Long Carrier Lifetimes in PbI2‑Rich PerovskitesRationalized by Ab Initio NonadiabaticMolecular DynamicsChuan-Jia Tong,†,‡,§ Linqiu Li,§ Li-Min Liu,*,†,‡ and Oleg V. Prezhdo*,§

‡School of Physics, Beihang University, Beijing 100191, China†Beijing Computational Science Research Center, Beijing 100193, China§Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States

ABSTRACT: Hybrid organic−inorganic perovskites have at-tracted considerable interest due to their impressive performancein solar energy applications. Many experiments show that a slightexcess of PbI2 significantly enhances the properties of the moststudied CH3NH3PbI3 compound. We use real-time time-depend-ent density functional theory and nonadiabatic moleculardynamics to demonstrate that the effect arises due to decreasedelectron−phonon interactions responsible for nonradiative chargerecombination. The fast organic CH3NH3

+ (MA) cations, presenton surfaces of stochiometric and MAI-rich perovskites, areparticularly mobile and introduce high-frequency phonons andstrong electric fields that couple to the charge carriers and createlarge nonadiabatic coupling. Excess PbI2 decreases MA surfacecoverage, reduces the nonadiabatic coupling by up to an order ofmagnitude, and extends the charge carrier lifetime. Generally, charges in perovskites are long-lived because thenonadiabatic coupling is very small, less than 1 meV, and quantum coherence formed during charge recombination isshort, less than 10 fs. Our results rationalize why decreasing the concentration of the organic cations on perovskitesurfaces can suppress nonradiative charge carrier recombination and improve material performance.

Methylammonium lead iodide CH3NH3PbI3(MAPbI3) solar cells are attracting considerableinterest because of their high photovoltaic perform-

ance.1−3 Following the first report of a perovskite solar cell in2009 with the power conversion efficiency of 3.8%,4 it has hadvery quick development. After several key advances in thefollowing years, the perovskite efficiency increased rapidly, nowreaching beyond 22%.5 The state-of-the-art performancemainly stems from the large optical absorption crosssection,6−10 easy band gap tuning by chemical composi-tion,11,12 efficient charge-carrier generation,13−15 and very longelectron and hole diffusion lengths.16,17 Apart from theirexcellent photoelectric properties, hybrid perovskites attract somuch attention due to their low production cost.18,19

Although perovskite solar cells show outstanding perform-ance, there still remain several phenomena that require clearunderstanding, such as the current−voltage hysteresis20−25 andstability upon exposure to humidity.26−31 Recently, manyexperiments have reported beneficial effects of a slight excess ofPbI2 in perovskite films.32−37 For example, Roldan-Carmona etal.32 observed improvement of crystallinity and electrontransfer by incorporating excess PbI2 as an additive in theperovskite film. Kim et al.36 showed an improved open-circuit

voltage and field factor by incorporating excess PbI2 into theperovskite phase. They deduced that excess PbI2 can suppressnonradiative charge carrier recombination. However, thereason why a few percent excess PbI2 is essential to achievehigh-efficiency devices remains unclear, motivating theoreticalanalysis of the microscopic mechanistic details of charge carrierrecombination.In this Letter, we report time-domain ab initio simulations of

the nonradiative electron−hole recombination process in PbI2-rich and MAI-rich perovskites. The simulations show that thecharge carrier lifetime is several times longer in the PbI2-richsystem due to weaker nonadiabatic coupling (NAC). Surfacesof stoichiometric and MAI-rich systems contain significantconcentrations of MA cations, which are mobile, exhibit high-frequency motions, and create strong electric fields that coupleto the charge carriers. Lower concentrations of MA cations inPbI2-rich systems decrease electron−phonon interactions andprolong charge carrier lifetimes. Other factors governing

