Stabilizing Perovskite Structures by Tuning Tolerance Factor

Dec 18, 2015 - ABSTRACT: Goldschmidt tolerance factor (t) is an empirical index for predicting stable crystal structures of perovskite materials. A t ...
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Stabilizing Perovskite Structures by Tuning Tolerance Factor: Formation of Formamidinium and Cesium Lead Iodide Solid-State Alloys Zhen Li,† Mengjin Yang,† Ji-Sang Park,† Su-Huai Wei,†,§ Joseph J. Berry,† and Kai Zhu*,† †

National Renewable Energy Laboratory, Golden, Colorado 80401, United States Beijing Computational Science Research Center, Beijing 100094, China

§

S Supporting Information *

ABSTRACT: Goldschmidt tolerance factor (t) is an empirical index for predicting stable crystal structures of perovskite materials. A t value between 0.8 and 1.0 is favorable for cubic perovskite structure, and larger (>1) or smaller (1) or lower ( 1. More than one structure is usually found for a perovskite material with a given chemical composition, depending on the temperature and preparation methods. For easy comparison in this study, we denote the phase with cubic structure as α-phase and the phase with nonperovskite structures as δ-phase.23 Unlike inorganic perovskite, in inorganic−organic hybrid perovskite, the organic cation usually has a nonspherical geometry and rotates constantly in the lattice.24,25 Thus, it is difficult to determine the exact size of the organic cation and calculate the absolute tolerance factor for a particular compound. However, qualitative analysis is still helpful to understand the structure transition in such materials. For example, formamidinium lead iodide, HC(NH2)2PbI3 (FAPbI3), has a larger A cation than methylammonium lead iodide, CH3NH3PbI3 (MAPbI3). Although the exact tolerance factor is difficult to attain due to the geometrical shape of the FA+ cation, a larger cation would normally result in a higher tolerance factor t. Two phases with distinct crystal structures could be attained in solution-processed FAPbI3 materials. One is the photoactive α-phase (black phase) with perovskite structure, and the other one is nonphotoactive phase (yellow phase) with hexagonal structure, which we denote as the δH-phase.17 According to Goldschmidt’s rule, it is reasonable to assume that the tolerance factor is larger than 1 for hexagonal δH-FAPbI3. Recently, inorganic perovskite solar cells with Cs+ as the A cation have demonstrated decent efficiencies.26,27 Inorganic halide perovskite materials often exhibit a higher thermal-decomposition temperature range than their organic hybrid counterparts. This additional design flexibility therefore offers new potential avenues to create stable PSCs. However, the small-size Cs+ cation results in a tolerance factor too low to sustain a cubic perovskite structure. The photoactive α-CsPbI3 with a bandgap of 1.77 eV is usually attained at a temperature higher than 300 °C.28 However, the stable phase of CsPbI3 at room temperature is a nonphotoactive yellow phase with orthorhombic structure (denoted as δOphase), which is consistent with the tolerance-factor analysis. Solid-state alloying is a common tool for tailoring the optical absorption and chemical stability of perovskite materials.29−32 Reports are available about doping with methylammonium lead bromide (MAPbBr3) or partially replacing FA+ with MA+ in FAPbI3 to enhance the stability of the α-phase of FAPbI3.33,34 Both of these alloying compositions have smaller tolerance factors than pure FAPbI3, so the effective tolerance factor is reduced. These observations have prompted us to hypothesize that the crystal structure of inorganic−organic hybrid perovskite can be controlled by tuning the effective tolerance factor of the materials. Here, we propose a general chemical composition design protocol to stabilize the perovskite structure in PSC materials, which is by balancing a material having a large tolerance factor with a material having a small tolerance factor, or vice versa, through solid-state alloying to achieve a more optimum effective tolerance factor. As an example of this general approach, we examine the solid-state alloying of FAPbI3 (large t) and CsPbI3 (small t) and show that, with proper tuning of the tolerance factor, the alloyed material displays a more stable α-phase, leading to better stability in the active layer and, ultimately, better

stability in the PV device. We also show that not only is the effective tolerance factor of solid-state alloys a useful figure of merit for predicting the structure stability of halide perovskite materials, for the (FA-Cs)PbI3 system in this study, but also, it can be extended to explain other stable compositions proposed elsewhere.

