Hysteresis, Stability, and Ion Migration in Lead Halide Perovskite

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Hysteresis, Stability, and Ion Migration in Lead-Halide Perovskite Photovoltaics Kenjiro Miyano, Masatoshi Yanagida, Neeti Tripathi, and Yasuhiro Shirai J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b00579 • Publication Date (Web): 26 May 2016 Downloaded from http://pubs.acs.org on May 28, 2016

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The Journal of Physical Chemistry Letters

Hysteresis, Stability, and Ion Migration in Lead-halide Perovskite Photovoltaics Kenjiro Miyano,∗,† Masatoshi Yanagida,†,‡ Neeti Tripathi,†,¶ and Yasuhiro Shirai†,‡ †Global Research Center for Environment and Energy based on Nanomaterials Science (GREEN), National Institute for Materials Science (NIMS), 1–1 Namiki, Tsukuba, Ibaraki 305-0044, Japan. ‡Center for Green Research on Energy and Environmental Materials, National Institute for Materials Science (NIMS), 1–1 Namiki, Tsukuba, Ibaraki 305-0044, Japan. ¶Current address: Organic and hybrid solar cells group, CSIR–National Physical Laboratory, New Delhi –110012, INDIA E-mail: [email protected]

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Abstract Ion migration has been suspected as the origin of various irreproducible and unstable properties, most notably the hysteresis, of lead-halide perovskite photovoltaic (PV) cells since the early stage of the research. Although many evidences of ionic movement have been presented both numerically and experimentally, a coherent and quantitative picture that accounts for the observed irreproducible phenomena is still lacking. At the same time, however, it has been noticed that in certain type of PV cells the hysteresis is absent or at least within the measurement reproducibility. We have previously shown that the electronic properties of hysteresis-free cells are well represented in terms of the conventional inorganic semiconductors. The reproducibility of these measurements was confirmed typically within tens of minutes under the biasing field of -1V to +1.5V. In order to probe the effect of ionic motion in the hysteresis-free cells, we extended the time scale and the biasing rage in the electronic measurements, from which we conclude the following; (1) From various evidences, it appears that ion migration is inevitable. However, it does not cause detrimental effects to the PV operation. (2) We propose, based on the quantitative characterization, that the degradation is more likely due to the chemical change at the interfaces between the carrier selective layers and perovskite rather than the compositional change of the lead-iodide perovskite bulk. Together, they give much hope in the use of the lead-iodide perovskite in the use of actual application.

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Keywords ion migration, hysteresis, long-term stability, degradation

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The progress in the photovoltaics (PVs) based on lead-halide perovskite has been enormous in the past few years and the power conversion efficiency is now above 22%. 1 Realization of cells with better than 15% efficiencies having an active area of 1 cm2 together with the relatively stable operation over 1000 hrs is the landmark toward their application to the real world. 2 Despite these amazing achievements, one issue has been left open from the outset of the current surge of the research; the origin of the irreproducibility in the current/voltage (J/V) traces depending on the scan direction and the scan speed (the "hysteresis") observed in many devices. The complexity of the problem was already obvious from the beginning. The hysteresis behavior reported in two pioneering works 3 4 differs each other although the cell structure was similar. For example, the magnitude of the hysteresis, ∆J(V), at a given bias voltage V increases monotonically with decreasing the scan speed and, at 10mV/s scan speed, it exceeds 10 mA/cm2 in Ref. 3 while the hysteresis loop is closed at this speed in Ref. 4. Already in both references, many potential mechanisms for the hysteresis have been proposed including the ion diffusion. Although we are still far from the understanding, the following rough estimate makes a scenario of simple ion motion difficult to accept in many cases. Let us assume that I− ions move. Since there are three ions in a pseudocubic lattice with 0.6 nm lattice constant, the ion density is n=12/nm3 . If all I− ions drift unidirectionally at a velocity, v, the induction current density, J, observed between the cell electrodes is J=env, where e is the elementary charge. Therefore, the ionic contribution of J=2mA/cm2 gives v=10nm/s. If we assume that the hysteresis ∆J=5mA/cm2 and the scan duration of 50s, the entire iodine in the perovskite layer (typically 300 to 500 nm thick) must be swept away. While the debate over the origin of the hysteresis was going on, the hysteresis has not been a big issue in a different type of cells, most notably perovskite layer sandwiched between PEDOT:PSS and PCBM. 5 It was already noticed in Ref. 4 that this type of cells behave differently. Using similar cell design, we succeeded in fabricating practically hysteresis-free cells. 6 Needless to say, the hysteresis-free operation of a device is essential to characterize

