Tensile strain regulation via grain boundary buffering for flexible perovskite solar cells

Domain: physics
Published: 2025-12-02
Editorial outcome: minor_revision

Abstract
Flexible perovskite solar cells show promise in photovoltaics due to their high energy-to-power efficiency and adaptability, making them a top choice for third-generation thin-film solar applications. However, the inherent defect and mechanical fragility of polycrystalline films pose a challenge that limited their photovoltaic and mechanical performance. Here, the nanomechanical properties of perovskite films are regulated to varying degrees by introducing metal chelates. Specifically, the metal chelates are embedded into the grain boundaries of perovskite, thereby creating a uniformly distributed tensile strain field. Through nanomechanical investigations of the tensile strain-induced modifications in the microstructure and photovoltaic performance of perovskite films, the flexible perovskite solar cells achieve a power conversion efficiency of 24.47%. This regulation strategy not only focuses on the nanomechanical properties of perovskite films but also reveals the correlation between the physical properties and the mechanical flexibility of perovskite solar cells.

Introduction
Flexible devices are receiving increasing attention for their applications in non-planar areas such as building-integrated photovoltaics, unmanned aerial vehicles, smart cars, and wearable electronic devices1–3. Among them, flexible perovskite solar cells (f-PSCs) have emerged as a research focus due to their high energy-to-mass ratio, high efficiencies, and suitability for low-temperature processing4,5. To date, the reported high power conversion efficiency (PCE) of the f-PSCs has reached 25% through various regulations for perovskite films and devices6–9. However, due to the thermo-mechanical behavior of residual macro- or micro-stresses in perovskite films, their polycrystalline nature, and poor interface contact, most f-PSCs still struggle to achieve a balance between photovoltaic performance and mechanical flexibility10–14.

The intrinsic flexibility of perovskite materials (ABX) arises from the coordination bond between the A–site cation and the B–X framework, but the polycrystallinity of perovskite films hinders their intrinsic flexibility15–18. In general, grain boundaries (GBs) in perovskite films are associated with several shortcomings, such as charge transport barriers and electron-hole recombination, which would harm the performance of f-PSCs19–21. GBs are transition zones between crystallites of differing orientation, typically characterized by atomic-scale disorder and incomplete chemical coordination. Additionally, the mismatch in thermal expansion coefficients between perovskite and the substrate can induce either tensile or compressive strain in the perovskite films. Therefore, the chemical bonds at GBs experienced higher stress than those within the grains, resulting in stress concentration and increasing the modulus within the grains, which leads to an increased tendency for fracture along GBs22–24. Specifically, GBs have become a significant restriction for the bendability and recoverability of f-PSCs, which restricts their further development. Addressing or releasing GB-induced stress concentration in perovskite films is an indispensable part of polycrystalline films with enhanced flexibility.

Elastomers or self-healing materials such as polyurethane, polyacrylamide, and polybutylacrylate have been utilized to bond GBs25–28. Although additives with self-healing properties could repair the damaged perovskite films, the random distribution of these blended elastomers at GBs tended to cause entanglement with perovskite crystals, thereby hindering their growth and resulting in uneven grain formation. Even cross-linked monomers based on small molecules instead of polymers typically exhibit poor electrical conductivity, which impedes charge transfer.

In contrast to these challenges, metal chelates could play a multifunctional role in perovskite films by forming geometrically directed self-assembly through dynamic coordination bonds and building charge transfer channels through coordination with perovskite29,30. The multidentate ligands on metal chelates have two critical advantages: (i) spatially selective anchoring on perovskite at GBs through Lewis acid-base interactions, which eliminates random entanglement with perovskite grains, and (ii) extended π-conjugation within the ligand framework coupled with electron delocalization, ensuring efficient charge transfer across the reconstructed lattice31,32. Unlike conventional self-healing agents or crosslinking monomers, metal chelates synergistically achieve defect remediation and electrical enhancement, addressing both morphological and electronic deficiencies through a single-component strategy.

Herein, a series of metal chelates involving aluminum, including aluminum acetylacetonate (Al(acac)3), aluminum benzoylacetone (Al(acB)3), and aluminum 4-(dimethylamino)benzoylacetone (Al(NB)3), were synthesized and applied to regulate nanomechanical properties and enhance the charge transfer of perovskite film. The phenyl exhibited electron-withdrawing effects, reducing the delocalization of electrons on Al(acac)3, and exhibiting conjugation effects. After grafting the dimethylaniline group, the lone electron pairs on the nitrogen atom not only overlap with the π electron system of the benzene ring through conjugation, but also push the electrons between the grains via resonance in the metal chelates. As a result, the metal chelates can join adjacent perovskite grains and form bridges through their chelating ligands. Furthermore, the introduction of metal chelates disturbs the perovskite lattice, gradually turning its Young’s modulus within the polycrystalline film. Consequently, by tailoring their functional groups of chelating ligands, internal stress within the perovskite film was effectively released, and tensile strain progressively reduced. Finally, the metal chelates modified f-PSCs presented a PCE of 24.47%. Benefiting from the metal chelates, the modified f-PSCs emerged with mechanical reliability and operational stability.

Results
Molecular interaction between metal chelates and perovskite
To improve the nanomechanical properties of the polycrystalline film, we designed two β-diketone aluminum chelates, Al(acB)3 and Al(NB)3, compared with Al(acac)333,34. While the polarized Al–O bonds in Al(acac)3 already form strong covalent chelate bonds, the ligands were tailored to strengthen anchoring with the perovskite surface and bridge adjacent grains. According to Supplementary Fig. 1, the metal chelates were synthesized via β-diketone complexation procedures, and the details of the synthesis method are described in the Supplementary Information. The molecular structures were confirmed using the 1H and 13C nuclear magnetic resonance (NMR) and mass spectra (Supplementary Figs. 2–8). The β-diketone ligands exhibit keto–enol tautomerism, enhancing their dynamic reactivity. To further tune intermolecular interactions and hydrogen-bond interactions at the perovskite surface, phenyl and N,N-dimethylaniline substituents were introduced, respectively. We analyzed the charge distribution of the three ligands by calculating the electrostatic potential map (ESP), as shown in Supplementary Fig. 9. The introduction of phenyl and N,N-dimethylaniline substituent has less effect on the electronegativity of β-diketone, but rather the phenyl ring with the electron-withdrawing groups helped to reduce the electron delocalization in the metal chelates, thus weakening the ligand bonding (O–Al…O=C) valence-donating properties. After grafting the dimethylamine group, the lone electron pairs on the nitrogen atom not only provided the coordination site but also engaged in overlap with the π bond on the benzene ring to form an n–π conjugation, which increased the local electron density and facilitated efficient charge transport channels. We also analyzed the ESP mapping of the three metal chelates to identify the active sites (Fig. 1a). It can be seen from the ESP that the dynamic changes in the structure of the metal chelate do not show any significant effect on the electronic structure of the molecule and its active sites. The C=O was chelated to metals, displaying a strongly negative charge center (highlighted in the blue regions on the maps). The chelation between C=O and the metal changed the charge characteristics of the ligand. It can be seen that after the grafting of phenyl and N,N-dimethylaniline on the ligand, the electronegativity of C=O on the ligand was weakened owing to the electron delocalization of the end group.

X-ray photoelectron spectroscopy (XPS) was performed to confirm the chelate state. As shown in Supplementary Fig. 10–11, the bimodal peaks of Al 2p and O 1s in Al(acac)3 were attributed to the O–Al bond and the coordination bond (O–Al…O=C), respectively. For the perovskite film doped with Al(acac)3, the binding energy of Al 2p and O 1s showed a chemical redshift. Similarly, the binding energies of Al 2p and O 1s both showed a chemical redshift in the Al(acB)3-modified and Al(NB)3-modified perovskite film. These differences in chemical shift may stem from the electron-withdrawing ability of phenyl and N,N-dimethylaniline, and the difference in peaks also showed that ligands had varying degrees of electron-withdrawing or electron-donating effects on the central metal. These results indicated that this series of metal chelates has generated electrostatic interactions of varying degrees with perovskites. The binding energies of the dynamic chelate bonds in these metal chelates exhibit varying degrees of redshift, indicating differing electrostatic interactions between the metal chelates and the perovskite, which may exert differential regulatory effects on the residual strain within the perovskite film. Additionally, to verify whether the metal chelates underwent denaturation during the experiment, the metal chelates were subjected to heat treatment individually at 150 °C for 15 min under an ambient condition of relative humidity ranging from 30–40%, and the heated metal chelates underwent XPS testing (Supplementary Fig. 12). The binding energy peaks of the heated metal chelates exhibited numerous differences compared to those of the isolated metal chelates and those doped into perovskite films. After heat treatment at the same ambient conditions, the metal chelates were partially converted into certain metal oxides after isolated heating, while those embedded at GBs retained their chelated state.