Received: June 9, 2018Accepted: July 9, 2018Published: July 9, 2018

LetterCite This: ACS Energy Lett. 2018, 3, 1868−1874

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nonradiative relaxation, such as the electronic energy gap andquantum coherence time, are less important in distinguishingthe properties of the PbI2-rich and MAI-rich systems. Thereported results rationalize the experimental observations atthe atomistic level and demonstrate how control overconcentration of the organic cations on perovskite surfacesprovides a mechanism to improve performance of theperovskite materials.The electronic structure and molecular dynamics (MD)

trajectories were obtained using plane-wave density functionaltheory (DFT) as implemented in the Quantum Espresso38

package. The exchange−correlation energy was calculated withthe Perdew−Burke−Ernzerhof (PBE) functional39 and ultra-soft pseudopotentials. To improve the description of the long-range van der Waals interactions, the DFT-D2 correction wasemployed.40 The periodic slab was constructed to representthe (001) surface of tetragonal MAPbI3. The slab was threelayers thick and contained 2 × 2 MAPbI3 unit cells along theperiodic x−y plane. A 20 Å vacuum layer was added in the zdirection to eliminate interactions between slab images. Thebasis set energy cutoff was set to 50 Ry. A uniform 3 × 3 × 1Monkhorst−Pack k-point mesh was used for the structuraloptimization, MD, and density of states (DOS) calculations.The NAC and NAMD calculations for the charge recombina-tion dynamics were performed at the Γ-point only forcomputational efficiency because MAPbI3 is a direct-band-gap semiconductor with the conduction and valence bandedges located at the Γ-point. Excitonic effects were notincluded in simulations both due to high computational costand because the exciton binding energy in hybrid perovskites isquite low, 20−60 meV.41−43 This value is comparable to kBT atroom temperature, and therefore, excitons in perovskites areeither bound very weakly or exist as free electron−hole pairs.Analysis of the transient photoluminescence data has led to theconclusion that the properties of the excited states in leadhalide perovskite are dominated by free charge pairs ratherthan bound excitons.44 The structures were fully relaxed untilthe calculated Hellmann−Feynman forces were smaller than0.05 eV/Å. Then, the systems were heated to 300 K throughrepeated velocity rescaling. An adiabatic MD trajectory with a1 fs atomic time step was produced. The electron−holerecombination was modeled with the decoherence-inducedsurface hopping (DISH) approach45 to NAMD, implementedin the PYXAID package.46,47 One thousand initial conditionswere selected from the adiabatic MD trajectory, and NAMDsimulations were performed using 300 random numbersequences to sample surface hopping probabilities for eachinitial condition. The technique has been used successfully tostudy excited-state dynamics in other perovskite sys-tems.7,17,28,48−54

We focus on the tetragonal phase of MAPbI3 at roomtemperature, as proposed in our previous report.55 Accordingto the previous DFT calculations,56,57 two (001) surfacemodels with different terminations are employed to representPbI2-rich (Figure 1a) and MAI-rich (Figure 1c) perovskites.Both models consist of three repeated layers of PbI6 octahedrawith organic MA molecules between the layers. The surfaces ofthe MAI-rich perovskite are terminated with the MAmolecules, while the surfaces of the PbI2-rich perovskite areterminated with the inorganic component. The partial densitiesof states (PDOSs) of the PbI2-rich and MAI-rich perovskitestructures are presented in Figure 1b,d. Consistent with theprevious reports,58,59 only lead and iodine atoms contribute to

the DOS around the valence band maximum (VBM) and theconduction band minimum (CBM). Essentially, no contribu-tions from the organic MA molecules are seen around the bandgap, suggesting that the MA molecules do not directlyparticipate in the charge generation and recombinationprocesses. Surfaces of the perovskite do not introduce midgapstates, as confirmed by our work and previous reports.56,57,60 Inagreement with the previous results,60 the PbI2-rich systemshows a smaller band gap, which can be rationalized byregarding unsaturated chemical bonds of the surface Pb and Iatoms as shallow trap states. One expects48 that the smallerband gap should accelerate charge recombination in PbI2-richperovskites. However, many experiments suggest that theenhanced performance of PbI2-rich systems stems from slownonradiative recombination and the long lifetime of chargecarriers. Therefore, the band gap is not the main factor thatdetermines the observed behavior, and it remains to beestablish what other factors play key roles during charge carrierrecombination in the perovskites.In order to investigate in detail the nonradiative charge

carrier recombination process, we performed NAMD simu-lations on both PbI2-rich and MAI-rich perovskite structures.The results are summarized in Table 1 and Figures 2−4. The