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RESULTS AND DISCUSSION We first studied the structure and stability of solid-state alloys of FAPbI3 and CsPbI3. Figure 2a shows the temperature-dependent X-ray diffraction patterns of FAPbI3 and FA1−xCsxPbI3 alloys with Cs ratio of 15, 30, and 45 at. % (denoted as Cs15, Cs30, and Cs45, respectively). A hot stage was used to heat the substrate from room temperature to 200 °C with a ramping rate of 1 °C/ min in a N2-purged dry atmosphere. The reflection at 2θ = 12° is correlated to δH-FAPbI3 (yellow phase), while the peak at 2θ = 14° represents the α-FAPbI3 (black phase). The δH-to-α phase transition for pure FAPbI3 occurs sharply at about 165 °C. By alloying with the lower-t material CsPbI3, the δH-to-α transition temperature decreases with an increase of Cs ratio. The phasetransition temperature of Cs15 alloy drops to 125 °C, and the phase transition becomes less sharp due to the alloying effects. For the Cs30 sample, the transition occurs below 100 °C and the transition edge is further broadened. The Cs45 compound contains α-phase even at room temperature. The decrease of phase-transition temperature suggests that the stability of the αFAPbI3 perovskite structure could be enhanced at room temperature by CsPbI3 alloying. The weaker Bragg diffraction peaks were seen in the Cs30 and Cs45 samples, which could be attributed to the apparent phase separation and potentially poorer crystallinity despite the larger grain size (Figure S9) of the films at high Cs doping ratios. Standard θ−2θ X-ray diffraction (XRD) data of FA1−xCsxPbI3 thin films with different Cs ratios are shown in Figure 2d. In this case, all films were annealed at 170 °C in air for 10 min. The (110) peaks of the α-phase (2θ ∼ 14°) consistently shift to higher angles with higher Cs ratio, corresponding to smaller lattice constants. Fitting of the lattice constant and its relationship with the Cs alloy ratio are shown in Figure S1 (Supporting Information). The near-linear decrease of the lattice constant with increasing Cs amount indicates successful mixing of Cs+ and FA+ cations in the solid-state alloys. It is evident that the δH-phase (peak near 12°) still exists in the FAPbI3 film under such an annealing condition. The absorption peak of δH-FAPbI3 can also be seen in the absorbance spectrum of FAPbI3 films, consistent with the XRD results. For the Cs15 film, a neat XRD pattern shows only the pure black (α) phase in the alloying film. The Cs15 film also exhibits a sharper absorption edge than the FAPbI3 ones, which indicates better optical properties of the Cs15 films than the pure FAPbI3 film (Figure S2). For materials with Cs ratio higher than 45 at. %, a new peak appears at 2θ = 13°, which corresponds to an orthorhombic structure (δO-phase) of CsPbI3 denoted by δO-CsPbI3. The δO-CsPbI3 phase also has a yellow color and poor photoresponse. Ultraviolet−visible (UV− vis) absorbance and XRD of δO-CsPbI3 films are shown in Figure S3 (Supporting Information). This phase separation can be attributed to the large lattice mismatch between FAPbI3 and CsPbI3. Phase separation is another issue to be considered when engineering composition via guidance by tolerance factor. Significant lattice mismatch can likely prevent some possible material alloy compositions that would otherwise be stable according to the effective tolerance-factor prediction. A number of different forces potentially drive the phase separation in 286

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Figure 3. Calculated energy difference between α-phase and different δ-phases for FA1−xCsxPbI3 alloys with different Cs ratios.

Figure 4. Stability of FAPbI3 and FA0.85Cs0.15PbI3 alloy films: (a) UV−vis spectra changes of FAPbI3 in 18 days; (b) UV−vis spectra changes of FA0.85Cs0.15PbI3 in 18 days; (c) XRD pattern of original FAPbI3 and FA0.85Cs0.15PbI3 films and after 30 days of storage; (d) XRD change of FAPbI3 thin film after exposing to high humidity; (e) photos of FAPbI3 and FA0.85Cs0.15PbI3 thin films under high-humidity conditions.