Next, upon the addition of the metal chelates within PbI2 or perovskite films (Fig. 1b, c), the Pb 4f peaks shifted to a lower binding energy, with Al(NB)3 demonstrating the most significant shift. These results likely arise from the electron-rich nature of the N,N-dimethylaniline group, which increased the electron cloud density around Pb2+. Meanwhile, the binding energy of N 1s revealed distinct chemical environments. As shown in Supplementary Fig. 13, the N 1s peak of the control perovskite film was located at 400.52 eV, whereas the N 1s peaks shifted to 400.16 eV, 400.13 eV, and 400.29 eV for the perovskite films doped with Al(acac)3, Al(acB)3, and Al(NB)3, respectively. This shift suggested the presence of hydrogen bonds between FA+ and metal chelates. Attenuated total reflectance infrared spectroscopy (ATR-IR) was undertaken to confirm the interaction of hydrogen bonding between metal chelates and N–H groups (Fig. 1d), as evidenced by slight redshifts in the N–H peaks from 3413.4 cm−1 to 3415.3 cm−1, while the C–N and C=N peaks remained unchanged at 1712.7 cm−1 and 1615.0 cm−1, respectively.

To investigate the charge interaction between metal chelates and perovskite films, we performed density functional theory (DFT) calculations on a regularized perovskite model using the Vienna Ab initio Simulation Package35,36. As shown in Fig. 1e, Al(acac)3, Al(acB)3, and Al(NB)3 manifested different affinities at the Pb–I-terminated lattice surface, and the binding energy formed between the metal chelates and perovskite is collected in Supplementary Fig. 14. The binding energy between Al(acac)3 and the Pb–I-terminated model surface was only 0.017 eV, while that between Al(acB)3 and the same model reached 0.120 eV, causing a mild distortion in the perovskite model. Notably, Al(NB)3 demonstrated a much stronger binding (0.614 eV), and this additional coordination of the N,N-dimethylaniline ligand induced a substantial lattice distortion of the Pb–I-terminated perovskite model. To investigate how metal chelates affect the electronic structure of perovskites, we calculated the density of states of the chelate-modified perovskite using the Perdew–Burke–Ernzerhof functional37,38. As illustrated in Supplementary Fig. 15, after being modified with metal chelates, the band gap of perovskite changed significantly, which indicated that less energy is required for electrons to transfer from the valence band to the conduction band. Besides, from the ultraviolet-visible (UV–Vis) spectroscopy, it can be seen that the absorption edges remained unchanged after incorporating a low dose of metal chelates (Supplementary Fig. 16). The photoluminescence (PL) intensity of the perovskite film was also enhanced after being treated with metal chelates. Besides, the charge density of the perovskite increased, which suggested that the electrical conductivity and carrier mobility were improved39. Through analyzing the charge density difference of the perovskite model doped with various metal chelates (Supplementary Fig. 17), a pronounced charge rearrangement appeared on the Pb−I-terminated model surface upon coordination with Al(NB)3. These results indicated that the bond interaction between Al(NB)3 and the perovskite surface was stronger than that with Al(acac)3 or Al(acB)3, and the redistribution of charge density likely induces the distortion of the Pb–I framework (such as the stretching or compression of Pb–I bonds). Moreover, compared with the Al(acac)3- or Al(acB)3-treated models, the charge separation was effectively enhanced after bonding with Al(NB)3, which is more beneficial for improving the overall performance of perovskite films.

Mechanical property regulation of perovskite film
The physical characteristics of the perovskite film are crucial for explaining its mechanical properties. We studied the nanomechanical properties of perovskite films using the peak force quantitative nanomechanical atomic force microscopy (PFQNM-AFM)8,9,40. As illustrated in Fig. 2a, the modulus mapping correlates strongly with the grains, where Young’s modulus in the grains was significantly higher than that at GBs. The control perovskite film exhibited a non-homogeneous average Young’s modulus of 12.16 GPa. After incorporating Al(acac)3, Al(acB)3, and Al(NB)3, the average modulus decreased to 11.26, 10.11, and 8.52 GPa, respectively. This could be attributed to the metal chelates interfering with the lattice structure of the perovskite through electrostatic interactions, alleviating the concentration of high modulus within the grains, thereby resulting in a decrease in the average modulus. These results suggested that the films modified with metal chelates exhibited lower stiffness than the control film, as the GBs (typically lower-modulus regions) may act as preferential sites for energy dissipation through interfacial sliding (Supplementary Note (1)). The approximate distribution of modulus within the perovskite film was also examined and presented in Fig. 2b. For the control perovskite film, the Young’s modulus distributed along the diagonal varied heterogeneously, where the localized stress concentration could initiate cracks during bending. Instead, the films modified with metal chelates displayed a homogeneous modulus distribution. Specifically, the modulus values measured along both diagonals are closely aligned with the overall average, showing only minor fluctuations. Finally, to quantify these nanomechanical properties, we performed continuous nanoindentation on both control and modified films, enabling a direct comparison of their stiffness and plasticity profiles. Under low applied load (Z, approach distance), the approach and the withdrawal curves nearly overlapped, indicating an entirely elastic response41–43. As the load increased (Fig. 2c), the approach and the withdrawal curves diverged significantly on the control perovskite film, whereas the Al(acac)3-, Al(acB)3-, and Al(NB)3-modified perovskite films showed far better overlap, especially the Al(NB)3-modified film, whose curves almost coincided. These data implied that metal-chelate modification enhanced film elasticity, with the Al(NB)3-modified film achieving the optimal balance of reduced stiffness and superior elastic recovery.

Besides, the grazing incident X-ray diffraction (GIXRD) technique was carried out to analyze the stress-strain behavior of the perovskite film, and the high diffraction angle and the multiplication coefficient corresponding to the (012) plane provide the most reliable structural symmetry information44. GIXRD spectra for the (012) crystal plane of the control and modified films present in Fig. 3a–d testing at different instruction tilt angles (ψ), and the 2θ–sin2ψ relationship was also fitted44,45. The diffraction peaks of the control film gradually shifted to low angles as ψ increased, signifying that the film experienced tensile stress46. In comparison, Al(acac)3-, Al(acB)3-, and Al(NB)3-modified perovskite films exhibited varying peak shifts with ψ, reflecting different levels of stress release across the three metal chelates. According to the 2θ–sin2ψ relationship depicted in Fig. 3e and calculated with Supplementary Note (2) and (3), the control film exhibited a residual tensile strain (ε) of 0.58%40. The tensile strain of Al(acac)3-, Al(acB)3-, and Al(NB)3-modified perovskite films was 0.43%, 0.28%, 0.24%, respectively. Due to the larger molecular volumes and stronger electrostatic interaction of Al(acB)3 and Al(NB)3 than Al(acac)3, Al(acB)3 and Al(NB)3 significantly reduced the tensile stress of the perovskite film, and caused the crystal packing more compact, resulting in a decrease in the interfacial spacing and a blue shift of the diffraction peaks. These results concluded that the tensile stress was released gradually with the assistance of Al(acac)3, Al(acB)3, or Al(NB)3, which were beneficial for the mechanical stability of the perovskite film. Confocal Raman spectroscopy was also supported as the stress variation within the perovskite film after modification by metal chelates47,48. As shown in Fig. 3f, the Raman spectra of the control film were fitted to obtain three peaks located at 124.7, 160.8, and 231.9 cm−1, and the fitting information was listed in Supplementary Table 1. The peaks at 124.7 and 160.8 cm−1 were assigned to the stretching of the I–Pb–I bond, whereas the peak at 231.9 cm−1 was attributed to the vibratory and torsional motions of FA+ within the [PbI6]4− framework. These findings indicated that the control film underwent significant tensile stress49. After doping with Al(acac)3, Al(acB)3, and Al(NB)3 in perovskite film, the peaks correspond to the I–Pb–I bond split into 124.8/157.4 cm−1, 123.8/156.1 cm−1, and 122.2/156.8 cm–1, respectively, as summarized in Supplementary Tables 2–4. The redshift of the shoulder peaks from 160.8 to 156.8 cm–1 was attributed to the compression of the in-plane Pb–I bond, while the shift of the main peaks from 124.7 to 122.2 cm–1 was derived from the stretching of the out-of-plane48. The difference in the redshift indicated that the in-plane compressive stress was higher than the out-of-plane tensile stress, bringing about a smaller tensile strain. As the split Raman peaks gradually converged, the tensile strain in the metal chelates-modified perovskite films also decreased, corresponding to the results of GIXRD spectra.

