Symmetry Breaking at MAPbI3 Perovskite Grain Boundaries

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Energy Conversion and Storage; Plasmonics and Optoelectronics 3

Symmetry Breaking at MAPbI Perovskite Grain Boundaries Suppresses Charge Recombination: Time-Domain Ab Initio Analysis Yutong Wang, Weihai Fang, Run Long, and Oleg V. Prezhdo J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b00763 • Publication Date (Web): 20 Mar 2019 Downloaded from http://pubs.acs.org on March 20, 2019

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The Journal of Physical Chemistry Letters

Symmetry Breaking at MAPbI3 Perovskite Grain Boundaries Suppresses Charge Recombination: Time-Domain Ab Initio Analysis

Yutong Wang,1 Wei-Hai Fang1, Run Long1, Oleg V. Prezhdo2

1College

of Chemistry, Key Laboratory of Theoretical & Computational

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

of Chemistry, University of Southern California, Los Angeles, CA 90089, USA

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 

Corresponding author, E-mail: [email protected] 1

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The Journal of Physical Chemistry Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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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Hybrid organic-inorganic halide perovskite (HOIP) solar cells have attracted great interest since the first report in 2009, with the power conversion efficiency increasing rapidly from 3.8%1 to 23.7%.2 A conventional HOIP, CH3NH3PbI3 (MAPbI3) has shown superior photovoltaic properties, including bandgap suitable for harvesting visible and near-infrared light,3 large absorption coefficient,4 large carrier diffusion length,5 high carrier mobility,6 and small exciton binding energy.7 In addition to solar cells, MAPbI3 forms the basis for lasers,8 light-emitting diodes,9 and photodetectors.10 Low-temperature solution growth provides an efficient and inexpensive route to synthesize MAPbI3. The films produced this way are typically polycrystalline,11-15 and therefore, they necessarily contain multiple grain boundaries (GBs). Experiments have produced contradictory results, suggesting that GBs can have both negative and positive effects on the charge carrier lifetimes and device performance.16 Thus, Kim et al. have reported that films with large grains show greater open‐circuit voltage than small grain films, due to reduced trap‐assisted recombination.17 Giesbrecht et al. have demonstrated that the increased MAPbI3 grain size, obtained by a new synthesis procedure, can improve the device performance due to a reduction in GBs.18 By correlating confocal fluorescence microscopy with scanning electron microscopy, de Quilettes et al. have been able to resolve spatially photoluminescence and carrier decay dynamics, illustrating that the MAPbI3 carrier lifetimes vary between different grains, and that GBs exhibit rapid nonradiative decay compared to other regions in the films.19 Our previous work20 have demonstrated that a GB can notably accelerate the nonradiative electron-hole recombination in MAPbI3, and that boundary doping by Cl 3



atoms can slow down the recombination. In order to eliminate the negative effect of GBs, interfaces and surfaces on excited-state lifetimes and device performance, several strategies have been demonstrated, involving Lewis base passivation,21 hydrogen bond interactions,22 and addition of organic dopants to mixed precursor solutions.23-26 In contrast to the reports highlighting the negative role of GBs,17-19 Zhu and coworkers have demonstrated that charge recombination happens primarily in non-GB regions of MAPbI3 thin films,27,28 arguing that GBs are benign to carrier lifetimes. Yin et al. have argued that GBs in MAPbI3 can be electrically clean.29,30 Yun et al. have used Kelvin probe force microscopy and conductive-atomic force microscopy to show that GBs facilitate charge carrier separation and collection.31 The diverse experimental evidence regarding the critical roles perovskite GBs play in the material performance strongly motivates theoretical studies into charge carrier dynamics in GB regions. Stimulated by the recent work describing both positive and negative influence of GBs on the HOIP performance,16-19,27,28,31-41 we apply time-dependent density functional theory (TDDFT) and nonadiabatic molecular dynamics (NAMD) to investigate in detail charge carrier recombination in a GB region of MAPbI3, and compare it with recombination in equivalent pristine MAPbI3. We show that MAPbI3 is sufficiently adaptive to heal a major GB defect created in a relatively small 240 atom simulation cell. The relaxed GB structure exhibits only shallow defect states within 0.1 eV from band edges. These states localize electrons and holes, facilitating charge separation. The relaxed structure is tight with some atomic motions even reduced compared to the pristine system. Even though charges in the GB states couple more 4


