Symmetry Breaking at MAPbI3 Perovskite Grain BoundariesSuppresses Charge Recombination: Time-Domain ab Initio AnalysisYutong Wang,† Wei-Hai Fang,† Run Long,*,† and Oleg V. Prezhdo‡

†College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing NormalUniversity, Beijing 100875, P. R. China‡Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States

*S Supporting Information

ABSTRACT: The influence of grain boundaries (GBs) on charge carrier lifetimes inmethylammonium lead triiodide perovskite (MAPbI3) remains unclear. Someexperiments suggest that GBs promote rapid nonradiative decay and deteriorate deviceperformance, while other measurements indicate that charge recombination happensprimarily in non-GB regions and that GBs facilitate charge separation and collection. Bycombining time-domain density functional theory and nonadiabatic (NA) moleculardynamics, we demonstrate that charge separation and localization happening at MAPbI3GBs due to symmetry breaking suppresses charge recombination. Even though GBslower the MAPbI3 bandgap and charge localization enhances interactions with phonons,electron−hole separation decreases the NA coupling, and the excited state lifetimeremains virtually unchanged compared to the pristine perovskite. Our study rationalizeshow GBs can have a positive influence on perovskite optoelectronic properties andadvances fundamental understanding of charge carrier dynamics in these fascinating materials.

Hybrid organic−inorganic halide perovskite (HOIP) solarcells have attracted great interest since the first report in

2009, with the power conversion efficiency increasing rapidlyfrom 3.8%1 to 23.7%.2 A conventional HOIP, CH3NH3PbI3(MAPbI3), has shown superior photovoltaic properties,including a bandgap suitable for harvesting visible and near-infrared light,3 a large absorption coefficient,4 a large carrierdiffusion length,5 a high carrier mobility,6 and a small excitonbinding energy.7 In addition to solar cells, MAPbI3 forms thebasis for lasers,8 light-emitting diodes,9 and photodetectors.10

Low-temperature solution growth provides an efficient andinexpensive route to synthesize MAPbI3. The films producedthis way are typically polycrystalline,11−15 and therefore, theynecessarily contain multiple grain boundaries (GBs). Experi-ments have produced contradictory results, suggesting thatGBs can have both negative and positive effects on the chargecarrier 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 demonstratedthat the increased MAPbI3 grain size, obtained by a newsynthesis procedure, can improve the device performance dueto a reduction in GBs.18 By correlating confocal fluorescencemicroscopy with scanning electron microscopy, de Quilettes etal. have been able to resolve spatially photoluminescence andcarrier decay dynamics, illustrating that the MAPbI3 carrierlifetimes vary between different grains, and that GBs exhibitrapid nonradiative decay compared to other regions in thefilms.19 Our previous work20 has demonstrated that a GB cannotably accelerate the nonradiative electron−hole recombina-

tion in MAPbI3 and that boundary doping by Cl atoms canslow down the recombination. In order to eliminate thenegative effect of GBs, interfaces, and surfaces on excited-statelifetimes and device performance, several strategies have beendemonstrated, involving Lewis base passivation,21 hydrogenbond interactions,22 and addition of organic dopants to mixedprecursor solutions.23−26

In contrast to the reports highlighting the negative role ofGBs,17−19 Zhu and co-workers have demonstrated that chargerecombination happens primarily in non-GB regions ofMAPbI3 thin films,27,28 arguing that GBs are benign to carrierlifetimes. Yin et al. have argued that GBs in MAPbI3 can beelectrically clean.29,30 Yun et al. have used Kelvin probe forcemicroscopy and conductive-atomic force microscopy to showthat GBs facilitate charge carrier separation and collection.31

The diverse experimental evidence regarding the critical rolesperovskite GBs play in the material performance stronglymotivates theoretical studies into charge carrier dynamics inGB regions.Stimulated by the recent work describing both positive and

negative influence of GBs on the HOIP perform-ance,16−19,27,28,31−41 we apply time-dependent density func-tional theory (TDDFT) and nonadiabatic molecular dynamics(NAMD) to investigate in detail charge carrier recombinationin a GB region of MAPbI3 and compare it with recombinationin equivalent pristine MAPbI3. We show that MAPbI3 is

