Long-Term Stability of Perovskite Solar Cells under Different Growth

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Long-Term Stability of Perovskite Solar Cells under Different Growth Conditions: A Defects-Controlled Diffusion Mechanism Cang-Lang Yao, Jian-Chen Li, Wang Gao, and Qing Jiang J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b02265 • Publication Date (Web): 30 Aug 2018 Downloaded from http://pubs.acs.org on August 30, 2018

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The Journal of Physical Chemistry Letters

Long-term Stability of Perovskite Solar Cells under Different Growth Conditions: A Defects-controlled Water Diffusion Mechanism Cang-Lang Yao, Jian-Chen Li, Wang Gao* and Qing Jiang* Key Laboratory of Automobile Materials, Ministry of Education, and College of Materials Science and Engineering, Jilin University, Changchun, 130022 (P. R. China)

Corresponding author

Email: [email protected], [email protected]

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Abstract: Understanding the water-infiltration process is crucial for improving the long-term stability of perovskite solar cells (PSC). Although many attempts have been made in this regard, the role of growth condition in the PSC synthesis, which have been observed experimentally to be essential for the stability of PSC, remains elusive. Using first-principles tools, we demonstrate that the growth condition strongly controls the water-infiltration process of PSC by dictating the formation of point defects on PSC surfaces. The resulting point defects are found to alter both the rate and the pathways of water-infiltration process substantially. Our work builds a new scenario for understanding the relation between PSC decomposition mechanism and its preparation methods, it not only sheds new insights for decrypting experimental phenomenon, but also provide important guidance for future preparation of PSC with improved water resistance.

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The robust growth of hybrid lead halide perovskite during the last decade has made it a promising star among the third generation solar cells 1–3. With high power conversion efficiency (PCE), abundant precursors and simplified synthesis procedure, hybrid lead halide perovskite solar cells (PSC) seems to be fully prepared for large-scale commercialization. However, the long-term stability is the Achilles Heel of present hybrid perovskite solar cells 4–7. While massive efforts have been made to elongate the service time of PSC, a consistent and widely-accepted understanding of the relation between PSC’s preparation and its degradation has not been established yet. In specific, water/moisture poses the most damaging factor to PSC. Researchers found that the monohydrate of MAPbI3 can form in a time scale of seconds 8, and the following decomposition to PbI2 can happen within hours 9. First principle and molecular dynamics simulations identified the vulnerability of PSC is inherent to its porous framework and hydrophilic constituent, making it defenseless towards water infiltration 10,11. In practice, the long-term stability of PSC depends strongly on the choice of precursors and the detailed synthesis method 9,12. With MAI+PbI2 precursors, Petrus et al. obtained PSC with elongated service time by adding excessive PbI2 9, while Liu et al. and Zhang et al. found excessive PbI2 detrimental 13,14. Meanwhile, the role of MAI excess is also in controversy, with sharply different views towards its effect on the stability of PSC 12,15,16 . The PSC’s performance is thus assumed to be heavily dependent on the specific synthesis route 9. On the other hand, Yang et al. use MAI+PbCl2 as precursors for PSC growth, achieving a good long-term stability with only 9% degradation over 62 days 17. One may correlate this enhanced performance

to the incorporated Cl atoms or the improved crystallization of PSC, however, the underlying mechanism remains elusive. Overall, the effect of growth condition on the long-term stability has not been systematically studied, the complex synthesis details veil the real mechanism of degradation and deviate our focus from the essentials. From the microscopic viewpoint, it is suggested that the water-catalyzed degradation initiates at defected area of PSC surface 18–20. These surface defects open tunnels for the diffusion of H2O molecules, making the PSC even more vulnerable 10,21. The formation of defects is inevitable during PSC synthesis, and is a direct result of the macroscopic, controllable growth condition of PSC. However, an intended study of defect depended decomposition mechanism and its relation to PSC’s long-term stability has been rarely reported. This is partly due to the extremely small size of surface defects as well as the low concentration. In this work, we will explore the determinant of PSC’s long-term stability by combining studies of PSC’s growth conditions and the water diffusion mechanism. While, PSC’s growth is on a macroscopic level and water diffusion is on a microscopic level, we will bridge these two ingeniously through the basic surface point defects. Since grain boundaries contain sizable concentration of point defects and other more complex defect types like mismatches and dislocations, the result of point defects would also contribute understanding to GB related degradation mechanism. To achieve a thorough infiltration into PSC bulk, water movement inevitably contains two components, vertical penetration and horizontal extension. The former is along [001] direction, while the latter is along [110] direction (see Figure 1(a)

Figure 1. a) Schematic show of water penetration (side view), the red arrow represents a vertical step. b) Schematic show of water extension (top view)， the yellow arrow represent a horizontal step. c) Energy evolution of vertical penetration of water from surface. d) Energy evolution of horizontal extension of water along direction. The water molecule is stressed by using different ball-stick representation, with white ball representing H atom and red ball O atom.