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strongly to phonons than free charges, the electron-hole separation reduces the NA coupling, and the excited state lifetime remains the same as in the perfect MAPbI3. Charge localization and symmetry breaking allows higher frequency phonon modes to couple to electrons and holes. The spectrum of the active modes is broad in both pristine and GB systems, causing rapid sub-10fs loss of coherence in the electronic subsystem, favoring long-lived excitations. The simulations are performed using the mixed quantum-classical decoherenceinduced surface hopping (DISH) NAMD technique,42 implemented within the timedependent Kohn-Sham density functional theory.43-45 The method treats the lighter and faster electrons quantum mechanically, and the heavier and slower nuclei semiclassically. The DISH algorithm naturally incorporates quantum decoherence within the electronic subsystem arising due to interactions with the nuclei. The decoherence time is estimated as the pure-dephasing time of the optical response theory.46,47 The approach was applied successfully to investigate photoexcitation dynamics in a variety of systems, including perovskites containing dopants,48,49 defects,50 and GBs,20 TiO2 with GBs,51 etc.52-56 The geometry optimization, adiabatic molecular dynamics (MD) and NA coupling calculations are carried out using the Vienna Ab initio Simulation Package (VASP).57 The Pedrew-Burke-Ernzerhof (PBE) functional in the generalized gradient approximation is used to treat the electron exchange and correlation interactions.58 Projector-augmented wave (PAW) pseudopotentials are utilized to describe the core region,59 and a 400 eV plane-wave energy cutoff is used. The Grimme DFT-D3 5



method60 is employed to describe the van der Waals interactions, in order to maintain system stability during geometry optimization and molecular dynamics simulations. The structures are optimized employing the 3 × 3 × 1 Monkhorst–Pack k-point mesh61 for the pristine system and the 6 × 2 × 1 mesh for the GB systems, with the 0.01 eV/Å force convergence threshold. After the geometry optimization, the systems are heated to 300 K with repeated velocity rescaling for 2 ps. Then, 5 ps adiabatic MD trajectories are obtained for the R-point in the microcanonical ensemble with a 1 fs atomic time step. To simulate the electron-hole recombination processes, 3000 geometries are selected from the adiabatic MD trajectories as initial configurations for NAMD performed using the PYXAID code.62,63 Both pristine MAPbI3 and MAPbI3 with a GB contain 240 atoms, Figure 1, allowing equivalent representation of electronic structure and vibrational modes in the perfect and defective systems. The lattice constant of the 2×2×5 supercell of the cubic phase MAPbI3 is 6.290 Å, in agreement with the previous theoretical value of 6.310 Å.64 The Σ5 (310) GB structure is built using the same optimized cubic phase MAPbI3. The average Pb-I bond length in optimized pristine MAPbI3 is 3.156 Å, agreeing with the experimental value of 3.16 Å.65 The GB undergoes a considerable reconstruction already at 0 K, with many bond lengths and angles adjusting to minimize the penalty for creating unsaturated chemical bonds. Upon heating to 300 K, the Pb-I framework of pristine MAPbI3 distorts slightly, and MA molecules rotate, subject to a small barrier.35 Additional reconstruction of the GB region is seen at room temperature. New Pb-I bonds are formed and MA molecules reorient driven by electrostatic interaction 6


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with the inorganic lattice.

Figure 1. Optimized and room temperature structures of (a) 2×2×5 pristine MAPbI3, and (b) Σ5(310) grain boundary (GB). Each system contains 240 atoms. The GB region undergoes significant reconstruction at both 0K and room temperature, minimizing the penalty associated with formation of unsaturated chemical bonds.

