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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Grain Boundary Facilitates Photocatalytic Reaction in Rutile TiO2 Despite Fast Charge Recombination: A Time-Domain Ab Initio Analysis Yaqing Wei, Zhaohui Zhou, Weihai Fang, and Run Long J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b02761 • Publication Date (Web): 24 Sep 2018 Downloaded from http://pubs.acs.org on September 24, 2018

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The Journal of Physical Chemistry Letters

Grain Boundary Facilitates Photocatalytic Reaction in Rutile TiO2 Despite Fast Charge Recombination: A Time-Domain Ab Initio Analysis Yaqing Wei,1 Zhaohui Zhou,2 Wei-Hai Fang,1 Run Long1* 1

College of Chemistry, Key Laboratory of Theoretical & Computational

Photochemistry of Ministry of Education, Beijing Normal University, Beijing, 100875, P. R. China 2

Chemical Engineering and Technology, School of Environmental Science and

Engineering, and Key Laboratory of Subsurface Hydrology and Ecological Effects in Arid Region, Ministry of Education, Chang’an University, Xi’an 710064, China ABSTRACT: TiO2 is an excellent photocatalytic and photovoltaic material but suffers low efficiency because of deep trap states giving rise to fast charge and energy losses. Using a combination of time-domain density functional theory and nonadiabatic molecular dynamics, we demonstrate that grain boundaries (GBs), which are common in polycrystalline TiO2, accelerate nonradiative electron-hole recombination by a factor of 3. Despite GBs increase the band gap without creating deep trap states, and accelerate coherence loss, they enhance nonadiabatic electron-phonon coupling, and facilitate the relaxation. Importantly, electrons accumulated at the boundaries together with the relatively long-lived excite state *

Corresponding Author Email: [email protected] 1

ACS Paragon Plus Environment

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favor photocatalytic reaction. Our study rationalizes the experimental observations and provides valuable perspectives for improving the device performance by defect engineering.

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TOC only

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Stimulated by the increasing concerns for environmental pollutions and energy crisis, the use of metal oxides as photocatalysts and photovoltaics has been considerably investigated in the past few decades.1,

2

Photocatalysis is capable of

utilization of sunlight for the decomposition of organic contaminants and degradation of pollutants,3 for the production of hydrogen via driving water splitting,4 and the direct conversion of solar energy to electric power via photoelectric effect.5 Due to its abundance, nontoxicity, and high stability under a variety of conditions, titanium dioxide (TiO2) is the most widely used photocatalysts and photovoltaics since its discovery of generating solar fuel in 1972.6 Among the three (rutile, anatase, and brookite) natural polymorphs of TiO2, rutile is the most stable phase7 whose band gap is about 3 eV,8 which constitutes a major factor to limit the efficiencies of photocatalysts and photovoltaics because pristine rutile can only absorb ultraviolet light in the solar spectrum. In addition, the photogenerated electrons and holes can be easily quenched through electron-hole recombination due to the present of a variety of defects in the polycrystalline material, which forms another obstacle for the low efficiencies. To enhance light harvesting, either composites of TiO2 with other smaller band gap photoactive materials9, 10 or introduction of dopants11 into TiO2 can partially achieve this goal. Both strategies suffer different issues that either requires perfect interface formed between two materials to lower interfacial defects concentration, or experiences dopant-mediated electron-hole recombination and prevents from practical applications. It is evident that the limitation of both methods is directly related to the fate of photogenerated charge carrier inside the TiO2. It is reasonable because in all of 4


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these applications, nonradiative charge and energy losses in TiO2 always play a significantly important role. The nonradiative recombination of photogenerated carriers with the excess electronic energy is unavoidably dissipated into heat12 and also shorten of the service life for the device. Thus, a longer excited carrier lifetime is favorable for achieving a better performance of the aforementioned devices. Over the past few decades, tremendous time-resolved ultrafast spectroscopy experiments have been performed to detect the photoexcited carrier dynamics of rutile TiO2. The measured electron-hole recombination timescales by different groups vary notably, ranging from picoseconds to microseconds.13-17 Yamada et al. reported a carrier lifetime of about 5 ns in single rutile crystals using the time-resolved photoluminescence spectroscopy.14 Shortly after, the same group reported a longer excited states lifetime in rutile single crystal using the transient absorption and photoconductivity spectroscopy.15 Woll and coworkers suggested that the decay of excited states in rutile occurs within 1 ns, showing about an order of magnitude smaller than that of anatase.16 Li and coworkers also reported a similar electron-hole recombination time scale in rutile TiO2 of less than 1 ns due to charge trap filling.17 These rather complicated situations could be ascribed to bulk defects, impurities, size or surface effects. In addition to these usual defects, grain boundaries (GBs) inevitably exist in the polycrystalline TiO2 and have significant effect on the electronic properties.18, 19 Unlike GBs creating deep trap states in transition metal dichalcogenides, such as MoS2, which form deep charge trap states and accelerates