Subsequently, AFM and scanning electron microscopy (SEM) were conducted to observe the morphology of the control and modified perovskite films. As can be seen in Supplementary Fig. 18, the roughness of the control, Al(acac)3-, Al(acB)3-, and Al(NB)3-modified films was 26.4, 24.1, 29.0, and 22.6 nm, respectively. The distinct roughness within the Al(acac)3- and Al(NB)3-modified films illustrated that fewer potential defects or recombination centers were likely to form. The Al(acB)3-modified films exhibit an abnormally rough surface, which might be caused by the poor contact between the phenyl groups of Al(acB)3 and the perovskite. The SEM images of the control, Al(acac)3-, Al(acB)3-, and Al(NB)3-modified perovskite films are presented in Supplementary Fig. 19. Different perovskite films had similar grain sizes, but there was a larger bare leak at GBs on the Al(acac)3- and Al(acB)3-modified film surfaces, which was not beneficial for carrier transfer. In contrast, compact GBs took shape in the Al(NB)3-modified films. To determine the presence of metal chelates in the perovskite film, energy dispersive spectroscopy was undertaken for validation. As shown in Supplementary Fig. 20, the Al element was approximately distributed around the grains, which revealed that metal chelates tend to be buried in GBs. Based on these results, the control perovskite films prepared by the two-step method induced significant tensile stress and local modulus concentration within the grains, due to the crystal growth driven by the subsequent thermal decomposition of MACl and the thermal-driven lattice expansion, as well as the local lattice freely contraction during the subsequent cooling process, which is different from the bottom lattice attached to the substrate, as illustrated in Fig. 3g. Compared with the control film, due to the strong electrostatic interaction between the metal chelates buried at GBs and the perovskite lattice, the tensile strain caused by freely contraction was alleviated at the top lattice. Moreover, under the electrostatic interaction between the metal chelate and the grains, Young’s modulus within the grains has been slowed down, thereby avoiding modulus concentration on the grain interiors.

Photovoltaic properties of f-PSCs
To further verify the advantage of releasing tensile stress, time-resolved PL (TRPL) spectroscopy was employed to analyze the impact of metal chelates in perovskite films (Supplementary Fig. 21), and the fitting data are listed in Supplementary Table 5. The control perovskite film without metal chelates displayed a carrier lifetime of 202.35 ns. Since the tensile stress was released with the help of Al(acac)3, Al(acB)3, and Al(NB)3, the corresponding perovskite films exhibited longer carrier lifetimes of 227.55, 212.58, and 236.18 ns, respectively. Among them, the Al(NB)3-modified perovskite film displayed the longest lifetime. Furthermore, the diffraction peaks in the GIXRD spectra of Al(acB)3-modified perovskite film were different from those of other films, and the morphology of the Al(acB)3-modified films also exhibited a rough surface, which may explain why the Al(acB)3-modified film showed a shorter PL lifetime than others.

The photovoltaic performances of f-PSCs modified by metal chelates were evaluated. The f-PSCs relying on the concentrations of metal chelates were systematically investigated, and the statistical photovoltaic parameters of devices were illustrated in Supplementary Figs. 22–25. Based on the statistical photovoltaic parameters, the photovoltaic performance of f-PSCs was dependent upon the doping concentration of metal chelates. The champion current density–voltage (J–V) curves of f-PSCs with the optimal concentration of each metal chelate are shown in Fig. 4a and Supplementary Fig. 26, and the corresponding photovoltaic parameters are listed in Table 1. The control f-PSCs exhibited a PCE of 22.67%, with an open-circuit voltage (VOC) of 1.155 V, a short-circuit current density (JSC) of 24.98 mA·cm−2, and a fill factor (FF) of 77.96%. The Al(NB)3-modified f-PSCs exhibited the best photovoltaic parameters, with a VOC of 1.181 V, a JSC of 25.67 mA·cm−2, an FF of 80.36%, and a high PCE of 24.47%. The Al(NB)3-modified f-PSC received a certified efficiency of 23.97% from a third-party organization (Supplementary Fig. 27). Although the nanomechanical properties of the Al(acB)3-modified perovskite film have been improved, poor morphology was observed in AFM and SEM. The strain of Al(acB)3-modified film might be the reason for the abnormal photovoltaic performance of Al(acB)3-modified f-PSCs. The external quantum efficiency (EQE) yielded the corresponding integrated JSC values of 23.82, 24.09, 23.16, and 24.60 mA·cm−2, respectively, close to the corresponding JSC values of the control and modified devices (Fig. 4b). The maximum power point track (MPPT) was tested to examine the operating stability of the devices (Fig. 4c). The output power of the control f-PSCs was reduced visually at a bias of 0.98 V, while the f-PSCs with metal chelates all showed a superior stable output power at the maximum power point. Then, the characteristics of the f-PSCs under different light intensities were probed to determine the electron-hole recombination behavior. The relationship between VOC and light intensity is shown in Supplementary Fig. 28. According to the linear dependence between VOC and light intensity, the slope of control f-PSC was calculated as 1.67 kBT/q, and the slopes of Al(acac)3-, Al(acB)3-, and Al(NB)3-modified f-PSCs were 1.55 kBT/q, 1.46 kBT/q, and 1.33 kBT/q, respectively. These results implied that the modified f-PSCs had a lower trap-related charge recombination than the control device. Through testing the single electron-carrier devices (structure: ITO/SnO2/perovskite/PC61BM/Ag) under dark conditions (Supplementary Fig. 29), the density of defect state was calculated based on the space-charge-limited current method. The electron defect state density of control device was 11.5 × 10−16 cm−3, while that of the Al(acac)3-, Al(acB)3-, and Al(NB)3-modified films was 8.7 × 10−16, 10.4 × 10−16, and 6.4 × 10−16 cm−3, respectively. The Al(NB)3-modified film exhibited the lowest defect state density among films modified with metal chelates.

Mechanical and operational stability of f-PSCs
The SEM images of the perovskite film after 3000 bending cycles at a radius of 5 mm are displayed in Supplementary Fig. 30. Continuous cracks were observed in the control and Al(acac)3-modified films, yet subtle cracks were detected in the Al(acB)3-modified films. Instead, no obvious cracks were found in the Al(NB)3-modified perovskite films. These results could be attributed to the release of internal residual strain and the reduced Young’s modulus, as evidenced by GIXRD and PFQNM-AFM measurements. Notably, modification with Al(NB)3 had significantly alleviated tensile strain, which led to the absence of subtle cracks within the perovskite film. To evaluate the mechanical stability of f-PSCs, bending resistance tests were performed at a 5 mm bending radius. Bending at different curvature radii (namely, R = 7, 6, 5, 4, 3, 2 mm) was tested (Fig. 4d). The control f-PSCs showed more efficiency attenuation than Al(NB)3-modified f-PSCs. The PCE of the Al(NB)3-modified f-PSCs maintains 90% of its initial value after 500 bending cycles at R = 2 mm, while the PCE attenuation of the control f-PSCs was about 30%. As shown in Fig. 4e, after 7,000 bend cycles, the PCE of Al(NB)3-modified f-PSCs declined to 80% of the initial value, whereas Al(acac)3- and Al(acB)3-modified just kept around 60%. The control f-PSCs began to degrade after just 2500 bending cycles, falling to nearly 20% of their initial PCE. These results implied that the Al(NB)3-modified f-PSCs exhibited excellent long-term mechanical stability, and the release of residual strain and low Young’s modulus are significant for the mechanical robustness of f-PSCs. Subsequently, a long-term operational stability test (ISOS-L-1 protocols) was performed under continuous light illumination under ambient air conditions50. As shown in Fig. 4f, the PCE of the encapsulated f-PSCs presented noticeable attenuation after 600 hours of testing. After about 200 hours, the PCEs of the control f-PSC dropped to 80% of its initial value and soon the device became inoperative. The Al(acac)3-modified f-PSCs also showed a continuous decrease, but performed slightly better than the control samples. The PCE of Al(acB)3-modified f-PSCs remained stable for up to 500 hours before declining sharply thereafter, which may be due to the abnormal crystallinity and morphology of Al(acB)3-modified perovskite films. Although the modification of Al(acB)3 can regulate the modulus and strain of perovskite films, the resulting in improved mechanical stability of f-PSCs, the photovoltaic performance of Al(acB)3-modified perovskite films exhibits slight abnormalities, such as lower current density. Differently, the Al(NB)3-modified f-PSCs maintained relatively steady output power, and demonstrated the best long-term operational stability, retaining 80% of their initial PCE after 600 h.