In order to characterize nuclear dynamics in the two systems, we report the canonically averaged standard deviation of the positions of each atom type, 𝝈𝒊 =

〈(𝒓𝒊 ― 〈𝒓𝒊〉)𝟐〉. Here,

𝒓𝒊 denotes the location of atom i, and the canonical averaging,

represented by the angular brackets, is performed over 5000 configurations from the 5 ps MD trajectories for each system. The Pb and I of the inorganic lattice are considered separately, since they support the electron and hole wavefunctions, while all atoms of the organic MA molecules are considered together, Table 1. A larger standard deviation indicates a stronger atom fluctuation, typically suggesting an enhanced NA electronphonon coupling. The data demonstrate that introduction of the GB has a small effect on atomic fluctuation, indicating that the reconstructed GB region is as stable as pristine 7



MAPbI3. Fluctuations of Pb and MA atoms are even slightly reduced. Interesting correlations between motions of the inorganic and organic subsystems have been observed recently rationalizing the unexpected enhancement of charge-carrier lifetimes in MAPbI3 at increased temperature.55

Table 1. Standard deviations in the positions of the Pb, I and MA atoms in pristine MAPbI3 and Σ5(310) GB. Pb

I

MA

Pristine

0.425

0.508

0.778

GB

0.393

0.534

0.756

Figure 2 shows the projected density of states (PDOS) for pristine MAPbI3 and the Σ5(310) GB system in their optimized geometries. The PDOS is split into contributions from the I, Pb and MA atoms. The HOMO is formed primarily by the I atomic orbitals, with minor contributions from the Pb atoms. The LUMO is of the complementary origin, arising primarily from the Pb atomic orbitals. The LUMO and HOMO constitute the initial and final states for the electron-hole recombination across the bandgap. The organic components do not contribute to the band edge states, and therefore, they have no direct effect on the NA coupling. However, MA motions influence the inorganic Pb-I framework mechanically, and interact with charge carriers electrostatically. The direct bandgap of pristine MAPbI3 calculated at the R-point is 1.55 eV, showing good agreement with the experimental value for cubic MAPbI3.65,66 The Σ5(310) GB 8


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introduces shallow trap states close to the band edges, and reduces slightly the HOMOLUMO gap, Figure 2b. Other types of GBs can introduce deeper trap states.20 To confirm the electronic structures obtained with the PBE functional, we performed additional calculations using the HSE06 hybrid functional. The HSE06 PDOS of the pristine and GB systems are presented in Figure S1 of the Supporting Information. The HSE06 bandgaps for the pristine MAPbI3 and GB systems are 2.06 eV and 1.89 eV, respectively, and are notably larger than the experimental value of 1.52 eV.65 Importantly, the defect states introduced by the GB are shallow at both PBE and HSE06 levels of description. Since the bandgap calculated at the PBE level shows much better agreement with experiment65 than the HSE06 bandgap, since the nonradiative relaxation times depend significantly on the bandgap, and since PBE is much more computationally efficient than HSE06 for periodic systems, we perform the NAMD calculations with the PBE functional.

Figure 2. Projected densities of states (PDOS) for (a) 2×2×5 240-atom pristine MAPbI3, 9



(b) 240-atom Σ5(310) GB in their optimized geometries, Figure 1. Electrons at the conduction band minimum are supported by Pb atoms, while holes at the valence band maximum are located on I atoms. The GB creates only shallow trap states, maintaining the overall PDOS shape.

The nonradiative electron-hole recombination rate is governed by the NA coupling between the initial and final states, and the NA coupling strength depends on overlap of the electron and hole wavefunctions. Figure 3 presents distribution of the HOMO and LUMO charge densities for the pristine and GB systems, at both 0K and ambient temperature. Electrons and holes are localized on the Pb-I lattice, with holes supported primarily by the I atoms, and electrons localized on the Pb atoms. At 0K, the HOMO and LUMO are delocalized in pristine MAPbI3, while they are localized in the GB system due to symmetry breaking. Notably, the HOMO and LUMO are located in different parts of the GB region, leading to electron-hole separation, in agreement with experiment.31 GBs split the lattice, creating unsaturated chemical bonds on some Pb and I atoms. The electrons and holes localize in the regions of the corresponding missing bonds. Thus, the HOMO of the GB structure has a strong contribution from the two iodines located next to each other and missing the Pb atom between them, see the bottom of the HOMO charge densities in Figure 3b. Correspondingly, the LUMO has a strong contribution from the middle pair of Pb atoms next to each other in the top part of the GB structure, see the 0K LUMO in Figure 3b. The GB structure has two equivalent GBs in the middle and the sides of the shown figures. An equivalent pair of 10


