1
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Yang Y, Zhang Y, Fernandez-Alberti S, Long R. Resolving the Puzzle of Charge Carrier Lifetime in ZnO by Revisiting the Role of Oxygen Vacancy. J Phys Chem Lett 2024; 15:1-8. [PMID: 38126721 DOI: 10.1021/acs.jpclett.3c03195] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2023]
Abstract
Zinc oxide (ZnO) is a wide bandgap prototypical n-type semiconductor due to the presence of intrinsic oxygen vacancies (VO). The VO can readily transfer to the most energetically favorable +2 charged VO (VO2+) by losing two electrons mediated by the metastable VO1+ defect. Nevertheless, the influence of charged VO on the charge dynamics in ZnO and the underlying mechanisms remain elusive. By performing nonadiabatic molecular dynamics simulations of the charge trapping and recombination processes, we show that both VO1+ and VO2+ slow down the nonradiative electron-hole recombination via assisted defect states and, thus, extending charge carrier lifetime compared to pristine ZnO. Our study contributes to identifying the different recombination pathways that take place in VO1+ and VO2+ of n-type ZnO systems, providing useful guidance for designing high-performance ZnO-based devices.
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Affiliation(s)
- Yating Yang
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing 100875, P. R. China
- Department of Radiochemistry, China Institute of Atomic Energy, Beijing 102413, P. R. China
| | - Yitong Zhang
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing 100875, P. R. China
| | | | - Run Long
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing 100875, P. R. China
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2
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Narindri Rara Winayu B, Weng WC, Chu H. Introduction of Fe on rGO/TiO2 improves styrene visible light-driven photocatalytic oxidation: Characterization, stability, kinetics, and mechanism. J Photochem Photobiol A Chem 2023. [DOI: 10.1016/j.jphotochem.2023.114613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2023]
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3
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Uner D, Yilmaz B. Elucidating the role of adsorption during artificial photosynthesis: H 2O and CO 2 adsorption isotherms over TiO 2 reveal thermal effects under UV illumination. PHOTOSYNTHESIS RESEARCH 2022; 154:353-367. [PMID: 35687276 DOI: 10.1007/s11120-022-00924-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2022] [Accepted: 05/09/2022] [Indexed: 06/15/2023]
Abstract
Adsorption measurements of CO2 and H2O over TiO2 surfaces in dark and under illumination were carried out to reveal the ensuing bottlenecks of the initial steps of the artificial photosynthesis reaction. When the adsorption isotherms of both CO2 and H2O were measured under illumination, the results were comparable to isotherms measured at higher temperatures in dark. This evidence is interpreted as the presence of hot spots, due to charge carrier recombination reactions. Differential heat of adsorption measurements revealed that H2O adsorption on TiO2 is stronger, and with a higher coverage than that of CO2. Dissociation of water is an energetically uphill reaction, and the local hot spots due to charge carrier recombination in indirect bandgap semiconductors can enhance the reaction probability. At higher temperatures, higher reaction probabilities are expected and estimated by a thermodynamic analysis for water splitting reaction. The potential role of these hot spots during natural and artificial photosynthetic reactions is discussed.
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Affiliation(s)
- Deniz Uner
- Department of Chemical Engineering, Faculty of Engineering, Middle East Technical University, Ankara, Turkey.
| | - Begum Yilmaz
- Department of Chemical Engineering, Faculty of Engineering, Middle East Technical University, Ankara, Turkey
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4
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Cheng C, Zhu Y, Fang WH, Long R, Prezhdo OV. CO Adsorbate Promotes Polaron Photoactivity on the Reduced Rutile TiO 2(110) Surface. JACS AU 2022; 2:234-245. [PMID: 35098240 PMCID: PMC8790733 DOI: 10.1021/jacsau.1c00508] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/09/2021] [Indexed: 06/14/2023]
Abstract
Polarons play a major role in determining the chemical properties of transition-metal oxides. Recent experiments show that adsorbates can attract inner polarons to surface sites. These findings require an atomistic understanding of the adsorbate influence on polaron dynamics and lifetime. We consider reduced rutile TiO2(110) with an oxygen vacancy as a prototypical surface and a CO molecule as a classic probe and perform ab initio adiabatic molecular dynamics, time-domain density functional theory, and nonadiabatic molecular dynamics simulations. The simulations show that subsurface polarons have little influence on CO adsorption and CO can desorb easily. On the contrary, surface polarons strongly enhance CO adsorption. At the same time, the adsorbed CO attracts polarons to the surface, allowing them to participate in catalytic processes with CO. The CO interaction with polarons changes their orbital origin, suppresses polaron hopping, and stabilizes them at surface sites. Partial delocalization of polarons onto CO decouples them from free holes, decreasing the nonadiabatic coupling and shortening the quantum coherence time, thereby reducing charge recombination. The calculations demonstrate that CO prefers to adsorb at the next-nearest-neighbor five-coordinated Ti3+ surface electron polaron sites. The reported results provide a fundamental understanding of the influence of electron polarons on the initial stage of reactant adsorption and the effect of the adsorbate-polaron interaction on the polaron dynamics and lifetime. The study demonstrates how charge and polaron properties can be controlled by adsorbed species, allowing one to design high-performance transition-metal oxide catalysts.