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its electrical property. They enable us to demonstrate that perovskite PVs show electrical properties typical of p-i-n diodes made of inorganic semiconductors. 7 8 Although the cause of the hysteresis is yet to be clarified by microscopic measurement tools, an interesting observation has been published recently, 9 in which the hysteresis is the result of electro-chemical reaction in the carrier extraction layers. If this is the case, the major cause of the hysteresis does not lie in the bulk property of the perovskite; an encouraging sign. At least we have a design guidance for cells with much reduced hysteresis. This is the first step to be able to compare the device performance fabricated in different laboratories. However, hysteresis-free does not imply ion-migration-free, of course. The purpose of this Perspective is to trace the effect of ion migration in our nominally hysteresis-free cells. The ion-migration issue was reviewed (among other things) recently. 10 Before going into experimental data, let us make a detour to the theoretical predictions. Although there are some variations in the details, theoretical predictions agree in that there are extremely large number of vacancies. For example, the vacancy formation enthalpy of methyl-ammonium iodide is calculated to be only 80 meV; so low that the defect concentration would be 2×1020 cm−3 at room temperature. 11 The activation energy over the potential hill toward the neighboring vacansies is also low. For I− anions, it is calculated to be 0.58 eV. 12 If one assumes an attempt frequency of 1012 Hz and a jump distance of 0.5 nm, a backof-the-envelope calculation shows that the diffusion constant would be 0.5×10−12 cm2 /s at room temperature making the diffusion length of an iodine vacancy to be a few nm in 1 s. 13 In a PV cell with 300 nm thickness, this is a considerable distance. The exact ion species depends on the model. It is suggested that not only I− anions but also methyl-ammonium+ cations could move, 14 although without experimental support up to now. In any case, it should be reminded that all these numerical studies were made in attempt to explain the hysteresis. Experimentally, ion migration in solids is well known. Notable and most studied example

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is AgI. (For a review, see for example Ref. 15). The ionic motion in materials similar to CH3 NH3 PbI3 has long been studied as well using various techniques. The dominant current carrying species was shown to be halogen anions in CsPbCl3 and CsPbBr3 by Tubandt method. 16 The ionic conductivity is high (≥ 10−3 S/cm) albeit at elevated temperatures (> 600K). From NQR of

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Cl, a large Cl− conductivity of 0.2 S/cm was deduced at 450K in

CH3 NH3 GeCl3 . 17 If the Arrhenius plot can be extrapolated to the room temperature, the conductivity is still as high as mS/cm. Recently, studies along the same line have been applied to lead-iodide perovskite. 18 By using various combinations of ion-blocking and ion-permeating (-supplying) electrodes, one can differentiate the electronic and ionic contributions to the total current. Most notably, the movement of I− ions accounts for a signifiant portion of the observed current even with the ion-blocking electrodes (lead-iodide perovskite sandwiched between graphite electrodes). 19

In this case, because the ions cannot pass through the electrodes, compositional gradient

(causing the chemical potential gradient) appears in the perovskite, which manifests as an open-circuit voltage across the cell after removal of the external current. Naturally the ionic motion is slow; the typical time scale of these experiments is in the range of 104 ∼ 106 s. However, if we translate these results to the case of PV cells, it can be much faster. Let us assume that the relevant ionic process is predominantly governed by a diffusion equation in these experiments. Then, the time t associated with this ionic motion scales inversely with the driving force (the strength of the electric field) and quadratically with the length scale. In other words, in terms of the sample thickness D, the electric field scales as 1/D for a given potential difference applied to the external electrodes and the diffusion time as D2 . Thus, under a fixed potential drop across a sample, the time it takes for ions to migrate through the sample scales as D3 . The sample thickness used in Ref. 18 was 0.6 mm while the typical perovskite film thickness used in PV cells is 300 nm. This means that the migration time is sped up by 10 orders of magnitude ((2 × 103 )3 ) because the externally applied potential is similar in both cases. It is clear that the most

