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Hole Trapping by Iodine Interstitial Defects Decreases Free Carrier Losses in Perovskite Solar Cells: a Time-Domain Ab Initio Study Wei Li, Jin Liu, Fu-Quan Bai, Hong-Xing Zhang, and Oleg V. Prezhdo ACS Energy Lett., Just Accepted Manuscript • Publication Date (Web): 05 May 2017 Downloaded from http://pubs.acs.org on May 5, 2017

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ACS Energy Letters

Hole Trapping by Iodine Interstitial Defects Decreases Free Carrier Losses in Perovskite Solar Cells: a Time-Domain Ab Initio Study Wei Li,1,2 Jin Liu,3 Fu-Quan Bai,1 Hong-Xing Zhang1*, and Oleg V. Prezhdo2* 1

Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, 130023, People’s Republic of China 2 Department of Chemistry, University of Southern California, Los Angeles, CA 90089, United States 3 Department of Chemical Engineering, University of Rochester, Rochester, NY 14627, United States

Abstract: We present a time-domain ab initio study of electron-hole recombination in pristine MAPbI3, and compare it to the trap mediated recombination in MAPbI3 with the iodine interstitial defect. Non-adiabatic molecular dynamics combined with time-domain density functional theory show that the iodine interstitial defect creates a sub-gap state capable of trapping both electrons and holes. Hole trapping occurs much faster than electron trapping or electron-hole recombination. The trapped hole survives for hundreds of nanoseconds, since, rather surprisingly, recombination of electrons with the trapped hole takes several times longer than recombination of electrons with holes in the valence band. Since the hole trap is relatively shallow, the hole can escape into the valence band prior to recombining with the electron. The differences are rationalized by variation in non-adiabatic electron-phonon couplings, phonon-induced pure-dephasing times and electronic energy gaps. The time-domain atomistic simulations contribute to understanding of the experimentally known defect-tolerance of perovskite solar cells, which is of great importance to the solar cell performance.

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Methylammonium (MA) lead halide perovskite solar cells (PSC), with chemical formula as MAPbX3 (X = Cl, Br, I), are attracting wide interest due to their high and rapidly evolving solar-to-electricity conversion efficiency.1-6 The certified 22.1% efficiency is almost twice as much as that in most efficient dye-sensitized solar cells.7 Experimental works have revealed that the high efficiency of PSC originates from their superior photovoltaic properties, including extremely large absorption cross section, low exciton binding energy, high carrier mobility, and super long carrier diffusion lengths.8-10 Despite the impressive optoelectronic performance, the recorded conversion efficiency of 22.1% still falls below the thermodynamic limit.11, 12 It is, therefore, essential to understand the fundamental physics underlying the device performance. Carrier dynamics in PSC is of particular interest, 1, 13-20 because long carrier lifetimes suggest good photovoltaic performance. Experimentally, the carrier recombination process in PSC is extremely slow, and the reported lifetimes extend beyond nanoseconds. For instance, the longest component of the bi-exponential fit can give the timescale up to ~200 ns.14, 16, 21 It is established that the dominant pathway for carrier recombination is non-radiative.12, 22, 23

Defects in perovskite materials have been under intense scrutiny in recent years. Organohalide perovskites tend to form defects due to the low thermal stability of the crystal.24 The reasons for the superior performance in PSC can be partly attributed to its unusual defect physics.17,

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Defect

migration due to ions diffusion could be the source of the slow response, and helping to understand the anomalous current-voltage hysteresis.29-38 By using first-principles calculations, a large number of native point defects have been studied.25, 39-47 Most common defects in perovskite are demonstrated to be benign.20 Intrinsic defect states can significantly modulate the carrier dynamics in perovskite material.12, 15-19, 48-51 However, the nature of the defect states and its impact on carrier dynamics in PSC has not been fully understood. In this work, we report a time-domain ab initio study comparing carrier relaxation and recombination in pristine lead halide perovskite MAPbI3 with those in MAPbI3 containing an iodine interstitial defect. In its neutral form, the iodine interstitial defect was predicted by DFT calculations to be a deep trap with a relatively low formation energy.39, 41, 42 In our simulation, we consider various carrier relaxation pathways that follow absorption of a photon and formation of electron and hole in conduction band (CB) and valence band (VB), Figure 1. In addition to the non-radiative electron-hole recombination in pristine MAPbI3, we investigate recombination of CB electron with VB hole in the 2


