Flexible perovskite/silicon monolithic tandem solar cells approaching 30% efficiency

SJ_Zhang
Jul. 7, 2025

Abstract

Thanks to their excellent properties of low cost, lightweight, portability, and conformity, flexible perovskite-based tandem solar cells show great potentials for energy harvesting applications, with flexible perovskite/c-silicon tandem solar cells particularly promising for achieving high efficiency. However, performance of flexible perovskite/c-silicon monolithic tandem solar cells still greatly lags, due to challenges in simultaneously achieving both efficient photocarrier transport and reliable mitigation of residual stress. Here, we reveal the critical role of perovskite phase homogeneity, for achieving highly-efficient and mechanical-stable flexible perovskite/c-silicon heterojunction monolithic tandem solar cells (PSTs) with textured surface. Through ensuring high phase homogeneity, which promotes charge transfer across all facets of the pyramid on the textured substrates and releases the residual stress at the perovskite/c-silicon interface, we demonstrate flexible PSTs with a bending curvature of 0.44 cm^-1, and a certified power conversion efficiency of 29.88% (steady-state 29.2%, 1.04 cm² aperture area), surpassing all other types of flexible perovskite-based photovoltaic devices. Our results can lead to broad applications and commercialization of flexible perovskite/c-silicon tandem photovoltaics.

Introduction

Metal halide perovskites have been widely used for ultra-thin, flexible solar cells, thanks to their high absorption coefficient and low Young’s modulus^1,2,3, offering great promises for wearable electronic devices, building-integrated photovoltaics (BIPV), portable energy systems, and aerospace technologies^4,5. Both single-junction flexible perovskite solar cells (f-PSCs)^6,7,8 and flexible perovskite-based tandem devices, such as perovskite/perovskite⁹, perovskite/Cu(In,Ga)Se₂ (CIGS)^10,11, and perovskite/organic photovoltaics (OPV)¹², have been actively and broadly developed, demonstrating their excellent potential in enabling next-generation high-efficiency flexible photovoltaics (PV) devices.

Among them, tandem structure based on wide-bandgap perovskite and narrow-bandgap c-silicon (c-Si) heterojunction solar cell, with its promising power conversion efficiency (PCE) and good stability, has demonstrated great promise to become a mainstream technology in the PV market^13,14,15,16. Especially, using c-Si wafers with reduced thickness (to less than 100 µm)^17,18 and blunted edges¹⁹, superb foldability and high response to infrared wavelengths can be simultaneously achieved, offering excellent potential for designing efficient flexible perovskite/c-Si tandem solar cells.

However, such great opportunities have remained largely unexplored to date²⁰, significantly limiting the improvement of PCE in perovskite-based flexible PVs. The primary challenge lies in simultaneously achieving both efficient longitudinal transport of photocarriers^21,22, and reliable mitigation of residual stress, which could induce delaminating and fracturing^23,24, crucial for flexible tandem devices. This is mainly caused by inadequate reaction^25,26 and nonideal cation distribution^27,28, which are further complicated by the use of perovskite/c-Si tandem solar cells with textured surface for enhanced light-trapping.

Here, we tackle these challenges to demonstrate highly efficient and reliable flexible perovskite/c-Si heterojunction monolithic tandem solar cells (PSTs). We reveal the critical role of phase homogeneity of perovskite films in flexible PSTs with textured substrates. We find that a highly homogeneous phase distribution of perovskite films not only effectively promotes the charge transport and extraction across all facets of the pyramid on the textured substrates, but also efficiently releases the tensile stress between the perovskite layer and textured c-Si bottom cell during bending. The optimized flexible PSTs achieve a champion certified PCE of 29.88% (steady-state 29.2%), along with superior mechanical endurance of maintaining initial efficiency after 2000 bending cycles. Furthermore, we demonstrate that the mechanical endurance of flexible PSTs can be extended to the fracture limit of the c-Si substrate, only when highly phase-homogeneous perovskite is achieved. Our findings pave the pathway toward high-performance flexible perovskite-based solar cells for high-power-to-weight-ratio, high-conformability, and high-integrability power applications.