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To examine the material stability of the Cs-doped FAPbI3 compound, thin films of FAPbI3 and FA0.85Cs0.15PbI3 were deposited and kept in a dry desiccator with a constant humidity of 15%. UV−vis spectra of these thin films were taken on different days of storage and compared in Figure 4a,b. The UV− vis spectrum of δH-FAPbI3 (yellow phase) is also plotted as a dotted curve in Figure 4a as a reference. For FAPbI3, the peak corresponding to the yellow phase is indicated for the asdeposited film, and its intensity increased in the first several days. From 10 to 18 days, the absorption above 400 nm dropped significantly, probably due to the material decomposition to form PbI2. In contrast, the UV−vis spectra of FA0.85Cs0.15PbI3 showed no obvious change during the same storage period. XRD pattern of fresh films and films after 30 days of storage were taken to examine the degradation product of the materials, as shown and compared in Figure 4c. The peaks at 2θ = 11.5° and 12.5° are from δH-FAPbI3 and PbI2, respectively. For pure FAPbI3, the intensities of these two peaks both increase after 30 days of storage in the desiccator. These results suggest that phase transition and material decomposition both contributed to the degradation of FAPbI3, which agrees with the observed UV−vis changes. Interestingly for FA0.85Cs0.15PbI3, no yellow-phase peak appears after 30 days of storage, and only a small change of the PbI2 peak can be seen from the XRD pattern. Thus, the Cs alloying appears to not only stabilize the perovskite phase of the FAPbI3 compound, but also suppress the decomposition to PbI2. Accelerated degradation experiments were also carried out to gain more insight into the degradation pathway. FAPbI3 and FA0.85Cs0.15PbI3 thin films were kept at about 90% relative humidity (RH) for 4 h. Analysis of the XRD pattern of FAPbI3 films in Figure 4d shows that the dominant peaks change from original α-FAPbI3 to δH-FAPbI3. The phase transition can also be seen by the color change from black to yellow of the FAPbI3 film (Figure 4e). The film color can be recovered to black after heating the film at 170 °C for 5 min, showing that the phase transition is reversible. XRD showed only a small amount of δHFAPbI3 phase after heating, with a slight increase of the PbI2 signal. Thus, it is evident that moisture triggers and accelerates the phase transition of FAPbI3 films. The α-to-δH phase transition occurs at a much faster rate than the chemical degradation of FAPbI3 perovskite materials. Even without a significant composition change, the phase transition could dramatically change the property of FAPbI3 thin films and further affect the performance of solar cells. In contrast, when the FA0.85Cs0.15PbI3 thin film was kept at the same humidity level (90% RH) for 4 h, no obvious color changes were observed (Figure 4e). There is no obvious change in the XRD pattern, and no δ-FAPbI3 peak can be seen even after storage in the 90% RH condition for 4 h (Figure S4). It is clear that Cs doping stabilizes the cubic perovskite structure, and the film shows better resistance to moisture. These results suggest that, under certain circumstances, phase transitions could be more catastrophic than chemical degradation in FAPbI3-based solar cells, although additional studies are required to determine the roles of each degradation pathway. These results indicate that the structural stability of the active layer plays an important role in the overall stability of FAPbI3-based PSCs. During preparation of this manuscript, one study from Lee et al. showed similar improved photostability and moisture stability for FA0.90Cs0.10PbI3 than the pure FAPbI3 solar cell, which is attributed to the enhanced interaction between FA+ and I−.35 Our results suggested a different mechanism that the enhanced moisture stability could