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presence of the iodine interstitial. We also study electron trapping, hole trapping, and recombination of the trapped charges with the corresponding free carriers. We aim to elucidate how the presence of the iodine interstitial defect changes free carrier lifetimes and charge recombination rates, and to establish the factors that cause these changes. Our simulations show that the non-radiative electron-hole recombination in pristine perovskite happens on a nanosecond timescale, which agrees with experiment. The slow non-radiative electron-hole recombination can be rationalized by the weak electron-phonon coupling and rapid phonon-induced decoherence in the electronic subsystems. The interstitial iodine atom introduces a trap state close to the VB. The defect already accelerates slightly the recombination of free charge carriers directly between the CB and VB. More importantly, the defect leads to rapid hole trapping, while electron trapping takes a long time. The hole trapping is fast because the non-adiabatic (NA) electron-phonon coupling is large due to significant overlap between the wave-functions of the trap and VB states, because the quantum coherence between the initial and final states is maintained for a relatively long time, and because the energy gap between the trap and VB states is small. Moreover, the trapped holes are surprisingly long-lived. Recombination of the trapped holes with CB electrons takes longer than recombination of the VB holes with the CB electrons. Since the hole trap is relatively shallow, the holes can escape into the VB prior to recombining with electrons. These factors can lead to reduction in charge and energy losses, and contribute to high efficiencies of PSC. The simulations are performed using a combination of non-adiabatic molecular dynamics (NAMD) and time-dependent Kohn-Sham density functional theory,52, 53 implemented within the Pyxaid software package,54, 55 as described in Supporting Information. In particular, Tully’s fewest switches surface hopping56 (FSSH) and decoherence induced surface hopping57 (DISH) are employed. FSSH is the most widely used NAMD simulation technique; however, the DISH data show better agreement with the available experiment,14, 16, 21 and should be regarded as the main results. Figure 2 shows the optimized ground geometries at 0 K, and compound images of 2000 frames from MD simulation at 300 K for pristine MAPbI3 perovskite and MAPbI3 with a neutral iodine interstitial defect. The (CH3NH3)+ group can rotate at room temperature in the cubic phase of the perovskite crystal. The optimized ground state structure shows that the C-N bond of the (CH3NH3)+ group is oriented along the (1 1 1) direction, facilitating formation of hydrogen bonds between (CH3NH3)+ groups and nearby iodine atoms, further stabilizing the perovskite crystal. The formation of 3


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hydrogen bonds in perovskite has, indeed, been demonstrated by static first-principle calculations.58, 59 The introduction of the interstitial iodine atom leads to a large distortion of the Pb-I octahedron. The rotational motions of the organic cation shows is strongly coupled to the Pb-I inorganic cage, as shown in the MD snapshots of the two structures. The organic cation does not leave the interstice of the Pb-I octahedral, and the Pb and I atoms fluctuate at their equilibrium positions during MD, indicating that the structures are stable. The light atoms of the organic species undergo much larger fluctuations than the heavier atoms of the inorganic lattice, as should be expected. The iodine interstitial defect inhibits rotations of the adjacent (CH3NH3)+ groups due to steric hindrance. This is particularly important, since reduced motions can weaken the NA electron-phonon coupling and slow down non-radiative charge relaxation. The projected density of states (pDOS) of the pristine and defective perovskite structures are shown in Figure 3. It can be seen that only iodine and lead orbitals contribute to DOS around the band gap. The CB minimum (CBM) mainly consists of Pb 6p orbitals with negligible component of iodine orbitals, while iodine 5p orbital form the VB maximum (VBM). The trap state is closer in energy to the VBM, because it is composed by the same iodine 5p orbitals. The charge density plots of the corresponding states in Figure 3 illustrate the above points further. The CBM and VBM charge densities are delocalized around the entire cell and are separated in space, indicating small overlap of the electron and hole wave-functions, and hence weak non-adiabatic coupling (NAC) and slow electron-hole recombination. Our results are consistent with the previous works.60-62 On the contrary, the charge density of the trap state is distributed over the interstitial iodine atom. The adjacent iodine atoms are also involved due to strong interaction between the interstitial and main iodines. It is worth to emphasize that there is almost no contribution from the organic cation to the DOS around the band gap, indicating that the organic cation does not participate directly in the photoexcitation process. The organic cation neutralizes the PbI3- framework and tunes the I-Pb-I backbone. Additionally, the motions of the organic cation can contribute electrostatically to the NAC electron-phonon coupling, and promote non-radiative charge relaxation. It is established that spin-orbit coupling (SOC) is significant in lead halide perovskites due to presence of Pb, which is a heavy element. By excluding the SOC effect, a direct band gap of 1.53 eV is obtained, which is in line with the experimental value of ~1.6 eV.63 Generally, incorporation of SOC shifts the CBM down by nearly 1 eV.39, 64 A more accurate value of 1.67 eV was predicted by de Angelis 4