Results

We use a flexible c-Si heterojunction solar cell with a thickness of ~70 µm and blunted edges as the bottom cell and fabricate perovskite layer on top to form tandem solar cells (Fig. 1a, b), which contains the indium tin oxides (ITO) recombination layer, the hybrid hole-transporting layer ([2-(9H-carbazol-9-yl)ethyl]phosphonic acid (2PACz)/nickel oxide (NiO_x) layer composite), the perovskite layer, and other functional layers.

Fig. 1: Schematics of flexible PSTs.

a Structural schematic of flexible PSTs. b Digital photo of the flexible tandem solar cells. c Schematic illustration of the synthesis process of perovskite on flexible textured c-Si heterojunction bottom cells.

We start with vapor-phase growth by evaporating Cs source to provide an ultra-uniform inorganic framework, followed by spinning organic cation solution (Fig. 1c). Particularly, we focus on the distribution of organic cations, which determines the phase homogeneity throughout the perovskite films and thus the band alignment, carrier transport, and residual stress. Homogeneity of perovskite phase distribution is critical for perovskite solar cells on flat substrate²⁸, which is both more important and challenging on textured substrates. Specifically, we compare the effects of mixed cations (formamidinium, FA/methylammonium, MA, control film) and single cation (FA, target film) during the liquid-phase fabrication, aiming to form homogeneous perovskite phases on the textured substrates.

To directly observe the phase distribution on textured substrates from a microscopic perspective, we first use cross-sectional transmission electron microscope (TEM) to examine the lattice homogeneity for top, middle, and bottom parts of perovskite films (Fig. 2a, b). In stark contrast to the control film (Fig. 2a), which exhibits varying lattice spacings d (ranging from 3.45 to 2.79 Å), the target film (Fig. 2b) exhibits high identical lattice spacing throughout (3.42 Å). The consistent pattern of lattice spacing along the depth direction is also observed at the crest and trough of the pyramids (Supplementary Fig. 1). This observation suggests that the use of single organic cation can produce homogeneous perovskite lattice, while the mixed organic cations with different ionic radii give rise to varied lattice spacing, with organic cations more accumulated on the top and lacking at the bottom. Notably, perovskite on textured substrates is much more sensitive and selective to the choice of cations than those on flat substrates (Supplementary Fig. 2). This underscores that achieving phase homogeneity is fundamentally more challenging on textured substrates. Such contrast in homogeneity between control and target samples is further evidenced by photoluminescence (PL): the control film exhibits different PL peak positions (by ~14 nm) for top and bottom surface of the film, while the target film shows much more consistent emission peaks (Fig. 2c and Supplementary Fig. 3).

Fig. 2: Investigation of perovskite phase homogeneity on textured silicon substrates and its impacts on carrier transfer.

a, b High-resolution TEM images collected from the corresponding squares of a control and b target perovskite (Perov.) film, respectively. c PL emissions of 20 points from the top and bottom surface, respectively. d Calculated formation energies for perovskites. e Real-time in situ CLSM. f Direct observation of PL quenching of control and target films by the extraction effect of HTL. g 3D c-AFM images (5 × 5 μm, electrical current) of the samples with a structure of c-Si/ITO/NiO_x/2PACz/Perov./C₆₀. h Schematics for the band alignment of perovskite film.

