronic trap states, which affect the charge transport and catalytic activity of mesoporous TiO2 films and aerogels. Unlike trap states associated with point defects and surfaces, the energetic and spatial distributions of interfacial trap states are not known. We have calculated the electronic structure of attached anatase nanoparticles to search for molecular orbitals localized at the particle interfaces and to identify their energetic positions in the nominal band gap. We found that orbitals localized at the interfaces had energies near the edge of the nominal conduction band and that such trap states localized at the interface between (001) facets were lower in energy than those localized at the interface between (101) facets. The spatial distributions of the interfacial trap states were similar between different levels of theory; however, hybrid density functional theory (DFT) predicted the trap states to be deeper than those predicted by DFT within the generalized gradient approximation or by density functional tight binding (DFTB).

Introduction The catalytic performance of porous, nanocrystalline anatase is strongly affected by the presence of electronic trap states, which arise from various types of defects and exhibit energies across a wide range within the band gap. 1,2 Trapping is the limiting phenomenon in electron transport within nanocrystalline TiO2 , 3 which in turn limits the overall transport in TiO2 –electrolyte systems. 4 Trap states also delay exciton recombination and act as active sites for catalysis, 5 which explains experiments showing that increasing trap density can dramatically increase overall photocatalytic performance. 6 The density of various types of trap states can be controlled by material synthesis and processing, 6,7 which should enable the development of materials that balance these competing effects. The most thoroughly investigated defects in TiO2 are oxygen vacancies and titanium interstitials, point defects which reduce TiO2 and produce excess electrons that occupy deep trap states ∼1 eV below the conduction band minimum (CBM). 1,2 Trap states associated with surfaces and 2 ACS Paragon Plus Environment

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interfaces are less understood, despite evidence from experiments and charge transport models suggesting that they are critical to transport and catalytic activity. 6–10 Scanning tunneling microscopy experiments have directly observed shallow traps (∼40 meV) on a clean anatase (101) surface associated with slight lattice distortion by dopants, compared with deep traps (∼1 eV) due to O vacancies. 11 Photoelectron spectroscopy experiments have also revealed shallow trap states (∼0.2 eV) in porous nanocrystalline anatase and single-crystal anatase, which were associated with edge-like features on surfaces. 12 We are not aware of direct experimental measurements of the trap states associated with interfaces between nanoparticles, although there is experimental evidence that they play an important role in charge transport. 6,13 Theoretical modeling of single truncated, bipyramidal anatase nanoparticles has predicted shallow trap states that are localized on their surfaces, although there is uncertainty in the preferred surface sites, whether near (001) facets 14 or on the equatorial plane at ridges between (101) facets. 15 To our knowledge, the work by Nunzi et al. 15 includes the only theoretical investigation of electronic structure in systems of attached nanoparticles. They concluded that joining two nanoparticles does not change the nature of trap states compared to the single particle, since they observed no significant difference in the curvature of the density of states at the CBM. These studies primarily used density functional theory within the generalized gradient approximation (GGA-DFT) and the semi-empirical density functional tight binding (DFTB) method, and the effect of level of theory on the description of these trap states in nanoparticles is also not yet clear. In modeling point defects, DFT is known to predict anomalously shallow traps due to the self-interaction error, and either a Hubbard U correction or some fraction of Hartree–Fock (HF) exchange is necessary to correctly predict deep trap states. 16 Such corrections are also necessary to model the band gap of bulk TiO2 , which DFT underpredicts. However, the magnitude of U or the fraction of HF exchange is determined empirically, and no single method correctly describes both the band gap and defect states. 17 In this work, we examined the spatial and energetic distributions of electronic states in anatase nanoparticles attached in two common orientations: one pair of particles attached by their (001)



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facets and one pair attached by (101) facets. Since there is no consensus on whether including a fraction of non-local exchange is necessary to obtain a better description of surface or interfacial states in anatase, we compared Kohn-Sham (KS) orbitals and their energies predicted at three levels of theory: hybrid DFT, GGA-DFT, and DFTB. To identify orbitals localized near the interfaces, we defined a scalar localization metric and computed it for each KS orbital. We found that all three levels of theory predict that KS orbitals spatially localized to the interfaces have energies near the CBM. To our knowledge, this constitutes the first computational evidence for electronic trap states localized at interface between anatase nanoparticles. The absolute depth of the trap states was dependent on the method, with hybrid DFT predicting deep interfacial traps (∼1 eV below the CBM), while DFTB and GGA-DFT predicting shallow traps (< 0.2 eV below the CBM). Despite this difference, all three methods predicted consistently that the trap states localized at the (101) interface lay shallower in energy below the CBM and exhibited a broader distribution than those at the (001) interface.

