Abstract

Despite improvements in the power conversion efficiency (PCE) of perovskite solar cells (PSCs), stability issues due to ion migration and phase separation remain critical concerns. Given the ionic crystal nature of perovskites, the use of multivalent cations is supposed to effectively suppress ionic migration. However, multivalent metal cations produce deep-level trap states, thus impairing device efficiency. Therefore, a multivalent cation replacement strategy that minimizes interstitial defects is desirable. Here we develop a divalent cation replacement strategy that mitigates ionic migration while limiting phase segregation. We demonstrate that the replacement of the A-site cations in the perovskite lattice with methylenediammonium cations (MDA²⁺) substantially suppresses the above issues in wide-bandgap perovskites. This is mainly due to the bivalent state of MDA²⁺ generating a strong interaction with the inorganic framework and reducing the mobility of halide ions and the formation of defects. As a result, the stability and efficiency of the fabricated PSCs are substantially improved. We demonstrate a champion PCE of 23.20% (certified 22.71%) for a single-junction PSC with a bandgap between 1.67 eV and 1.68 eV. Furthermore, a PCE of 30.13% is obtained for mechanically stacked perovskite/Cu(In,Ga)Se₂ tandem devices, and a PCE of 21.88% for translucent perovskite devices. Finally, we obtain a steady-state PCE of 23.28% (certified 22.79%) for flexible monolithic perovskite/Cu(In,Ga)Se₂ tandem cells.

Main

Halide perovskites are attractive materials for photovoltaics owing to their exceptional optoelectronic properties^1,2,3,4,5. Perovskite-based tandem solar cells have attracted increasingly more research attention because of their potential to achieve higher power conversion efficiencies (PCEs) than their single-junction counterparts^6,7,8,9. The construction of an efficient tandem cell requires the use of a wide-bandgap perovskite material as the light-absorbing layer of the top subcell, generally enabled by the inclusion of more bromide. However, the concomitant instability issue, especially phase separation, has become a major barrier to the commercialization of the perovskite-based tandem photovoltaics^10,11,12.

A variety of methods have been reported to enhance the longevity of perovskites and suppress ion migration and phase segregation, including crystallographic modulation¹², formation of two-dimensional/three-dimensional heterojunctions^13,14, polymer modification¹⁵, inorganic layer coating¹⁶, utilization of ionic liquids¹⁷, chlorine alloying¹⁸, inclusion of pseudo-halide anion^19,20, interstitial doping by multivalent alkali metal cation²¹ and so on. Given the ionic migration in this soft ionic crystal, the use of multivalent cations is supposed to be very effective owing to the enhanced electrostatic interactions. However, multivalent metal cations in perovskites, as interstitial defects due to small ionic radii, generally produce deep-level trap states, thus impairing the device efficiency. Although trace amounts may minimize the sacrificial trade-off²¹, precise control of the dosage is challenging and, thus, not conducive to industrial implementation. Therefore, a multivalent cation replacement strategy that involves entering the perovskite lattice without forming interstitial defects may be desirable.

Here we report the partial replacement of the A-site in the perovskite lattice by using methylenediammonium cations (MDA²⁺) to inhibit halide migration in wide-bandgap perovskites. We show that MDA²⁺ bears the strongest interactions with the corner-sharing octahedral sublattice, compared with the univalent methylammonium (MA⁺), formamidinium (FA⁺) and guanidinium (GA⁺) cationic species. This is primarily due to the divalent state of MDA²⁺, enabling a stronger electrostatic interaction with the inorganic framework. Therefore, the incorporation of MDA²⁺ significantly increases the energy barrier of ionic movement and, thus, inhibits ion migration and photoinduced halide segregation. The as-resulted wide-bandgap single-junction perovskite solar cells (PSCs) obtained a champion PCE of 23.20% with a bandgap of 1.67–1.68 eV (certified 22.71% efficiency). The unencapsulated target cells maintained approximately 80% of their initial efficiency at maximum power point (MPP) tracking for 750 h at around 45 °C, whereas the control device lost 50% after 700 h. Semitransparent PSCs were fabricated, delivering a champion PCE of 21.88%. We applied them to four-terminal perovskite/Cu(In,Ga)Se₂ (CIGS) tandem devices and achieved a high PCE of 30.13%. An efficiency of 23.41% obtained from current density–voltage (J–V) sweep with a steady-state efficiency of 23.28% (a certified efficiency of 22.79%) was also demonstrated on flexible monolithic perovskite/CIGS tandem solar cells.