Figure 1. Side view of the optimized MAPbI3 structures withexposed (001) surfaces for two stoichiometric ratios: (a) highconcentration of PbI2 (PbI2-rich) and (c) high concentration ofMAI (MAI-rich). PDOS of (b) PbI2-rich and (d) MAI-richperovskites. Lead is dark gray, iodine is purple, carbon is brown,nitrogen is blue, and hydrogen is pink.

Table 1. Optimized Geometry Band Gap, and CanonicallyAveraged Pure-Dephasing Time (τd), Absolute Value ofNAC, and Nonradiative Electron−Hole RecombinationTime (τ) for the Studied Perovskites

form band gap (eV) τd (fs) |NAC| (meV) τ (ns)

PbI2-rich 1.24 3.29 0.011 23.08MAI-rich 1.78 3.57 0.096 3.56

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time-dependent population of the photoexcited state is shownin Figure 2. The carrier recombination time τ is obtained usingthe short-time linear approximation to the exponential decay,f(t) = exp(−t/τ) ≈ 1 − t/τ. Compared with many otherphotocatalytic materials,61−63 both MAI-rich and PbI2-richperovskites exhibit long, nanosecond recombination times,matching well the previous experimental42,64,65 and theoreti-cal7,28,48−50,52,66 reports. Further, we calculated the radiativelifetimes using the Einstein coefficient for spontaneousemission and obtained 63.1 and 31.7 μs for the MAI-richand PbI2-rich perovskites, respectively, in agreement with theprevious experimental and theoretical reports.44,67−69 Theradiative lifetime is several orders of magnitude longer than thenonradiative lifetime, indicating that nonradiative relaxationconstitutes the main mechanism of charge recombination.Such long nonradiative and radiative recombination timesresult in large electron and hole diffusion lengths observed inthe perovskite materials. The current calculations show thatthe excited-state population decays by nearly an order ofmagnitude more slowly in the PbI2-rich than that in the MAI-rich system, rationalizing the experimentally establishedenhanced performance of PbI2-rich perovskites.32−37

To elucidate the origin of the difference in the chargerecombination rates in the PbI2-rich and MAI-rich systems, weconsider in detail the factors affecting quantum transition rates.The rate of the nonradiative electron−hole recombinationdepends on the electronic energy gap, quantum coherence, andNAC. Generally, loss of quantum coherence decreases thetransition rate.70,71 We estimate the quantum coherence timeas the pure-dephasing time, τd, of the optical response theoryby computing the second-order cumulant approximation to thepure-dephasing function71 and fitting it by the Gaussian, D(t)= exp(−0.5(t/τd)2). The computed pure-dephasing functionsare plotted in Figure 3a. The functions are nearly identical, andthe fitted pure-dephasing times are very short, 3.29 fs in PbI2-rich and 3.57 fs in MAI-rich. The similar time scales indicatethat a slight excess of either PbI2 or MAI has little effect onquantum coherence during electron−hole recombination inthe perovskite. The pure-dephasing is very fast because theelectrons and holes are localized on different parts of theinorganic subsystem, Pb and I, respectively, and the overlap

between their wave functions is small. Fast decoherence is animportant factor in achieving the slow recombination rates andlong charge carrier lifetimes in the perovskite materials.Because there is essentially no difference in the quantum