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of the electronic characterization data 7 8 are not immune to the ionic motion. We have to conclude that, even in an ideal PV cell equipped with ion-blocking electrodes, the ionic redistribution is completed under the external potential before we notice it under most experimental conditions and the data must be convoluted with such motion. We will come back to this point later. One exception may be the impedance spectroscopy in which the frequency range (sub Hz ∼ MHz) can cover the relevant time range. So far, we have considered only the time scale associated with the motion of a single ion. If the perovskite layer is bounded by inert and ion-blocking boundaries, the above discussion should cover the time scale associated with the ion migration . The fact that the observed hysteresis is orders of magnitude slower implies that there must be some additional process. Several mechanisms have been proposed; (1) there is a source of ions that replenish the ones removed from the perovskite layer (not necessarily the same ion species), 18 (2) electrochemical reaction takes place at the perovskite/electrode boundary, 9 20 and (3) ion migration combined with deep traps at the boundary results in bias voltage history dependent recombination loss. 21 In the first case, the phenomenon lasts until the ion source is empty. In the second case, the speed of the reaction is the speed of hysteresis. In the third case, the ion accumulation near the recombination centers varies depending on the bias voltage history. Regarding the electrochemical scenario above, the treatment of typical mixed conductors such as Ag2 S, 22 in which the stoichiometry of chemical species (Ag+ and Ag atoms) is analyzed using electrochemical potentials, is simple and clear. On the other hand, in the current case, the chemical components to be taken into account are probably I – , iodine vacancy V•I , and I. 20 Quantitative analysis of the experimental data from the point of the ionic motion including the vacancies in lead-iodide perovskite is yet to appear. In this respect, the observation of the apparent complete depletion of one type of ions from some region in the perovskite film under relatively low applied voltage is interesting as shown in the following.

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Using cells with Au/perovskite/Au or Au/perovskite/PEDOT:PSS electrode pairs, extremely large hysteresis, even the reversal of the polarity, has been observed. 23 Because both Au and PEDOT:PSS do not likely act as ion source for perovskite, the hysteresis must be the manifestation of charged vacancy gradient. In fact, the Kelvin force microscopy observation is in accordance with the macroscopic motion of charged species. The in situ optical microscope observation showed the growing front of chemically modified region under an external electric field. The speed of the growth is not unreasonably different from the one expected from Ref. 18 either. One question remains, though. The charged species forming the growing front are likely to be negatively charged vacancies (rather than V•I ) because they grow from the positive electrode. The facile polarization reversal mentioned above is surprising and alarming. If this is caused by the inherent property of the bulk lead-iodide perovskite, not much could be done. Fortunately, this is not the case. In Figure 1, we show J/V traces over the bias voltage range wider than usually presented. The basic structure of our cell is PEDOT:PSS/perovskite/PCBM. 6 Both in the dark and illuminated with 1 sun (100 mW/cm2 ), the cell is stable, reproducible, and hysteresis-free, within the time scale of the measurements, typically seconds to tens of minutes. The internal field in the perovskite layer must vary drastically according to the illumination conditions and the bias voltage. The reverse bias voltage of -2 V on top of the chemical potential difference between the p- and n- electrodes amounts to the internal electric field of the order of 105 V/cm in the dark. We performed photocurrent spectroscopy at -2 V and the same dark current was recovered after the measurement, which took tens of minutes. No sigh of slow charge migration or creep-like behavior was noticed within this period even in the semi-log scale in Figure 1b, which should make the minute current anomaly visible if present. As was estimated earlier, if any ionic movement is possible, the ions must redistribute themselves in the film faster than our changing the experimental parameters so that we always observe the "renormalized" electronic properties. However, it is clear that whatever

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the effect of this ion redistribution would be, it is not detrimental to the extent to kill the PV action significantly. A drift-diffusion model including the ionic contribution has been numerically studied and it was found that the ion migration alone does not affect the PV performance. 21 This is reassuring. At the same time, though, the striking difference between our data in Figure 1 and the creep-like behavior observed around the applied bias of ±0.6 V in Ref. 23 still needs closer inspection.

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Figure 1: Wide voltage range (±2V) J/V scan. The red circles are data for the cell in the dark and the blue ones under illumination of 1 sun. (a) is a linear plot and (b) is a semi-log plot in order to magnify the low current behavior in the negative bias region. The black dashed curve is the J/V relationship if the shunt resistance Rsh of the cell is 1 MΩcm2 . No additional current contribution is discernible. Note in passing, that the J/V curves in Figure 1 represent electronic parameters similar to those in our previous publication. 8 In addition, we found that the dark J/V curve in the negative bias voltage can be fitted well if we assume that this part is governed by the leakage through the cell, the shunt resistance, Rsh . In Figure 1b, we show the J/V curve for Rsh =1 MΩ cm2 in a dashed line. It is clear that there appears no additional leak or creep current. 9



