Control of Charge Recombination in Perovskites by Oxidation State of

Article Cite This: J. Am. Chem. Soc. 2018, 140, 15753−15763

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Control of Charge Recombination in Perovskites by Oxidation State of Halide Vacancy Wei Li,† Yi-Yang Sun,‡ Linqiu Li,§ Zhaohui Zhou,∥ Jianfeng Tang,*,† and Oleg V. Prezhdo*,§ †

College of Science, Hunan Agricultural University, Changsha 410128, People’s Republic of China State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 201899, People’s Republic of China § Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States ∥ Chemical Engineering and Technology, School of Environmental Science and Engineering, and Key Laboratory of Subsurface Hydrology and Ecological Effects in Arid Region, Ministry of Education, Chang’an University, Xi’an 710064, People’s Republic of China

J. Am. Chem. Soc. 2018.140:15753-15763. Downloaded from pubs.acs.org by UNIV OF LOUISIANA AT LAFAYETTE on 11/30/18. For personal use only.

‡

S Supporting Information *

ABSTRACT: Advances in perovskite solar cells require development of means to control and eliminate the nonradiative charge recombination pathway. Using ab initio nonadiabatic molecular dynamics, we demonstrate that charge recombination in perovskites is extremely sensitive to the charge state of the halogen vacancy. A missing iodine anion in MAPbI3 has almost no effect on charge losses. However, when the vacancy is reduced, the recombination is accelerated by up to 2 orders of magnitude. The acceleration occurs due to formation of a deep hole trap in the singly reduced vacancy, and both deep and shallow hole traps for the doubly reduced vacancy. The shallow hole involves a significant rearrangement of the Pb− I lattice, leading to a new chemical species: a Pb−Pb dimer bound by the vacancy charge, and under-coordinated iodine bonds. Hole trapping by the singly reduced iodide vacancy operates parallel to recombination of free electron and hole, accelerating charge losses by a factor of 5. The doubly reduced vacancy acts by a sequential mechanism-free hole, to shallow trap, to deep trap, to free electron, and accelerates the recombination by a factor of 50. The study demonstrates that iodine anion vacancy can be beneficial to the performance, because it causes minor changes to the charge carrier lifetime, while increasing charge carrier concentration. However, the neutral iodine and iodine cation vacancies should be strongly avoided. The detailed insights into the charge carrier trapping and relaxation mechanisms provided by the simulation are essential for development of efficient photocatalytic, photovoltaic, optoelectronic and related devices.

1. INTRODUCTION

heat or moisture, and current−voltage hysteresis due to ion migration.18−27 Numerous experiments have been devoted to investigating charge carrier trapping and relaxation processes in perovskite materials.3,8,11,28−41 Nonradiative electron−hole recombination is extremely slow in perovskites, e.g., on the order of hundreds of nanoseconds in MAPbI3.42 However, the role of defects, especially their impact on carrier dynamics involving charge trapping and recombination, has not been studied in sufficient detail. It has been commonly accepted that perovskite materials exhibit unusual defect tolerance.43−45 First-principles calculations suggest that most point defects in perovskite materials are shallow and benign when carrier recombination is concerned, whereas deep level defects are hard to form in these materials.46−55 Yet, recent experiments reveal unexpected roles of some of the defects. Shallow defects in perovskite films could produce an unintentional doping.56

Hybrid organic−inorganic perovskite solar cells (PSCs) are attracting wide attention because of the rapid evolution of the power conversion efficiency.1−15 Perovskite materials, such as the now classic methylammonium lead halide (MAPbX3, X = Cl, Br, I), benefit from their superior optoelectronic properties, such as long carrier lifetime, high carrier mobility and high optical absorption coefficient, as well as from low-cost fabrication. Despite the impressive performance, the certified highest efficiency of 23.2% of PSCs16 is still below the thermodynamic limit of ∼31% for a single-junction device,17 suggesting the presence of channels for electron and energy losses. A fundamental understanding of the mechanisms of nonradiative electron−hole recombination and development of techniques to eliminate the recombination pathways are of great importance for the PSCs community. Intrinsic defects are inevitable in solution-processed perovskite films. Defects in perovskite are believed to correlate with such challenging issues as instability upon exposure to light, © 2018 American Chemical Society