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Affiliation(s)
- Cheng Cheng
- College
of Chemistry, Key Laboratory of Theoretical and Computational Photochemistry
of Ministry of Education, Beijing Normal
University, Beijing 100875, P.R. China
| | - Yonghao Zhu
- College
of Chemistry, Key Laboratory of Theoretical and Computational Photochemistry
of Ministry of Education, Beijing Normal
University, Beijing 100875, P.R. China
| | - Wei-Hai Fang
- College
of Chemistry, Key Laboratory of Theoretical and Computational Photochemistry
of Ministry of Education, Beijing Normal
University, Beijing 100875, P.R. China
| | - Run Long
- College
of Chemistry, Key Laboratory of Theoretical and Computational Photochemistry
of Ministry of Education, Beijing Normal
University, Beijing 100875, P.R. China
| | - Oleg V. Prezhdo
- Department
of Chemistry, University of Southern California, Los Angeles, California 90089, United States
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5
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Cheng C, Fang WH, Long R, Prezhdo OV. Water Splitting with a Single-Atom Cu/TiO 2 Photocatalyst: Atomistic Origin of High Efficiency and Proposed Enhancement by Spin Selection. JACS AU 2021; 1:550-559. [PMID: 34467318 PMCID: PMC8395698 DOI: 10.1021/jacsau.1c00004] [Citation(s) in RCA: 43] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2021] [Indexed: 05/26/2023]
Abstract
Anatase TiO2 is an intensely investigated photocatalytic material due to its abundance and chemical stability. However, it suffers from weak light harvesting and low photocatalytic efficiency. Experiments show that light absorption and photocatalytic properties can be enhanced simultaneously by TiO2 doping with well-dispersed Cu atoms, forming a single-atom catalyst (Cu/TiO2) that can be used for solar water splitting and other applications. By performing ab initio nonadiabatic molecular dynamics simulations, we demonstrate that Cu/TiO2 is inactive before light irradiation due to rapid electron-hole recombination via both shallow and deep traps. Surprisingly, the shallow trap is more detrimental to the Cu/TiO2 performance than the deep trap because it couples better to free carriers. After light irradiation, leading to electron transfer and Cu/TiO2 protonation, the shallow trap is eliminated, and a local distortion around the Cu atom stabilizes the deep trap state on the Cu d-orbital, decoupling it from free charges and giving rise to high photocatalytic hydrogen generation activity. We further demonstrate that the photocatalytic performance of Cu/TiO2 can be enhanced by spin selection, achievable experimentally via optical intersite spin transfer or chiral semiconductor coating. Both H adsorption and spin selection enhance charge carrier lifetimes by an order of magnitude. The spin selection mechanism does not require formation of the H species, which necessitates concurrent sources of electrons and protons and which is intrinsically unstable because water splitting involves frequent proton shuffling. Our results rationalize the experimental observations at the atomistic level, provide mechanistic insights into operation of single atom photocatalysis, and demonstrate that spin selection can be used to develop advanced and efficient systems for solar energy conversion.