Received: March 17, 2019Accepted: March 20, 2019Published: March 20, 2019

Letter

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sufficiently adaptive to heal a major GB defect created in arelatively small 240 atom simulation cell. The relaxed GBstructure exhibits only shallow defect states within 0.1 eV fromband edges. These states localize electrons and holes,facilitating charge separation. The relaxed structure is tightwith some atomic motions even reduced compared to thepristine system. Even though charges in the GB states couplemore strongly to phonons than free charges, the electron−holeseparation reduces the NA coupling, and the excited statelifetime remains the same as in the perfect MAPbI3. Chargelocalization and symmetry breaking allows higher frequencyphonon modes to couple to electrons and holes. The spectrumof the active modes is broad in both pristine and GB systems,causing rapid sub-10 fs loss of coherence in the electronicsubsystem, favoring long-lived excitations.The simulations are performed using the mixed quantum-

classical decoherence-induced surface hopping (DISH)NAMD technique,42 implemented within the time-dependentKohn−Sham density functional theory.43−45 The methodtreats the lighter and faster electrons quantum mechanicallyand the heavier and slower nuclei semiclassically. The DISHalgorithm naturally incorporates quantum decoherence withinthe electronic subsystem arising due to interactions with thenuclei. The decoherence time is estimated as the pure-dephasing time of the optical response theory.46,47 Theapproach was applied successfully to investigate photo-excitation dynamics in a variety of systems, includingperovskites containing dopants,48,49 defects,50 GBs,20 TiO2with GBs,51 etc.52−56

The geometry optimization, adiabatic molecular dynamics(MD) and NA coupling calculations are carried out using theVienna Ab initio Simulation Package (VASP).57 The Pedrew−Burke−Ernzerhof (PBE) functional in the generalized gradientapproximation is used to treat the electron exchange andcorrelation interactions.58 Projector-augmented wave (PAW)pseudopotentials are utilized to describe the core region,59 anda 400 eV plane-wave energy cutoff is used. The Grimme DFT-D3 method60 is employed to describe the van der Waalsinteractions, in order to maintain system stability duringgeometry optimization and molecular dynamics simulations.The structures are optimized by employing the 3 × 3 × 1Monkhorst−Pack k-point mesh61 for the pristine system andthe 6 × 2 × 1 mesh for the GB systems, with the 0.01 eV/Åforce convergence threshold. After the geometry optimization,

the systems are heated to 300 K with repeated velocityrescaling for 2 ps. Then, 5 ps adiabatic MD trajectories areobtained for the R-point in the microcanonical ensemble witha 1 fs atomic time step. To simulate the electron−holerecombination processes, 3000 geometries are selected fromthe adiabatic MD trajectories as initial configurations forNAMD performed using the PYXAID code.62,63

Both pristine MAPbI3 and MAPbI3 with a GB contain 240atoms, Figure 1, allowing equivalent representation ofelectronic structure and vibrational modes in the perfect anddefective systems. The lattice constant of the 2 × 2 × 5supercell of the cubic phase MAPbI3 is 6.290 Å, in agreementwith the previous theoretical value of 6.310 Å.64 The Σ5 (310)GB structure is built using the same optimized cubic phaseMAPbI3. The average Pb−I bond length in optimized pristineMAPbI3 is 3.156 Å, agreeing with the experimental value of3.16 Å.65 The GB undergoes a considerable reconstructionalready at 0 K, with many bond lengths and angles adjusting tominimize the penalty for creating unsaturated chemical bonds.Upon heating to 300 K, the Pb−I framework of pristineMAPbI3 distorts slightly, and MA molecules rotate, subject to asmall barrier.35 Additional reconstruction of the GB region isseen at room temperature. New Pb−I bonds are formed, andMA molecules reorient driven by electrostatic interaction withthe inorganic lattice.In order to characterize nuclear dynamics in the two

systems, we report the canonically averaged standard deviation

of the positions of each atom type, σ = − r r( )i i i2 . Here, ri

denotes the location of atom i, and the canonical averaging,represented by the angular brackets, is performed over 5000configurations 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 wave functions, whileall atoms of the organic MA molecules are considered together,Table 1. A larger standard deviation indicates a stronger atomfluctuation, typically suggesting an enhanced NA electron−

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

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 0.778GB 0.393 0.534 0.756

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phonon coupling. The data demonstrate that introduction ofthe GB has a small effect on atomic fluctuation, indicating thatthe reconstructed GB region is as stable as pristine MAPbI3.Fluctuations of Pb and MA atoms are even slightly reduced.Interesting correlations between motions of the inorganic andorganic subsystems have been observed recently, rationalizingthe unexpected enhancement of charge-carrier lifetimes inMAPbI3 at increased temperature.55

Figure 2 shows the projected density of states (PDOS) forpristine MAPbI3 and the Σ5(310) GB system in their

optimized geometries. The PDOS is split into contributionsfrom the I, Pb, and MA atoms. The HOMO is formedprimarily by the I atomic orbitals, with minor contributionsfrom the Pb atoms. The LUMO is of complementary origin,

arising primarily from the Pb atomic orbitals. The LUMO andHOMO constitute the initial and final states for the electron−hole recombination across the bandgap. The organiccomponents do not contribute to the band edge states, andtherefore, they have no direct effect on the NA coupling.However, MA motions influence the inorganic Pb−I frame-work mechanically and interact with charge carriers electro-statically. The direct bandgap of pristine MAPbI3 calculated atthe R-point is 1.55 eV, showing good agreement with theexperimental value for cubic MAPbI3.