Received: August 7, 2018 Published: October 26, 2018 15753

DOI: 10.1021/jacs.8b08448 J. Am. Chem. Soc. 2018, 140, 15753−15763

Article

Journal of the American Chemical Society

acts as an electron donor, creates a hole trap near the conduction band (CB), increases nonadiabatic electron− phonon coupling, and accelerates charge recombination by a factor of 5. The I+1 V vacancy produces an additional hole trap near the valence band (VB) by a different chemical mechanism. The negative charge occupying the vacancy attracts the two nearby Pb atoms that form a stable dimer and detach from iodines, leaving them chemically unsaturated. By introducing both shallow and deep trap states, IV+1 accelerates charge recombination by a factor of 50 compared to pristine MAPbI3. The results indicate strongly that the conditions of synthesis and operation of perovskite materials should be carefully controlled to suppress formation of neutral iodine and iodine cation vacancies, in order to optimize material performance.

Shallow defects may also play important roles in reducing the carrier lifetime,56−62 contrary to the general theoretically predicted properties of point defects. Observation of a monomolecular decay component by photoluminescence decay in PSCs suggests that trap-assisted recombination is the dominant loss mechanism,19,63,64 which is in contrast to the bimolecular recombination via direct band-to-band transition or Auger recombination.35,61 Charged ionic defects can be formed in the presence of external and built-in electric fields65 or light illumination.66,67 This is likely related to ionic conductivity of perovskite materials. Xiao and co-workers pointed out that the giant photovoltaic effect switchable by electric field in PSCs can be ascribed to the drift of charged defects.68 Sherkar and coworkers reported that the nonradiative charge recombination is sensitive to the charge state of defects.3 The presence of the iodide vacancy at room temperature could be responsible for ion migration, and the current−voltage hysteresis.67,69 The correlation between the current−voltage hysteresis and ion migration by charged defects was investigated theoretically.21−24 Though it is generally perceived that ionized defects are responsible for charge trapping in PSCs,10,15,70,71 Frolova et al. reported recently an uncommon enhancement of PSCs performance in the presence of iodine anion vacancy under bias voltage.28 The diverse experimental and theoretical observations raise important questions regarding the role of charged defects in nonradiative charge recombination in PSCs, calling for detailed theoretical investigations. In this work, we demonstrate that charge recombination in PSCs depends strongly on the oxidation state of the halide vacancy, which constitutes the most common type of defect due to its low formation energy.48,51,72−75 Utilizing the ab initio nonadiabatic molecular dynamics (NAMD) methodology,76−79 we consider MAPbI3 with neutral (IV), anion (I+1 V ) and cation (I−1 V )iodine vacancies and investigate the nonradiative carrier relaxation processes depicted in Figure 1. The simulations show that I−1 V creates no trap states and has little influence on charge recombination. The neutral iodine vacancy

2. SIMULATION METHODOLOGY The ab initio NAMD simulations are performed using the decoherence-induced surface hopping (DISH) approach.80 DISH is a quantum/semiclassical approximation,81 in which the heavier nuclei are treated semiclassically whereas the lighter electrons maintain their quantum character. The original version of DISH has been adapted to the classical path approximation (CPA) and implemented in the PYthon eXtension for Ab Initio Dynamics (PYXAID) code.76,77 The methodology has been used successfully to investigate excited state dynamics in a wide range of systems, including perovskites and other materials.82−94 The simulation cell is formed from (2 × 2 × 2) unit cells of pseudocubic perovskite95 and contains 96 atoms. Initially, the MA cations point along the [100] direction which creates a more stable structure compared to the [110] and [111] directions.96 The neutral iodine vacancy defect is obtained by removing an iodine atom from the pristine system. The charged vacancy defects are achieved by removing or adding one electron from the neutral vacancy supercell. Spin-polarized calculations are performed for the neutral vacancy system that has an odd number of electrons. The geometric and electronic structure calculations, and adiabatic molecular dynamics are carried out using the VASP code.97 The simulations use the PBE functional,98 400 eV plane-wave energy cutoff, and Γ-centered 4 × 4 × 4 Monkhorst−Pack k-point mesh. Atomic positions are relaxed until the calculated Hellmann−Feynman forces on the atoms are smaller than 0.02 eV/Å. After the structure optimization, the system is brought up to 300 K in the canonical ensemble using the Nosé thermostat. Then, a 3 ps trajectory is obtained in the microcanonical ensemble and used for the nonadiabatic coupling calculations. The 3 ps NA Hamiltonian is repeated twice to obtain 6 ps of input for NAMD and to allow good averaging over initial conditions. The averaging is done over 3000 initial geometries and 1000 stochastic realizations of the DISH process for each geometry. The 3 million DISH trajectories can be generated due to application of the CPA to surface hopping, as described in the papers accompanying the release of PYXAID.76,77 The trajectory and the NA Hamiltonians are precomputed, allowing one to achieve a large number of stochastic realizations of the surface hopping algorithm. A large number of DISH trajectories is needed in order to sample properly the slow hopping processes, which have low probability during the simulation time. Similarly to other surface hopping procedures, DISH involves a stochastic process that determines when hops occur. A uniform random number between 0 and 1 is generated, and the DISH probability is compared to this number in order to decide whether or not to hop. Nonradiative electron−hole recombination in perovskites can take a few hundred nanoseconds, and it is computationally very expensive to model charge trapping and recombination processes on such time scale by solving the time-dependent Schrodinger equation. Instead, we consider all possible pairs of states, model quantum dynamics between the state pairs using DISH, and obtain rates constants for each process depicted in Figure 1. The set of considered states