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Affiliation(s)
- Cheng Cheng
- College
of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry
of Ministry of Education, Beijing Normal
University, Beijing 100875, P.R. China
| | - Wei-Hai Fang
- College
of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry
of Ministry of Education, Beijing Normal
University, Beijing 100875, P.R. China
| | - Run Long
- College
of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry
of Ministry of Education, Beijing Normal
University, Beijing 100875, P.R. China
| | - Oleg V. Prezhdo
- Department
of Chemistry, University of Southern California, Los Angeles, California 90089, United States
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6
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Cheng C, Fang Q, Fernandez-Alberti S, Long R. Controlling Charge Carrier Trapping and Recombination in BiVO 4 with the Oxygen Vacancy Oxidation State. J Phys Chem Lett 2021; 12:3514-3521. [PMID: 33793248 DOI: 10.1021/acs.jpclett.1c00713] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The lack of an in-depth understanding of the intrinsic oxygen vacancy (OV) defect properties in the photoanode BiVO4 limits the further improvement of its photoelectrochemical water splitting performance. To address this issue, nonadiabatic molecular dynamics simulations are performed to study the impact of OV on charge carrier lifetimes in BiVO4. The simulations show that a neutral OV gives rise to local structural distortions due to the formation of V-O-V bonds, forcing the electrons trapped on the nearer of the two V atoms to form two deep polaron-like V4+ hole traps. These localized midgap states greatly accelerate nonradiative electron-hole recombination compared to that of pristine BiVO4, reaching a time scale of several nanoseconds in good agreement with experiments. The ionized OV state restores the bandgap to its value in pristine BiVO4 and restores the charge carrier lifetimes due to the fast loss of coherence time. Our study reveals the mechanism of the detrimental role of OV in BiVO4 and provides valuable insights for improving the performance of the BiVO4 photoanode by ionizing the oxygen vacancy.
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Affiliation(s)
- Cheng Cheng
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing 100875, P. R. China
| | - Qiu Fang
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing 100875, P. R. China
| | - S Fernandez-Alberti
- Departamento de Ciencia y Tecnologia, Universidad Nacional de Quilmes/CONICET, B1876BXD Bernal, Argentina
| | - Run Long
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing 100875, P. R. China
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Smith B, Shakiba M, Akimov AV. Crystal Symmetry and Static Electron Correlation Greatly Accelerate Nonradiative Dynamics in Lead Halide Perovskites. J Phys Chem Lett 2021; 12:2444-2453. [PMID: 33661640 DOI: 10.1021/acs.jpclett.0c03799] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Using a recently developed many-body nonadiabatic molecular dynamics (NA-MD) framework for large condensed matter systems, we study the phonon-driven nonradiative relaxation of excess electronic excitation energy in cubic and tetragonal phases of the lead halide perovskite CsPbI3. We find that the many-body treatment of the electronic excited states significantly changes the structure of the excited states' coupling, promotes a stronger nonadiabatic coupling of states, and ultimately accelerates the relaxation dynamics relative to the single-particle description of excited states. The acceleration of the nonadiabatic dynamics correlates with the degree of configurational mixing, which is controlled by the crystal symmetry. The higher-symmetry cubic phase of CsPbI3 exhibits stronger configuration mixing than does the tetragonal phase and subsequently yields faster nonradiative dynamics. Overall, using a many-body treatment of excited states and accounting for decoherence dynamics are important for closing the gap between the computationally derived and experimentally measured nonradiative excitation energy relaxation rates.
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Affiliation(s)
- Brendan Smith
- Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States
| | - Mohammad Shakiba
- Department of Materials Science and Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
| | - Alexey V Akimov
- Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States
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8
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Ballestas-Barrientos A, Murdock AT, Liu H, Masters A, Maschmeyer T. Understanding the link between solid/liquid interfaces and photoelectrochemical activity in novel thin-film photoanodes of preferentially oriented high-index rutile TiO2 facets – A work inspired by Michel Che’s research on surface chemistry. J Catal 2020. [DOI: 10.1016/j.jcat.2020.09.028] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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9
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Wang Y, Long R. Rapid Decoherence Induced by Light Expansion Suppresses Charge Recombination in Mixed Cation Perovskites: Time-Domain ab Initio Analysis. J Phys Chem Lett 2020; 11:1601-1608. [PMID: 32017852 DOI: 10.1021/acs.jpclett.0c00139] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Using time-domain density functional theory combined with nonadiabatic molecular dynamics, we have investigated the effect of light-induced lattice expansion on the nonradiative electron-hole recombination in the mixed-cation perovskite FA0.75MA0.25PbI3. We demonstrate that charge carrier lifetime extends by a factor of 1.5 within 1% lattice expansion; the bandgap grows only by 0.04 eV; the electron-phonon coupling increases by 13%; and the decoherence time shortens by 37%. The small bandgap change has negligible influence on recombination times. Lattice expansion enhances atomic fluctuations that lead to the enhancement of electron-phonon coupling and acceleration of decoherence. By creating several high-frequency phonon modes, the lattice expansion shortens the decoherence time further. As a result, rapid decoherence beats an enhanced electron-phonon coupling, playing the dominant role in suppressing the nonradiative electron-hole recombination. The light-induced lattice expansion or strain effects provide a rational route to improve the perovskite photovoltaic and photoelectronic device performance.