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charge recombination significantly.20 Experiments correlated with theoretical simulations illustrated that GBs do not generate deep trap states in the band gap of rutile TiO2.21 Bak et al. reported that the concentration of electrons locating in the GBs is larger than that in the bulk phase of polycrystalline rutile, causing influence on charge transport and reactivity.22, 23 Wallace and McKenna demonstrated that GBs in rutile TiO2 reduce electron mobility by several orders of magnitude due to enhanced electron trapping at boundaries.24 However, Masayuki Kamei suggested that GBs localized chare at the boundaries and were beneficial for photocatalytic reaction of bicrystalline TiO2.25 It is evident that detailed nonradiative charge recombination dynamics in rutile TiO2 containing GBs following ultrafast photoexcitation remains poorly understood. One of the main reasons for this lack of understanding is that, in most cases, there exist many of photoinduced dynamics processes that can be mixed. Experiments alone is difficult to interpret quantitatively the measured data. Furthermore, the role and exact nature of GBs are tightly depending on materials.26-28 We have shown that GBs notably accelerates charge recombination in hybrid inorganic-organic perovskite27 while which significantly suppresses the energy losses in monolayer black phosphorous.28 Thus, it is of great importance to understand the influence of GBs on the decay of excited state in the rutile TiO2 at the atomistic level to explore how this geometry disorder affects the charge recombination dynamics and further the performance of photocatalysts and photovoltaics. To address this issue, a time-domain density functional study of nonradiative electron-hole recombination in rutile TiO2 containing GBs is needed. 6


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Motivated by the recent experimental works,14, 15, 19 we report a time-domain density functional theory (TD-DFT) combined with nonadiabatic molecular dynamics (NAMD) study of the nonradiative electron-hole recombination in rutile TiO2 with and without GBs. The simulations reproduce the electron-hole recombination timescales in rutile TiO2 reported experimentally,14, 15 and establish the factors of GBs accelerating charge recombination. GBs accelerate electron-hole recombination and shorten excited state lifetime for several reasons. GBs increase the NA electron-phonon coupling between the conduction band minimum (CBM) and the valence band maximum (VBM). The coupling is enhanced mostly because the CBM is localized at the GB and significantly depends on the nuclear displacement arising from crystal symmetry breaking, giving rise to increased nuclear motion. Rutile TiO2 containing GBs mildly increases the band gap by 0.2 eV without introducing any deep trap states, showing good agreement with previous theoretical studies.21 The decay of quantum coherence between the CBM and VBM changes slightly due to the lack of introduction of foreign light atoms into the lattice. The enhanced NA coupling competes successfully with the increased band gap and shortened decoherence time, and constitutes the major factor for determining the charge recombination rate and as a result of accelerated charge recombination. More importantly, the electron accumulated at boundaries together with the relatively long-lived excited state lifetime, favor photocatalytic reaction.22 Overall, the excited state lifetimes are long, because the NA coupling is small, about sub-1 meV, and the time of quantum coherence between the initial and final states is short, about sub-4fs. 7



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The NAMD simulations employ the quantum-classical decoherence induced surface hopping (DISH) approach29 implemented within the framework of time-dependent Kohn-Sham theory.30 DISH is derived from surface hopping approach31 that treats nuclear degrees of freedom classically and electronic degrees of freedom quantum mechanically. DISH brings the quantum decoherence into the quantum-classical approximation, capturing the physical nature of nuclear wave function branching for surface hops.29, 32 Decoherence is included in the calculation because it occurs significantly faster than the electron-hole recombination.33 The classical path approximation (CPA) is used to save the computational cost.34 CPA is valid when the changes in the nuclear geometry upon photo-excitation are negligible compared with the amplitude of the thermally induced nuclear fluctuations. The simulation cells of rutile used here are rigid and large, satisfying with the applicable conditions of CPA. The state-of-the-art real-time NAMD approach has been applied to study photoinduced charge dynamics in a broad range of systems,27, 35-41 including black phosphorus,27 TiO2 sensitized by MoS235 and quantum dots (QD),36 TiO2 nanotube,37 a polymer interfaced with QD,38 as well as TiO2/perovskite,39 high-temperature cuprite superconductors40 and TiS3 nanoribbons.41 Geometry optimization, adiabatic MD, and NA coupling calculations are carried out using the Vienna ab initio simulation package (VASP).42 The electron exchange and correlation interactions are treated with the Perdew-Burke-Ernzerhof (PBE) functional.43