Figure 1. Investigated charge carrier trapping, detrapping and relaxation processes in pristine MAPbI3 and MAPbI3 with (a) I−1 V , (b) IV, and (c) I+1 V defects. ① Formation of electrons and holes via photoexcitation across the band gap. ② Nonradiative electron−hole recombination between conduction band minimum (CMB) and valence band maximum (VBM), bypassing traps. ③, ⑤ Capture of hole by a trap state in IV and I+1 V . ④, ⑧ Recombination of trapped holes with electrons in the CBM (trap-assisted recombination) in IV and I+1 V . ⑥ Detrapping of holes by excitation from the shallow trap to the CBM in I+1 V . ⑦ Decay of trapped holes from the shallow trap to the deep trap. Blue (red) ball refers to hole (electron). The dashed lines denote the Fermi level. 15754


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Journal of the American Chemical Society includes VBM, CBM and all midgap states for each system. We compute pairwise transition rates between all pairs of states in this set, with the data shown in Supporting Information. Then, we construct coupled differential equations and integrate them using these rate constants, in order to produce time-dependent populations of each state. The details of construction of coupled kinetics equations are shown in Supporting Information. Previous works highlighted the importance of spin−orbit coupling (SOC) in MAPbI3 due to presence of the heavy Pb atom.99,100 However, SOC has a negligible effect on the geometric structure,101,102 while accurate electronic structure calculations require simultaneous inclusion of SOC and a correction for the electron self-interaction error, making such calculations much more computationally expensive than PBE.47,103−105 Pure DFT functionals, such as PBE, exhibit a cancelation of the errors associated with SOC and self-interaction. In particular, the earlier calculation shows that the PBE functional provides the iodine vacancy energy levels that are similar to those obtained with the high level methods.75

pristine MAPbI3, each Pb atom is bound to six iodine atoms to form the PbI6 octahedron, and the organic cations, MA+, are inside the Pb−I inorganic cage. Such hybrid perovskite materials are soft, allowing for considerable thermal atomic motions.20 The organic cations fluctuate more than the inorganic lattice, both because the organic cations are composed of lighter atoms, and because the Pb−I octahedrons are relatively rigid and define the overall structure of the material. It has been reported that organic cations are rotationally mobile at room temperature, changing their orientation on a picosecond time scale.106 The iodine vacancy leads to formation of under-coordinated Pb cations, which can create defect states and/or form new chemical bonds. The Pb−Pb distance between the neighboring under-coordinated atoms is 6.2 Å in neutral IV at 0 K. The distance increases by 0.7 Å in the I−1 V system, and decreases dramatically by about 3 Å in the I+1 V system. The evolution of the Pb−Pb distances around the vacancy site at 300 K is shown in Figure 2e. The distances fluctuate around the average values +1 of 5.8, 6.8, and 3.7 Å for IV, I−1 V and IV , following the same order as in the static structures. The Pb−Pb distance is longer in I−1 V than IV, because removal of an iodine anion (iodide) leaves a positive charge between the Pb cations, increasing their repulsion. On the contrary, Pb−Pb distance becomes shorter in the I+1 V system, which contains a negative charge in the vacancy between the two Pb cations. After capture of an extra electron, the vacancy attracts the two Pb cations that move toward each other and form a Pb dimer. Formation of the stable Pb dimer in the presence of the negatively charged halogen vacancy has been confirmed theoretically.49 The oscillation of Pb−Pb distance in the I+1 V system is less significant than in IV and I−1 V , Figure 2e, indicating that the Pb−Pb dimer remains stable at ambient conditions. In order to characterize how the iodine vacancy defects influence nuclear dynamics, we calculated the root-meansquare displacement velocity of atoms in the four systems. Then, we grouped the atoms into organic (MA) and inorganic (Pb and I) components. Further, in the defective perovskites, we categorized the Pb and I atoms into those neighboring the vacancy site and away from it. The data are shown in Table 1.