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Affiliation(s)
- Yutong Wang
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education , Beijing Normal University , Beijing 100875 , P. R. China
| | - Run Long
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education , Beijing Normal University , Beijing 100875 , P. R. China
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10
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Wang Y, Long R. Anomalous Temperature-Dependent Charge Recombination in CH 3NH 3PbI 3 Perovskite: Key Roles of Charge Localization and Thermal Effect. ACS APPLIED MATERIALS & INTERFACES 2019; 11:32069-32075. [PMID: 31424190 DOI: 10.1021/acsami.9b12478] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Optimizing metal halide perovskite solar cells necessitates understanding of nonradiative electron-hole recombination because it comprises a dominant route for charge and energy losses. In principle, the electron-hole recombination rate increases as temperature grows due to enhanced electron-phonon coupling. Experiments defy this expectation in MAPbI3 (MA = CH3NH3+). By performing nonadiabatic (NA) molecular dynamics analyses combined with time-domain density functional theory simulations, we demonstrate that nonradiative electron-hole recombination in MAPbI3 at high temperature occurs more slowly than that at low temperature. First and most important, increasing temperature enhances thermal disorder and leads to significant distortion of the inorganic Pb-I framework, giving rise to electron and hole wave functions locating spatial separation and reducing NA coupling by a factor of 28% in comparison with low temperature. Second, rising temperature enhances the thermal fluctuations of both the inorganic and organic components that accelerate decoherence process by a factor of 12%. Both factors, particularly the small NA coupling, contribute to suppressing electron-hole recombination at high temperature. The simulations show excellent agreement with experiments and emphasize how the charge localization driven by thermal effects impacts electron-hole recombination in perovskites and advances our understanding of the unusual charge dynamics.
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Affiliation(s)
- Yutong Wang
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education , Beijing Normal University , Beijing , 100875 , PR China
| | - Run Long
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education , Beijing Normal University , Beijing , 100875 , PR China
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11
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Wang Y, Long R. Unravelling the Effects of Pressure-Induced Suppressed Electron-Hole Recombination in CsPbBr 3 Perovskite: Time-Domain ab Initio Analysis. J Phys Chem Lett 2019; 10:4354-4361. [PMID: 31317740 DOI: 10.1021/acs.jpclett.9b01678] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Using nonadiabatic (NA) molecular dynamics simulations, we demonstrate pressure-dependent electron-hole recombination in all-inorganic CsPbBr3 perovskite. In particular, electron-hole recombination under 1 atm takes place in several hundred picoseconds, agreeing well with experiments. An increase of pressure causes PbBr6 octahedron distortion, including contraction of both Pb-Br-Pb angles and Pb-Br bond lengths, leading to a decrease in decoherence time and NA coupling and thus slowing electron-hole recombination. When the pressure reaches a critical pressure of 1.20 GPa, a phase transition occurs in which the charge carrier lifetime is longest and extends to several nanoseconds. When the pressure is increased over the threshold, the shrinkage of Pb-Br bond length is inhibited and the contraction of Pb-Br-Pb angles primarily induced the PbBr6 octahedron distortion. Such a situation gives rise to a mild NA coupling and decoherence time, restoring the recombination time to over half of a nanosecond. Our study uncovers the mechanisms for the pressure-suppressed charge recombination and provides an advanced route toward further development of photovoltaic performance of perovskite materials.