65,66 The Σ5(310) GBintroduces shallow trap states close to the band edges andreduces slightly the HOMO−LUMO gap, Figure 2b. Othertypes of GBs can introduce deeper trap states.20 To confirmthe electronic structures obtained with the PBE functional, weperformed additional calculations using the HSE06 hybridfunctional. The HSE06 PDOS of the pristine and GB systemsare presented in Figure S1 of the Supporting Information. TheHSE06 bandgaps for the pristine MAPbI3 and GB systems are2.06 and 1.89 eV, respectively, and are notably larger than theexperimental value of 1.52 eV.65 Importantly, the defect statesintroduced by the GB are shallow at both PBE and HSE06levels of description. Since the bandgap calculated at the PBElevel shows much better agreement with experiment65 than theHSE06 bandgap, since the nonradiative relaxation timesdepend significantly on the bandgap, and since PBE is muchmore computationally efficient than HSE06 for periodicsystems, we perform the NAMD calculations with the PBEfunctional.The nonradiative electron−hole recombination rate is

governed by the NA coupling between the initial and finalstates, and the NA coupling strength depends on overlap of theelectron and hole wave functions. Figure 3 presentsdistribution of the HOMO and LUMO charge densities forthe pristine and GB systems, at both 0 K and ambienttemperature. Electrons and holes are localized on the Pb−Ilattice, with holes supported primarily by the I atoms, and

Figure 2. Projected densities of states (PDOS) for (a) 2 × 2 × 5 240-atom pristine MAPbI3 and (b) 240-atom Σ5(310) GB in theiroptimized geometries, Figure 1. Electrons at the conduction bandminimum are supported by Pb atoms, while holes at the valence bandmaximum are located on I atoms. The GB creates only shallow trapstates, maintaining the overall PDOS shape.

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

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electrons localized on the Pb atoms. At 0 K, the HOMO andLUMO are delocalized in pristine MAPbI3, while they arelocalized in the GB system due to symmetry breaking. Notably,the HOMO and LUMO are located in different parts of theGB region, leading to electron−hole separation, in agreementwith experiment.31 GBs split the lattice, creating unsaturatedchemical bonds on some Pb and I atoms. The electrons andholes localize in the regions of the corresponding missingbonds. Thus, the HOMO of the GB structure has a strongcontribution from the two iodines located next to each otherand missing the Pb atom between them; see the bottom of theHOMO charge densities in Figure 3b. Correspondingly, theLUMO has a strong contribution from the middle pair of Pbatoms next to each other in the top part of the GB structure,see the 0 K LUMO in Figure 3b. The GB structure has twoequivalent GBs in the middle, and the sides of the shownfigures. An equivalent pair of two Pb atoms next to each other,analogous to the middle pair, is present in the bottom left andright corners (consider periodic images of the shownstructure). The 300 K LUMO in Figure 3b has strongcontributions from these atoms and not from the middle pairof Pb atoms, due to thermal fluctuations that break thesymmetry further. Thermal fluctuations enhance chargelocalization in both systems, as seen in experiment.67 Still,the charges are localized much more and the orbitals overlapmuch less at the GB than in pristine MAPbI3. Since theHOMO−LUMO overlap decreases at the GB, the NAcoupling responsible for the charge recombination shoulddecrease as well.In order to characterize the phonon modes that participate

in the electron−hole recombination, we compute Fouriertransforms (FTs) of the phonon-induced fluctuations for theHOMO−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 nonradiativecharge recombination and accept the energy lost by theelectronic subsystem reside in the low frequency region of thespectrum. No contributions from high frequency modes, suchas stretching and bending of MA molecules, are seen. Thestrong peak around 100 cm−1 can be assigned to the Pb−Istretching, and the peak below 60 cm−1 can be assigned to thePb−I−Pb bending. Both Pb−I stretching and bending modesinfluence geometry of the inorganic lattice and create the NA

coupling. Higher frequency peaks at around 150 and 200 cm−1

can be attributed to librations of the organic MA cations. Sincethe charges are supported only by the inorganic lattice, theorganic cations influence charge dynamics indirectly, eitherelectrostatically or by mechanical coupling to the inorganiclattice. The peaks at 300 and 400 cm−1 can be assigned to theMA torsional modes, proposed as a marker of the orientationaldisorder of the material.68−70