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two Pb atoms next to each other, analogous to the middle pair, is present in the bottom left and right corners (consider periodic images of the shown structure). The 300K LUMO in Figure 3b has strong contributions from these atoms and not from the middle pair of Pb atoms, due to thermal fluctuations that break the symmetry further. Thermal fluctuations enhance charge localization in both systems, as seen in experiment.67 Still, the charges are localized much more and the orbitals overlap much less at the GB than in pristine MAPbI3. Since the HOMO-LUMO overlap decreases at the GB, the NA coupling responsible for the charge recombination should decrease as well.

Figure 3. Distributions of HOMO and LUMO charge densities for (a) pristine MAPbI3 and (b) Σ5(310) GB in their optimized structures and at room tempearture. The electron and hole are localized in different regions of the GB. Thermal disorder enhances the 11



localization.

In order to characterize the phonon modes that participate in the electron-hole recombination, we compute Fourier transforms (FTs) of the phonon-induced fluctuations for the HOMO–LUMO energy gaps. The resulting influence spectra, also known as spectral densities, are shown in Figure 4. The majority of the phonon modes that promote the nonradiative charge recombination and accept the energy lost by the electronic subsystem reside in the low frequency region of the spectrum. No contributions from high frequency modes, such as stretching and bending of MA molecules, are seen. The strong peak around 100 cm-1 can be assigned to the Pb-I stretching, and the peak below 60 cm-1 can be assigned to the Pb-I-Pb bending. Both Pb-I stretching and bending modes influence geometry of the inorganic lattice and create the NA coupling. Higher frequency peaks at around 150 cm-1 and 200 cm-1 can be attributed to librations of the organic MA cations. Since the charges are supported only by the inorganic lattice, the organic cations influence charge dynamics indirectly, either electrostatically or by mechanical coupling to the inorganic lattice. The peaks at 300 and 400 cm-1 can be assigned to the MA torsional modes, proposed as a marker of the orientational disorder of the material.68-70

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Figure 4. Fourier transforms of the autocorrelation functions for the HOMO-LUMO energy gap in (a) pristine MAPbI3 and (b) Σ5(310) GB. Many types of motions, including bending and stretching of the Pb-I lattice, and librations and torsions of MA, contribute to the signal.

Electron-vibrational interactions involve both inelastic and elastic scattering. Quantified by the NA coupling, inelastic scattering gives energy losses from electron to phonons during the electronic transition from LUMO to HOMO. Elastic scattering destroys quantum coherence formed between LUMO and HOMO during the recombination process, and is characterized by the pure-dephasing time of the optical response theory.46 Figure 5 gives the pure-dephasing functions calculated using the second-order cumulant approximation.46,47 Reported in Table 2, the pure-dephasing times, τ, are obtained by Gaussian fitting, exp[-0.5(t/τ)2]. The short, sub-10fs coherence times contribute to the long charge carrier lifetimes in HOIPs, which can be understood as a manifestation of the quantum Zeno effect.71-73 13



The inset in Figure 5 present the unnormalized autocorrelation functions (un-ACF) of the HOMO-LUMO energy gap fluctuations, entering the calculation of the puredephasing functions.46,47 Electronic coherence is short in HOIPs because the electronic subsystem couples to a variety of phonon modes, arising from both the inorganic lattice and the organic cations, Figure 4. Participation of many modes leads to fast ACF decay and low recurrences. Coherence is also short, because electrons and holes are localized on different atoms, Pb and I, respectively, Figure 2, and in the GB system, on different parts of the simulation cell, Figure 3. Localization of HOMO and LUMO on different atoms allow the HOMO and LUMO energies fluctuate independently of each other, leading to a large HOMO-LUMO energy gap fluctuation, reflected in the initial values of the un-ACF.47 The lightly higher initial un-ACF value for the GB system, inset in Figure 5, indicates that elastic electron-phonon scattering is slightly stronger, and rationalizes why the pure-dephasing time is somewhat shorter, Table 2.