The phase inhomogeneity observed in the control film can be caused by the difference in perovskite formation energy involving FA⁺ and MA⁺ cations. MA⁺ cations give a lower formation energy (ΔE = −1.67 eV) for the perovskite crystallization (Fig. 2d and Supplementary Fig. 4), and tend to form perovskite crystals at the surface before diffusing into the inorganic framework. This is also confirmed by focused ion beam time-of-flight secondary-ion mass spectroscopy (FIB-ToF-SIMS), showing accumulation of MA⁺ and FA⁺ ions on the control film top surface (Supplementary Figs. 5, 6). In contrast, FA⁺ cations in the target film can diffuse more uniformly throughout the inorganic framework thanks to its higher formation energy (ΔE = 0.23 eV), resulting in retarded crystallization for the target film. Such difference is further evidenced by real-time in situ confocal laser scanning microscopy (CLSM), with the target film showing a delayed rise of PL lifetime (indicating crystallization) of 25 s compared to the control film (13 s) (Fig. 2e and Supplementary Fig. 7). Therefore, using single organic cation with higher formation energy is desirable for achieving phase-homogeneous perovskite films.

To evaluate the enhancement of charge transfer by the phase homogeneity, we compare the quenching effect by depositing a hole transport layer (HTL) or electron transport layer (ETL) on half of each perovskite film. CLSM mapping shows more effective carrier extraction (larger color contrast in Fig. 2f and Supplementary Fig. 8) by either the HTL or ETL in the target film. This is further confirmed by charge selectivity measurements using conductive atomic force microscope (c-AFM), with larger current (Fig. 2g) found for the target film in both positive and negative bias.

Such superior charge transfer is attributed to the highly aligned band structure, thanks to the phase homogeneity. Ultraviolet photoelectron spectroscopy (UPS) results of the top and bottom surface of the perovskite film show much better band alignment in the target film, while the control film shows skewed band structure (Fig. 2h and Supplementary Fig. 9), in which tilted bands hinders charge transfer along the depth direction^29,30.

The lattice and phase homogeneity along the depth of perovskite films regulates the residual stress, and thus adhesion at textured interfaces, which is particularly crucial for flexible tandem solar cells during bending^31,32. We correlate the residual stress with the perovskite lattice using grazing-incidence X-ray diffraction (GIXRD). The lattice spacing of the target film exhibits minimal variation with Ψ angles (Supplementary Fig. 10), with a residual stress as low as 23.3 MPa. In contrast, the control film shows a significant increase in lattice spacing, with a residual stress as high as 48.7 MPa, more than doubling that of the target film.

To visualize the resistance to bending as a result of stress release, we compare the thin-film topology and cross-sectional structure of the two perovskite films before and after bending. The top-view scanning electron microscope (SEM) images (Fig. 3a–d) show that the control film exhibits multiple distinct fracture lines (indicated by the arrows) upon bending, while such defects are not observed in the target film. To further analyze the effects of fracture lines on the textured substrates, we use focused ion beam (FIB)-cutting to examine the cross section of the perovskite layer on textured c-Si bottom cell (Fig. 3e–h). As seen in Fig. 3g, h, after 2000 cycles, the control film suffers from cracks and delamination from the textured substrates, while the target film remains largely intact. Notably, the appearance of fracture lines and interfacial delamination is spatially highly correlated. We also perform in situ TEM tests during bending using a specialized insert that allows application of force inside TEM. We observe that the stress lines tend to aggregate on the troughs of the pyramids (Supplementary Fig. 11), indicating that the interfacial delamination is highly concentrated spatially (Fig. 3g). This further indicates the importance of the perovskite phase homogeneity along the depth from crest to trough of such pyramids on the textured substrates, which can effectively facilitate the release of the residual stress and thus significantly enhances endurance during bending.

Fig. 3: Film morphology of perovskite films on textured substrates before/after mechanical durability tests.

a–d Top-view SEM images of control and target perovskite on flexible textured silicon substrates (a, b) before and (c, d) after 2000 bending cycles, respectively. e, f, Cross-section SEM images of e control and f target perovskite on flexible textured silicon substrate before 2000 bending cycles. g, h Cross-section FIB-SEM images of g control and h target perovskites on flexible textured silicon substrate after 2000 bending cycles.