Methods
Materials
Isopropanol (IPA, 99.7%), Chlorobenzene (99.8%), N,N-dimethylformamide (DMF, 99.8%), and dimethyl sulfoxide (DMSO, 99.8%) were purchased from Acros Organics. Flexible conductive substrates and n-hexylammonium bromide (HABr, Greatcell) were purchased from Yingkou Libra. Technology Co., LTD. Methylammonium chloride (MACl, Greatcell), formamidinium iodide (FAI, Greatcell), lead(II) iodide (PbI2, 99.99%), spiro-OMeTAD (99.8%), and 4-tert-butylpyridine (TBP) were purchased from Advanced Election Technology Co., Ltd. Li-bis(trifluoromethanesulfonyl) imide (Li-TFSI) was purchased from Xi’an E-Light New Material Co., Ltd. Rubidium(I) chloride (RbCl) and Rubidium(I) iodide (RbI) were purchased from Sigma-Aldrich. Tin(IV) oxide colloid precursor (SnO2, 15% in H2O colloidal dispersion) and molybdenum oxide (MoO3) were purchased from Alfa Aesar. Silver (99.999%) was purchased from ZhongNuo Advanced Material (Beijing). All the chemicals and solvents were used without further purification.

Preparation of perovskite precursor solution
In detail, PbI2 (691.5 mg) and RbCl (9.2 mg) were dissolved in 1 mL mixed solvent of DMF:DMSO (V:V = 9:1). For the metal chelates modified solution, the different metal chelate was dissolved in the PbI2 mixed solution, respectively. FAI (90 mg) and MACl (15 mg) were dissolved in 1 mL IPA. 72.5 mg spiro-OMeTAD, 17.5 μL Li-TFSI stock solution (520 mg Li-TFSI in 1 mL acetonitrile), and 29 μL TBP were dissolved in 1 mL chlorobenzene, used as the precursor solution of the hole transporting layer.

Device fabrication
After cleaning with ethanol, ITO/PET is treated with UV ozone for 15 minutes and can be used for spin-coating. SnO2 solution (diluted with water in a volume ratio of 1:4) was spin-coated on ITO substrates at 3000 rpm for 30 s, and then baked on a hot plate in ambient air at 120 °C for 40 minutes. After cooling down, RbI solution (dispersed in the water, 2 mg/mL) was spin-coated on ITO substrates at 3000 rpm for 30 s, and then baked on a hot plate in ambient air at 100 °C for 5 minutes. Before depositing the perovskite film, the substrate was cleaned with ultraviolet ozone for 10 minutes to improve the surface. Then, the substrate covered with mixed PbI2 precursor solution was first spun at 1500 rpm for 30 s and annealed at 70 °C for 1 minutes. After cooling to room temperature, 100 µL FAI precursor solution was spin-coated on the PbI2 film at 1800 rpm for 30 s. The substrate attached with the perovskite film was taken out from the nitrogen glove box to ambient air and annealed at 150 °C for 15 minutes in humidity conditions (30–40% humidity). After annealing, the samples were transferred to a nitrogen-filled glove box for further processing. The HABr solution (2 mg/mL in IPA) was spin-coated on the perovskite surface at 5000 rpm for 30 s, followed by annealing at 100 °C for 5 minutes. Afterward, the hole transporting layer was deposited on top of the passivation layer at 3000 rpm for 30 s, and the hole transporting layer was put in a desiccator for 16 hours oxidation of spiro-OMeTAD. Finally, MoO3 (10 nm) and Ag (100 nm) were successively thermally evaporated on the hole-transporting layer.

GIXRD and photoluminescence measurement
Grazing incident X-ray Diffraction (GIXRD) experiment was performed using a Rigaku SmartLab five-axis X-ray diffractometer equipped with Cu K radiation at 45 kV and 200 mA (λ=1.54050 Å), parallel beam optics, and a secondary graphite monochromator. The angle of the grazing incidence was 0.3°. GIXRD patterns were obtained by fixing the 2θ and varying the instrument tilt angle (ψ) and scanning rate at 0.02° min−1 with a step of 0.01°. The measurements were conducted through different instrument tilt angles from 0° to 50°.

Device characterization
The J–V characteristics were measured using a solar simulator (Enlitech, SS-F5-3A) with standard AM 1.5G (100 mW cm−2) illumination and a Keithley B2901A source, and the light intensity was calibrated using a KG-5 Si diode (SRC-00209). The J–V curves of devices were measured in reverse (from 1.2 V to −0.1 V) and forward (from −0.1 V to 1.2 V) scan modes with a scan step length of 0.01 V and a dwell time of 10 ms for each voltage. External quantum efficiency (EQE) data were obtained using QE-R3018, Enlitech. The continuous light test was measured by an LED simulator (spectra region: 410-850 nm) at ISOS-L-1 standard from Suzhou D&R Instruments Co., Ltd. All bending test results were obtained from the average of 12 cells.

Other characterization
The thermogravimetric analysis curves were obtained on a synchronous thermal analyzer (TGA/DSC 3+). The 1H and 13C NMR spectra were recorded on a Bruker AVANCE III 400 MHz. The mass spectrum was obtained from Agilent GC-MS/FID. ATR-IR was obtained on Thermo Scientific IS5. The Raman spectrum was measured using a Witec RAS300 Alpha300R with a 473 nm laser. XPS was performed on a Thermo Scientific ESCALab 250 using 200 W monochromated Al Kα (1486.6 eV) radiation. The PFQNM-AFM test was using Bruker Dimension ICON SPM (USA). PL and TRPL were obtained using an FLS980 spectrometer with a 475 nm EPL laser (Edinburgh Instruments Ltd.). Ultraviolet-visible absorption spectra were obtained using a SHIMADZU UV-2700. SEM and EDS were used on a Hitachi SU8600. AFM was used with Bruker DMFASTSCAN2-SYS.