decoherence rates in the MAI-rich and PbI2-rich systems andthe lower band gap in the PbI2-rich system favors fasterrelaxation, in contrast to the NAMD and experimental results,NAC must be the dominant factor rationalizing the differencebetween the two cases. As shown in Table 1, the canonicallyaveraged absolute NAC value is extremely small in the PbI2-rich perovskite, 0.011 meV. While also small, the correspond-ing value for the MAI-rich system is almost 9 times larger,0.096 meV. Thus, indeed, the smaller NAC in the PbI2-richperovskite explains its longer excited-state lifetime and betterphotovoltaic performance. In addition to computing theaverages, we monitor the NAC fluctuation during thedynamics. Figure 3b presents the absolute NAC values over3000 fs in both MAI-rich and PbI2-rich systems. The NACfluctuates a lot, in particular, because it is proportional to thenuclear velocity, which changes significantly during MD. Thedifference between the instantaneous NAC values for the MAI-rich and PbI2-rich systems is very significant. The NAC in thePbI2-rich perovskite is always small, remaining less than 0.2meV. In contrast, the NAC can exceed 1 meV in the MAI-richperovskite, in particular, around 1600 and 2450 fs. In general,the small, sub-meV NAC values and rapid decoherence explainthe long, nanosecond electron−hole recombination times inthe perovskites.In order to characterize the nuclear motions that determine

the large NAC values in the MAI-rich system, we checkedseveral configurations during the 2200−2500 fs time intervalwhen the NAC reaches high magnitude (see Figure 3b). Figure4 demonstrates that the MA cations located on the perovskitesurface exhibit the largest motions. Because the MA species arecharged and carry significant dipole moments, they can couplestrongly to electrons and holes. There exists a significantamount of theoretical and experimental work showing that theorganic molecules can rotate inside of inorganic cages at roomtemperature.72−74 Indeed, the MA molecules in both theoutermost and subsurface layers rotate significantly, as shownby the curved arrows in Figure 4. The MA molecules in the

Figure 2. Evolution of the excited-state population in (a) PbI2-rich and (b) MAI-rich perovskites during the electron−hole recombinationdynamics. The red dotted lines show linear fits.

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outermost layer exhibit larger-amplitude motions and fasterrotations and even show a tendency for out-of-surfacemovement. For example, compared with the originalconfiguration at 2200 fs, the outermost MA molecules showsignificant displacement in the vertical direction during thenext few 100s of femtoseconds, as large as 1.38 Å at 2500 fs.The enhanced motions of the MA molecules on the perovskitesurface induce strong electron−phonon interactions in theMAI-rich perovskites. Generally, charge separation andrecombination are determined by both electronic couplingand electron−phonon interactions. The latter are particularlyimportant for the recombination process. Therefore, we canconclude that it is the strong electron−phonon coupling

induced by intense vibrations of the organic molecules thatresults in large NAC values in the MAI-rich perovskite, leadingto faster electron−hole recombination.In order to confirm the above conclusions and to obtain

further insights into the electron−phonon interactions in thetwo systems, we report the influence spectra calculated asFourier transforms of the autocorrelation functions of thephonon-induced fluctuations of the electronic energy gaps.The influence spectra characterize the phonon modes thatcouple to the electronic subsystem. Presented in Figure 3c, thespectra exhibit dominant peaks near 100 and 200 cm−1.Compared to the PbI2-rich system, the MAI-rich perovskiteshows many signals in the high-frequency area (>250 cm−1).High-frequency phonons are particularly important becausethey have higher velocities (for a given kinetic energy ortemperature) and create larger NAC that is proportional to thevelocity. The Pb−I inorganic sublattice of the MAPbI3perovskite shows only low-frequency vibrations, with thePb−I bending and stretching modes at 62 and 90 cm−1,respectively.75 The higher-frequency modes in the rangebetween 250 and 400 cm−1 arise from the much lighter MAcations, in particular, their hindered rotations.75−77 The modesabove 500 cm−1 show very little intensity in the computedinfluence spectra. The broader range of phonon modes and, inparticular, participation of the higher-frequency modesenhance electron−phonon interactions and increase NAC inthe MAI-rich system. The excess of PbI2 used in theexperiments decreases the concentration of MA molecules onthe perovskite surface, weakens electron−phonon interactions,and decreases the NAC responsible for the electron−holerecombination. This conclusion rationalizes the experimentalfindings.32−37