The

electron

and

ion

cores

interaction

8


are

described

by

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projector-augmented wave pseudopotentials.44 To correct the self-interaction error and approach band gap of rutile with experiment,45 the DFT+U method is adopted with the on-site U = 4.2 eV applied to the Ti 3d electrons.46 The energy cutoff of plane-wave basis is set to 400 eV. The geometry optimization is performed with the Γ point while a much denser Monkhorst-Pack grid of 1 × 3× 5 Γ-centered k-point is used for density of states calculation.47 The adiabatic MD and NAMD simulations are carried out at the Γ point, which gives the direct band gap of both the studied systems. The band structure of the two systems are shown in Figure S1 of the Supporting Information. After relaxing the geometry at 0 K, the temperatures of the two systems were brought to 300 K using repeated velocity rescaling. Then, two ps adiabatic MD trajectories are generated in the microcanonical ensemble with a 1 fs atomic time-step. To simulate the electron-hole recombination, 500 initial conditions are selected randomly from the adiabatic MD trajectories for the NAMD simulations of electron-hole recombination using the PYXAID code.34 A detailed description of the theoretical approach can be found elsewhere.34, 48 The rutile TiO2 with the optimized lattice constant of a=b= 4.60 Å and c=2.96 Å has been used to create both the (10 × 2 × 2) 240-atom supercell (Figure 1a) and the Σ5 (210) GB containing 240 atoms (Figure 1b), in order to eliminate the size effect on the dynamics. The GB system contains two identical Σ=5 tilt boundaries and which are symmetrically equivalent, relating each other by inversion symmetry. The deformation of geometric structure reflects the nuclei coupling to the electronic

9



degrees of freedom. In particular, thermal fluctuations at room temperature may affect the structure, we present both the geometries optimized at 0 K and averaged geometry of the overall MD trajectory at 300 K, Figure 1. The geometries of the pristine rutile TiO2 change little upon heating, because they preserve crystal symmetry in the presence of strong perfect bulk Ti-O covalent bonds, Figure 1a. The averaged Ti-O bond length lengthens slightly from 1.966 Å at 0 K to the canonically averaged value of 1.977 Å at 300 K. While in the GBs contained system (Figure 1b), the Ti atoms remain largely unchanged, and the large changes are associated with the significant displacements of the O atoms out of the equilibrium sites, in particular for the O atoms at the boundaries, because the GBs break the symmetry, introduce notable strain and distort the geometry. Furthermore, the right panel of Figure 1b clearly displays that some of Ti-O bonds are broken and some of new Ti-O bonds are formed at the boundaries at 300 K, giving rise to large atomic fluctuations and enhanced NA electron-phonon coupling relative to the pristine system. Here in the optimized GB geometry at 0 K, the averaged Ti-O bond length is 1.997 Å while it increases to 2.003 Å in the canonically averaged geometry, separated the contributions from the averaged Ti-O bond lengths of 1.993 Å in bulk regime and 2.023 Å at boundaries, respectively.

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Figure 1. Simulation cell showing the geometry at 0 K (left panel) and 300 K (right panel) of (a) 240-atom (10 × 2 × 2) pristine rutile supercell, (b) 240-atom Σ5 (210) [001] tilt grain boundary (GB). Because nuclear dynamics creates the NA electron-phonon coupling for nonradiative electron-phonon recombination, we investigate the geometry fluctuations further. In addition to the average bond lengths reported here, we compute the ensemble-averaged standard deviation of the position of each atom i in the pristine and GB-contained rutile at room temperature. The algorithm used here is expressed as 〈 〈 〉 〉. Here, represents the location of atom i at time t along the 2 ps MD trajectories, and the angular bracket represents the ensemble averaging over time. Then, we average the standard deviations over all Ti and O atoms in both systems. Generally, larger standard deviation represents greater atomic fluctuation. As shown in Table 1, the overall standard deviation decreases from 0.151 in the pristine system to 0.186 in the system with GBs, promoting the entire atoms’ fluctuation by 23%. The atomic fluctuations are enhanced because the GBs relax the symmetry and induce local strain, reflecting by the standard deviations of GBs’ atoms and those in the bulk region: 0.189 vs 0.185. Thus, both bond lengths and atomic fluctuation 11