Figure 5. Pure-dephasing functions for the HOMO-LUMO transition in the pristine and GB MAPbI3. The inset shows the unnormalized autocorrelation functions, Fourier transformed in Figure 4. 14


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Figure 6 presents evolution of the excited state populations during the nonradiative electron-hole recombination in pristine MAPbI3 and at the Σ5(310) GB. The recombination times, summarized in Table 2, are obtained using the short-time linear approximation to exponential decay, f(t) = exp (−t/τ) ≈ 1 – (t/τ). The data agree with the experimental MAPbI3 carrier lifetimes, ranging from tens of picoseconds to hundreds of nanoseconds.74-77 Introduction of the Σ5(310) GB has little effect on the recombination, because the GB region undergoes significant reconstruction, Figure 1, compensating unsaturated chemical bonds and reducing the bandgap only slightly, Figure 2 and Table 2, and since symmetry breaking separates electron and hole, Figure 3, reducing the NA coupling, Table 2. The result rationalizes the experiments showing that charge recombination happens primarily in non-GB regions of MAPbI3 films, and that GB facilitating charge carrier separation.31 Thus, while some GBs20 constitute a major source of charge carrier losses,17-19 it is possible to obtain polycrystalline MAPbI3 films in which carrier losses are not accelerated at GBs, and in which GB help to separate electrons and holes.

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Figure 6. Nonradiative electron-hole recombination dynamics in the pristine and GB MAPbI3. GB has little influence on the recombination timescale, because it creates only shallow trap states, and separates electron and hole, reducing the NA coupling, Table 2.

Table 2. Bandgap, absolute NA coupling, pure-dephasing time, and nonradiative electron-hole recombination time for pristine MAPbI3 and the Σ5(310) GB. Bandgap

NA Coupling

Dephasing

Recombination

(eV)

(meV)

(fs)

(ns)

Pristine

1.55

0.56

6.23

2.89

GB

1.34

0.44

5.19

2.93

In summary, we have performed a time-domain ab initio NAMD simulation of the nonradiative electron-hole recombination in pristine MAPbI3 and MAPbI3 with a Σ5(310) GB. The study demonstrates that GBs can have a positive effect on 16


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performance of perovskite-based devices. On the one hand, GBs help to separate electrons and holes, and dissociate photo-generated excitons. On the other hand, GBs do not necessarily accelerate charge recombination. The ability of the relatively soft perovskite structure to rearrange and heal unsaturated chemical bonds created in GB regions is the key property in this regard. Charges are separated because GBs break perfect crystalline symmetry and create trap states. However, because the trap states are shallow, due to reconstruction of the GB region, the charges can escape back to delocalized bands and continue long-distance transport. Charge separation by shallow traps is also responsible for slow charge recombination, with a timescale similar to that in bulk MAPbI3. In addition to defect healing, the soft, multi-component structure of MAPbI3 provides a broad spectrum of phonon modes that induces rapid loss of quantum coherence during charge recombination, making it slow. The study suggests that a moderate annealing of polycrystalline MAPbI3 can facilitate GB reconstruction and significantly improve its performance. The detailed time-domain atomistic analysis of charge carrier dynamics in MAPbI3 advances our understanding of the key factors governing the unique properties of HOIPs.

Notes The authors declare no competing financial interest.

Acknowledgements The authors are grateful to the National Science Foundation of China, Grant Nos. 17



21573022, 51861135101, 21590801, and 21421003. R. L. acknowledges financial support by the Beijing Normal University Startup and the Fundamental Research Funds for the Central Universities. O. V. P. acknowledges funding from the U.S. Department of Energy, grant No. DE-SC0014429, and thanks Beijing Normal University for hospitality during manuscript preparation.

Supporting Information Available: Description of the theoretical methodologies, additional simulation details, and densities of states obtained with the HSE06 functional. The material is available free of charge via the Internet at http://pubs.acs.org.

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Symmetry Breaking at MAPbI3 Perovskite Grain Boundaries

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