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and co-workers using SOC and many-body GW self-energy corrections.65 The good agreement of the bandgap obtained in this work with the experiment value is due to cancellation of errors arising from neglect of SOC and bandgap underestimation by pure DFT functionals, including PBE functional. We use the current approach for the following reasons. First, inclusion of both SOC and GW correction is computationally expensive and extends far beyond the current capabilities, especially for NAMD that requires many repeated energy and NAC calculations. Second, the interstitial iodine defect acts as a hole trap that located near the VBM. SOC modifies strongly the CB, whereas the top of VB is almost unchanged.66 Most importantly, pure DFT calculations provide the same trend as the higher level methods. For instance, Sun et al. found that there is a scale shift in the positions of the Kohn-Sham levels in perovskite materials calculated with hybrid DFT/SOC and pure DFT, while at the same time, the relative positions of the energy levels predicted by the two methods do not change.67 Recent theoretical work has shown that the combination of hybrid DFT and SOC is not fully sufficient to reproduce the experimental band gap.68 GW calculations can correctly address this problem, as demonstrated by de Angelis and coworkers.65 Turning attention to the iodine interstitial defect, Du and co-authors have shown, using hybrid DFT and SOC, that the iodine interstitial defect induces deep traps in all its charge states (-1, 0, +1).47 Our bare DFT calculations agree with this result, Figures 3 and S1. Generally, pure DFT calculations have been used widely to treat defective perovskites, achieving good results.25, 42, 69 Pure and hybrid DFT produce similar defect Kohn-Sham levels.70 To test our simulation setup, we carried out a hybrid DFT calculation on the neutral iodine interstitial defect using the HSE functional, and similarly to the PBE calculation, we found that the defect is still a deep trap. It should be noted that, even though pure DFT gives good band gap due to the fortuitous error cancelation, it underestimates other parameters, including band dispersion and carrier effective masses. Thermal motion of atoms drives fluctuations of the electronic energy levels, and the fluctuations reflect the strength of elastic and inelastic electron-vibrational interactions that, respectively, induce coherence loss and are responsible for NA transitions between electronic states. The fluctuations can be characterized by the ACF, eq (S3). Figure 4 (top) shows the u-ACF of the relevant energy gaps at 300 K in pristine and defective perovskite. In pristine perovskite, the gap for electron-hole recombination is defined as the energy difference between CBM and VBM. In defective perovskite, the gap is between CBM and trap state for hole trapping, CBM and trap state for electron trapping, and CBM and VBM for electron-hole recombination. All u-ACF decay on similar timescales, however, their initial values differ 5


