Control of Charge Recombination in Perovskites by Oxidation State of

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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 J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b08448 • Publication Date (Web): 26 Oct 2018 Downloaded from http://pubs.acs.org on October 26, 2018

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Journal of the American Chemical Society

Control of Charge Recombination in Perovskites by Oxidation State of Halide Vacancy

Wei Li,1 Yi-Yang Sun,2 Linqiu Li,3 Zhaohui Zhou,4 Jianfeng Tang,1* Oleg V. Prezhdo3*

1

College of Science, Hunan Agricultural University, Changsha 410128, P. R. China

2

State Key Laboratory of High Performance Ceramics and Superfine Microstructure,

Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 201899, China 3

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

United States 4

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, China

*Corresponding authors, email: [email protected] (J. F. T.); [email protected] (O. V. P.)

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Abstract Advances in perovskite solar cells require development of means to control and eliminate 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 two 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 PbPb 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, since 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.


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1. Introduction 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, 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 3 ACS Paragon Plus Environment


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 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 coworkers 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 While 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.


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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 (𝐼𝐼𝑉𝑉 ),

anion (𝐼𝐼𝑉𝑉+1) and cation (𝐼𝐼𝑉𝑉−1 )iodine vacancies and investigate the nonradiative relaxation processes depicted in Figure 1. The simulations show that 𝐼𝐼𝑉𝑉−1 creates no trap states and

has little influence on charge recombination. The neutral vacancy acts as an electron donor, creates a hole trap near the conduction band (CB), increases electron-phonon coupling, and

accelerates charge recombination by a factor of five. The 𝐼𝐼𝑉𝑉+1 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, 𝐼𝐼𝑉𝑉+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.

2. Simulation Methodology. The ab initio NAMD simulations are performed using the decoherence-induced surface hopping (DISH) approach.80 DISH is a quantum/semi-classical approximation,81 in which the heavier nuclei are treated semi-classically 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 pseudo-cubic 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 4x4x4 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, 6 ACS Paragon Plus Environment

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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 timescale 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 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 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 7 ACS Paragon Plus Environment


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

3. Results and Discussion 3.1 Geometric Structure and Thermal Fluctuations The optimized structures of pristine MAPbI3, and MAPbI3 with the 𝐼𝐼𝑉𝑉 , 𝐼𝐼𝑉𝑉−1 and 𝐼𝐼𝑉𝑉+1

vacancies are shown in Figure 2a-d. The vacancy sites are highlighted by the black circles. In 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 since 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 timescale.106 The iodine vacancy leads to formation of under-coordinated Pb ions, 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 𝐼𝐼𝑉𝑉 at 0 K. The distance increases by 0.7 Å in the 𝐼𝐼𝑉𝑉−1 system, and decreases dramatically by about 3 Å in the 𝐼𝐼𝑉𝑉+1 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 of 5.8, 6.8 and 3.7 Å for 𝐼𝐼𝑉𝑉 , 𝐼𝐼𝑉𝑉−1 and 𝐼𝐼𝑉𝑉+1 , following the same order as in the static structures. The Pb-Pb distance is longer in 𝐼𝐼𝑉𝑉−1 8

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than 𝐼𝐼𝑉𝑉 , 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 𝐼𝐼𝑉𝑉+1 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 ions that move towards 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 𝐼𝐼𝑉𝑉+1 system is less significant than in 𝐼𝐼𝑉𝑉 and 𝐼𝐼𝑉𝑉−1 , 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-mean-square 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. 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, since 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 𝐼𝐼𝑉𝑉 and 𝐼𝐼𝑉𝑉−1 systems compared with the pristine system. This is because the inorganic lattice has lost two bonds associated with the

missing iodines. The enhanced motions of the inorganic ions 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 𝐼𝐼𝑉𝑉+1 system, especially for the atoms next to the vacancy, Table 1. The result can be ascribed to the formed Pb 9 ACS Paragon Plus Environment


dimer, Figures 2d,e and 3d, that is stable under thermal fluctuations. Formation of the Pb dimer stabilizes the vacancy site in the 𝐼𝐼𝑉𝑉+1 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 pDOS 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 inserts. The calculated band gap of pristine perovskite is 1.65 eV, consistent with the previous calculations 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 𝐼𝐼𝑉𝑉 vacancy creates only a trap state that derives from the CB. The state

is populated by an electron, and therefore, 𝐼𝐼𝑉𝑉 acts as an n-type dopant and introduces negative charge carriers near the CB. In the spin-polarized calculation, the trap state is halfoccupied, 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 𝐼𝐼𝑉𝑉 is formed due to hybridization of dangling bonds from the nearby Pb ions, i.e., 10 ACS Paragon Plus Environment

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it is a predominantly Pb-6p state. However, there is no sufficient hybridization of the Pb6p orbitals around the vacancy site to form a deep bound state, because the distance between the Pb ions around the vacancy site is larger. Since the trap is an occupied state, it acts as a hole trap, i.e., holes created in VB upon photo-excitation can recombine with electrons in both the CB and the trap state. The 𝐼𝐼𝑉𝑉−1 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 𝐼𝐼𝑉𝑉+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 𝐼𝐼𝑉𝑉+1

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 timescale. 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 11 ACS Paragon Plus Environment


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 band gap. Such changes can have a strong influence on the charge carrier trapping and relaxation processes.