DFT simulation
First-principles calculations in this work were performed using the Vienna Ab initio Simulation Package35,36. The generalized gradient approximation by Perdew–Burke–Ernzerhof was employed to describe the exchange-correlation function37. The ion-electron interaction was estimated by the projector-augmented wave model38. The energy cutoff for the plane wave expansion was set to 450 eV. A 2 × 2 × 1 Monkhorst Pack k-point setup was used for geometry optimization. The energy convergence for terminating the electronic self-consistent field was 10−6 eV/atom, and the force convergence on each atom for geometric optimization was 10−2 eV/Å. The electrostatic potentials (φ) of the passivation were calculated using the Gaussian 09 package at the B3LYP/def2TZVP level with DFT-D3. The electrostatic potential maps were drawn by Multiwfn and VMD software51,52.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript proposed a metal chelates (Al(acac)3, Al(acB)3, Al(NB)3) strategy to turn grain boundaries of perovskite with less tensile strain and better mechanical and optoelectronic performances. Although various DFT calculation and surface characterizations are employed to validate the hyposis of metal chelates, the key argument of this manuscript may need a further investigation. It is quite a common precursor for metal chelates as a metal oxide precursor, then how could these chelates remain to be the same chemical after a thermal processing with humid air? A number of published manuscripts have proposed the formation of GaOx, SiOx with metal chelates (https://doi.org/10.1039/C7EE03113K, https://doi.org/10.1002/aenm.201800232).\nIn addition to the major issue, authors should clarify a couple of items as shown below:\n1) For high efficiency acclaim, device efficiency should be certified\n2） For tensile strain from incompatible thermal expansion coefficients, authors should elaborate more about the correlation between grain boundary and perovskite layer so that observed low strain can be interpreted smoothly\n3) metal chelates was introduced in PbI2 first in this manuscript, and will this addition will be valid for one step processed perovskite film?", "reviewer_2": "This work provided by Tan et al. designed a series metal chelated to modify the Young’s modulus and residual stress of perovskite film with varying degrees. More importantly, the study analyzed the functions and role of metal chelates at grain boundary and how physical and mechanical characteristics of perovskite film correlate with the operating or mechanical flexibility of flexible devices. This work proposes a feasible approach for the preparation of flexible perovskite solar cells. This manuscript can be recommended to be published after solving the following problems.\n1.Despite the gradient modulation of film modulus and stress by the designed series of metal chelates, why does the second metal chelate yield the lowest PCEs when compared with those modified by Al(acac)3 and Al(acB)3?\n2.According to the structure of the three ligands, highly reactive carbonyl moiety on the ligand displays pronounced coordination activity. But it wonders that how individual ligands influence the performance of perovskite film and flexible devices.\n3.The comments for Fig. 3g focus on the working mechanism of Al(NB)3 in the perovskite film. However, less information can be obtained from Fig. 3g. It is suggested to revise the comments or update the schematic diagram.\n4.As the author said“The chelation between C=O and the metal changed the charge characteristics of the asymmetric ligand.”First, the charge distribution of ligand has not been investigated and it can be seen not all ligands are asymmetric. Please provide the supporting data and refine the description.\n5.Some descriptions are ambiguous to understand. For example, “After doping with Al(acB)3 and Al(NB)3 in the perovskite film, respectively;”, “After about 200 hours, the PCEs of the control and Al(acac)3-modified f-PSCs dropped to 80% of their initial value, indicating that the control f-PSCs had essentially degraded.” Please check and improved the manuscript.\n6.The authors mentioned electrostatic interaction in the conclusion many times but rarely explain in the whole text. Please examine this part.", "reviewer_3": "It is an interesting work in which the authors designed and introduced metal chelates to regulate the tensile strain of perovskite, in order to improve the mechanical properties of perovskite films on flexible devices. The metal chelates are embedded into the grain boundaries of perovskite, thereby creating an even-distributed tensile strain field. The author analyzed the effect of residual stress in perovskite films on the mechanical stability and operational stability of flexible devices and obtained flexible perovskite solar cells with an efficiency of 24.47%. After careful consideration of the work, I believe that this manuscript has the potential to bring inspiration for the perovskite-based flexible devices and deserves to be published in Nature Communications, provided that the authors address the concerns raised.\n1.The author focuses on the Young's modulus of perovskite film, and analyzes that after the metal chelate was doped into the perovskite film, the high modulus was transferred from the grains to the grain boundaries. The author should provide more explanations here so as to correspond to the schematic diagram of Figure 3g. Also, the manifestations of metal complexes in Figure 3g are not uniform. Does this have any special significance?\n2.The author has mentioned the dynamic reactivity of metal complexes in the material design part. But the authors have not mentioned what is the role of dynamic coordination in its application in flexible perovskite film.\n3.Some descriptions are obscure to understand. For example, “These results suggested that the modified films exhibited reduced global stiffness and enhanced plasticity, as the GBs (typically lower-modulus regions) may act as preferential sites for energy dissipation through interfacial sliding (Supplementary Formula 1).” Please revise the comments and improve the whole article.\n4.The diffraction peak positions of the Al(acB)3- and Al(NB)3-modified perovskite films show a high-angle offset compared with the control and Al(acac)3-modified perovskite films. This indicates that the interplanar spacing has decreased. However, Al(acB)3 and Al(NB)3 have larger molecular volumes than Al(acac)3. Why do metal chelates with larger volumes cause in the interplanar spacing of perovskites to decrease? Please explain or supplement the evidence for it.\n5.The caption of Figure 1c does not exactly match the content of the figure.\n6.The authors tested the long-term operational stability of the devices under ISOS-L-1 conditions. In Figure 4f, why did the operational stability of the Al(acB)3-modified devices suddenly drop after 500 h?"}, "author_response": "Point-by-point response to the reviewer’s comments:\nREVIEWER COMMENTS\nReviewer #1 (Remarks to the Author):\nThis manuscript proposed a metal chelates (Al(acac) , Al(acB) , Al(NB) ) strategy to\n3 3 3\nturn grain boundaries of perovskite with less tensile strain and better mechanical and\noptoelectronic performances. Although various DFT calculation and surface\ncharacterizations are employed to validate the hyposis of metal chelates, the key\nargument of this manuscript may need a further investigation. It is quite a common\nprecursor for metal chelates as a metal oxide precursor, then how could these chelates\nremain to be the same chemical after a thermal processing with humid air? A number\nof published manuscripts have proposed the formation of GaOx, SiOx with metal\nchelates (https://doi.org/10.1039/C7EE03113K,\nhttps://doi.org/10.1002/aenm.201800232).\nResponse:\nWe sincerely appreciate the reviewer’s insightful and constructive comments, which\nhave been invaluable in helping us further enhance the quality of this study.\nDuring the experiment, the metal chelate was mixed with the perovskite precursor\nsolution, and finally, the metal chelate was embedded in the grain boundaries of the\nperovskite film. The preparation of the perovskite film was carried out in an air\nenvironment with a relative humidity of 30%-40% and on a heating platform at 150 ℃\nfor 15 minutes. We conducted XPS tests and analyses on the powder of the three metal\nchelates and the perovskite film doped with the metal chelates. In these cases, the\nbinding energies of Al 2p and O 1s appear as double peaks, respectively. We reviewed\na large number of published reports (Sol. RRL 2021, 5, 2000795; Appl. Phys. Lett. 2009,\n94, 222108; Surf. Sci. Spectra 1994, 3, 135–140; Vacuum 2015, 113, 52e58; Procedia\nEngineering 2017, 216, 175–181; and Database: http://xpsdatabase.net), and found that\nthe binding energies of Al 2p and O 1s in aluminum oxide generally range from around\n74.6 eV and 531.6 eV, and their binding energy are all single peaks. This is quite\ndifferent from our experimental results. For instance, 1) there is a significant difference\nin the position of the binding energy; 2) the number of peaks is also different. Therefore,\nwe classified the binding energy of Al 2p in the XPS spectrum as belonging to the O−Al\nbonds and O−Al…O=C coordination bonds. The XPS spectrum and the data analysis\nare presented in the supplementary information, as follows:\nIn the Supplementary information:\nSupplementary Fig. 9 XPS spectra of Al 2p before and after incorporation of metal\nchelates into perovskite films. (a) Al(acac) , (b) Al(acB) , (c) Al(NB) , (d) Al(acac) in\n3 3 3 3\nperovskitefilm, (e) Al(acB) in perovskitefilm, (f) Al(NB) in perovskitefilm.\n3 3\nSupplementary Fig. 10 XPS spectra of O 1s before and after incorporation of metal\nchelates into perovskite films. (a) Al(acac) , (b) Al(acB) , (c) Al(NB) , (d) Al(acac) in\n3 3 3 3\nperovskitefilm, (e) Al(acB) in perovskitefilm, (f) Al(NB) in perovskitefilm.\n3 3\nFurthermore, we carefully reviewed the reference provided by the reviewers\n(https://doi.org/10.1039/C7EE03113K; https://doi.org/10.1002/aenm.201800232) and\nlearned a lot about metal and non-metal complexes from these two reports. Thermal\nstability and water stability are very important characteristics of such complexes. We\nhave doped metal complexes into perovskites, so it is also necessary to pay attention to\nthe stability of metal complexes during the processing. Therefore, we added\nexperiments to illustrate whether metal complexes can still maintain the same chemical\nproperties during the processing of perovskite thin films.