In addition to the crack/delamination, another considerable difference observed between the perovskite films is the quality of crystallization. The target film exhibits a much higher level of crystallization with well-defined grain boundaries, in contrast to the control film. This again showcases the benefit of the retarded crystallization, which enhances the charge transport in the resulting flexible device by reducing the density of the grain boundaries (which are likely to impair charge transfer under mechanical deformation).

We also evaluate the PV performance of the flexible PSTs, prepared with device architecture of Ag/ITO/a-Si(p)/a-Si(i)/n-Si/a-Si(i)/a-Si(n)/ITO/HTL/Perovskite/ETL/SnO₂/Indium Zinc Oxide (IZO)/Ag/LiF (Fig. 4a). The devices using the target films show superior performance compared with the control ones. The optimized device exhibits a short-circuit current density (J_sc) of 19.51 mA/cm², a fill factor of 0.809, and an open-circuit voltage (V_oc) of 1.89 V, yielding a champion PCE of 29.83% with an active area of 1.04 cm² (surpassing the control device with 27.45% PCE) measured under simulated sunlight (Fig. 4b and Supplementary Figs. 12–15). The integrated J_SC from external quantum efficiency (EQE) response of perovskite and silicon subcells are 19.10 and 19.21 mA/cm², respectively (Fig. 4d). We also determine the stabilized power output of this champion flexible PSTs by measuring the current at the maximum power point (MPP) voltage over 80 s with a stabilized PCE of 29.20% (Fig. 4c). To further validate our results, we send our devices to National Institute of Measurement and Testing Technology (NIMTT, Chengdu, China) and China Electronic Product Reliability and Environmental Testing Research Institute (CEPREI, Guangzhou, China). The best device achieves a certified PCE of 29.88% and a certified stabilized PCE of 29.20%, respectively (Fig. 4e and Supplementary Figs. 16, 17). We further evaluate the stability of the devices using the procedure specified in the ISOS-L-1 protocols³³, and age them under one-sun LED illumination (25 °C). After 1000 h of continuous illumination at the MPP in a nitrogen atmosphere, the unencapsulated target device remains stable and constant, while the control device drops to 92% of its initial efficiency (Fig. 4f). These results again demonstrate the superiority of perovskite films with uniform phase distribution, even at the device level.

Fig. 4: Device performance of flexible PSTs.

a An artist’s schematic illustration of the flexible tandem device. b The J-V curves and PV parameters of control and target devices. The device performance of single-junction silicon solar cells and perovskite solar cells are shown in Supplementary Figs. 12, 13. c Steady-state PCE and current density of the champion target devices. d EQE plots for the target device. e Independent performance certification from the National Institute of Measurement and Testing Technology. f Normalized power output evolution of flexible PSTs after continuous exposure to one-sunlight in N₂ environment for 1000 h. g Photo of the Discovery dynamic mechanical analyzer (DMA) 850 used for the three-point bending test. h, i Bending tests of flexible tandem devices with h different bending radii and i different bending cycle numbers at a bending radius of 3.2 cm. Additional data is presented in Supplementary Fig. 22 and Supplementary Table 1.

To demonstrate the flexibility of PSTs from a practical level, we develop a three-point bending test and observe that our flexible tandem devices can endure significant deformation (Fig. 4g and Supplementary Figs. 18, 19). We further investigate the endurance to repeated bending of flexible tandem devices by assessing the PCE variation with different bending radii (Supplementary Fig. 20). As the bending radius decreases to 2.25 cm, corresponding to a curvature of 0.44 cm⁻¹, the target device is able to maintain its initial efficiency, while the control device shows significantly degradation and falls to 52% of its initial efficiency (Fig. 4h and Supplementary Fig. 21). We also study device durability under 3.2 cm radius bending. The target devices maintain their 100% initial value after full 2000 cycles, while the PCE of control devices drops by more than 60% after just 1000 cycles (Fig. 4i). This suggests that the mechanical endurance of flexible PSTs can be extended to the fracture limit of c-Si substrate. The improved mechanical durability of the target device is consistent with the enhanced interfacial adhesion at the perovskite/textured silicon interface, thanks to the uniform phase distribution of perovskite films by releasing residual stress. Overall, our findings provide an in-depth investigation of phase homogeneity in flexible perovskite/c-Si monolithic tandem solar cells and suggest a promising path for further promoting the application of flexible photovoltaic technology.