The shunt resistance more than ∼ 10 kΩcm2 does not influence the fitting of the J/V curve in the positive bias voltage, and hence does not degrade the PV performance. Therefore, its value is usually quoted as larger than some arbitrary number. 24 The observed Rsh is as good as those found in high quality inorganic semiconductors. 25 What is remarkable in Figure 1 is not only the stability under a large negative bias voltage but also the durability. In the forward direction, the cell withstands current density of more than 300 mA/cm2 . The Joule heating in the series resistance, Rs , amounts to 0.3 W/cm2 . In fact the cell cannot tolerate too much current. In Figure 2, we show two rounds of bias voltage scans ±3 V. In the first forward scan in the dark, part of the cell gave way and the J/V curve does not trace the initial curve (Figure 2 black arrow). However, this happens locally. Probably the most defective part "burned" but the rest was intact. The subsequent scan under illumination (Figure 2, red curve) is normal except for the extra leak due to the failed part (red arrow). This part should be more square (as shown in the first voltage increase run in the dark) but it now resembles the J/V curve indicated by the black arrow, the return scan in the dark. Of course, this reduces the FF and thus the efficiency. 100 0 -100

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Figure 2: Wider voltage range (±3V) J/V scan. Part of the cell broke in the first positive bias voltage scan in the dark (blue curve) at the highest current density and the J/V curve in the reverse scan does not trace the initial curve (black arrow). The red curves are taken subsequently under illumination of 1 sun. Both forward and reverse bias voltage scans are plotted. The curves lost squareness (red arrow) indicating the enhanced leakage but no further sign of degradation is observed. 10


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Now that perovskite passed our short term scrutiny, the nest item of our concern is the long term stability of the material, especially under light exposure. Long term stability can be tested in various modes. Our cells are stable for a long period (more than 6 mo.) if stored in the ambient condition 6 (long shelf life). Some degree of degradation is obvious if they are under continuous illumination of 1 sun and kept at the maximum power point (MPP). The degradation is rapid in the initial 10 hrs or so and the pace slows down subsequently. In one study, the power conversion efficiency (PCE) decreases from 12% to 7% after 150 hrs of continuous exposure. 26 However, the degradation is worse when no current is extracted (open circuit condition) under illumination. 27 The much enhanced rate of degradation observed in the cells under open circuit condition compared to that in the MPP operation indicates that it is unlikely that the degradation occurs inside the bulk perovskite. Because the entire perovskite layer is swamped with photo-carriers under the 1 sun illumination, there will be little potential gradient inside in both cases. Especially, in the open circuit case, the internal electric field should be very small, i.e., the quasi Fermi levels for electrons and holes are almost flat since no current flows out of the cell. It is expected thus the ion-migration in the bulk perovskite is unlikely. The difference between the MPP operation and the open circuit condition is that all photo-generated current must be dissipated internally in the latter case. One mechanism for the internal carrier dissipation is recombination in the bulk of perovskite; radiative and nonradiative mediated by the ingap states. However, the nonradiative recombination in the perovskite seems rather low: the reverse saturation current that accounts for the nonradiative recombination is only J02 ∼ 10−11 A/cm2 . 8 Another more plausible mechanism is recombination in the electrodes. Intense charge injection, electrons and holes or into HOMO and LUMO of the electrode materials, followed by recombination must be very harsh to organic molecules. In Figure 3, we show J/V curves of a cell before and after the exposure to 1 sun for 7.5 hours in the open circuit condition. The J/V curve after the light soaking treatment

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and under illumination exhibits a slope that extends to the negative bias voltage, reducing the FF (and hence the efficiency) significantly. We frequently encounter similar behavior in inorganic PV cells with carrier trapping structure. 28 The photo-generated carriers must escape from the potential well and extra external electrical field is necessary to extract the carriers from the traps. Eventually the current should saturate at the Jsc level of the fresh cell. The relationship between the J/V curve and the trap characteristics depends on the details, e.g., position and the depth of the traps.