\nTherefore, the metal chelates were heated on a hotplate at 150 ℃ for 15 minutes under\nan environmental condition of relative humidity ranging from 30%-40%, and then the\nheated metal chelate was subjected to XPS testing. The data graph is shown below.\nAccording to the XPS test results, we found that some new binding energy peaks (Al\n2p: 74.58, 74.81, 74.78 eV; O 1s: 536.64 and 532.08, 536.10 and 532.05, 535.92 and\n532.28 eV) appeared for the heated metal chelates in the Al 2p and O 1s spectra, and\nwe attributed these to the formation of oxidized aluminum. It is worth noting that these\nbinding energy peaks are different from those of the individual metal chelates and those\nof the metal chelates incorporated into the perovskite film. Therefore, we speculate that\nthe metal chelates incorporated into the perovskite film have not or have very little been\naffected by the environment with RH 30%-40%. And we revised and added a\nsupplement to the manuscript and supplementary information. As follows:\n“X-ray photoelectron spectroscopy (XPS) was performed to confirm the chelate state.\nAs shown in Supplementary Fig. 9-10, the bimodal peaks of Al 2p and O 1s in\nAl(acac) were attributed to the O−Al bond and the coordination bond (O−Al…O=C),\n3\nrespectively. For the perovskite film doped with Al(acac) , the binding energy of Al 2p\n3\nand O 1s showed a chemical redshift. Similarly, the binding energies of Al 2p and O 1s\nboth showed a chemical redshift in the Al(acB) -modified and Al(NB) -modified\n3 3\nperovskite film.”\n“Additionally, to verify whether the metal chelates underwent denaturation during the\nexperiment, the metal chelates were subjected to heat treatment individually under at\n150 ℃ for 15 minutes under an environmental condition of relative humidity ranging\nfrom 30%-40%, and the heated metal chelates underwent XPS testing (Supplementary\nFig. 11). The binding energy peaks of the heated metal chelates exhibited numerous\ndifferences compared to those of the isolated metal chelates and when doped into\nperovskite films. After heat treatment at same environment conditions, the metal\nchelates partially converted into certain metal oxides after isolated heating, while those\nembedded at GBs retained their chelated state.”\nSupplementary Fig. 11 The binding energies of (a, b, c) Al 2p and (d, e, f) O 1s of\nthree metal chelates heated for 15 minutes at a temperature of 150 °C with an RH 30-\n40% environment.\nIn addition to the major issue, authors should clarify a couple of items as shown below:\n1) For high efficiency acclaim, device efficiency should be certified.\nResponse:\nThank you for your constructive comments, which are invaluable for enhancing the\nquality of our manuscript. As follows:\nSupplementary Fig. 26 The efficiency certification report for the camphor-based f-\nPSCs at the IEE, Chinese Academy of Sciences, China.\nOn page 15, “The Al(NB) -modified f-PSC received a certified efficiency of 23.97%\n3\nfrom a third-party organization (Supplementary Fig. 26).”\n2) For tensile strain from incompatible thermal expansion coefficients, authors should\nelaborate more about the correlation between grain boundary and perovskite layer so\nthat observed low strain can be interpreted smoothly.\nResponse:\nThank you for your detailed feedback and constructive criticism, which are invaluable\nfor enhancing the quality of our manuscript. Our description of the regulation of tensile\nstrain is not clear enough, which may mislead the readers. We have made revisions in\nthe manuscript, as follows:\nOn page 3, in the section of introduction, “Since GBs of perovskite are transition zones\nbetween two grains with different orientations, the atomic arrangement is disordered,\nand the chemical bonds are incompletely coordinated. Additionally, due to the\nmismatch in thermal expansion coefficients between perovskite and the substrate,\nperovskite films often give rise to tensile or compressive strain. Therefore, the chemical\nbonds at GBs experienced higher stress than those within the grains, resulting in stress\nconcentration and increasing the modulus within the grains, which leads to an increased\ntendency for fracture along GBs.22-24”\nOn page 13, regarding the description of Fig. 3g, “Based on these results, the control\nperovskite films prepared by the two-step method induced significant tensile stress and\nlocal modulus concentration within the grains, due to the crystal growth driven by the\nsubsequent thermal decomposition of MACl and the thermal-driven lattice expansion,\nas well as the local lattice freely contraction during the subsequent cooling process,\nwhich is different from the bottom lattice attached to the substrate, as illustrated in Fig.\n3g. Compared with the control film, due to the strong electrostatic interaction between\nthe metal chelates buried at GBs and the perovskite lattice, the tensile strain caused by\nfreely contraction was alleviated at the top lattice. Moreover, under the electrostatic\ninteraction between the metal chelate and the grains, Young's modulus within the grains\nhas been slowed down, thereby avoiding modulus concentration on the grain interiors.”\nAnd we have also made new revisions to Fig. 3g, as follows:\nFig. 3 g, Schematic diagram of residual strain regulation by metal chelates at GBs\nduring the heating and cooling process.\n3) metal chelates was introduced in PbI first in this manuscript, and will this addition\n2\nwill be valid for one step processed perovskite film?\nResponse:\nThank you for the reviewers' suggestions. We conducted experiments in perovskite\nfilms prepared by the one-step method. However, since the PCE of the n-i-p type\nflexible perovskite solar cells prepared by the one-step method was not as high as that\nof the devices prepared by the two-step method, we mainly focused on the effects in\nthe n-i-p type flexible perovskite solar cells prepared by the two-step method.\nFurthermore, according to most reports in n-i-p-type devices (one-step method: ACS\nNano 2025, 19, 4867−4875; Energy Environ. Sci., 2024, 17, 2621–2630; Joule 2024,\n8, 1–22; two-step method: Nat. Commun. 2025, 16, 1771; Angew. Chem. Int. Ed. 2025,\ne202421063; Adv. Mater. 2023, 35, 2300513), the reference perovskite films generally\nhave significant residual tensile strain, and the researchers have all controlled the\nresidual tensile strain. This indicates that the residual strain of the perovskite film is\ndetermined by the bottom interface rather than the preparation method of the perovskite\nfilm. Therefore, we adopt the two-step method here as the fabrication method for the\ndevice. Below is the J-V curve of the flexible perovskite devices prepared by the one-\nstep method, and PCEs of the control and metal chelate modified f-PSCs were 21.5%\nand 23.7%, respectively.\nReviewer #2 (Remarks to the Author):\nThis work provided by Tan et al. designed a series metal chelated to modify the Young’s\nmodulus and residual stress of perovskite film with varying degrees. More importantly,\nthe study analyzed the functions and role of metal chelates at grain boundary and how\nphysical and mechanical characteristics of perovskite film correlate with the operating\nor mechanical flexibility of flexible devices. This work proposes a feasible approach\nfor the preparation of flexible perovskite solar cells. This manuscript can be\nrecommended to be published after solving the following problems.\nResponse:\nThank you for your detailed feedback and constructive criticism, which are invaluable\nfor enhancing the quality of our manuscript.\n1. Despite the gradient modulation of film modulus and stress by the designed series of\nmetal chelates, why does the second metal chelate yield the lowest PCEs when\ncompared with those modified by Al(acac) and Al(acB) ?\n3 3\nResponse:\nWe are grateful for the comments provided by the reviewers, as they are crucial for our\nmanuscript. From the SEM images of the perovskite films, we can observe that the\nmorphology of the perovskite films modified with Al(acB) is slightly worse compared\n3\nwith other modifications. Moreover, from the GIXRD analysis, we can also see that the\ncrystallinity of the perovskite films modified with Al(acB) is slightly poorer. It may be\n3\nthat the influence of the benzene ring structure on the ligands causes a larger spatial\nsteric hindrance in the interfacial embedding of the film, as we mentioned in the\nmanuscript:\n“Furthermore, the diffraction peaks in the GIXRD spectra of Al(acB) -modified\n3\nperovskite film were different from those of other films, and the morphology of the\nAl(acB) -modified films also exhibited an extremely rough surface, which may explain\n3\nwhy the Al(acB) -modified film showed a shorter PL lifetime than others.”\n3\nis not the best, but the mechanical properties and light stability of the modified flexible\ndevice show certain regular changes. The regulation of the mechanical properties of the\nfilm enables the device to obtain improved mechanical performance, while the\nmorphology and crystalline characteristics of the film do not affect the photovoltaic\nperformance of the device. This precisely reflects the topic we have described: the\nmodulus and stress of perovskite films are of great importance for flexible perovskite\nsolar cells.\n2. According to the structure of the three ligands, highly reactive carbonyl moiety on\nthe ligand displays pronounced coordination activity. But it wonders that how\nindividual ligands influence the performance of perovskite film and flexible devices.\nResponse:\nThank you for the comments from the reviewers. We attempted to introduce the ligand\ninto the perovskite film with a concentration of 1 mg/mL, and prepared a flexible\nperovskite solar cell. The J-V curve is as follows, and the introduction of the ligand led\nto a significant hysteresis effect on the J-V curves.\nFigure** a, The molecular structure of the third type of ligand. b, The J-V curves of\nflexible perovskite solar cells that were respectively doped with the third ligand.