3.3 Electron-Vibrational Interactions Electron-vibration interactions produce elastic and inelastic scattering events. Elastic scattering leads to loss of quantum coherence in the electronic subsystem, while 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


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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 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 2nd cumulant approximation.107–111 Loss of coherence influences quantum dynamics, as exemplified by the quantum Zeno effect,113 since transition between a pair of states requires formation of a superpositions between them. In the present case, superpositions are formed due to NA coupling. Loss of coherence destroys the superpositions, collapsing the wavefunction 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 timescale, 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 𝐼𝐼𝑉𝑉+1 system, Table 2, because these states have small energy gap, Figure 3d,

and since they both are composed of I-5p orbitals. The other considered pairs of states have larger gaps and are localized on 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 Golden rule expression for the transition 13 ACS Paragon Plus Environment


rate. One can show that the decoherence function, defined in the time-domain, is directly related to the Franck-Condon factor, defined in the energy 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 timescales reported in Figure 5 are obtained by exponential fitting. The rise and decays components in the populations of trap states are fitted separately, and timescales 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 data 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 as the 𝐼𝐼𝑉𝑉−1 vacancy is reduced to 𝐼𝐼𝑉𝑉 and 𝐼𝐼𝑉𝑉+1 , respectively. Electron-hole recombination in the pristine perovskite takes 152.7 ns. This timescale 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 wavefunctions 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 𝐼𝐼𝑉𝑉−1 14 ACS Paragon Plus Environment

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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 geometric structure associated with the vacancy causes minor perturbations to the CBM and VBM wavefunctions, insert in Figure 3b. The neutral 𝐼𝐼𝑉𝑉 and 𝐼𝐼𝑉𝑉+1 vacancies accelerate electron-hole recombination by

providing new relaxation pathways. The trap state located near the CBM in the 𝐼𝐼𝑉𝑉 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 𝐼𝐼𝑉𝑉 accelerates by a factor of

5 compared to the 𝐼𝐼𝑉𝑉−1 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

𝐼𝐼𝑉𝑉+1 vacancy, since the system contains several defect states in the gap. Recombination of free electron and hole directly between CBM and VBM is no longer important in the 𝐼𝐼𝑉𝑉+1

system, while 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 15 ACS Paragon Plus Environment


applications, since 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 charges trapped 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 allinorganic 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 cation may influence the charge carrier dynamics through a complex interplay of motions of the 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 16 ACS Paragon Plus Environment

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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 gap. 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.

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. Out time-domain ab initio simulations show that nonradiative charge recombination remains essentially unaffected in the presence of the 𝐼𝐼𝑉𝑉−1 vacancy (missing I-). Once the vacancy gets reduced, charge losses are accelerated by up to two 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 vacancy 𝐼𝐼𝑉𝑉 creates a state near the CB, while 𝐼𝐼𝑉𝑉+1 produces both shallow and deep hole traps.

There are no midgap defect states in the 𝐼𝐼𝑉𝑉−1 system. In comparison, a defect state

splits off the CB into the bandgap in the presence of the 𝐼𝐼𝑉𝑉 vacancy, since acts as a n-dopant

and places an electron into the CB. This defect state exists in the 𝐼𝐼𝑉𝑉+1 system as well, and 17

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it is deeper inside the gap, because it is now doubly occupied. The shallow hole trap seen in the 𝐼𝐼𝑉𝑉+1 system slightly above the VB is formed by a different mechanism. The negative

charge left in the vacancy site by the 𝐼𝐼𝑉𝑉+1 defect interacts so strongly with the nearby Pb2+

cations that they form a dimer, which remains stable at room temperature. Since the Pb-Pb bond distance in the Pb dimer is much shorter than in the pristine perovskite as well as in the systems containing the 𝐼𝐼𝑉𝑉−1 and 𝐼𝐼𝑉𝑉 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. While on the one hand, the 𝐼𝐼𝑉𝑉+1 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 𝐼𝐼𝑉𝑉 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 𝐼𝐼𝑉𝑉+1 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 since the shallow-to-deep trap transition takes longer than escape of the hole from the shallow trap. 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 𝐼𝐼𝑉𝑉 and negatively charged 𝐼𝐼𝑉𝑉+1 vacancies. The problem

can arise both during perovskite synthesis and under device operating conditions involving 18 ACS Paragon Plus Environment

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flow of charges. The simulations suggest that 𝐼𝐼𝑉𝑉−1 vacancies can have a positive effect on

PCS performance as observed in experiments.28 The understanding of the defect chemistry and photo-physics provided by the simulations assists in the development of highefficiency PSCs and other devices.