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significantly. Typically, a larger initial value of u-ACF, corresponding to the energy gap fluctuation squared, is indicative of a faster accumulation of the wave-function phase diﬀerence for the two energy levels, and thus a short coherence time.71 The data shown in Figure 4 (top) indicate that the initial value of u-ACF is largest for electron trapping and smallest for hole trapping, suggesting and decoherence should be fast in the former case and slow in the latter case. The differences in the initial values of the u-ACF can be rationalized further by considering the charge density for the corresponding states, as shown in Figure 3. For the defective perovskite, the trap state is close to the VBM in energy, and thus the fluctuation of the VBM-trap energy gap is small. In addition, both the trap state and VBM mainly locate at iodine atoms, leading to similar chemical environment and correlated fluctuations of energy levels. Both factors facilitate long coherence between the trap state and VBM. In contrast, coherence between the trap and CBM is short. This is because the energy gap and its fluctuation are large in this case, and because the trap state involves contribution from I 5p orbitals, while the CBM arises from the Pb 6p orbitals, leading to uncorrelated fluctuations of the two levels. The pure-dephasing functions can be calculated using second-order cumulant approximation of the optical response theory,72 eq (S4), are shown in the middle panel of Figure 3. The Gaussian fits, exp[-0.5(t/τ)2], give the decoherence times, presented in Table 1. As anticipated based on the properties of the u-ACF, the hole trapping process involves longest coherence (~13 fs), while electron trapping gives the shortest coherence time (~3 fs), at room temperature. Generally, shorter coherence leads to slower dynamics, as exemplified by the quantum Zeno effect.73 Table 1 also shows the average absolute values of the NAC. The coupling leading to hole trapping is an order of magnitude larger than the coupling responsible for electron trapping and recombination of free charge carriers. The difference can be understood by considering the atomic origin of the corresponding electronic state, Figure 3. The VBM and trap states involve in hole trapping arise from 5p orbitals of iodine atoms, and therefore the overlap between these states is large, leading to large NAC electron-phonon for hole trapping. Conversely, the CBM is localized on 6p orbitals of lead atoms, and its overlap with the VBM and trap state wave-functions is small. As a result, the NAC responsible for the electron trapping and recombination of free electron and hole in the CB and VB are small, Table 1. The influence spectrum, eq. (S5), characterizes the frequencies of the phonon modes that couple to the given electronic transition. Figure 4 (bottom) presents the power spectra for electron-hole 6


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recombination between CB and VB in the pristine and defective perovskites, for the electron trapping and for the hole trapping. For the pristine perovskite, the dominant peaks appear near 50 cm-1 and 200 cm-1, which can be assigned to the I-Pb-I bending mode and the torsional mode of the organic cation, repectively.74 In contrast, the charge relaxation processes taking place in the defective perovskite couple primarily to vibrations below 100 cm-1. The coupling to the vibrational mode at 200 cm-1 is absent, because the interstitial defect constrains rotation of the organic cations. Participation of slow modes in the electronic transitions is not surprising, because the electronic states involved in the transitions are localized on heavy elements, Figure 3. Previous calculations of metal nanoclusters75 and semiconductor quantum dots76, 77 show similar behavior. High-frequency modes above 100 cm-1 are absent in the power spectra, indicating that the stretching and bending motions of the light atoms of the organic cation carry no contribution to the charge relaxation processes near and across the bandgap. Non-radiative electron-phonon relaxation is of great relevance semiconductor materials, since it is responsible for energy losses to heat. Figure 5 presents the relaxation dynamics starting from the initial state in the pristine and defective perovskite obtained using the FSSH and DISH approaches. To determine the relaxation timescales, τ, we fit the first 2000 fs of NAMD data to the first-order expansion of the exponential decay, f(t) = 1 - exp(t/τ) ≈ t/τ. The relaxation time estimated for the non-radiative electron-hole recombination in pristine perovskite is 1.2 ns by FSSH, as shown in Table 1. Inclusion of decoherence significantly slows down the relaxation to 114.8 ns, bringing the results in agreement with experiments.14, 16, 21 The electron-hole recombination across the fundamental bandgap is about 30% faster in the presence of the interstitial defect, because the defect increases the NAC. The relaxation times decrease to 0.8ns for FSSH and 78.3ns for DISH, primarily due to increased NAC in the defective perovskite, Table 1. Next, we consider processes involving the interstitial defect state. Figure 5 and Table 1 present the data for the electron and hole trapping processes. The hole trapping proceeds on a fast time scale, 0.005 ns according to FSSH and 0.03 ns according to DISH. This is several orders of magnitude faster than the electron trapping, which requires 5.4 ns according to FSSH and 449.2 ns according to DISH. The hole trapping is also faster than the electron-hole recombination across the fundamental bandgap, as discussed in the previous paragraph. The electron trapping is very slow even compared to the electron-hole recombination across the bandgap, and therefore, it can be ignored. The hole trapping is the dominant process in the defective perovskite, with the trapping time on the order of a few tens of 7