It is important to note that the effects of excess PbI2 on thedisorder and morphology of perovskite crystals are not trivial,and it is not absolutely clear if the PbI2 excess is incorporatedin the perovskite upon its growth. The current work focuses onthe effect of a PbI2 excess on the relative stability andabundance of the differently terminated surfaces. Otherprocesses related to the formation of defects, both in thebulk and at the surface, upon nonstoichiometric growth of theperovskite, can also play a prominent role in determining theproperties of the final material. For example, a MAI-deficientenvironment can hinder the formation of charge trap defects,such as iodine interstitials,78,79 leading to concomitantimprovement of the photoluminescence properties.In summary, using a combination of real-time TDDFT and

NAMD, we have investigated nonradiative electron−holerecombination in PbI2-rich and MAI-rich perovskites. Theinvestigation has been motivated by multiple experimentalpublications that report longer charge carrier lifetimes andbetter photovoltaic performance of PbI2-rich perovskites. Wehave analyzed the three factors that govern the nonradiativecharge carrier recombination, including the electronic energygap, the nonadiabatic electron−phonon coupling, andquantum coherence. The analysis shows that the NAC is themain factor rationalizing the improved properties of the PbI2-rich systems. The coupling is nearly an order of magnitudesmaller in the PbI2-rich perovskite compared to that in theMAI-rich perovskite. The electronic energy gap is smaller inthe PbI2-rich system, having a modest opposite effect on thecharge carrier recombination, while quantum coherence isessentially the same in the two cases. Further analysesdemonstrate that the increased NAC in the MAI-rich system

Figure 3. (a) Pure-dephasing functions. (b) Time-dependentabsolute NAC. (c) Phonon influence spectra.

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can be attributed to stronger electron−phonon interactionsinduced by rotating MA cations, especially those exhibitinglarge-amplitude motions on the perovskite surface. Accord-ingly, a slight excess of PbI2 in a perovskite decreases theconcentration of MA molecules and removes them from thesurface, weakening electron−phonon interactions. As a result,the decreased NAC suppresses nonradiative electron−holerecombination. In general, the charge carrier lifetimes in theperovskites are long because the NAC is very small, less than 1meV, and quantum coherence during charge recombination isshort, less than 10 fs. By providing clear atomistic ration-alization of the improved properties of the PbI2-rich perov-skites, our work clarifies the experimental results and generatesguidelines for improving the performance of the perovskitematerials.

■ AUTHOR INFORMATIONCorresponding Authors*E-mail: liminliu@buaa.edu.cn (L-.M.L.).*E-mail: prezhdo@usc.edu (O.V.P.).ORCIDOleg V. Prezhdo: 0000-0002-5140-7500NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSC.-J.T. and L.-M.L. acknowledge support by the National KeyResearch and Development Program of China Grant No.2016YFB0700700 and the National Natural Science Founda-tion of China (No. 51861130360, 51572016 and U1530401).L.-Q.L. and O.V.P. acknowledge support of the U.S. NationalScience Foundation, Grant No. CHE-1565704. We acknowl-edge computational support from the Special Program forApplied Research on Super Computation of the NSFC−Guangdong Joint Fund (the second phase) under Grant No.U1501501.

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Figure 4. Characteristic snapshots of the MAI-rich perovskite along the MD trajectory at successive times (a) 2200, (b) 2300, (c) 2400, and(d) 2500 fs in the region of large NAC (Figure 3b). The dashed circles demonstrate the original arrangement of the MA molecules in (a).The curved and straight arrows indicate rotation and upward movement, respectively.

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