perovskite alloys, and determining how each factor affects the perovskite stability will be the subject of future studies. It has been shown that reducing the effective tolerance factor of FAPbI3 by adding the smaller-size Cs+ cation can stabilize the α-phase perovskite structure. On the other hand, the CsPbI3 with small tolerance factor can also be stabilized to an α-phase by mixing with the large-size FA+ cation. Temperature-dependent XRD in Figure 2b shows that the δO-to-α transition of CsPbI3 occurs at about 315 °C. After cooling to room temperature, the black color of α-CsPbI3 fades quickly in ambient air, indicating a conversion back to δO-CsPbI3. The high transition temperature and phase instability in air make it impractical for conventional solar cells. However, for a 30 at. % FA+-doped FA0.30Cs0.70PbI3 (Cs70) alloy, the transition temperature is greatly reduced to about 160 °C, as shown in Figure 2c. The phase transition back to δO-CsPbI3 is also suppressed so that the perovskite α-phase can be detected at room temperature in film XRD pattern. Figure 2e shows the XRD pattern of FA1−xCsxPbI3 films with different FA+ ratios; all films were annealed at 170 °C for 10 min. Pure CsPbI3 exhibits the orthorhombic structure. At an alloying ratio of 20 at. % FA+, the peak for perovskite structure starts to appear at 2θ = 20°. With increasing FA+ content, the XRD pattern become distinct from pure CsPbI3, showing a dominant phase with perovskite structure. The strong diffraction peak from the (120) plane of Cs70 alloy (2θ = 20°) can be attributed to a preferential crystal orientation in the film. By partially replacing Cs+ with large-size FA+, the effective tolerance factor is increased toward the range of stable perovskite structure; thus, the stability of the perovskite structure is also improved. The dramatic decrease of δO-to-α phase-transition temperature and stabilization of αphase in the FA+-doped CsPbI3 alloys suggest that the balancing tolerance-factor protocol is promising for both materials with either too high or too low a tolerance factor. We also performed hybrid density functional theory calculations to investigate the formation energy of different phases of FAPbI3 and CsPbI3, and their alloys. The formationenergy difference of the hexagonal and orthorhombic phases to the cubic phase is attained and shown in Figure 3. The lower the formation energy, the more thermodynamically favorable and stable is the corresponding phase. The green line follows the lowest formation energy for crystal structures with different Cs ratios. The large-tolerance-factor FAPbI3 (Cs ratio = 0%) shows the lowest energy with a hexagonal structure, which is consistent with the prediction of tolerance factor. On the other hand, the small-tolerance-factor CsPbI3 (Cs ratio = 100%) shows lower energy with an orthorhombic structure. The energy of the hexagonal structure increases, and the energy of the orthorhombic structure decreases, with increasing Cs %, intersecting one another at a composition of about 30% Cs ratio. At the intersection, the stable ground-state structure changes from δH to δO, and the phase-transition energy from the α-phase to the two different δ-phases reaches a minimum, which explains the observed higher stability of the α-phase in FA1−xCsxPbI3 solid-state alloys. It is worth mentioning that our calculation is based on the ground-state situation without considering the contribution of phonon and configurational entropies. Because we study only the relative stability of the δphases and α-phase, we expect that the alloy-induced effect is largely canceled in a comparison of different phases, and thus, the trend of the relative stability on the amount of Cs composition is expected to be well-described by comparing the enthalpy differences in Figure 3. 288

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Figure 5. Photovoltaic performance of FA1−xCsxPbI3 alloy solar cells: (a) J−V curves of Cs+-doped FAPbI3 solar cells with different Cs+ ratios of 0 at. %, 15 at. %, 30 at. %, and 45 at. %; (b) J−V curves of δO-CsPbI3 and FA+-doped FA0.30Cs0.70PbI3 solar cells; (c) J−V curves of best device with FA0.85Cs0.15PbI3 composition; (d) IPCE spectrum and integrated photocurrent of the best device.

were fabricated using the same device architecture, and their device characteristics are shown in Figure S5 (Supporting Information). The cells with δ-phases demonstrate reasonable Voc values of 0.8−0.9 V, but very poor incident photon-toelectron conversion efficiency (IPCE), less than 20%, compared to their α-phase counterparts. These results indicate that the materials in δ-phases not only are low in light absorption, but also may suffer from higher recombination rates and poor chargetransport properties. The δH-FAPbI3 impurities in the FAPbI3 and δO-CsPbI3 in Cs45 films both could act as recombination centers, thus affecting the Voc and FF in the corresponding solar cells. Because the Cs15 composition produces the best solar cell performance, the subsequent device optimization of the Cs+doped FAPbI3 is focused on the composition of 15 at. % Cs+ ratio. Meanwhile, J−V curves of CsPbI3 and FA+-doped CsPbI3 are shown in Figure 5b for comparison. Due to the large bandgap of about 2.7 eV, δO-CsPbI3 solar cells can only generate a low JSC of 0.22 mA/cm2 and low PCE of 0.12%. Stabilization of the CsPbI3 perovskite α-phase by incorporating 30 at. % FA+ greatly improves the solar cell performance, with a JSC of 18.1 mA/cm2 and PCE of 10.1%. IPCE of FA0.30Cs0.70PbI3 solar cells shows a wide absorption range of 300−750 nm (Figure S6), indicating that perovskite structure α-phase is stabilized with this alloy composition. It is important to mention that an α-CsPbI3 solar cell can also be fabricated with care using dimethyl sulfoxide (DMSO) as solvent in a nitrogen glovebox. The α-CsPbI3 solar cells yielded an efficiency of 8.4% (Figure S7, Supporting Information), although the solar cells degraded in ambient air within 1 h. The J−V curve of the best device attained with FA0.85Cs0.15PbI3 composition is shown in Figure 5c. Under reverse voltage scan,