3. RESULTS AND DISCUSSION 3.1. Geometric Structure and Thermal Fluctuations. The optimized structures of pristine MAPbI3, and MAPbI3 +1 with the IV, I−1 V and IV vacancies are shown in Figure 2a−d. The vacancy sites are highlighted by the black solid circles. In

Table 1. Root-Mean-Square Velocity (Å/fs) of Atomic Positions in Pristine and Defective MAPbI3 pristine IV I−1 V I+1 V

totala

MAb

Pb−Ic

Pb−Id

Pb−Ie

0.065 0.049 0.058 0.055

0.093 0.069 0.081 0.079

0.009 0.011 0.011 0.0071

− 0.010 0.0092 0.0049

− 0.011 0.011 0.008

a

Averaged over all atoms. bAveraged over atoms in MA. cAveraged over Pb and I atoms. dAveraged over Pb and I atoms around the vacancy site. eAveraged over Pb and I atoms away from the vacancy site.

Figure 2. Optimized structures of (a) pristine MAPbI3, and MAPbI3 +1 with (b) I−1 V , (c) IV and (d) IV defects. (e) Evolution of the Pb−Pb distance around the vacancy site. The numbers represent canonically averaged Pb−Pb distances along the MD trajectory and, in parentheses, Pb−Pb distances in the optimized ground state structure. The Pb−Pb distance is longest in I−1 V because Coulomb repulsion separates the Pb cations after removal of the iodine anion. The Pb− Pb distance is shortest in I+1 V , because the Pb atoms are attracted to the negative charge left in the vacancy. The two Pb atoms in I+1 V are sufficiently close to form a stable dimer, as evidenced by the small fluctuation in the Pb−Pb distance, compared to the other two cases.

The results demonstrate that the iodine vacancy in all charge states (0,+1,−1) suppresses vibrations of the organic cations. This fact is perhaps surprising, because removal of an iodine atom creates additional space. It can be rationalized by distortion of the inorganic lattice, creating additional constraints on the MA cations and inorganic octahedra. In contrast to the motions of the organic species, vibrations of the Pb−I octahedra are enhanced in the IV and I−1 V systems compared with the pristine system. This is because the 15755


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+1 Figure 3. Projected density of states (pDOS) for (a) pristine MAPbI3, and MAPbI3 with (b) I−1 V , (c) IV and (d) IV defects obtained for the optimized geometry. The inserts show charge densities of the band edge and trap states, with the organic cations removed for better visualization because the contributions from the organic subsystem are zero. I−1 V creates no gap states. The neutral iodine vacancy IV introduces an occupied trap state below the Fermi level. I+1 V introduces both deep and shallow occupied trap states below the Fermi level.