Electron-vibrational interactions involve both inelastic andelastic scattering. Quantified by the NA coupling, inelasticscattering gives energy losses from electron to phonons duringthe electronic transition from LUMO to HOMO. Elasticscattering destroys quantum coherence formed betweenLUMO and HOMO during the recombination process andis characterized by the pure-dephasing time of the opticalresponse theory.46 Figure 5 gives the pure-dephasing functions

calculated using the second-order cumulant approxima-tion.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-10 fs coherence times contribute to the long charge carrierlifetimes in HOIPs, which can be understood as amanifestation of the quantum Zeno effect.71−73

The inset in Figure 5 present the unnormalizedautocorrelation functions (un-ACF) of the HOMO−LUMOenergy gap fluctuations, entering the calculation of the pure-dephasing functions.46,47 Electronic coherence is short inHOIPs because the electronic subsystem couples to a variety ofphonon modes, arising from both the inorganic lattice and theorganic cations, Figure 4. Participation of many modes leads tofast 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, ondifferent parts of the simulation cell, Figure 3. Localization ofHOMO and LUMO on different atoms allows the HOMO and

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

Figure 5. Pure-dephasing functions for the HOMO−LUMOtransition in the pristine and GB MAPbI3. The inset shows theunnormalized autocorrelation functions, Fourier transformed inFigure 4.

Table 2. Bandgap, Absolute NA Coupling, Pure-DephasingTime, and Nonradiative Electron−Hole RecombinationTime for Pristine MAPbI3 and the Σ5(310) GB

bandgap(eV)

NA coupling(meV)

dephasing(fs)

recombination(ns)

pristine 1.55 0.56 6.23 2.89GB 1.34 0.44 5.19 2.93

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LUMO energies to 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 lightlyhigher initial un-ACF value for the GB system, inset in Figure5, indicates that elastic electron−phonon scattering is slightlystronger and rationalizes why the pure-dephasing time issomewhat shorter, Table 2.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 recombinationtimes, 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 MAPbI3carrier lifetimes, ranging from tens of picoseconds to hundredsof nanoseconds.74−77 Introduction of the Σ5(310) GB haslittle effect on the recombination, because the GB regionundergoes significant reconstruction, Figure 1, compensatingfor unsaturated chemical bonds and reducing the bandgap onlyslightly, Figure 2 and Table 2, and since symmetry breakingseparates electron and hole, Figure 3, reducing the NAcoupling, Table 2. The result rationalizes the experimentsshowing that charge recombination happens primarily in non-GB regions of MAPbI3 films and that GB facilitates chargecarrier separation.31 Thus, while some GBs20 constitute amajor source of charge carrier losses,17−19 it is possible toobtain polycrystalline MAPbI3 films in which carrier losses arenot accelerated at GBs, and in which GB helps to separateelectrons and holes.In summary, we have performed a time-domain ab initio

NAMD simulation of the nonradiative electron−hole recombi-nation in pristine MAPbI3 and MAPbI3 with a Σ5(310) GB.The study demonstrates that GBs can have a positive effect onperformance of perovskite-based devices. On the one hand,GBs help to separate electrons and holes and dissociatephotogenerated excitons. On the other hand, GBs do notnecessarily accelerate charge recombination. The ability of therelatively soft perovskite structure to rearrange and healunsaturated chemical bonds created in GB regions is the keyproperty in this regard. Charges are separated because GBsbreak perfect crystalline symmetry and create trap states.However, because the trap states are shallow, due toreconstruction 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 slowcharge recombination, with a time scale similar to that in bulkMAPbI3. In addition to defect healing, the soft, multi-component structure of MAPbI3 provides a broad spectrumof phonon modes that induces rapid loss of quantumcoherence during charge recombination, making it slow. Thestudy suggests that a moderate annealing of polycrystallineMAPbI3 can facilitate GB reconstruction and significantlyimprove its performance. The detailed time-domain atomisticanalysis of charge carrier dynamics in MAPbI3 advances ourunderstanding of the key factors governing the uniqueproperties of HOIPs.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.jp-clett.9b00763.

Description of the theoretical methodologies, additionalsimulation details, and densities of states obtained withthe HSE06 functional (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: runlong@bnu.edu.cn.ORCIDWei-Hai Fang: 0000-0002-1668-465XRun Long: 0000-0003-3912-8899Oleg V. Prezhdo: 0000-0002-5140-7500NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe authors are grateful to the National Science Foundation ofChina, Grant Nos. 21573022, 51861135101, 21590801, and21421003. R.L. acknowledges financial support by the BeijingNormal University Startup and the Fundamental ResearchFunds for the Central Universities. O.V.P. acknowledgesfunding from the U.S. Department of Energy, grant No. DE-SC0014429, and thanks Beijing Normal University forhospitality during manuscript preparation.

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