be associated with the suppressed black-to-yellow phase transition by structure stabilization. FA1−xCsxPbI3 solar cells were fabricated with different Cs doping ratios, and their photocurrent density−voltage (J−V) curves under simulated one-sun illumination are compared in Figure 5a,b. Table 1 summarizes the corresponding PV Table 1. Performance Parameters of FA1−xCsxPbI3 Alloy Solar Cells composition

VOC (V)

JSC (mA/cm2)

FF

PCE (%)

FAPbI3 FA0.85Cs0.15PbI3 FA0.70Cs0.30PbI3 FA0.55Cs0.45PbI3 FA0.30Cs0.70PbI3 δO-CsPbI3

1.06 1.06 1.04 0.94 1.00 0.90

19.69 20.39 19.46 18.09 18.08 0.22

0.68 0.74 0.73 0.56 0.56 0.61

14.2 16.1 14.8 9.60 10.2 0.12

performance parameters including short-circuit current density (Jsc), open-circuit voltage (Voc), fill factor (FF), and power conversion efficiency (PCE). For Cs-doped FAPbI3, The best device performance is attained with Cs15 composition. The pure FAPbI3 attained a similar Voc as Cs15, but Jsc and FF values are lower, leading to a lower overall efficiency. For a high Cs ratio of 30 at. %, the Jsc and FF were lower than those for Cs15 devices, which are probably associated with larger bandgap and the existence of PbI2 impurity in the absorber, as shown in the XRD pattern in Figure 2d. Due to the large amount of δO-CsPbI3 impurity in the Cs45 perovskite composition, the corresponding solar cell performance decreases to an unacceptable level. Solar cells with δH-FAPbI3 and δO-CsPbI3 yellow phases as absorbers 289

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Figure 6. Shelf life stability of FAPbI3 and FA0.85Cs0.15PbI3 solar cells: J−V curves of (a) FAPbI3 and (b) FA0.85Cs0.15PbI3 solar cells at 0−15 days of storage under 15% RH. Normalized (c) JSC and (d) PCE of FAPbI3 and FA0.85Cs0.15PbI3 solar cells with different storage time.

unchanged afterward. The increase of efficiency during the first several days can be attributed to oxidation of spiro-OMeTAD. Although there are clearly other mechanisms at play in the device stability, these results indicate that the stability of FAPbI3 PSCs strongly depends on the phase stability of their absorber materials. Thus, by stabilizing the perovskite α-phase in FAPbI3, the PSC stability can be improved. The success of stabilizing the perovskite structure by tuning the tolerance factor in the (FA-Cs)PbI3 alloying system encourages us to extend the concept to other alloy systems. The effective tolerance factor of different alloys is calculated using a previously published approach.22 The atomic-ratio weighted average of the two different cations is used as the estimated effective cation size. For a composition of AxB1−xPbI3

the device showed a Voc of 1.08 V, Jsc of 21.5 mA/cm2, FF of 0.75, and PCE of 17.3%. The cell showed moderate hysteresis when scanned in forward and reverse directions. The forward-scan efficiency is 13.2%, which is 76% of the reverse-scan efficiency. It is common to have hysteresis for planar devices, which, in general, could be overcome by adding a mesoporous TiO2 layer.36 Stable output of the device is shown in Figure S8. The device output at 0.9 V reached a stable output efficiency of ∼16.4% at about 30 s after light-soaking. IPCE of the bestperformance device is shown in Figure 5d, with a plateau above 80% in the wavelength range 400−650 nm. The cutoff wavelength is around 815 nm, corresponding to a bandgap of 1.52 eV. As shown in the same figure, the photocurrent density integrated from the IPCE spectrum reaches 21.4 mA/cm2, matching well the JSC of the J−V curve. On the basis of the phase-stability difference discussed above, we further compared the device stability of pure FAPbI3 and Cs15 solar cells kept in a dark desiccator with constant RH of 15%. J−V curves of the as-fabricated solar cells are denoted as data of 0 day in Figure 6a,b. The subsequent J−V curves of the same pure FAPbI3 and Cs15 devices measured repeatedly after 3, 6, 9, 12, and 15 days of storage are also plotted in Figure 6a,b, respectively. For easy comparison, the JSC and PCE values extracted from these J−V curves are plotted in Figure 6c,d. As can be seen, the pure FAPbI3-based solar cell continuously degrades to about 50% of the initial efficiency after 15 days. The biggest drop of these parameters is seen in JSC and FF. JSC decreases monotonically to 80% of the initial value at 15 days, which could be due to lower light absorption caused by α-to-δH phase transition in the perovskite absorber. The degradation of FF may also be attributed to the increased amount of δH-phase that increases the recombination in solar cells. In contrast to behavior of the pure FAPbI3-based device, the performance of Cs15 cell increased during the first 3 days and then remained almost