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V (V) Figure 3: J/V scan before (in red curves) and after (in blue curves) the light soaking for 7.5 hours under 1 sun illumination. The dark curves, after 0 hour and 7.5 hours exposure, are on top of each other. Note in passing that the bulk recombination processes are proposed to dominate the efficiency loss in lead-iodide perovskite PVs. 29 This may well be the case in our cells as well. However, in the present case, we conclude that the additional loss mechanism caused by the prolonged light exposure is not in the bulk; numerical simulations using SCAPS 30 indicate 12


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that if the loss mechanism is introduced in the bulk, the current loss should accompany the Voc reduction. This is not the case in Fig. 3 The J/V curves in the dark before and after the light soaking test are identical as shown in Figure 3. The deep traps do not affect the current in the dark and thus are likely to be photo-activated as we noted earlier in the fresh cell. 8 Under prolonged exposure, the J/V curves change qualitatively. In Figure 4, we show J/V curves before and after 18 hrs of light soaking. The curves after the light soaking are in blue. The blue curve in the dark and that under illumination overlap above ∼ 1.1 V. The curves before the light soaking are in red. Note that only the positive bias voltage side is shown. Below ∼ 1.1 V and in the dark, the red curve is nearly identical to the blue curve. Again, the red curve in the dark and that under illumination overlap above ∼ 1.1 V. Note that the curve under illumination was taken with a monochromatic light source as a part of spectroscopic studies, which will be the subject of our future study. The dark curves before and after are now different. This means that the major defects are no longer lightactivated ones but permanent. However, even after the degradation, Rsh stays at relatively high level. In Figure 4, we show the leak current in a semi-log scale (inset), which implies Rsh ∼ 3 × 105 Ωcm2 . This is still insignificant. Of course, this does not prove that the bulk perovskite is intact. However, preliminary impedance spectroscopic studies show additional series capacitive element that reduces the total cell capacitance in the degraded cell. We speculate that we have additional layer of permanent deep traps that behaves as a thin insulator within the time scale of our impedance measurements. Earlier, we argued that under the open circuit light-soaking condition, there would be little electric field inside the bulk perovskite. Even during the MPP operation, the internal field should be low. This makes it likely that the additional defect layer to be located between the bulk perovskite and external electrodes. At the moment, we do not have a convincing argument to assume that the defects are induced in the carrier selective layers (as we commented earlier) or in the interfacial region but in the perovskite side or both.

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The nature of defects should be specified as well. 20 21 Detailed analysis of various means (spectroscopic, elemental, electrical, etc.) is clearly needed. We summarize our discussion as follows: We have mounting evidences to state that the ionic motion must be carefully taken into account in designing the PV cells and in analyzing the data. Especially, the choice of the proper interfacial conditions, both electrochemically inert and ion-blocking, is the minimal requirement. Other effects of ionic motion are not obvious. At least, we know that it is not detrimental but could be the cause of the obstacle against getting the best out of the material. For example, it may form the barrier that hinders the open circuit voltage (Voc) from reaching ∼ 0.3 V of the band gap, which has bee demonstrated in the best GaAs thin film devices. 31 This is not the thermodynamic limit but must be very close to the practical limit from the following observation. Recent search for the limiting factors in the high quality IIIV semiconductor PVs using the absolute EL intensity measurements 32 and numerical analysis 33 shows that the efficiency and hence Voc are strongly degraded from the ideal thermodynamic values by the presence of minute amount of nonradiative processes; a highly nonlinear dependence. This means that one has to surpass by far the perfection in defect-free crystal growth and light management achieved in thin-film GaAs PVs to go beyond the 0.3V barrier. Maybe one can exploit the ionic motion for a better performance, such as in situ regeneration of damaged cell. Our effort in this direction is under way, although systematic results are yet to be obtained. The degradation of the perovskite under photo-excitation augmented by the defect mediated recombination near the interface can be one path to the efficiency reduction. The same mechanism in the carrier selective layers may be the major cause of degradation. In the former case, the problem is very complex. In the latter case, we should look for electrochemically more robust materials as carrier selective layers. In either case, the interfacial control is the key. We have to have a microscopic picture of the ionic motion in the working cell. Fast and chemically sensitive probe is clearly needed in order to give a definitive answer.

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Acknowledgement The authors thank Dr. Giancarlo Lorena for contributing to the initial part of this research. Discussions with Drs. Ryo Tamaki and Dhruba Khadka are appreciated. This work was funded by MEXT under the Program for Development of Environmental Technology using Nanotechnology (GREEN).