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and 1(b)). The equivalent directions of [110] in a tetragonal 0] and [11 0], each of which belongs to lattice includes [110], [11 family. As shown in Figure 1 (a), the penetration process can be divided into five steps. In the first step, the adsorbed water molecule has to overcome the hindrance of MA+ and squeezes into the hollow site beneath the cation. The process is accompanied by the distortion of the inorganic framework, resulting in an energy barrier of 0.29 eV, compared to 0.31 eV of Tong’s result 10. The following steps of penetration generally proceed with more ease. From step v2 to step v4, the water molecule endures a vertical displacement and a rotation, moving from the upper part of sub-surface area to the lower part. Finally, with step v5, H2O squeezes into the hollow site beneath MA cation, preparing for the next penetration to the 3rd layer of PSC. From step v1 to step v5, H2O molecule goes for a quasi-cycle, through which H2O can move further and further into PSC inner bulk (penetration route in Figure S1 of supporting information). Following the same manner, the horizontal extension is also divided step by step (Figure 1(b)). Horizontal extension happens at step v3 of penetration, when H2O molecule is at the middle part of sub-surface area (Figure 1 (a)). Instead of further moving downward, molecule can move horizontally across the hollow site on the (110) plane, just as Caddeo suggested that water can jump horizontally from one PbI cage to another 22. To continue, water molecule rotates around (001) axis to another hollow site for next horizontal jump. The rotation comprises 3 steps, from h2 to h4. The final step (h5) is another horizontal transferring across the (110) hollow site, which is almost the same as step h1. The 5 steps from h1 to h5 also constitute a quasi-cycle, through which, H2O can traverse horizontally the whole PSC (extension route in Figure S2 of SI). The two movement components of diffusion show different energetics (Figure 1 (c) and (d)). We listed the detailed data in Table 1, as it shows, the rate-controlling step (RCS) of penetration is step v1, with an energy barrier of 0.29 eV, while the RCS of extension is step h4, with an energy barrier of 0.15 eV. Therefore, v1 is the overall RCS of diffusion. The transition state of v1 happens when water attempts to cross the hollow site on (001) plane, which is by nature narrower than the hollow site on (110) plane (Figure S3 and S4). The vertical penetration through the (001) hollow site causes relatively large distortion of the inorganic framework: the area of the hollow site projected on (001) plane is enlarged by 7.8% compared to that of original structure, and the average atom deviation along [001] direction is 0.142 Å (Figure S3). Contrarily, the horizontal movement across (110) hollow site gives rise to smaller distortion: the projected area of the hollow site on (110) plane is enlarged by 6.7%, and the average atom deviation along [110] is 0.128 Å

(Figure S4). In summary, the structural anisotropy of PSC determines the different diffusion energetics on different directions. Although H2O infiltration into PSC is an overall quite fast process, the diffusion speed on horizontal direction can still be 224.3 times faster than that on vertical direction, based on Boltzmann equation (assuming the same pre-exponential factor for the two diffusion components). Therefore, it is reasonable to predict that the vertical movement defines the overall infiltration rate in an ideal model. However, one may further asks, is the infiltration rate of water into PSC really a reflection of vertical penetration rate? Since experimental results of PSC’s long-term stability are often inconsistent and even conflicting 9,12,13, the surface model is therefore more likely to be an uncertain variant, instead of a constant with perfect and uniform structure. As described in previous part, the most basic method for introducing uncertainties to surface structure is to build the one containing defects, specifically, point defects. Three main types of point defects on surface are usually considered: vacancy, interstitial and antisite. However, intersitials at surface are instable adsorbates, while antisites do not change the structure considerably, based on our results. Therefore, in the following study, we focus on the surface vacancy using 4 models to test their resistance to water, they are MA vacancy, Pb vacancy, I-α vacancy and I-β vacancy (an I-α atom forms vertical Pb-I bonding, an I-β atom forms horizontal Pb-I bonding). Based on the results of water diffusion on perfect surface model, we no longer need to perform the whole diffusion process from the very beginning with every single vacancy model. Especially we are concerned about the controlling penetration step v1. Our transition state search indicates that two out of the four types of vacancy can remarkably lower the energy barrier for the