sufficient hybridization of the Pb-6p orbitals around the vacancy site to form a deep bound state, because the distance between the Pb ions around the vacancy site is larger. Because the trap is an occupied state, it acts as a hole trap, i.e., holes created in VB upon photoexcitation can recombine with electrons in both the CB and the trap state. The I−1 V system exhibits no gap states in the pDOS plot, Figure 3b. The defect states have energies within the CB. Removal of the iodine anion does not alter the oxidation states of the atoms in the perovskite structure, creating no unsaturated chemical bonds. The distance between the two Pb atoms, which used to be connected by the missing iodine, is the largest among the three vacancy cases, Figure 2e, indicating that the Pb atoms do not attempt to create new bonds. The IV+1 vacancy introduces a relatively deep, doubly occupied defect state below the CBM, Figure 3d. The negative charge that is left in the vacancy after removal of iodine cation attracts the Pb cations, which form a stable bond, insert in Figure 3d, with the bond distance twice shorter than the Pb− Pb distance in pristine perovskite and perovskite with the other two vacancies, Figure 2e. The doubly occupied defect state is localized on this Pb−Pb dimer bond and serves as a deep hole trap near the CBM. In addition to the deep trap, the I+1 V defect creates a shallow hole trap state near the VBM, as well as a state right at the VBM, Figure 3d. These state arise from I-5p atomic orbitals. Because the shallow hole trap is located within a few kBT of the VBM, the trapped hole can escape back to the VB on a relatively fast time scale. Figure 3 demonstrates that the electronic structure of the iodine vacancy site can be efficiently tuned by regulating the system charge, which depends, for instance, on operating conditions of a perovskite solar cell. As the system becomes more negative, the Pb−Pb distance around the iodine vacancy site is shortened, enhancing hybridization of the 6p orbitals of the Pb atoms around the vacancy, and lowering the trap state energy from inside the CB into the bandgap. Such changes can

inorganic lattice has lost two bonds associated with the missing iodines. The enhanced motions of the inorganic lattice are consistent with the previous static calculations showing that ion migration is likely mediated by vacancy defects.21,22 The displacement of the Pb and I atoms is smaller in the I+1 V system, especially for the atoms next to the vacancy, Table 1. The result can be ascribed to the formed Pb dimer, Figures 2d,e and 3d, that is stable under thermal fluctuations. Formation of the Pb dimer stabilizes the vacancy site in the I+1 V system and inhibits the migration of iodine ions. 3.2. Electronic Structure. The dependence of the electronic structure on the charge of the iodine vacancy can be understood by considering the projected density of states (pDOS) shown in Figure 3. The total DOS is separated into contributions from Pb-6s and -6p states, and I-5s and -5p states. The charge densities for the band edge states and the trap state are shown in the insets. The calculated bandgap of pristine perovskite is 1.65 eV, consistent with the previous calculation on cubic MAPbI3.50 The VB maximum (VBM) originates mainly from I-5p orbitals, whereas Pb-6p orbitals dominates the CB minimum (CBM). The VBM and CBM orbitals are separated in space, minimizing their overlap, and therefore, leading to weak electron−hole interaction and low recombination rate. The organic cations carry no contribution to the band edges states. Their role is to stabilize the Pb−I octahedra and neutralize the system. The neutral IV vacancy creates only a trap state that derives from the CB. The state is populated by an electron, and therefore, IV acts as an n-type dopant and introduces negative charge carriers near the CB. In the spin-polarized calculation, the trap state is half-occupied, and split into a lower lying occupied state near the CBM, Figure 3c, and a higher lying empty state above the CBM, Figure S1 of Supporting Information. The gap state in neutral IV is formed due to hybridization of dangling bonds from the nearby Pb cations, i.e., it is a predominantly Pb-6p state. However, there is no 15756


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Figure 4. Spectral densities characterizing phonon modes involved in charge carrier trapping and relaxation in (a) pristine MAPbI3, and MAPbI3 +1 with (b) I−1 V , (c) IV and (d) IV . Notice different y-axis scales, which use arbitrary but consistent units. The IV system shows the strongest electron− phonon coupling, whereas the I+1 V system involves the largest number of modes extending into the higher frequency region.