Computational Methods DFT calculations with the B3LYP 18 and PBE 19 functionals were performed with the double-zeta, polarized def2-SV(P) basis set 20 as implemented in NWChem. 21 A comparison with the larger def2-SVP set is given in Fig. S1 (Supporting Information). DFTB 22 calculations were performed using the “ti-org” set 23 of Slater–Koster parameters as implemented in DFTB+. 24 The geometries of individual and attached particles were prepared using the anatase crystal structure as described below and optimized at the PBE and DFTB levels of theory until forces were below 4.5 × 10−4 atomic units. The optimized atomic coordinates obtained for each system are provided in the Supporting Information. Prior work has shown that comparing the predictions of the hybrid and non-hybrid functionals is important, but geometry optimizations using the B3LYP functional were not feasible on the system sizes modeled in this work. Therefore, we report three sets of electronic structure calculations: B3LYP//PBE, PBE//PBE, and DFTB//DFTB, where the usual A//B notation


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indicates orbitals obtained at the level of theory “A” using the geometry optimized at the level of theory “B”. All orbital energies are reported below with respect to the nominal valence band maximum (VBM) aligned to zero. Electronic densities of states (DOS) are reported by applying a Gaussian broadening of width 0.08 eV to the KS eigenvalues. Once the electronic structure of each system was obtained, we sought to identify the subset of electronic states localized near the interface by calculating a scalar index λ for each orbital φ , defined by

λ=

R

w(r) |φ (r)|2 dr R |φ (r)|2 dr

(1)

where w(r) is a scalar function with high weight in a region R near the interface between the particles. For each system, we defined an interfacial region R as the convex hull formed by atoms that are within 3 neighbors of the interface (i.e., within 3 neighbors of any atom that shares a bond ˚ was used to identify neighboring with an atom in the other nanoparticle). A cutoff distance of 2.1 A atoms. We then set w(r) =

   1

r ∈ R, (2)

  0

otherwise,

in which case λ ∈ [0, 1]. Thus, the interfacial overlap metric λ represents the fraction of the density of each orbital that overlaps with the interfacial region R. In Fig. S2 (Supporting Information), we report calculations of λ using a region R that encompasses atoms within two neighbors of the interface instead of three, which decreases the overall magnitude of λ but does not affect its distribution in energy. In addition to identifying localized interfacial trap states and their energies, we found it useful to distinguish them from states localized elsewhere (e.g., surface states) and to identify bulk-like delocalized states. To that end, we use the radius of gyration of the density as a simple metric of spatial delocalization δ for each orbital:

δ=

R

|r − r0 |2 |φ (r)|2 dr R |φ (r)|2 dr

1/2

,


(3)


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where R

r0 = R

r |φ (r)|2 dr |φ (r)|2 dr

is the center of density of the orbital. The values of λ and δ were calculated for the highest 200 occupied orbitals and the lowest 200 unoccupied orbitals.