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picoseconds. The smaller energy gap, the larger NAC due to the VBM and trap state wave-functions origination from the same 5p orbitals of iodines, and the longer coherence time all contribute to the fast hole trapping. This result confirms clearly that the iodine interstitial defect serves as the hole trapping site in PSC. The trapped holes are surprisingly long lived. According to DISH, it requires over 300 ns for the hole to recombine with the electron in the CB, Figure 6. The recombination of the trapped hole with the CB electron is even slower than recombination of the VB hole with the CB electron. The long lifetime of the trapped hole can be attributed to the small NAC and fast decoherence between the trap state and the CBM, since they arise from atomic orbitals of different atoms, I and Pb respectively. Rather than recombining with the electron, the trapped hole can escape back to the VB on a sub-ns timescale indicated by our calculations, Figure 6. Therefore, hole trapping by the neutral iodine interstitial defect effectively increases the hole lifetime and decreases electron-hole recombination, and thus, it is benign to the device performance. The simulations agree with the recent experiments showing that excess iodine concentration in precursor solutions increase carrier lifetimes in perovskite films.78 Our simulations also rationalize the experimental work showing that perovskite material exhibits high tolerance towards the defect-induced mechanism of charge carrier losses.12, 79 Iodine interstitial defects at all charge states (-1, 0, +1) should be abundant in solution-processed perovskite films, as demonstrated by Mosconi and de Angelis.69 Several works reported the amphoteric behavior of the iodine interstitial,39, 41, 47 which can be stabilized thermodynamically by forming a charged state. Solution-processed perovskite film growth is an out-of-equilibrium process, and the thermodynamic equilibrium condition is likely not achieved. The concentration of neutral iodine interstitial defects can be controlled by regulating the growth conditions, as supported by the theoretical work of Yin et al.,25 who showed that the neutral iodine interstitial defect has a small formation energy of 0.23 eV under I-rich/Pb-poor conditions. Buin et al. showed that the neutral iodine interstitial defect can have a fairly small formation energy of 0.57 eV under the iodine-rich conditions.42 A high defect density is achieved during typical MAPbI3 film synthesis. A defect density as high as ~1016-1017 cm-3 was reported by Mosconi and de Angelis based on the analysis of photoluminescence rise dynamics.69 The defect concentration can be estimated as ܿ = ܰ௦ exp(−‫ܧ‬௙ /݇ܶ), where ‫ܧ‬௙ is the formation energy and ܰ௦ is the number of equivalent sites the defect can be placed in the supercell.80 The 0.23 eV energy of formation of the neutral iodine interstitial defect reported by Yin et al.,25 gives 8


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the ~2.5×1017 cm-3 defect concentration at ambient temperature, in excellent agreement with the experimental data analysis by Mosconi and de Angelis.69 Iodine atom is an open shell species with one unpaired electron. The NAMD simulations were performed using spin-restricted DFT for both pristine and defective perovskite. We also carried out an open-shell spin-polarized calculation. The corresponding pDOS is shown in Figure S1 of Supporting Information. The spin-up and spin-down components of the defect state are split by about ~0.4 eV. Most importantly, similarly to the spin-restricted result, Figure 3, the spin-polarized states are deep traps, and the hole trap state is much closer to the VB than the electron trap state is to the CB. Indeed, the gap between the hole trap and VB is ~0.25 eV for the spin-polarized case, Figure S1, and ~0.4 eV for the spin-restricted case, Figure 3, both value being much greater than ݇ܶ, qualifying them as deep traps. The gap between the electron trap and CB is ~1.2 eV for the spin-polarized case and ~1.4 eV for the spin-restricted case, much larger than the gaps between the hole traps and VB. In both spin-restricted and spin-polarized calculations the defect states arise from p-orbitals of I atoms. While the quantitative results on the charge trapping and relaxation dynamics may differ for the spin-polarized calculations, the key conclusion will remain the same. Our time-domain NAMD simulations of carrier relaxation and recombination in CH3NH3PbI3 give conclusions that are qualitatively similar to those of the lifetime calculations on the fully inorganic CsPbI3 by Kawai et al.81 The similarity can be explained by the fact that the organic cation in CH3NH3PbI3 does not directly participate in the charge trapping and recombination. The band gap and trap energy levels arise from the inorganic lattice (PbI3) and have very little contribution from the organic cation. The polar CH3NH3+ group can give rise to the exotic dielectric properties and the possible ferroelectric behavior in CH3NH3PbI3. The ferroelectric properties in perovskite materials have been correlated with the hysteretic behavior in the current-voltage curve, as demonstrated by de Angelis and coworkers.82 The effect of ferroelectric order on carrier relaxation has been investigated by Jankowska and Prezhdo.83 To recapitulate, by performing state-of-the-art time-domain ab initio simulations of carrier trapping and relaxation dynamics in pristine and defective MAPbI3 perovskite, we have identified the key roles played by traps. We demonstrated for the first time that transient charge trapping can be beneficial for solar cell performance, since it can extend carrier lifetimes. The simulations demonstrate that free electrons and holes live for hundreds of nanoseconds in pristine perovskite, in agreement with 9


