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 devices1,2,3. 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 devices6,7,8,9. 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 flexibility10,11,12,13,14.

The intrinsic flexibility of perovskite materials (ABX3) arises from the coordination bond between the A–site cation and the B–X framework, but the polycrystallinity of perovskite films hinders their intrinsic flexibility15,16,17,18. 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-PSCs19,20,21. 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 GBs22,23,24. 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 polybutyl acrylate have been utilized to bond GBs25,26,27,28. 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.

Fig. 1: The interaction between perovskite and metal chelates.
Fig. 1: The interaction between perovskite and metal chelates.The alternative text for this image may have been generated using AI.
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a Chemical structures and ESP maps (units: kcal mol−1) of metal chelates. b Pb 4f XPS spectra of PbI2 films modified by different metal chelates. c Pb 4f XPS spectra of perovskite films modified by different metal chelates. d ATR-IR spectra of perovskite film without or with different metal chelates. e The optimized adsorption structures of the binding interaction between Al(acac)3, Al(acB)3, Al(NB)3 and Pb–I-terminated surface.

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 nonhomogeneous 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 response41,42,43. 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.

Fig. 2: The nanomechanical characteristics of perovskite films.
Fig. 2: The nanomechanical characteristics of perovskite films.The alternative text for this image may have been generated using AI.
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a High-resolution quantitative mapping of Young’s modulus (E) of the control, Al(acac)3-, Al(acB)3-, and Al(NB)3-modified perovskite films conducted using PQFNM-AFM. b The variation of the modulus along the diagonal line in the mapping picture of control, Al(acac)3-, Al(acB)3-, and Al(NB)3-modified perovskite films, respectively. Two diagonal lines are taken from the corresponding high-resolution quantitative mapping of Young’s modulus. c The force indentation curves of control, Al(acac)3-, Al(acB)3-, and Al(NB)3-modified perovskite films, respectively. The arrows indicate the direction of the indentation force when it approaches and withdraws. Z represents the depth at which the indentation force acts.

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.

Fig. 3: Strain regulation within perovskite films.
Fig. 3: Strain regulation within perovskite films.The alternative text for this image may have been generated using AI.
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a–d GIXRD with different instrumental ψ values of (a) control, (b) Al(acac)3-, (c) Al(acB)3-, and (d) Al(NB)3-modified perovskite films. e Linear fitting of the 2θ–sin2ψ relationships of perovskite films. f Raman spectra of perovskite films excited at 473 nm. The orange and green peaks represent Pb–I–Pb bonds subjected to residual strain. With increasing residual strain, the peak gradually blueshifts as the bond becomes more rigid. The blue peak was attributed to the librational and torsional motions of FA+ within the [PbI6]4− framework. g Schematic diagram of residual strain regulation by metal chelates at GBs during the heating and cooling process.

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.

Fig. 4: Photovoltaic and mechanical bending performances of f-PSCs.
Fig. 4: Photovoltaic and mechanical bending performances of f-PSCs.The alternative text for this image may have been generated using AI.
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a J–V curves of control and Al(NB)3-modified f-PSCs. b EQE spectra of control and modified f-PSCs. c MPPT of control f-PSC and those modified by different metal chelates. The vertical coordinate on the left represents the output current density under the voltage at the maximum power point. The vertical coordinate on the right represents the output power under the voltage at the maximum power point. d PCE decay of the control and Al(NB)3-modified f-PSCs versus bending radius after 500 bending cycles. Error bars represent the standard deviations from the statistical results of 12 devices. e PCE decay of control and metal chelate-modified f-PSCs during long-term mechanical bending cycles at a radius of 5 mm. Error bars represent the standard deviations from the statistical results of 12 devices. f long-term operating test (ISOS-L-1 Protocol) of the encapsulated control and metal chelate-modified f-PSCs under continuous 100 mW·cm−2 LED illumination in an air atmosphere with RH ~ 60%.

Table 1 The champion photovoltaic parameters of f-PSCs modified with different metal chelates
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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, 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.

Discussion

In summary, we investigated how metal chelates influence tensile strain in perovskite films and assessed the photovoltaic performance and mechanical stability of f-PSCs under varying strain levels. The nanomechanical property of perovskite films could be significantly altered by hydrogen bonding and electrostatic action between perovskite and metal chelates. In addition, the metal chelates would form bridges between grains through hydrogen bonding and electrostatic action, which would form less recombination of non-radiative carriers. The Al(NB)3-modified perovskite films showed the lowest Young’s modulus and residual strain, making them more flexible and resistant to bending than other films. Furthermore, this strain-regulated method had a significant effect on improving the photovoltaic performance and mechanical flexibility of f-PSCs. The PCE was improved significantly from 22.67% to 24.47% with the modification of Al(NB)3, and the PCE maintained 80% of its initial value after 7000 bending cycles at a radius of 5 mm. This work explored the effect of different degrees of tensile strain on perovskite films relying on metal chelates and demonstrated that the physical and nanomechanical properties of the perovskite films significantly affect the photovoltaic and mechanical performance of f-PSCs.

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 1.5 G (100 mW cm−2) illumination and a Keithley B2901A source, and the light intensity was calibrated using a KG-5Si 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/DSC3+). 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.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.