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analyses indicate that GBs distort the system geometry, leading one to expect stronger electron-phonon coupling, and shorter quantum coherence time between the initial and final states. Because the two facts have opposite effect on nonradiative electron-hole recombination times and therefore relaxation dynamics necessitates explicit simulations. Table 1. Standard deviations of the atomic position in the pristine and GB-contained systems. Overall

Atoms around the GB/rest

Pristine

0.151

-

GB

0.186

0.189/0.185

Figure 2 presents the local density of states (LDOS) of the pristine rutile and GB-contained system calculated using the optimized structure. The LDOS of the pristine rutile TiO2 is separated into the contributions from Ti and O atoms (Figure 2a). It shows that the VBM is composed primarily by O atoms, while the CBM originates mostly from Ti atoms. The charge densities shown in Figure 3 confirms this observation. The calculated band gap increases from 1.98 eV in the pristine TiO2 to 2.20 eV in the system GBs, Interestingly, GBs avoid deep electron trap states (Figure 2b), showing an good agreement with previous DFT calculations.49 These electronic energies are dissipated into lattice during electron-hole recombination. Figure 2b demonstrates that the side GBs atoms contribute significantly to the CBM whereas 12


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bulk atoms devote to the VBM.

Figure 2. The local density of states (LDOS) of (a) the pristine rutile and (b) Σ5 (210) GB, obtained using optimized geometries with the PBE+U approach. The LDOS of the pristine rutile shows that the VBM is primarily formed by O orbitals and CBM is mainly composed of Ti orbitals. GBs increase band gap without introducing any deep trap states. The boundaries atoms contribute notably to the CBM. Zero energy is set to the Fermi level.

The CBM and VBM constitute the initial and final states for the electron-hole recombination because the photoexcitation charge carriers can rapidly relax to the band edge states within (sub)picosecond timescales before recombination. The mixing of VBM and CBM wave functions is directly reflecting the strength of electron-phonon coupling. Figure 3 presents the chare densities of the VBM and CBM 13



in the two systems. Figure 3a shows that the VBM and CBM are primarily localized on the oxygen atoms and titanium atoms, respectively. The conclusion is in consistent with the analysis of LDOS (Figure 2a). The CBM of the Σ5 (210) GB is entirely localized on the side GB titanium atoms, while the VBM is localized on the oxygen atoms of the left-hand side bulk region, also agreeing well with the LDOS shown in Figure 2b. By watching the VBM/CBM overlap, one may expect that the NA coupling is larger for the pristine system than for the GB system. However, this is not true, Table 2, because the NA coupling is determining by both the matrix element -iħ⟨ϕj│∇R│ϕk ⟩, and the nuclear velocity dR/dt, it is larger in the system with GBs due to larger atomic fluctuations, Table 1.

Figure 3. VBM and CBM charge density in (a) pristine rutile and (b) Σ5 (210) GB. The charge density of the VBM and CBM are delocalized on the overall O and Ti atoms in the pristine rutile, whereas VBM and CBM localize on O and Ti atoms and in the vicinity of GBs in the Σ5 (210) GB system. In addition to band gap and NA electron-phonon coupling, electronic decoherence time, known as the pure-dephasing time in the optical response theory,50 also influences nonradiative electron-hole recombination times. It can be calculated 14


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using the second order cumulant approximation to the pure-dephasing function. The pure-dephasing functions of two systems are shown in Figure 4. The times of pure-dephasing, , obtained by fitting the data with Gaussian: 0.5/

, are summarized in Table 2. The pure-dephasing times are very short, 3.7 fs for the pristine system and 3.4 fs for the GBs system. The small reduction of pure dephasing time in system with GBs stems from the larger amplitude of atomic fluctuation, Table 1. As exemplified by the quantum Zeno effect,51 shorter coherence leads to slower quantum dynamics. To gain further the origin of the difference in pure-dephasing time scales in the two systems, we computed the unnormalized autocorrelation functions (un-ACF) of the fluctuations of the VBM-CBM energy gaps, inset of Figure 4. Under the cumulant approximation, the dephasing function is computed by integrating un-ACF. Generally, the greater initial value, slower and more asymmetric decay of the un-ACF favor faster dephasing.34 Here, the un-ACFs of the both systems show similar oscillations. The initial value of un-ACF for the system with GBs is larger than that of the pristine system, leading to a faster dephasing process for the band gap transition in the system with GBs.