Methods

Materials

All reagents and solvents are used without purification. Lead iodide (PbI₂, 99.99%), Cesium bromide (CsBr), and methylammonium chloride (MACl) are purchased from Xi’an Polymer Light Technology Corp. Formamidine iodide (FAI), methylammonium bromide (MABr) and formamidine bromide (FABr) are purchased from Greatcell Solar Materials. Fullerene (C₆₀), lithium fluoride (LiF), and ethanol are purchased from Sigma-Aldrich. The ceramic 2-inch NiO_x, indium-doped tin oxide (ITO, In:Sn = 95:5 wt%) and indium zinc oxide (IZO, In:Zn = 90:10 wt%) targets are purchased from Kairui New Materials Co. Ltd.

Device fabrication

Flexible silicon heterojunction solar cell

The n-type Czochralski (CZ) c-Si wafers with 70 µm thickness are used as the bottom subcells. The Czochralski n-type c-Si wafers initially hold a thickness of 160 μm. To remove the saw damage, they are treated in a 20.0 vol% alkaline water solution at 80 °C, with varying treatment times to achieve various wafer thicknesses. Subsequently, the wafers are immersed in a 2.1 vol% alkaline solution at 80 °C for 10 min to form a microscale pyramid on both sides of the wafer surface. Approximately 2 mm wide edge region of these 70 µm textured wafers are passivated in a HF: HNO₃ (10: 90 vol%) solution for 90 s at 25 °C to achieve better flexibility. All wafers are cleaned through the standard RCA cleaning process and subsequently soaked in a 2.0% hydrofluoric acid aqueous solution to eliminate organic matter and metal ions and etch surface oxides, respectively. Then, 5 nm i-a-Si: H and 15 nm p-a-Si:H, as well as 4 nm i-a-Si:H and 6 nm n-a-Si:H, are deposited on the back and front, respectively, at a process temperature of 200 °C in two RF plasma-enhanced chemical vapor deposition (PECVD). Indium tin oxide (ITO) is sputtered on the surface of the N-type layer and P-type layer, respectively. The thickness of ITO on the surface of the N-type layer is 20 nm, and the series resistance is 300 Ω per square; the thickness of ITO on the surface of the P-type layer is 80 nm, and the series resistance is 50 Ω per square. Following that, 200 nm of Ag is evaporated as the back electrode.

Flexible tandem solar cell

The flexible silicon bottom cells were cut into 2 × 2 cm² or 2 ×6 cm² squares by laser and heated for 30 min. Then, at 0.37 Pa, 25 °C and 90 W power, the hole transfer NiO_x layer was RF sputtered on the surface of the textured silicon for 10 min. The final thickness of the NiO_x layer is 30 nm. The 50 μL of 2PACz (1 mg/mL in anhydrous EtOH) solution was spin-coated on the NiO_x layer at 3000 rpm for 30 s and then annealed at 100 °C for 10 min. The perovskite film is deposited using a vapor/solution hybrid two-step method, with PbI₂ and CsBr co-evaporated at a rate of 10:1 to a thickness of 350 nm. Then, a mixture of FAI/FABr(MABr) is dissolved in ethanol at concentrations of 61/20(15) mg/mL. 5 mg/ml MACl is added to achieve better crystallinity. The solution is spin-coated at 4000 rpm for 30 s in ambient air with 5% RH, followed by an annealing step at 150 °C for 30 min in ambient air with 75% RH. The final composition of the control perovskite is Cs_xFA_yMA_1-(x+y)Pb(I,Br)₃ (0<x + y < 1) and that of the target perovskite is Cs_xFA_1-xPb(I,Br)₃ (0<x < 1). Following the thermal evaporation of a 20 nm thick C₆₀ film as the electron transport layer (ETL), a 10 nm thick layer of SnO₂ is subsequently deposited via atomic layer deposition to serve as a buffer layer, which aims to prevent sputtering damage. Thereafter, a 120 nm indium zinc oxide (IZO) film is deposited by direct current (DC) sputtering at 25 °C. A 600 nm thick Ag grid is thermally evaporated onto the front surface using a shadow mask, and subsequently, a 200 nm thick Ag grid is also evaporated onto the back surface. Eventually, an antireflection layer of LiF of 100 nm thickness is evaporated.