Acknowledgements O. V. P. acknowledges funding from the U.S. Department of Energy (grant no. DESC0014429). W. L. acknowledges startup funding from Hunan Agricultural University (grant 540499818006) and Dr. Liujiang Zhou for fruitful discussions. J. F. T. acknowledges support by the National Nature Science Foundation of China (grant 51301066). Y.Y.S acknowledges support by the 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).

Supporting Information Available: Density of states for the spin-down component in the 𝐼𝐼𝑉𝑉 system; data fitting for the state-to-state transition rates; and coupled kinetics

equations. The material is available free of charge via the Internet at http://pubs.acs.org.



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Figure Captions.

Figure 1. The investigated charge carrier trapping, detrapping and relaxation processes in pristine MAPbI3 and MAPbI3 with (a) 𝐼𝐼𝑉𝑉−1 , (b) 𝐼𝐼𝑉𝑉 , and (c) 𝐼𝐼𝑉𝑉+1 defects. ① Formation of electrons and holes

via photo-excitation 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 𝐼𝐼𝑉𝑉 and 𝐼𝐼𝑉𝑉+1 . ④, ⑧ Recombination of trapped holes with electrons

in the CBM (trap-assisted recombination) in 𝐼𝐼𝑉𝑉 and 𝐼𝐼𝑉𝑉+1 . ⑥ Detrapping of holes by excitation from the shallow trap to the CBM in 𝐼𝐼𝑉𝑉+1 . 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.

Figure 2. Optimized structures of (a) pristine MAPbI3, and MAPbI3 with (b) 𝐼𝐼𝑉𝑉−1 , (c) 𝐼𝐼𝑉𝑉 and (d) 𝐼𝐼𝑉𝑉+1

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 𝐼𝐼𝑉𝑉−1 because Coulomb repulsion separates

the Pb cations after removal of the iodine anion. The Pb-Pb distance is shortest in 𝐼𝐼𝑉𝑉+1 , because the Pb atoms are attracted to the negative charge left in the vacancy. The two Pb atoms in 𝐼𝐼𝑉𝑉+1 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.

Figure 3. Projected density of states (pDOS) for (a) pristine MAPbI3, and MAPbI3 with (b) 𝐼𝐼𝑉𝑉−1 , (c) 𝐼𝐼𝑉𝑉 and (d) 𝐼𝐼𝑉𝑉+1 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 since the



contributions from the organic subsystem are zero. 𝐼𝐼𝑉𝑉−1 creates no gap states. The neutral iodine

vacancy 𝐼𝐼𝑉𝑉 introduces an occupied trap state below the Fermi level. 𝐼𝐼𝑉𝑉+1 introduces both deep and shallow occupied trap states below the Fermi level.

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

Figure 5. Evolution of populations of the key states involved in charge trapping and recombination in pristine and defective MAPbI3. The 𝐼𝐼𝑉𝑉−1 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 𝐼𝐼𝑉𝑉 system and by a factor of 50 in the 𝐼𝐼𝑉𝑉+1 system.


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Figure 1



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Figure 2


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Figure 3



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Figure 4


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Figure 5


Journal of the American Chemical Society 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|NAC| 40 41Dephasing 42 43Rate 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 44 of 45

Table 1. Root-mean-square velocity (Å/fs) of atomic positions in pristine and defective MAPbI3. totala

MAb

Pb-Ic

Pb-Id

Pb-Ie

pristine

0.065

0.093

0.009

-

-

𝐼𝐼𝑉𝑉

0.049

0.069

0.011

0.010

0.011

0.058

0.081

0.011

0.0092

0.011

𝐼𝐼𝑉𝑉+1

0.055

0.079

0.0071

0.0049

0.008

𝐼𝐼𝑉𝑉−1 a

averaged over all atoms

b

averaged over atoms in MA

c

averaged over Pb and I atoms

d

averaged over Pb and I atoms around the vacancy site

e

averaged over Pb and I atoms away from the vacancy site

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.

vbm-

vbm-

vbm-

vbm-

cbm-

vbm-

vbm-

𝐼𝐼𝑉𝑉+1

shallow

vbm-

cbm-

cbm-

cbm

cbm

cbm

trap

trap

cbm

shallow

-deep

deep

shallow

deep

0.44

0.43

0.58

0.56

3.99

0.43

15.9

0.68

0.91

0.53

0.46

6.2

6.0

5.8

5.3

8.6

5.9

13.2

6.3

7.4

5.0

6.3

0.0065

0.0073

0.018

0.018

92.59

0.0074

29.58a/

0.47

0.70

0.014

0.83

pristine

𝐼𝐼𝑉𝑉−1

𝐼𝐼𝑉𝑉

4.33b a

trapping and bdetrapping.


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TOC graphic


Control of Charge Recombination in Perovskites by Oxidation State of

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