Table 2. Averaged Absolute Value of Nonadiabatic Coupling (|NAC|, meV), Pure-Dephasing Time (fs), and Rate Constant (ns−1) for Pairs of Electronic States in Pristine and Defective Perovskites

|NAC| Dephasing Rate

pristine

I−1 V

vbm-cbm

vbm-cbm

vbm-cbm

vbm-trap

cbm-trap

vbm-cbm

vbm-shallow

shallow-deep

vbm-deep

cbm-shallow

cbm-deep

0.44 6.2 0.0065

0.43 6.0 0.0073

0.58 5.8 0.018

0.56 5.3 0.018

3.99 8.6 92.59

0.43 5.9 0.0074

15.9 13.2 29.58a/4.33b

0.68 6.3 0.47

0.91 7.4 0.70

0.53 5.0 0.014

0.46 6.3 0.83

I+1 V

IV

a

Trapping. bDetrapping.

experimental Raman spectra.112 Defects create localized states, inserts in Figure 3, and introduce higher frequency motions, Figure 4. The pure-dephasing times, shown in Table 2, are obtained using the optical response function formalism in the second cumulant approximation.107−111 Loss of coherence influences quantum dynamics, as exemplified by the quantum Zeno effect,113 because transition between a pair of states requires formation of superpositions between them. In the present case, superpositions are formed due to NA coupling. Loss of coherence destroys the superpositions, collapsing the wave function to one of the states. For example, if the system starts in state 1, rapid decoherence collapses the system back to state 1 before the system is able to form a significant superposition with state 2. Thus, the system is never able to make the transition, leading to the quantum Zeno effect.113 Decoherence proceeds on a 10 fs time scale, which is typical for solid materials,84 with exception of carbon-based nanoscale systems.114,115 The pure-dephasing time is significantly faster than inelastic electron−phonon energy exchange that occurs over hundreds of ns in perovskite materials. Quantum coherence is longest, 13.2 fs, for the transition between the VBM and the shallow hole trap in the I+1 V system, Table 2, because these states have small energy gap, Figure 3d, and because they both are composed of I-5p orbitals. The other considered pairs of states have larger gaps and are localized on

have a strong influence on the charge carrier trapping and relaxation processes. 3.3. Electron-Vibrational Interactions. Electron-vibrational interactions produce elastic and inelastic scattering events. Elastic scattering leads to loss of quantum coherence in the electronic subsystem, whereas inelastic scattering dissipates electronic energy to heat through nonradiative relaxation. Both types of scattering events influence quantum dynamics of charge trapping and recombination. In order to characterize the phonon modes that couple to the electronic transitions between the key pairs of states, Figure 1, we compute autocorrelation functions (ACF) of the energy gap fluctuations and their Fourier transforms (FT). The ACF are used to compute the pure-dephasing/decoherence times according to the optical response theory.107−111 The FT spectrum is known as the influence spectrum, or the spectral density. The intensity of each peak in the influence spectrum characterizes the electron−phonon coupling strength at the particular phonon frequency. The influence spectra shown in Figure 4 are dominated by low frequency modes originating from motions of the heavy Pb and I atoms that support all states involved in charge trapping and recombination. High frequency modes are absent because the organic cations do not contribute to the band edge and trap states. The dominant peaks around 100 cm−1 and below can be assigned to Pb−I stretching and bending modes, in agreement with the 15757


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Figure 5. Evolution of populations of the key states involved in charge trapping and recombination in pristine and defective MAPbI3. The I−1 V defect creates no trap states inside the bandgap, Figure 3, and accelerates the recombination only slightly. The recombination is accelerated by a factor of 5 in the IV system and by a factor of 50 in the I+1 V system.

vacancy causes minor perturbations to the CBM and VBM wave functions, insert in Figure 3b. The neutral IV and I+1 V vacancies accelerate electron−hole recombination by providing new relaxation pathways. The trap state located near the CBM in the IV system provides an additional channel for hole trapping. Once trapped, the hole rapidly recombines with a CB electron, such that the trap state population never builds up appreciably, blue line in Figure 5c. Overall, the electron−hole recombination in IV accelerates by a factor of 5 compared to the I−1 V vacancy and a factor of 6 relative to the pristine system. The charge trapping and recombination accelerate by another order of magnitude in the doubly reduced I+1 V vacancy, because the system contains several defect states in the bandgap. Recombination of free electron and hole directly between CBM and VBM is no longer important in the I+1 V system, whereas it is significant in the other three cases. Judging by the state-to-state rate constants shown in Table 2, the dominant mechanism involves hole trapping by the shallow trap, 29.58 ns−1, transition of the hole from the shallow to the deep trap, 0.47 ns−1, and recombination of the deep trap hole with the CBM electron, 0.83 ns−1. Note that the shallow trap can be populated and depopulated multiple times before the hole hops to the deep trap: compare the 0.47 ns−1 rate for the transition from the shallow to the deep trap with the 4.33 ns−1, for the transition from the shallow trap back to the VBM. The above results suggest that a flow of electrons in PSCs and other devices can shorten significantly charge carrier lifetimes in the presence of iodine vacancies. This can be a common problem in applications, because iodides tend to diffuse in perovskites, forming iodide rich and pure phases. It is important to note that defect concentration is not considered explicitly in our work. The experimental range of defect concentration is on the order of 1016−1017 cm−3.66 We use a 2 × 2 × 2 cubic supercell of the MAPbI3 perovskite containing 96 atoms. The supercell volume is 1.988 × 10−21 cm3. The defect concentration is higher in the current calculation than in the experiments due to computational limitations on the simulation cell size. For this reason, our calculation focuses on the lifetime of charge carriers trapping