reffective = xr A+ + (1 − x)r B+

teffective =

reffective + rI − 2 (rPb2+ + rI−)

The effective tolerance factors from some previous reports and our results are summarized in Figure 7.30,31,33,34 As seen, for the alloy compositions studied, the best device performance is for absorbers with tolerance factors around 0.94−0.98 (red circle). Pure FAPbI3 is not usually believed to be thermodynamically stable at room temperature, because the δH-to-α phase transition is an endothermic process.33 These studies usually claim better device performance with the alloys, as well as enhanced stability. The improvement in stability is consistent with lower effective tolerance factor in the alloy materials. On the other hand, studies of (MA-Cs)PbI3 alloys and our result from (FA-Cs)PbI3 alloys showed some compositions with poor photoactivity (wide bandgap, yellow phase). Such poor-photoactive alloys assemble at the low tolerance region with t < 0.85 (green area). There are more factors in addition to the size of the organic cation, such as 290

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work at the National Renewable Energy Laboratory is supported by the U.S. Department of Energy under Contract DE-AC36-08-GO28308. We acknowledge the support by the hybrid perovskite solar cell program of the National Center for Photovoltaics funded by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Solar Energy Technologies Office.

Figure 7. Summary of the effective tolerance factors of different mixed perovskite alloys from the literature and our results.30,31,33,34

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cation geometry and interactions between organic R groups,37 that affect the structure of organic−inorganic hybrid perovskites. However, it is shown here that the effective tolerance factor can be a simple figure of merit to roughly predict the stable structure of the mixed perovskite alloys. An effective tolerance factor of around 0.95 but not exceeding 1 is good for maintaining a cubic perovskite structure. However, an effective tolerance factor lower than 0.85 would cause too much distortion in the lattice; thus, a nonperovskite structure is easily formed.

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CONCLUSIONS In conclusion, the correlation between the Goldschmidt tolerance factor and crystal structure is discussed and applied in lead halide perovskites to explain the PV nonfavorable yellow phases in FAPbI3 and CsPbI3. The δH-FAPbI3 and δO-CsPbI3 (yellow phases) could be attributed to large and small tolerance factors, respectively. The tolerance factor could be tuned by alloying the large-tolerance-factor FAPbI3 and small-tolerancefactor CsPbI3, so that α-phase (black phase) was stabilized in the mixed perovskite. FA1−xCsxPbI3 alloys showed lower δ-to-α phase-transition temperature compared to pure FAPbI3 and CsPbI3. High humidity can trigger the α-to-δH phase transition in FAPbI3 films, but not in the Cs-doped FA0.85Cs0.15PbI3 films, showing the importance of phase stability in FAPbI3-based materials. Due to stabilized structure, FA0.85Cs0.15PbI3 alloy solar cells showed better performance and device stability against their FAPbI3 counterparts. Tuning the tolerance factor through solidstate alloying is proposed as a general composition design strategy to stabilize the perovskite structure. The effective tolerance factor of alloy materials could serve as a figure of merit to assess the perovskite structure stability and successfully explain our result in (FA-Cs)PbI3 alloys and in other similar alloy systems.

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.5b04107. Experimental details, calculation methods, XRD data, absorption spectra, IPCE spectra, device performances, stable output of solar cells, SEM images, and EDS elemental mapping (PDF) 291

DOI: 10.1021/acs.chemmater.5b04107 Chem. Mater. 2016, 28, 284−292

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DOI: 10.1021/acs.chemmater.5b04107 Chem. Mater. 2016, 28, 284−292