Table 1. Energy change (∆E) and barrier of vertical and horizontal steps Step

1

2

3

4

5

Vertical

0

0.006

0.122

0.038

-0.080

Horizontal

-0.091

-0.122

-0.020

0.122

-0.061

Vertical

0.290

0.024

0.151

0.044

0.255

Horizontal

0.079

0.029

0.125

0.151

0.122

∆E/eV

Energy barrier/ eV

Figure 2. Schematic illustration of the first step of vertical penetration on MA removed surface ((a) and (b)), on I-α removed surface ((c) and (d)), different rate controlling step of water diffusion on different defect types (e). Note that RCS here only corresponds to the water diffusion through vacancies.

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penetration: MA vacancy and I-α vacancy. For MA removed surface, water directly adsorbs on the hollow site, and the penetration can proceed without the hindrance of MA cation (Figure 2 (a) and (b)). Meantime, the close interaction between H2O and the hollow site distorts the inorganic framework and enlarges the hollow site, which also facilitates the penetration. Here, ∆E of step v1 on MA removed surface is -0.27 eV, much smaller than that on perfect surface (-0.0002 eV, Figure 1 (c)), and the energy barrier is reduced from 0.29 eV to 0.04 eV. Similarly, for I-α removed surface, the energy barrier of step v1 is decreased sharply to 0.02 eV (Figure 2 (c) and (d)). To the contrary, for Pb removed or I-β removed surface, the barrier of step v1 increases to 0.74 eV and 0.46 eV respectively. This is because the water molecule will get stuck on Pb and I-β vacancy by the unsaturated surface I atoms which have accumulated more electron density due to decreased coordination numbers (Figure S18 and S19). Clearly, the formation of surface defects turns over the diffusion energetics of water. As shown in Figure 2 (e), on MA and I-α removed surfaces, the controlling step for water’s extension is no longer v1, but the horizontal step h4, whose energy barrier is only 0.15 eV. Therefore, the diffusion speed is no longer limited by the vertical penetration. In this case, water can rapidly penetrate and extend to all the hollow sites of sub-surface area, forming MAPbI3∙H2O monohydrate. Our calculation indicates that the lattice constant mismatch between bulk PSC and its monohydrate is up to 6.6% (lattice constants in Figure S5), suggesting that monohydrate cannot form compatible interface upon PSC. Instead, more point defects and even cracks would form at the interface, destructing the PSC layer by layer, creating new penetration tunnels and leading to disastrous degradation. Indeed, the lattice expansion has been observed in experiments, and was suggested to be an intermediate step during PSC decomposition 6,18. This again, displays the intrinsic instability of MAPbI3 type PSC whose inorganic framework cannot resist the tension caused by water infiltration. It is predicable that the fast diffusion of water and the layer exfoliation of PSC are more difficult to happen within the stiffer and more compact MAPbBr3 cell and thermodynamically more stable FAPbI3 counterpart, which are actually being used for mixed perovskite hybrids to improve the long-term stability 23–25 . Nevertheless, for MAPbI3 type PSC, the devastating consequence caused by point defects can be alleviated to certain extents. In fact, the types and concentrations of point defects can be greatly varied by the growth condition of PSC. We measure the relative stability of point defects with their formation energies (Ef), as shown in Figure 3 (complete data of other defects in Figure S6 and S7). Formation energies of each vacancy are categorized into I rich condition and I poor (Pb rich) condition. In theoretical calculations, the difference between the two conditions results from the choice of chemical potential of the vacant atom. In practice, the MAI+PbI2 precursors can lead to I rich condition due to the abundant PbI3- complex ion in the synthesis process, while MAI+PbCl2 lead to I poor condition due to lower PbI3- concentration 26. We find that MA vacancy is the most stable type under I rich condition with Ef=0.88 eV, while I-α vacancy is the most stable type under I poor condition with Ef=1.19 eV, both in qualitatively consistency with previous report 27 . Part of the difference of Ef with Uratani’s result arises from the inclusion of van der Waals interaction 27, which generally