different atoms. Consequently, all other coherence times are shorter, less than 10 fs. The fast coherence loss contributes to long charge carrier lifetimes in halide perovskites, as exemplified by the quantum Zeno effect.113 An additional argument can be given by the Fermi’s golden rule expression for the transition rate. One can show that the decoherence function, defined in the time-domain, is directly related to the Franck−Condon factor, defined in the frequency domain.116,117 A shorter coherence time corresponds to a smaller Franck−Condon factor and a smaller transition rate. 3.4. Charge Trapping and Recombination Dynamics. Finally, we consider the charge carrier trapping and relaxation processes defined in Figure 1, and characterized in Table 2 and Figure 5. The time scales reported in Figure 5 are obtained by exponential fitting. The rise and decay components in the populations of trap states are fitted separately, and time scales correspond to the decay components. The rate constants presented in Table 2 are obtained by performing DISH simulations for each pair of states, with the corresponding data and fits shown in Supporting Information. The plots shown in Figure 5 are solutions of kinetics equations with the rates reported in Table 2. The strong dependence of the charge carrier trapping and recombination on the oxidation state of the iodine vacancy constitutes the main result of the current work. The charge carrier lifetime decreases by one and two orders of magnitude +1 as the I−1 V vacancy is reduced to IV and IV , respectively. Electron−hole recombination in the pristine perovskite takes 152.7 ns. This time scale is consistent with our earlier simulation82 and agree with experiment.30,118 The slow recombination owes to small NA coupling (0.44 meV) and fast decoherence (6.2 fs). The coupling is small because the CBM and VBM wave functions are localized on different subsystems, lead and iodine atoms, and because the coupling is generated by slow motions of the heavy elements, Figure 4. The I−1 V vacancy has little influence on the nonradiative charge recombination because it creates no states inside the bandgap, Figure 3b, and its NA coupling and pure-dephasing times are comparable to those of the pristine system, Table 2. The local distortion of the octahedral structure associated with the 15758


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dimer is much shorter than in the pristine perovskite as well as in the systems containing the I−1 V and IV defects, the Pb atoms move away from iodines. The under coordinated iodine atoms formed this way are responsible for the shallow hole trap near the VBM. On the one hand, the I+1 V vacancy accelerates charge trapping and recombination; on the other hand, the dimer formation in this case stabilizes the vacancy and prevents its migration, thereby reducing the current−voltage hysteresis observed in PCSs. The electron−hole recombination in the presence of the IV vacancy occurs by two parallel channels, including direct recombination of electron and hole between the VBM and the CBM, and hole trapping followed by rapid recombination with the CB electron. The recombination in the I+1 V system occurs by the sequential mechanism, involving transitions of the hole from the VBM to the shallow trap, to the deep trap, and to the CBM. The first step is reversible because the shallow-to-deep trap transition takes longer than escape of the hole from the shallow trap to the VB. The nonradiative charge relaxation is facilitated by low frequency vibrations of the inorganic Pb−I lattice. Higher frequencies appear due to defects that create localized states and exhibit stronger electron−phonon coupling. The study indicates strongly that perovskite films need to be carefully manipulated to avoid formation of the neutral IV and negatively charged I+1 V vacancies. The problem can arise both during perovskite synthesis and under device operating conditions involving flow of charges. The simulations suggest that IV−1 vacancies can have a positive effect on PCS performance as observed in experiments.28 The in-depth understanding of the defect chemistry and photophysics provided by the simulations assists in the development of high-efficiency PSCs and other related devices.