Results and Discussion Single-particle models. Single particles were prepared by cleaving the tetragonal crystal structure ˚ c = 9.514 A ˚ 25 ) on (001) and (101) facets, resulting in a truncated of bulk anatase (a = 3.785 A, bipyramidal shape characteristic of anatase nanoparticles. 26 The geometric aspect ratio of single particles is governed by the thermodynamic stability of the associated surfaces. The ratio is thus dependent on particle size 7 and on synthesis and processing procedures, as has been observed in TEM images. 6,13 We chose an aspect ratio of d[001] /d[100] ∼ 1.3, which falls within the range of ∼1.0–1.5 commonly observed experimentally. 14 Limited by the computational cost of the B3LYP calculations, 27 in what follows we use nanoparticles with 70 TiO2 units to construct the interfacial systems. Each particle occupies a volume equivalent to a sphere of 1.7 nm diameter, which is 6–12 times smaller than the 10–20 nm sizes of particles in typical nanocrystalline anatase. 6,13 To test the effect of surrounding water on both the atomic and electronic structure of the model particle, we performed a geometry optimization of a single Ti70 O136 particle surrounded by 200 water molecules distributed over all ten facets, resulting in roughly one monolayer of coverage. During optimization, we observed near-instantaneous dissociation of H2 O molecules along edges of the (001) facets, resulting in the hydroxylation of 4-coordinated Ti sites as, shown in Fig. 1. The changes near (101) facets were limited to water molecules reorienting to coordinate to 5coordinated Ti sites. Therefore, in what follows, we consider model particles with hydroxylated (001) facets, but do not include explicit physisorbed water molecules on the (101) facets, similar to in other theoretical work. 14,15,28 Regarding the effect of surrounding water on electronic structure, we found that the projected 6 ACS Paragon Plus Environment

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the CBM+1 level, which is localized symmetrically on the opposite particle (Table S2). Orbitals computed at the PBE//PBE and DFTB//DFTB levels of theory also exhibit a manifold of occupied orbitals with predominantly O 2p character separated by a gap from a manifold of unoccupied orbitals with predominantly Ti 3d character, along with four states of Ti 3d character occupied by excess electrons within the gap below the CBM. These states also exhibit high degrees of overlap with the interfacial region, consistent with characteristics of interfacial traps. However, the energies of these trap states with respect to the CBM depend significantly on the level of theory. Selected orbitals at the PBE and DFTB levels of theory are given in Tables S4 and S5 (Supporting Information). The DOS curves as well as λ and δ values computed at the three levels of theory for particles attached on (001) faces are summarized in Fig. 4. As discussed above, the B3LYP calculations (Fig. 4, bottom panel) predict well-separated manifolds (4.0 eV) of valence and conduction states with relatively low overlap with the interfacial region (small λ values) and moderately delocalized character (large δ values). The first two states occupied by the excess electrons are clearly identifiable by their large overlap with the interface (large λ ) and high degrees of localization (small

δ values). These states are separated by ∼1.1 eV from the CBM. The other two states occupied by excess electrons have smaller overlap with the interface and slightly larger degree of delocalization. The effect of implicit solvation on the electronic structure of the system of (001)-attached particles at the B3LYP//PBE level was also tested using the COSMO model. 30 We observed a nearly uniform upward shift on the DOS, as shown in Fig. S5 (Supporting Information), which is consistent with the results of the explicit solvation of the single particle. The PBE calculations (Fig. 4, center panel) predict more narrowly separated (2.4 eV) manifolds of valence and conduction bands with spatial characteristics similar to B3LYP. The first two states occupied by the excess electrons are again clearly identifiable by their large overlap with the interface and strong degree of localization. These states are however separated by only ∼0.2 eV from the CBM, five times closer than the separation predicted by B3LYP. Because of the smaller separation, the other two states occupied by the excess electrons are nearly overlapping in energies




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Table 2: Orbital energies with respect to the VBM and values of λ for the four states occupied by excess electrons and two lowest unoccupied states for (001) and (101) interfaces.

Orbital type

Trap

Conduction

Trap

Conduction

B3LYP ε, λ 2.87 eV, 3.00 eV, 3.11 eV, 3.15 eV, 4.01 eV, 4.01 eV, 3.26 eV, 3.34 eV, 3.43 eV, 3.50 eV, 3.81 eV, 3.89 eV,

PBE ε, λ

(001) interface 0.93 2.11 eV, 0.98 2.21 eV, 0.49 2.25 eV, 0.55 2.28 eV, 0.07 2.34 eV, 0.06 2.35 eV, (101) interface 0.60 2.20 eV, 0.35 2.23 eV, 0.21 2.30 eV, 0.14 2.35 eV, 0.26 2.36 eV, 0.29 2.37 eV,