15



Figure 4. Pure-dephasing function computed using the unnormalized autocorrelation function (un-ACF) of the fluctuations of the VBM-CBM energy gap. The inset shows the un-ACF. Larger initial value leads to faster dephasing process.

Figure 5 shows the evolution of the population of the CBM in the pristine rutile and GB-contained system. The electron-hole recombination times summarized in Table 2 are obtained by fitting the data with an exponential function:

exp / . The calculated electron-hole recombination time of 12.7 ns for the pristine rutile TiO2 agrees well with the data reported experimentally.15 Such slowly nonradiative electron-hole recombination facilitates to achieve high photocatalytic and photovoltaic efficiencies. Introduction of GBs into the pristine rutile TiO2 notably accelerates the electron-hole recombination by a factor of 3, achieving 3.9 ns excited state lifetime. The lifetime is longer than the most systems we studied, including TiO2 sensitized by MoS235 and PbSe QD,36 MoS2/MoSe2 junctions,27 etc., together with the 16


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localized electrons at boundaries, suggesting that rutile TiO2 contained GBs favor photocatalytic reaction.25

Figure 5. Electron-hole recombination dynamics of pristine and GB contained rutile. The observed change in electron-hole recombination upon GBs formation can be rationalized by the band gap, the strength of the NA electron-phonon coupling and the pure-dephasing time, Table 2. GBs shorten dephasing time and increase the band gap, favoring to slow charge recombination. Generally, quantum transition is fast if coupling is strong. In the present work, the amplitude of NA electron-phonon coupling constitutes the primary factor to affect the nonradiative electron-hole recombination dynamics, rationalizing the acceleration in charge recombination of system with GBs compared to the pristine rutile TiO2. These results suggest that the 17



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GBs in rutile TiO2 should be modulated or engineered with great caution, intentionally doping for example, to retard the electron-hole recombination further for photovoltaic or photocatalytic applications.

Table 2. Band gap, Pure-Dephasing Time, Average absolute NA coupling, Nonradiative electron-hole recombination Time for pristine and GB contained rutile system. Bandgap (eV)

Dephasing (fs)

NA coupling (meV)

Recombination (ns)

Pristine

1.98

3.7

0.45

12.7

GB

2.20

3.4

0.83

3.90

By performing ab initio time-domain simulations, we investigated the nonradiative electron-hole recombination in pristine rutile TiO2 with and without grain boundaries. The recombination constitutes a main route for charge and energy losses in the TiO2-based photocatalysts and photovoltaics, in particular limiting the device efficiency. The simulations demonstrate that grain boundaries accelerate moderately electron-hole recombination. The obtained results are rationalized at the atomistic level by the changes in the band gap, dephasing time, and electron-phonon coupling. Grain boundaries decrease mildly the dephasing time and increase moderately the band gap that are beneficial for slowing recombination down. At the same time, the boundaries break the system symmetry, induce large atomic fluctuations, and enhance the electron-phonon coupling, thereby accelerating the 18


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nonradiative electron-hole recombination. The enhanced coupling competes successfully with the reduced dephasing time and increased band gap, giving rise to fast charge loss. The relatively long-lived excited state lifetime and localized electron at the boundaries facilitates photocatalytic reaction. The study demonstrates that the grain boundaries play a key role in the nonradiative electron-hole recombination, and suggest the deep reasons responsible for the experimentally reported enhanced photocatalytic efficiency in polycrystalline TiO2.

ACKNOWLEDGEMENTS This work was supported by the National Science Foundation of China (Grant Nos. 51861135101, 21573022 to R. L. and 21520102005, 21421003 to W. -H F.). R. L. is grateful to the Fundamental Research Funds for the Central Universities, the Recruitment Program of Global Youth Experts of China, and the Beijing Normal University Startup Package. Z.H. Z. acknowledges the Fundamental Research Funds for the Central Universities from Chang’an University (300102298106).

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