\nWe conducted X-ray photoelectron spectroscopy tests on the lead iodide films doped\nwith ligands and the perovskite films, as shown in the figure below. Before and after\ndoping the ligands, the binding energy of Pb4f in the lead iodide films showed almost\nno change; however, in the perovskite films before and after doping the ligands, the\nbinding energy of Pb4f changed significantly. Therefore, we speculate that during the\n150 °C annealing process of the films, the ligands alone formed a new chelation with\nthe perovskite. Moreover, although the ligands alone can form coordination bonds with\nthe perovskite, they cannot form bridging structures between the grains, and thus cannot\nprovide a buffering effect to alleviate the stress and modulus of the films.\nFigure** a, XPS spectra of PbI film and PbI film with the third ligand. b, XPS spectra\n2 2\nof perovskite film and perovskite film with the third ligand. c, Theoretical speculation\nbased on the experimental results.\n3. The comments for Fig. 3g focus on the working mechanism of Al(NB) in the\n3\nperovskite film. However, less information can be obtained from Fig. 3g. It is suggested\nto revise the comments or update the schematic diagram.\nResponse:\nThanks for your comment. The comments for Fig. 3g might cause misunderstandings\nand it is not clear. We have revised the description in the manuscript and revised Fig.\n3g. As follow:\nOn page 13, “Based on these results, the control perovskite films prepared by the two-\nstep method induced significant tensile stress and local modulus concentration within\nthe grains, due to the crystal growth driven by the subsequent thermal decomposition\nof MACl and the thermal-driven lattice expansion, as well as the local lattice freely\ncontraction during the subsequent cooling process, which is different from the bottom\nlattice attached to the substrate, as illustrated in Fig. 3g. Compared with the control film,\ndue to the strong electrostatic interaction between the metal chelates buried at GBs and\nthe perovskite lattice, the tensile strain caused by freely contraction was alleviated at\nthe top lattice. Moreover, under the electrostatic interaction between the metal chelate\nand the grains, the Young's modulus within the grains has been slowed down, thereby\navoiding modulus concentration on the grain interiors.”\nThe revised Fig. 3g is presented as follows:\nFig. 3 g, Schematic diagram of residual strain regulation by metal chelates at GBs\nduring the heating and cooling process.\n4. As the author said “The chelation between C=O and the metal changed the charge\ncharacteristics of the asymmetric ligand.” First, the charge distribution of ligand has not\nbeen investigated and it can be seen not all ligands are asymmetric. Please provide the\nsupporting data and refine the description.\nResponse:\nThank you to the reviewers for their suggestions. The ligands were modified based on\nβ-diketone, which is a common chelating ligand. We conducted DFT simulations on the\nchemical structures of the two synthesized ligands and analyzed the electrostatic\ndistribution of the ligands, as shown in the figure below. It was found that the carbonyl\ngroups of the two newly designed ligands have high activity, indicating that the ligands\ncan form chelates with metal ions. The asymmetric design did not have a significant\nimpact on the electrostatic potential distribution of the ligands. We added new\ndescriptions in the manuscript. As follow:\nOn page 5, “We analyzed the charge distribution of the three ligands by calculating the\nelectrostatic potential map (ESP), as shown in Supplementary Fig. 8. The introduction\nof phenyl and N,N-dimethylaniline substituents has less effect on the electronegativity\nof β-diketone, but rather the phenyl ring with the electron-withdrawing groups helped\nto reduce the electron delocalization in the metal chelates, thus weakening the ligand\nbonding (O−Al…O=C) valence-donating properties.”\n“The chelation between C=O and the metal changed the charge characteristics of the\nligand.”\nAnd we have added Supplementary Fig. 8 in the Supplementary information, as\nfollows:\nSupplementary Fig. 8 The electrostatic potential map of the three ligands (units:\nkcal/mol).\n5. Some descriptions are ambiguous to understand. For example, “After doping with\nAl(acB) and Al(NB) in the perovskite film, respectively;”, “After about 200 hours,\n3 3\nthe PCEs of the control and Al(acac) -modified f-PSCs dropped to 80% of their initial\n3\nvalue, indicating that the control f-PSCs had essentially degraded.” Please check and\nimproved the manuscript.\nResponse:\nThanks for the reviewers' valuable comments. We have made revisions to the\nmanuscript and carefully reviewed the manuscript, as follows:\nOn page 6, “Similarly, the binding energies of Al 2p and O 1s both showed a chemical\nredshift in the Al(acB) -modified and Al(NB) -modified perovskite film.”\n3 3\nOn page 18, “After about 200 hours, the PCEs of the control f-PSCs dropped to 80%\nof their initial value, and subsequently decreased rapidly and the device became\ninoperative. The Al(acac) -modified f-PSCs also showed a continuous decrease, but\n3\nperformed slightly better than the control samples.”\nAdditionally, we revised some descriptions in the manuscript. As follows:\nOn page 16, “The output power of the control f-PSCs was reduced visually at a bias of\n0.98 V, while the f-PSCs with metal chelates all showed a superior stable output power\nat the maximum power point.”\nOn page 16, “These results implied that the modified f-PSCs had a lower trap-related\ncharge recombination than the control device.”\nIn the section on Introduction, We revised “However, due to the thermo-mechanical\nbehavior of residual macro- or micro stresses in perovskite films, polycrystallinity of\nperovskite film, and poor interface contact, most f-PSCs still struggle to achieve a\nbalance between photovoltaic performance and mechanical flexibility.” to “However,\ndue to the thermo-mechanical behavior of residual macro- or micro-stresses in\nperovskite films, their polycrystalline nature, and poor interface contact, most f-PSCs\nstill struggle to achieve a balance between photovoltaic performance and mechanical\nflexibility.”\n6. The authors mentioned electrostatic interaction in the conclusion many times but\nrarely explain in the whole text. Please examine this part.\nResponse:\nThank you for the reviewers' corrections. We have made revisions to the manuscript\nand checked the whole manuscript. As follows:\n“These results indicated that the electrostatic interaction between Al(NB) and the\n3\nsurface was stronger than Al(acac) and Al(acB) ,”\n3 3\n“These data implied that the electrostatic interaction between metal chelates and\nperovskites effectively regulates the Young's modulus of perovskite films, and\nenhanced film elasticity, with the Al(NB) -modified film achieving the optimal balance\n3\nof reduced stiffness and superior elastic recovery.”\n“These results concluded that the tensile stress was released gradually with the\nelectrostatic interaction of Al(acac) , Al(acB) , and Al(NB) with perovskite, which\n3 3 3\nwere beneficial for the mechanical stability of the perovskite film.”\nReviewer #3 (Remarks to the Author):\nIt is an interesting work in which the authors designed and introduced metal chelates to\nregulate the tensile strain of perovskite, in order to improve the mechanical properties\nof perovskite films on flexible devices. The metal chelates are embedded into the grain\nboundaries of perovskite, thereby creating an even-distributed tensile strain field. The\nauthor analyzed the effect of residual stress in perovskite films on the mechanical\nstability and operational stability of flexible devices and obtained flexible perovskite\nsolar cells with an efficiency of 24.47%. After careful consideration of the work, I\nbelieve that this manuscript has the potential to bring inspiration for the perovskite-\nbased flexible devices and deserves to be published in Nature Communications,\nprovided that the authors address the concerns raised.\nResponse:\nThank you for your insightful and constructive comments. We greatly appreciate your\ndetailed feedback, which has helped to clarify and refine the discussion within our\nmanuscript.\n1. The author focuses on the Young's modulus of perovskite film, and analyzes that after\nthe metal chelate was doped into the perovskite film, the high modulus was transferred\nfrom the grains to the grain boundaries. The author should provide more explanations\nhere so as to correspond to the schematic diagram of Figure 3g. Also, the manifestations\nof metal complexes in Figure 3g are not uniform. Does this have any special\nsignificance?\nResponse:\nWe sincerely appreciate the reviewer’s insightful and constructive comments, which\nhave been invaluable in helping us further enhance the quality of this study. We\nprimarily regulated the spatial heterogeneity of Young's modulus on the perovskite film,\nwhich reduced the overall stiffness of the film. Additionally, this adjustment also\ndecreased the localized stress concentration and produced a more uniform stress\ndistribution in the film.\nWe have revised the description in the manuscript and revised Fig. 3g. As follows:\nOn page 13, “Based on these results, the control perovskite films prepared by the two-\nstep method induced significant tensile stress and local modulus concentration within\nthe grains, due to the crystal growth driven by the subsequent thermal decomposition\nof MACl and the thermal-driven lattice expansion, as well as the local lattice freely\ncontraction during the subsequent cooling process, which is different from the bottom\nlattice attached to the substrate, as illustrated in Fig. 3g. Compared with the control film,\ndue to the strong electrostatic interaction between the metal chelates buried at GBs and\nthe perovskite lattice, the tensile strain caused by freely contraction was alleviated at\nthe top lattice. Moreover, under the electrostatic interaction between the metal chelate\nand the grains, Young's modulus within the grains has been slowed down, thereby\navoiding modulus concentration on the grain interiors.”\nThe revised Fig. 3g is presented as follows:\nFig. 3 g, Schematic diagram of residual strain regulation by metal chelates at GBs\nduring the heating and cooling process.