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experiment. Iodine interstitial defects create trap state close to the VB, thereby facilitating hole trapping. Electron trapping by the same state is very slow and can be ignored. Most interestingly, the lifetime of the trapped hole is very long, because trapped hole recombines with a free electron is even slower than recombination of free electrons and holes. Because the trap state is close to the perovskite VB, the hole can escape the trap and become a free charge carrier on a sub-nanosecond timescale. The long lifetime of the trapped hole reduces the overall rate of electron-hole recombination, while efficient hole escape from the trap to the VB facilitates charge transport. The calculation results are rationalized by the differences in the NA electron-phonon coupling, quantum coherence times and energy gaps, which can be attributed to the particular details of the perovskite electronic structure. The slow rate of trap-mediated charge recombination can be responsible for relaxing the limit on attainable open-circuit voltage in the presence of a certain density of trap states, as suggested based on experimental data.17, 22, 23

Our simulations establish detailed mechanisms of phonon-mediated charge carrier dynamics, trapping

and relaxation, which are of crucial importance for understanding the device physics and improving performance of photovoltaic and photo-catalytic cells.

Acknowledgments We are grateful to Zhu-Feng Hou and Yi-Yang Sun for fruitful discussions. O.V.P. acknowledges financial support of the U.S. National Science Foundation, Grant No. CHE-1565704. H.X.Z. acknowledges support from the National Natural Science Foundation of China (Grant No. 21573088) and State Key Development Program for Basic Research of China (Grant No. 2013CB834801). F.Q.B. acknowledges support of the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (Second Phase) and Young Scholar Training Program of Jilin University. The simulations were performed at the University of Southern California’s Center for High-Performance Computing (hpc.usc.edu).

ASSOCIATED CONTENT Supporting Information. Description of the computational methodology and density of states for MAPbI3 with the iodine interstitial defect obtained from spin-polarized calculation. This information is available free of charge 10


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on the ACS Publications website at DOI: 10.1021/acsenergylett.6b00681.

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]; [email protected]