Material characterizations

Revealing the “Bottom” of perovskite film on the textured substrates^34,35

A solution of PTAA at a concentration of 10 mg/ml in chlorobenzene is spin-coated onto a silicon substrate, and the deposition of the perovskite is carried out as described in the “device fabrication” section. Following 2 h immersion in chlorobenzene, the bottom surface is delaminated from the textured silicon substrates.

Deriving the bandgap values from different transport layer sides

First, we place the sample in the CLSM setup, and select a test area of 200 × 200 μm. Then, we pick ten sample points in each of the two orthogonal directions, and all the 20 spectra are averaged. Finally, the bandgap of perovskite is deduced using the position of corresponding emission peaks.

Focused ion beam-transmission electron microscope (FIB-TEM)

The samples are prepared with c-Si/NiO_x + 2PACz/perovskite stacks. The surface of the sample is protected by depositing a Pt and carbon layer before thinning with focused ion beam (FIB) equipment (Thermo Fisher Helios 5 CX). Pt is deposited using 5 kV, 0.34 nA electron beams and 80 pA ion beams. After Pt deposition, excavation begins at 30 kV, 2.5 nA and thinned at 30 kV, 0.43 nA. After the extraction of the FIB sample, the thinning begins from a low voltage of 0.79 nA, followed by 0.23 nA, and finally decreases to 80 pA. Then the TEM test is carried out in the Thermo Fisher Talos F200S.

Focus ion beam-time-of-flight secondary-ion mass spectrometry (FIB-ToF-SIMS)

The test is conducted using a PHI nanoToF instrument equipped with a GA source and FIB accessories. The FIB processing is performed prior to the ToF-SIMS analysis, which is carried out directly afterward. During the analysis, the ion beam scans across the sample line by line, acquiring a mass spectrum at each pixel. To minimize interference and prevent unnecessary signals, the ion beam is blanked when transitioning between scan rows.

Steady-state photoluminescence (PL)

The PL emission test is performed by PicoQuant FluoTime 300 with a 405 nm laser (LDH-P-C-405, PicoQuant GmbH).

Conductive atomic force microscopy (c-AFM)

We deposit a 10 nm silver layer atop the c-Si/ITO/NiO_x/2PACz/perovskite/C₆₀ stack (on textured silicon) to improve conductivity during c-AFM testing. The c-AFM test is performed with a Bruker Dimension Icon instrument. The tip used is model TESPA-V2. The bias is applied to the sample.

Confocal laser scanning microscopy (CLSM)

The CLSM measurement is conducted by the TCSPC module (MT200, Pico Quant). And the in situ CLSM testing is carried out via continuously grabbing frames at the rate of 1 frame per second for a total time scale of 40 s immediately after dripping the organic cation solution. The instrument focal length is pre-aligned with a pre-prepared perovskite film before testing.

Ultraviolet photoelectron spectroscopy (UPS)

The UPS measurement is performed with a Thermo Scientific Escalab 250Xi instrument utilizing a He discharge lamp with a photon energy of 21.22 eV.