\n2. The author has mentioned the dynamic reactivity of metal complexes in the material\ndesign part. But the authors have not mentioned what is the role of dynamic\ncoordination in its application in flexible perovskite film.\nResponse:\nThanks for the comment from reviewer. Because the metal-ligand bonding in Al(acac) 3 is\ngenerally considered to be dynamically variable, the designed metal chelates based on\nAl(acac) are tentatively assumed to have this property. Secondly, aluminum and\n3\noxygen elements are both bonded in two ways in the XPS spectra of the metal chelates\n(in the Supplementary information).\nSecondly, an electrostatic potential diagram of another structure of metal chelates is\nadded here, and is added in Fig. 1, as follows:\nFig. 1 The interaction of perovskite films with metal chelates. a, Chemical structures\nand ESP maps (units: kcal/mol) of metal chelates.\nAnd we added some description about the dynamic structure, as shown on page 6:\n“It can be seen from ESP that the dynamic changes in the structure of the metal chelate\ndo not show any significant effect on the electronic structure of the molecule and its\nactive sites.”\nFurthermore, the dynamic coordination bond (−C=O...Al−) in the metal chelate\nundergoes a significant change before and after doping into the perovskite film,\nresulting in a redshift of the binding energy for the dynamic coordination bond in the O\n1s spectra of three metal chelates, as shown in Figure S10. This indicates a change in\nthe strength of the dynamic chelation interaction of the coordination bond. The varying\ndegrees of binding energy red shift also imply differing electrostatic interactions\nbetween the metal complexes and the perovskite. This may explain why the tensile\nstrain in the perovskite film was modulated to different extents.\nTherefore, we added a supplement in the manuscript, as follows:\nOn page 7, “The binding energies of the dynamic chelate bonds in these metal chelates\nexhibit varying degrees of redshift, indicating differing electrostatic interactions\nbetween the metal chelates and the perovskite, which may exert differential regulatory\neffects on the residual strain within the perovskite film.”\nSupplementary Fig. 10 XPS spectra of O 1s before and after incorporation of metal\nchelates into perovskite films. (a) Al(acac) , (b) Al(acB) , (c) Al(NB) , (d) Al(acac) in\n3 3 3 3\nperovskitefilm, (e) Al(acB) in perovskitefilm, (f) Al(NB) in perovskitefilm.\n3 3\n3. Some descriptions are obscure to understand. For example, “These results suggested\nthat the modified films exhibited reduced global stiffness and enhanced plasticity,\nas the GBs (typically lower-modulus regions) may act as preferential sites for energy\ndissipation through interfacial sliding (Supplementary Formula 1).” Please revise the\ncomments and improve the whole article.\nResponse:\nThanks to the suggestion from reviewers. We have revised the description in the\nmanuscript. As follows:\n“This could be attributed to the metal chelates interfering with the lattice structure of\nthe perovskite through electrostatic interactions, alleviating the concentration of high\nmodulus within the grains, thereby resulting in a decrease in the average modulus.\nThese results suggested that the films modified with metal chelates exhibited lower\nstiffness than the control film, as the GBs (typically lower-modulus regions) may act as\npreferential sites for energy dissipation through interfacial sliding (Supplementary\nFormula 1).”\n4. The diffraction peak positions of the Al(acB) - and Al(NB) -modified perovskite\n3 3\nfilms show a high-angle offset compared with the control and Al(acac) -modified\n3\nperovskite films. This indicates that the interplanar spacing has decreased. However,\nAl(acB) and Al(NB) have larger molecular volumes than Al(acac) . Why do metal\n3 3 3\nchelates with larger volumes cause in the interplanar spacing of perovskites to decrease?\nPlease explain or supplement the evidence for it.\nResponse:\nThank you for your thoughtful and important comments. The observed grains in SEM\nimages are generally formed by the stacking of multiple crystals rather than a single\ncrystal. The molecular volume of Al(acac) is relatively small, and it has a minor impact\n3\non the packing of perovskite crystals. The latter two metal chelates are grafted with\nfunctional groups that have a large volume, like phenyl and N,N-dimethylaniline\nsubstituents, causing an increase in the molecular volume. The metal chelates are\nusually embedded at the junctions between grains. Through DFT calculations and\nexperimental data, we can clearly see that stronger electrostatic interactions are formed\nbetween Al(acB) or Al(NB) and perovskite, which predicts that the interaction force\n3 3\ngenerated between Al(acB) or Al(NB) and perovskite is stronger than that of Al(acac) .\n3 3 3\nWhen Al(acB) and Al(NB) are embedded in the perovskite film, these may make the\n3 3\ngrain boundaries of perovskite more distinct, but the electrostatic interaction between\nthe metal chelates and the perovskite grains reduces the residual tensile stress in the\nfilm, weakens the distortion of the perovskite lattice, and makes the crystal packing\nmore compact. We have revised and added the new description in the manuscript, as\nfollows:\n“Due to the larger molecular volumes and stronger electrostatic interaction of Al(acB)\n3\nand Al(NB) than Al(acac) , Al(acB) and Al(NB) significantly reduced the tensile\n3 3 3 3\nstress of the perovskite film, and caused the crystal packing more compact, resulting in\na decrease in the interfacial spacing and a blue shift of the diffraction peaks.”\n“Al(acB) -modified films exhibit an abnormally rough surface, which might be caused\n3\nby the poor contact between the phenyl groups on Al(acB) and the perovskite, resulting\n3\nin an abnormal crystallization behavior.”\nIn addition, we conducted simulations on the perovskite model using VASP, as follows\nSupplementary Fig. 15. We found that the perovskite model with Al(acac) maintained\n3\nthe original configuration, while the octahedra of the perovskite models with Al(acB)\n3\nand Al(NB) exhibited slight distortions. Therefore, we infer that Al(acB) and Al(NB)\n3 3 3\nwill exert a greater electrostatic force on the lattice structure of the perovskite film,\nthereby alleviating the lattice expansion effect caused by the mismatch in thermal\nexpansion coefficients, and reducing the internal strain or distortion within the grains.\nThis is conducive to a more compact packing of the crystal and results in a reduction in\nthe lattice spacing.\nSupplementary Fig. 16 The calculated charge density difference (blue, depletion;\nyellow, accumulation) of the perovskite surface upon different metal chelate treatments\n(a) Al(acac) , (b) Al(acB) , and (c) Al(NB) .\n3 3 3\n5. The caption of Figure 1c does not exactly match the content of the figure.\nResponse:\nThanks to the reviewers for checking out the errors, and we have corrected them in the\nmanuscript, as follows:\nOn page 8, “Pb 4f XPS spectra of perovskite films modified by different metal chelates.”\n6. The authors tested the long-term operational stability of the devices under ISOS-L-1\nconditions. In Figure 4f, why did the operational stability of the Al(acB)3-modified\ndevices suddenly drop after 500 h?\nResponse:\nThe electrostatic interaction between the benzene group on Al(acB) and the perovskite\n3\nis relatively weak, and the molecular size is large, which makes it impossible to form a\ngood molecular contact with the perovskite, thus having a significant impact on the\ncrystallization of the perovskite film. Although it reduces the residual tensile stress and\nslightly improves the mechanical properties of the device, the defects within the\nperovskite film have increased significantly. As a result, the photovoltaic effect of the\ndevice modified by Al(acB) is slightly lower than that of other metal chelate modified\n3\ndevices, leading to poorer operational stability of the device. And we also offered a\nrevised description in the manuscript, as follows:\n“Furthermore, the diffraction peaks in the GIXRD spectra of Al(acB) -modified\n3\nperovskite film were different from those of other films, and the morphology of the\nAl(acB) -modified films also exhibited an extremely rough surface, which may explain\n3\nwhy the Al(acB) -modified film showed a shorter PL lifetime than others.”\n3\n“Although the nanomechanical properties of the Al(acB) -modified perovskite film\n3\nhave been improved, the poor morphology observed in AFM and SEM and the strain\nof Al(acB) -modified film might be the reason for the abnormal photovoltaic\n3\nperformance of Al(acB) -modified f-PSCs.”\nfilm in the mechanical stability of the device. The mechanical stability and photovoltaic\nperformance of flexible devices are respectively dominated by different factors.\nFig. 3 c, GIXRD with different instrumental ψ values of (c) Al(acB) -modified\n3\nperovskite films.\nSupplementary Fig. 17 AFM images of the control, Al(acac) -, Al(acB) -, and\n3 3\nAl(NB) -modified perovskite films.\n3 3\nAl(NB) -modified perovskite films.\nThe PCE of Al(acB) -modified f-PSCs remained stable for up to 500 hours before\n3\ndeclining sharply thereafter, which may be due to the abnormal crystallinity and\nmorphology of Al(acB) -modified perovskite films, as indicated by GIXRD and AFM\n3\ntests. Although the modification of Al(acB) can regulate the modulus and strain of\n3\nperovskite films, resulting in improved mechanical stability of f-PSCs, the photovoltaic\nperformance of Al(acB) -modified perovskite films exhibits slight abnormalities, such\n3\nas lower current density."}, {"round": 2, "reviewer_comments": {"reviewer_1": "Authors have provided reasonable surface analysis data to support the integrity of metal chelates after thermal annealing. I would like to recommend for the publication in Nature Communications.", "reviewer_2": "The authors have adequately addressed all reviewer comments, and the manuscript is now suitable for acceptance.", "reviewer_3": "The authors have adequately addressed the comments, and the manuscript is now suitable for acceptance."}, "author_response": ""}]

Decision letter