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(57) Jaeger, H. M.; Fischer, S.; Prezhdo, O. V., Decoherence-Induced Surface Hopping. J Chem Phys 2012, 137, 22A545. (58) Amat, A.; Mosconi, E.; Ronca, E.; Quarti, C.; Umari, P.; Nazeeruddin, M. K.; Gratzel, M.; De Angelis, F., Cation-Induced Band-Gap Tuning in Organohalide Perovskites: Interplay of Spin-Orbit Coupling and Octahedra Tilting. Nano Lett 2014, 14, 3608-3616. (59) Quarti, C.; Mosconi, E.; De Angelis, F., Interplay of Orientational Order and Electronic Structure in Methylammonium Lead Iodide: Implications for Solar Cell Operation. Chem Mater 2014, 26, 6557-6569. (60) Feng, J.; Xiao, B., Crystal Structures, Optical Properties, and Effective Mass Tensors of Ch3nh3pbx3 (X = I and Br) Phases Predicted from Hse06. J Phys Chem Lett 2014, 5, 1278-1282. (61) Wang, Y.; Gould, T.; Dobson, J. F.; Zhang, H.; Yang, H.; Yao, X.; Zhao, H., Density Functional Theory Analysis of Structural and Electronic Properties of Orthorhombic Perovskite Ch3nh3pbi3. Phys Chem Chem Phys 2014, 16, 1424-1429. (62) Lang, L.; Yang, J.-H.; Liu, H.-R.; Xiang, H. J.; Gong, X. G., First-Principles Study on the Electronic and Optical Properties of Cubic Abx3 Halide Perovskites. Phys Lett A 2014, 378, 290-293. (63) Baikie, T.; Fang, Y. N.; Kadro, J. M.; Schreyer, M.; Wei, F. X.; Mhaisalkar, S. G.; Graetzel, M.; White, T. J., Synthesis and Crystal Chemistry of the Hybrid Perovskite (Ch3nh3)Pbi3 for Solid-State Sensitised Solar Cell Applications. J Mater Chem A 2013, 1, 5628-5641. (64) Torres, A.; Rego, L. G. C., Surface Effects and Adsorption of Methoxy Anchors on Hybrid Lead Iodide Perovskites: Insights for Spiro-Meotad Attachment. J Phys Chem C 2014, 118, 26947-26954. (65) Umari, P.; Mosconi, E.; De Angelis, F., Relativistic Gw Calculations on Ch3nh3pbi3 and Ch3nh3sni3 Perovskites for Solar Cell Applications. Scientific reports 2014, 4, 4467-4473. (66) Even, J.; Pedesseau, L.; Jancu, J.-M.; Katan, C., Importance of Spin–Orbit Coupling in Hybrid Organic/Inorganic Perovskites for Photovoltaic Applications. J Phys Chem Lett 2013, 4, 2999-3005. (67) Sun, Y. Y.; Shi, J.; Lian, J.; Gao, W.; Agiorgousis, M. L.; Zhang, P.; Zhang, S., Discovering Lead-Free Perovskite Solar Materials with a Split-Anion Approach. Nanoscale 2016, 8, 6284-6289. (68) Giorgi, G.; Fujisawa, J.-I.; Segawa, H.; Yamashita, K., Cation Role in Structural and Electronic Properties of 3d Organic-Inorganic Halide Perovskites: A Dft Analysis. J Phys Chem C 2014, 118, 12176-12183. (69) Mosconi, E.; Meggiolaro, D.; Snaith, H. J.; Stranks, S. D.; De Angelis, F., Light-Induced Annihilation of Frenkel Defects in Organo-Lead Halide Perovskites. Energy & environmental science 2016, 9, 3180-3187. (70) Kerdsongpanya, S.; Alling, B.; Eklund, P., Effect of Point Defects on the Electronic Density of States of Scn Studied by First-Principles Calculations and Implications for Thermoelectric Properties. Phys Rev B 2012, 86, 195140. (71) Akimov, A. V.; Prezhdo, O. V., Persistent Electronic Coherence Despite Rapid Loss of Electron-Nuclear Correlation. J Phys Chem Lett 2013, 4, 3857-3864. (72) Mukamel, S., Principles of Nonlinear Optical Spectroscopy. Oxford University Press: New York: 1995. (73) Kilina, S. V.; Neukirch, A. J.; Habenicht, B. F.; Kilin, D. S.; Prezhdo, O. V., Quantum Zeno Effect Rationalizes the Phonon Bottleneck in Semiconductor Quantum Dots. Physical review letters 2013, 110, 180404. (74) Quarti, C.; Grancini, G.; Mosconi, E.; Bruno, P.; Ball, J. M.; Lee, M. M.; Snaith, H. J.; Petrozza, A.; Angelis, F. D., The Raman Spectrum of the Ch3nh3pbi3 Hybrid Perovskite: Interplay of Theory and Experiment. J Phys Chem Lett 2014, 5, 279-284. (75) Neukirch, A. J.; Guo, Z.; Prezhdo, O. V., Time-Domain Ab Initio Study of Phonon-Induced Relaxation of Plasmon Excitations in a Silver Quantum Dot. J Phys Chem C 2012, 116, 15034-15040. (76) Trivedi, D. J.; Wang, L.; Prezhdo, O. V., Auger-Mediated Electron Relaxation Is Robust to Deep Hole Traps: Time-Domain Ab Initio Study of Cdse Quantum Dots. Nano Lett 2015, 15, 2086-2091. 15


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ACS Energy Letters

Figure Captions

Figure 1. Diagram of the energy levels and charge transfer processes inside the perovskite material. Photo-excitation from the valence band maximum (VBM) to the conduction band minimum (CBM). Non-radiative electron-hole recombination in pristine MAPbI3. Non-radiative electron-hole recombination in MAPbI3 with the iodine interstitial defect. Capture of a hole by the trap state (hole trapping). Capture of an electron by the trap state (electron trapping). Non-radiative relaxation of the trapped holes into ground state. Non-radiative relaxation of the trapped electrons into ground state.