Grazing-incidence X-ray diffraction (GIXRD)

GIXRD test is conducted by Rigaku Smartlab 3kw using Cu Kα (λ = 1.5406 Å) radiation. And the data were detected at a grazing incident angle of 0.5° with various Ψ angles of 0, 25, 35, 45, and 55°. The scan rate is 2.5°/min. The samples are prepared on flat substrates, and the results show a clear difference between control and target samples. It is important to note that such a difference would be more significant for samples prepared on textured substrates, evidenced by data such as shown in Supplementary Fig. 2. Therefore, such a non-trivial difference observed using flat-substrate samples fully supports the conclusion for textured-substrate samples.

Scanning electron microscope (SEM)

Field-emission SEM (Thermo Scientific Helios 5 CX) are conducted to observe the film surface and cross-section morphologies before/after bending tests.

In situ transmission electron microscope (in situ TEM)

The in situ bending test is carried out on the FEI TECNAI F30 TEM system using the transmission in situ sample rod of picofemto model. A c-Si/ITO/HTL/perovskite half-stack sample is used. And it is cut from the top surface of the sample using the Thermo Fisher Scios 2 FIB-SEM system, and then a Pt film is deposited on the surface to protect the perovskite film. Then, the sample is welded to the 3 mm diameter copper FIB bracket. Contacting the left side of the sample with a tungsten tip; and the movement of the tungsten tip is controlled by piezoelectric ceramics at a rate of about 0.01 nm/s to apply a bending force on the edge of the sample. In all bending procedures, a 300 kV voltage and a weak electron beam are employed in the TEM system to reduce the potential influence of the beam on the bending deformation. The camera captures the real-time stress distribution at a frame rate of 20 frames per second.

Device characterizations

Photovoltaic performance characterization

The J-V curves are obtained using a Keithley 2400 source measurement unit in conjunction with a solar simulator from RAVI SYSTEMS CORP. under AM1.5 G illumination, utilizing a high spectral match solar simulator (RHS-50SS) equipped with a xenon lamp and a halogen lamp. The light in the short wavelength range was calibrated by the 91150V-KG5 reference cell, and then the entire light intensity was calibrated by the 91150 V reference cell. The tandem devices are exposed to light through a mask with an aperture area of 1.04 cm². The J-V curve measurements are conducted in an unencapsulated state in air. The external quantum efficiency (EQE) spectra are recorded with the Enli Technology QE-R system. −0.5 V bias is applied when measuring the current of perovskite subcells. For the maximum power point (MPP) tracking test, continuous illumination from an LED-based solar simulator, which provided a light intensity of 100 mW/cm² is conducted within a nitrogen atmosphere. Subsequently, PCE is measured and normalized before aging.

Bending durability test

The flexible tandems are secured to two horizontal fixed poles and perform horizontal reciprocating motion by adjusting the distance between the poles, thereby testing various bending radius and cycles. The bending radius is calculated according to the method we describe in Supplementary Fig. 20. And particularly to bending tests with different bending radii, we conduct 50 cycles of bending at each radius.

Three-point bending test

Place the flexible PSTs horizontally on two fixed poles, with one free pole exerting a vertical force. The force is gradually loaded to bend the samples. The force (F) and numerical displacement (D) applied by the free pole are record until the sample fractures.

Density functional theory calculation

Spin-polarized density functional theory (DFT) calculations are performed using the Vienna ab initio simulation package (VASP). The Perdew–Burke–Ernzerhof (PBE) generalized-gradient approximation is employed to characterize the electron-electron interactions. An energy cutoff of 400 eV is applied. The Monkhorst-Pack k-point grid is set to 1 × 2 × 2 for all computational tasks. The convergence threshold for energy and force is set to be less than 10⁻⁵eV and 0.02 eV/Å. Bottom layers are fixed during the calculations. All the structure is optimized.