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Affiliation(s)
- Yutong Wang
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education , Beijing Normal University , Beijing , 100875 , P.R. China
| | - Run Long
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education , Beijing Normal University , Beijing , 100875 , P.R. China
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12
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Wang Y, Fang WH, Long R, Prezhdo OV. Symmetry Breaking at MAPbI 3 Perovskite Grain Boundaries Suppresses Charge Recombination: Time-Domain ab Initio Analysis. J Phys Chem Lett 2019; 10:1617-1623. [PMID: 30892907 DOI: 10.1021/acs.jpclett.9b00763] [Citation(s) in RCA: 46] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The influence of grain boundaries (GBs) on charge carrier lifetimes in methylammonium lead triiodide perovskite (MAPbI3) remains unclear. Some experiments suggest that GBs promote rapid nonradiative decay and deteriorate device performance, while other measurements indicate that charge recombination happens primarily in non-GB regions and that GBs facilitate charge separation and collection. By combining time-domain density functional theory and nonadiabatic (NA) molecular dynamics, we demonstrate that charge separation and localization happening at MAPbI3 GBs due to symmetry breaking suppresses charge recombination. Even though GBs lower the MAPbI3 bandgap and charge localization enhances interactions with phonons, electron-hole separation decreases the NA coupling, and the excited state lifetime remains virtually unchanged compared to the pristine perovskite. Our study rationalizes how GBs can have a positive influence on perovskite optoelectronic properties and advances fundamental understanding of charge carrier dynamics in these fascinating materials.
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Affiliation(s)
- Yutong Wang
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education , Beijing Normal University , Beijing 100875 , P. R. China
| | - Wei-Hai Fang
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education , Beijing Normal University , Beijing 100875 , P. R. China
| | - Run Long
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education , Beijing Normal University , Beijing 100875 , P. R. China
| | - Oleg V Prezhdo
- Department of Chemistry , University of Southern California , Los Angeles , California 90089 , United States
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13
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Gao B, Gao P, Lu S, Lv J, Wang Y, Ma Y. Interface structure prediction via CALYPSO method. Sci Bull (Beijing) 2019; 64:301-309. [PMID: 36659593 DOI: 10.1016/j.scib.2019.02.009] [Citation(s) in RCA: 92] [Impact Index Per Article: 18.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2019] [Revised: 02/07/2019] [Accepted: 02/09/2019] [Indexed: 01/21/2023]
Abstract
The atomistic structures of solid-solid interfaces are of fundamental interests for understanding physical properties of interfacial materials. However, determination of interface structures faces a substantial challenge, both experimentally and theoretically. Here, we propose an efficient method for predicting interface structures via the generalization of our in-house developed CALYPSO method for structure prediction. We devised a lattice match toolkit that allows us to automatically search for the optimal lattice-matched superlattice for construction of the interface structures. In addition, bonding constraints (e.g., constraints on interatomic distances and coordination numbers of atoms) are imposed to generate better starting interface structures by taking advantages of the known bonding environment derived from the stable bulk phases. The interface structures evolve by following interfacially confined swarm intelligence algorithm, which is known to be efficient for exploration of potential energy surface. The method was validated by correctly predicting a number of known interface structures with only given information of two parent solids. The application of the developed method leads to prediction of two unknown grain boundary (GB) structures (r-GB and p-GB) of rutile TiO2 Σ5(2 1 0) under an O reducing atmosphere that contained Ti3+ as the result of O defects. Further calculations revealed that the intrinsic band gap of p-GB is reduced to 0.7 eV owing to substantial broadening of the Ti-3d interfacial levels from Ti3+ centers. Our results demonstrated that introduction of grain boundaries is an effective strategy to engineer the electronic properties and thus enhance the visible-light photoactivity of TiO2.
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Affiliation(s)
- Bo Gao
- State Key Laboratory of Superhard Materials & Innovation Center for Computational Physics Methods and Softwares, College of Physics, Jilin University, Changchun 130012, China
| | - Pengyue Gao
- State Key Laboratory of Superhard Materials & Innovation Center for Computational Physics Methods and Softwares, College of Physics, Jilin University, Changchun 130012, China
| | - Shaohua Lu
- State Key Laboratory of Superhard Materials & Innovation Center for Computational Physics Methods and Softwares, College of Physics, Jilin University, Changchun 130012, China
| | - Jian Lv
- State Key Laboratory of Superhard Materials & Innovation Center for Computational Physics Methods and Softwares, College of Physics, Jilin University, Changchun 130012, China
| | - Yanchao Wang
- State Key Laboratory of Superhard Materials & Innovation Center for Computational Physics Methods and Softwares, College of Physics, Jilin University, Changchun 130012, China
| | - Yanming Ma
- State Key Laboratory of Superhard Materials & Innovation Center for Computational Physics Methods and Softwares, College of Physics, Jilin University, Changchun 130012, China; International Center of Future Science, Jilin University, Changchun 130012, China.
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