Figure 2. Structures of pristine MAPbI3 (a), and MAPbI3 with the iodine interstitial defect (b) optimized at 0 K and sampled at 300 K. The blue circle depicts the location of the defect. For the structures at 300 K, snapshots of 2000 frames in the molecular dynamics simulation are presented. The iodine interstitial defect creates a large distortion in the Pb-I octahedron, indicating a strong interaction with the adjacent iodine atoms. In addition, the defect constrains rotation of the adjacent methylammonium molecules.

Figure 3. Total and projected density of states (DOS) of pristine MAPbI3 (top panel) and MAPbI3 with the iodine interstitial defect (bottom panel). Charge densities of VBM (a) and CBM (b) in pristine MAPbI3, and VBM (c), CBM (d), and trap state (e) in MAPbI3 with the iodine interstitial defect. The CBM of MAPbI3 is dominated by 6p orbitals of Pb, and the VBM is dominated by 5p orbitals of I. The defect introduces a state close to the VBM. The defect state is also formed by 6p orbitals of Pb, maximizing wavefunction overlap with the VBM.

Figure 4. Un-normalized autocorrelation function (u-ACF) (top), pure-dephasing function (middle), and spectral density (bottom) for the energy gaps in pristine MAPbI3 and MAPbI3 with the iodine interstitial defect. The spectral density is obtained by Fourier transform (FT) of 17


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normalized ACF. The gaps are between CBM-VBM in pristine perovskite, and CBM-VBM, VBM-trap (hole trapping), and CBM-trap (electron trapping) in defective perovskite. For the defective perosvkite, most peaks in the spectral density are below 300 cm-1, indicating that low frequency modes are responsible for non-radiative charge trapping and recombination. Pristine perovskite show torsional modes of the methylammonium molecules at 200-300 cm-1. These modes are absent in the defective perovskite, because the iodine interstitial defect inhibits re-orientation of the methylammonium molecules, see Figure 2b.

Figure 5. Time evolution of the final state population due to non-radiative electron-hole recombination in the pristine perovskite (black) and the defective perovskite (red), and the trap state population due to electron trapping (blue) and hole trapping (green) in defective perovskite obtained with FSSH and DISH. “IS” stands for initial photo-excited state. Exponential fitting of the data to the first-order, f(t) = 1 - exp(t/τ) ≈ t/τ, gives the relaxation time τ, Table 1. The relaxation from the VBM to the trap state shows a relatively high decay rate, indicating that hole trapping is the predominant decay path among the possible processes in the perovskite with the iodine interstitial defect.

Figure 6. Time evolution of the ground state population due to nonradiative relaxation of trapped electrons (blue) or holes (red), and the population of the VB state due to escape of the trapped holes (green) obtained with FSSH and DISH. Trapped holes are surprisingly long-lived compared with trapped electrons, and even with the electron-hole recombination across the fundamental bandgap, Figure 5 and Table 1. The trapped hole requires over 300 ns to return to the ground state, which is 2.5 times slower than the pristine system. At the same time, the trapped hole can escape to the VB on a sub-ns timescale.

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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

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Figure 6

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Table 1. Averaged absolute NA coupling, pure-dephasing time, and non-radiative relaxation time for charge recombination in pristine perovskite, and charge recombination and trapping in defective perovskite. NA coupling Dephasing time Relaxation time (meV) (fs) (ns) Pristine perovskite 0.43 5.5 1.2a/114.8b Defective perovskite 0.51 4.9 0.8/78.3

Hole trapping

2.77

13.0

0.005/0.03

Electron trapping

0.34

3.1

5.4/449.2

a b

FSSH, without decoherence; DISH, with decoherence, showing better agreement with experiment

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Hole Trapping by Iodine Interstitial Defects ... - ACS Publications

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