DFTB ε, λ 0.91 0.96 0.46 0.54 0.07 0.07

2.75 eV, 2.79 eV, 2.99 eV, 2.99 eV, 3.00 eV, 3.00 eV,

0.91 0.91 0.61 0.15 0.05 0.48

0.33 0.32 0.37 0.23 0.14 0.29

2.97 eV, 2.98 eV, 3.00 eV, 3.00 eV, 3.01 eV, 3.02 eV,

0.43 0.28 0.12 0.08 0.29 0.40

exhibit a broader distribution than those at the (001) interface. Furthermore, the states that are most strongly localized at the (101) interface are not necessarily the lowest-lying states in the Ti d manifold. As a result, the excess electrons in the (101) system do not necessarily occupy the localized interfacial states. This observation is common across the three levels of theory used here, even for DFTB and PBE calculations which showed little difference in the total DOS between the two systems. Although the two systems are formed from the same two anatase nanoparticles, the difference in interface orientation produces trap states of different character.

Conclusions We have obtained the optimized geometry and electronic structure of systems of attached nanoparticle, and we have found spatially localized states with energies near the CB edge that correspond qualitatively to trap states observed experimentally in porous nanocrystalline anatase. 12 The physical orientation of the interface was found to have significant effects on the depth and distribution 14 ACS Paragon Plus Environment

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of the associated trap states. The trap states localized at a (001)/(001) interface between anatase nanoparticles fell deeper in energy than the trap states localized at a (101)/(101) interface between the same two particles. In addition, the states localized at a (101)/(101) interface exhibit a broader distribution in energy. Excess electrons therefore tended strongly to occupy interfacial traps between the (001)-attached particles, but not necessarily those between the (101)-attached particles. The calculations were performed using three levels of theory: hybrid DFT using the B3LYP functional, GGA-DFT using the PBE functional, and DFTB. The effects of the interfacial orientation on the depth and distribution of the trap states were consistent at all levels of theory. The method did affect the depth of the predicted trap states in the same manner found in prior modeling of point defects; namely, DFTB and GGA-DFT predict that the traps are shallow (∼0.2 eV), while hybrid DFT predicts deep traps (∼1.1 eV). However, contrary to the case of deep traps associated with oxygen vacancies, 16 experimental measurements suggest that the traps associated with surface and edge sites are shallow, 12 in which case DFTB and GGA-DFT provide a better description of these states than hybrid DFT. These results suggest that electronic transitions in these interfacial systems would be very useful to investigate using DFT and time-dependent DFT, as has been done recently in single anatase clusters 32 and nanoparticles. 28,31 The combination of spatial and energetic information about interfacial states would be useful as input to Monte Carlo simulations of transport in nanocrystalline anatase, 3,33 which to date have depended on empirical measurements or assumed forms of the distribution of trap states. In light of experiments demonstrating the ability to control preferential oriented attachment of (001) facets vs. (101) facets, 8 the present results could also have useful implications for the development of porous networks of nanocrystalline anatase, whose photocatalytic performance has been shown to be very sensitive to the details of the inter-particle interfaces. 6 It would thus be useful in future work to more thoroughly investigate the connection between interface geometry and trap state depth and distribution by modeling a range of particle sizes, particle aspect ratios, and interface orientations.



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Acknowledgments The authors thank J. J. Pietron, P. A. DeSario, L. D. Gunlycke, and S. A. Fischer for their discussions. The authors thank anonymous reviewers for constructive comments and suggestions that were instrumental in revising the manuscript. This work was supported by the U.S. Naval Research Laboratory (NRL) via the National Research Council (NRC) and by the Office of Naval Research, both directly and through NRL. N.Q.L. is grateful for support from the NRC Research Associateship Program.

Supporting Information Comparison of basis sets, values of λ calculated with an alternate definition of R, electronic states of the single particle, effects of particle size, additional electronic states of interfacial systems, values of δ for (101) interfaces, and atomic coordinates of optimized geometries.

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Modeling Electronic Trap States at Interfaces between Anatase

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