and recombination by a single defect. Charges generated by light in a macroscopic perovskite sample diffuse, and get trapped and recombine, once they reach a defect site. Defect concentration would enter a higher level reaction-diffusion model, in which charge recombination on a defect site (reaction) is combined with charge diffusion within the material. The current results can be used as input to such reaction-diffusion calculations.19,66,119 The key result of this work is that the oxidation state of the halide vacancy can regulate formation of shallow or deep traps, and thus modulate the charge recombination process. Does this result apply to other perovskites, e.g., involving different halides or all-inorganic materials? It is quite likely that our conclusions apply to all-inorganic perovskites, given similarity in the defect chemistry and the fact that the A-site cation, such as MA+ and Cs+, does not contribute directly to the charge carrier states near the band edges and to the defect states. The A-site cation may influence the charge carrier dynamics through a complex interplay of motions of the A-site cation and the inorganic lattice. Cl and Br are more electronegative and smaller than I, and bonds of Pb with Cl/Br are more rigid than the Pb−I bond. Therefore, one expects that the inorganic octahedra distort less in the X = Cl/Br systems in the presence of a halide vacancy. Hence, it is possible that the X− and X vacancies are “healed” less, and the corresponding vacancy states are deeper inside the bandgap. Two effects should be considered regarding formation of the Pb−Pb dimer and the corresponding shallow hole trap in the presence of the X+ vacancy. On the one hand, the more rigid Pb−Cl/Br structure can prevent formation of the dimer, which requires significant displacements of Pb atoms. On the other hand, the Pb atoms are closer to each other in the tighter Pb−Cl/Br perovskite, and they need to move less to form the dimer. Given the strong effect of the oxidation state of the halide vacancy on charge trapping and recombination in MAPbI3, the importance of oxidation states of this and other defects in various halide perovskites merits further investigation.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.8b08448. Density of states for the spin-down component in the IV system; data fitting for the state-to-state transition rates; and coupled kinetics equations (PDF)

4. CONCLUSIONS In summary, we have demonstrated that oxidation state of the iodine vacancy defect in the MAPbI3 perovskite has a strong influence on charge carrier trapping and recombination. Our time-domain ab initio simulations show that nonradiative charge recombination remains essentially unaffected in the − presence of the I−1 V vacancy (missing I ). Once the vacancy gets reduced, charge losses are accelerated by up to 2 orders of magnitude. The effect arises due to formation of occupied midgap states that can trap the hole, facilitating its recombination with the electron. The neutral iodine vacancy IV creates a state near the CB, while I+1 V produces both shallow and deep hole traps. There are no midgap defect states in the I−1 V system. In comparison, a defect state splits off the CB into the bandgap in the presence of the IV vacancy, because it acts as a n-dopant and places an electron into the CB. This defect state exists in the I+1 V system as well, and it is deeper inside the bandgap, because it is now doubly occupied. The shallow hole trap seen in the I+1 V system slightly above the VB is formed by a different mechanism. The negative charge left in the vacancy site by the 2+ I+1 cations V defect interacts so strongly with the nearby Pb that they form a dimer, which remains stable at room temperature. Because the Pb−Pb bond distance in the Pb

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AUTHOR INFORMATION

Corresponding Authors

*[email protected] *[email protected] ORCID

Wei Li: 0000-0002-9999-5081 Zhaohui Zhou: 0000-0002-9131-6136 Oleg V. Prezhdo: 0000-0002-5140-7500 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS O.V.P. acknowledges funding from the U.S. Department of Energy (grant no. DE-SC0014429). W.L. acknowledges startup funding from Hunan Agricultural University (grant 540499818006) and thanks Drs. Liujiang Zhou, Zhufeng Hou, and Wanjian for fruitful discussions. J.T. acknowledges support by the National Nature Science Foundation of China (grant 51301066). Y.-Y.S. acknowledges support by the 15759


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National Natural Science Foundation of China (grant 11774365). The simulations were performed at the University of Southern California’s Center for High-Performance Computing (hpcc.usc.edu).

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Control of Charge Recombination in Perovskites by Oxidation State of

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