Figure 3. Formation energy of MA, Pb, I-α and I-β vacancies under (a) I rich condition (b) and I-poor condition.

increases the formation energy of vacancy, e.g. for VMA in I rich condition, such increase is 0.16 eV, for VI-α in I poor condition, such increase is 0.22 eV. It is noteworthy that two different vdW methods are employed for comparison, TS (Tkatchenko-Scheffler 28) and SCS (self-consistent screening 29). Although we use the data by PBE+SCS method throughout our work, it is found that PBE+TS generates quite similar results (maximum deviation less than 7%), which indicate minor screening effect in the hybrid perovskite system, corresponding to porous inorganic framework and hydrophilic constituent of PSC. As we find, both I rich and I poor conditions generate detrimental point defects. However, the large difference of formation energies between VMA and VI-α (0.31 eV) is indicative of the great difference of their concentrations. Our results corroborate the practices of using MAI+PbCl2 as precursors to create I poor growth condition for preparing PSC, which can effectively improve the surface quality, and thus alleviate the layer exfoliation. Actually, such synthesis route does have obtained PSC with elongated service time 17. Previous studies has ascribed the promotion of PSC performance to the incorporated Cl atom into PSC lattice (MAPbI3-xClx) 30,31, leading to unexpected optimization of PSC structure. However, the conflicting work observed that the additive chloride exists in an amorphous lead-containing phase, while without signal of lattice chloride atoms being detected (keynote lecture, 6th

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International Conference on Hybrid and Organic Photovoltaics, HOPV 14, 11–14 May 2014, Lausanne Switzerland) 32. This reminds us that the influence of precursors on PSC performance should be more correlated to the growth environment, which can greatly affects the surface quality, and the intrinsic water resistance of PSC. Herein, we show that our findings can be used to understand more experiments. Many pioneering attempts have been made to improve the stability of PSC, such as substitution, polymeric encapsulation, incorporation of stiffer phase, and construction of 2D/3D heterojunctions7,33–35. These treatments are beneficial to hinder the water diffusion into PSC according to our findings: e.g. polymeric encapsulation is unfavorable to the water adsorption and diffusion, while the stiffer phases and 2D structures display smaller lattice tunnels for water diffusion and stronger resistance to layer exfoliation (see Figure S20). In addition, the mixed PSC and the protection layer with derivatives of all-inorganic perovskites could be also the options for enhancing the stability of PSC. Of course, the constituents of these perovskite hybrids are more complex than pure phase, which requires accurate modelling of their atomic structures (especially of the interface) to understand defect properties and the relation to sophisticated synthesis routes and to complex precursors for experimental realization. In the aims of bridging PSC’s long-term stability and its growth condition, we studied the defect-depended water diffusion mechanism in PSC with first principle tools. Starting from the microscopic model of molecule movement, we confirmed the vertical penetration to be the controlling step in water diffusion process, which defines the overall decomposition rate of PSC. While, the macroscopic growth condition of PSC affects the formation of point defects on surface. We find the major point defects on surface (VMA and VI-α) can decrease the energy barrier of the controlling penetration step remarkably, and thus accelerate the degradation. Importantly, the devastating effect of surface point defect can be largely alleviated by tuning the growth condition to prevent the formation of detrimental defect types. Our results clarified the underlying relation between growth condition and PSC’s long-term stability from the puzzling experimental phenomenon, that the PSC’s service time can be tuned/improved at the very first time of its synthesis. It not only sheds new thoughts for understanding PSC’s degradation mechanism, but also inspires researchers new ideas and options to control the quality of PSC for real commercial use.

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fixed, while the other atoms are allowed to relax. More computational details and the schematic show of transition states can be seen in the Supporting Information.

Corresponding Author Email address: [email protected], [email protected]

Acknowledgements The authors thank the support from the Thousand Young Talents Plan, the National Natural Science Foundation of China (No. 21673095, 51631004), the Program of Innovative Research Team (in Science and Technology) in University of Jilin Province, and the computing resources of High Performance Computing Center of Jilin University and National Supercomputing Center in Jinan and Tianjin, China.

Supporting

Information

Available:

Additional

computational details of modeling. Transition states of each penetration and extension steps. Full formation energies of surface point defects (vacancy, interstitial, and antisite). Comparison of lattice constant between 2D and 3D PSC.

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Long-Term Stability of Perovskite Solar Cells under Different Growth

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