Notes and References (1) NREL, Best Research-Cell Efficiencies (last accessed on May 10, 2016). http://www. nrel.gov/ncpv/images/efficiency_chart.jpg. (2) Chen, W.; Wu, Y.; Yue, Y.; Liu, J.; Zhang, W.; Yang, X.; Chen, H.; Bi, E.; Ashraful, I.; Gratzel, M. et al. Efficient and Stable Large-Area Perovskite Solar Cells with Inorganic Charge Extraction Layers. Science 2015, 350, 944–948. (3) Snaith, H. J.; Abate, A.; Ball, J. M.; Eperon, G. E.; Leijtens, T.; Noel, N. K.; Stranks, S. D.; Wang, J. T.-W.; Wojciechowski, K.; Zhang, W. Anomalous Hysteresis in Perovskite Solar Cells. The Journal of Physical Chemistry Letters 2014, 5, 1511–1515, PMID: 26270088. (4) Unger, E. L.; Hoke, E. T.; Bailie, C. D.; Nguyen, W. H.; Bowring, A. R.; Heumuller, T.; Christoforo, M. G.; McGehee, M. D. Hysteresis and Transient Behavior in CurrentVoltage Measurements of Hybrid-Perovskite Absorber Solar Cells. Energy Environ. Sci. 2014, 7, 3690–3698. (5) Shao, Y.; Xiao, Z.; Bi, C.; Yuan, Y.; Huang, J. Origin and Elimination of Photocurrent Hysteresis by Fullerene Passivation in CH3 NH3 PbI3 Planar Heterojunction Solar Cells. Nat Commun 2014, 5 . (6) Tripathi, N.; Yanagida, M.; Shirai, Y.; Masuda, T.; Han, L.; Miyano, K. Hysteresis-free 16


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(23) Xiao, Z.; Yuan, Y.; Shao, Y.; Wang, Q.; Dong, Q.; Bi, C.; Sharma, P.; Gruverman, A.; Huang, J. Giant Switchable Photovoltaic Effect in Organometal Trihalide Perovskite Devices. Nat Mater 2015, 14, 193–198. (24) You, J.; Yang, Y.; Hong, Z.; Song, T.-B.; Meng, L.; Liu, Y.; Jiang, C.; Zhou, H.; Chang, W.-H.; Li, G. et al. Moisture Assisted Perovskite Film Growth for High Performance Solar Cells. Appl. Phys. Lett. 2015, 105, 183902–1–5. (25) Ogura, A.; Sogabe, T.; Ohba, M.; Okada, Y. Extraction of Electrical Parameters in Multi-junction Solar Cells from Voltage Dependent Spectral Response without Light Bias. Jpn. J. Appl. Phys. 2014, 53, 066601–1–5. (26) Tripathi, N.; Shirai, Y.; Yanagida, M.; Karen, A.; Miyano, K. Novel Surface Passivation Technique for Low-temperature Solution-processed Perovskite PV Cells. ACS Applied Materials & Interfaces 2016, 8, 4644–4650, PMID: 26821862. (27) This was first noted by Dr. George Dibb of National Physical Laboratory, U.K., during his stay in NIMS. (28) Fujii, H.; Toprasertpong, K.; Watanabe, K.; Sugiyama, M.; Nakano, Y. Evaluation of Carrier Collection Efficiency in Multiple Quantum Well Solar Cells. IEEE J. Photovolt. 2014, 4, 237–241. (29) Leong, W. L.; Ooi, Z.-E.; Sabba, D.; Yi, C.; Zakeeruddin, S. M.; Graetzel, M.; Gordon, J. M.; Katz, E. A.; Mathews, N. Identifying Fundamental Limitations in Halide Perovskite Solar Cells. Advanced Materials 2016, 28, 2439–2445. (30) Burgelman, M.; Nollet, P.; Degrave, S. Modelling Polycrystalline Semiconductor Solar Cells. Thin Solid Films 2000, 361, 527–532. (31) Green, M. A.; Emery, K.; Hishikawa, Y.; Warta, W.; Dunlop, E. D. Solar Cell Efficiency Tables (version 47). Prog. Photovolt: Res. Appl. 2016, 24, 3–11. 19



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(32) Chen, S.; Zhu, L.; Yoshita, M.; Mochizuki, T.; Kim, C.; Akiyama, H.; Kanemitsu, Y. Thorough Subcells Diagnosis in a Multi-junction Solar Cell via Absolute Electroluminescence-Efficiency Measurements. Sci. Rep 2015, 5, 7836–1–6. (33) Zhu, L.; Mochizuki, T.; Yoshita, M.; Chen, S.; Kim, C.; Akiyama, H.; Kanemitsu, Y. Conversion Efficiency Limits and Bandgap Designs for Multi-junction Solar Cells with Internal Radiative Efficiencies below Unity. Opt. Express 2016, 24, A740–A751.

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Hysteresis, Stability, and Ion Migration in Lead Halide Perovskite

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