Impedance of ion migration in wide-bandgap perovskite

As the simplest and smallest diammonium cation, MDA²⁺ was previously reported to be used in the FAPbl₃ perovskite to inhibit the transition of α-FAPbl₃ to its δ-phase^22,23. However, the potential of MDA²⁺ in other perovskite systems has remained largely unexplored. MDA²⁺ features a high charge number, rich –N–H bonds and an acceptable ionic size, which may allow substitutional doping at the A-site and the formation of stronger interactions with the inorganic sublattices over MA⁺ and FA⁺, thus holding the potential to suppress ion migration and photoinduced halide segregation in wide-bandgap perovskites. We compared the energy barriers of ion migration among the cases of MA⁺, FA⁺, GA⁺ and MDA²⁺ (see chemical structures and ionic radii in Supplementary Fig. 1) cationic dopants using density functional theory (DFT) calculations based on a MAFAPbI_xBr_3−x perovskite system. Figure 1a depicts a schematic illustration of the substitution of various organic cations at the A-site within the perovskite lattice. Figure 1b shows the most preferred migration path of iodide ion. Based on this path, we compared the energy barriers of migration in the case of four types of organic A-cation (Fig. 1c). The energy barrier for ion migration was significantly increased upon MDA²⁺ replacement as compared with the other three cationic substitution cases. Figure 1d showcases the crystal model for DFT calculations. The detailed manner of interactions between the four types of organic cation and the lead–halide frameworks are shown in Fig. 1e. Among them, the hydrogen on the MDA²⁺ has the closest interaction distance with the halogen atom, suggesting a stronger bonding. The total binding energy with respect to each kind of cation is compared in Fig. 1f, and MDA²⁺ features the strongest interaction with the inorganic octahedron compared with its counterparts (−6.5, −6.3, −6.7 and −8.4 eV for FA⁺, MA⁺, GA⁺ and MDA²⁺, respectively).

Fig. 1: Theoretical studies of the interactions between different organic A-cations with the perovskite.

Suppressed halide segregation and migration

We conducted temperature-dependent conductivity measurements following previous reports to verify the suppressed ion migration in the MDA²⁺-incorporated perovskite film (Fig. 2a)^16,26,27. The change of conductivity with temperature is determined by two regions. In the lower-temperature region, the conductivity is dominated by the conductance of electrons. At higher temperatures, the conductivity is instead dominated by ionic conductance. The transition of the two regions occurs at a higher temperature (245 K) for the MDA²⁺-doped sample compared with its undoped counterpart (192 K), indicating that ion migration is inhibited in the doped film. Furthermore, by linearly fitting the temperature-dependent conductivity data in the two regions to the Nernst–Einstein relation, we obtained the corresponding activation energies of electron transport and ion migration, respectively. The ion migration activation energy of MDA²⁺-doped perovskite films is 0.75 eV, much higher than that of undoped samples (0.43 eV). This is compelling evidence that MDA²⁺ cations stabilize halide perovskites and inhibit ionic movement.

Fig. 2: Suppressed ion migration and halide segregation enabled by MDA²⁺.

Improved optoelectronic properties

To gain insights into how the A-site substitution by MDA²⁺ would impact the defects in halide perovskite, we carried out DFT calculations to compare the formation energies of several types of point defect in the presence of MA⁺, FA⁺ and MDA²⁺ at the A-site, respectively (Fig. 3a and Supplementary Fig. 23). The defect formation energies of Pb–I antisite, I–FA antisite and iodide vacancy defects show the most notable increase with MDA²⁺ as compared with MA⁺ and FA⁺, suggesting that these types of imperfection in perovskite would be inhibited. Pb–I and I–FA antisite defects are deep-level defects that behave as non-radiative recombination centres²⁸. The iodide vacancy defects are characterized by low formation energy that induce only shallow trap states, which, however, help to ion migration because vacancy-mediated halide migration is considered a main ionic transport mechanism in halide perovskites²⁹.

Fig. 3: Improved optoelectronic properties of the perovskite films.

Photovoltaic performance and device stability

We prepared single-junction wide-bandgap (1.67–1.68 eV) PSCs with an inverted architecture (Fig. 4a). Figure 4b shows the J–V curves of the champion PSCs without or with MDA²⁺ doping with an optimal doping concentration (see the detailed results of optimization in Supplementary Text 5). The champion PCE of the MDA²⁺-doped solar cell (0.75 mol% MDA²⁺) is 23.20% obtained by reverse voltage sweep with an open-circuit voltage (V_OC) of 1.267 V, short-circuit current density (J_SC) of 21.52 mA cm⁻² and fill factor (FF) of 85.10%. It is one of the highest efficiencies of PSCs based on perovskite absorbers with 1.67–1.69 eV bandgaps (Supplementary Fig. 28 and Supplementary Table 4). The control devices yield a maximum efficiency of 22.22% with a V_OC of 1.246 V, J_SC of 21.26 mA cm⁻² and FF of 83.89%. Reverse- and forward-scanned J–V curves are shown in Supplementary Fig. 29. We sent it for certification (National Institute of Metrology), and a certified efficiency of 22.71% was obtained (Supplementary Fig. 30). Supplementary Fig. 31 shows the external quantum efficiency (EQE) spectra of the devices. A statistical comparison of photovoltaic parameters of the control and target devices is shown in Fig. 4c. Upon incorporation of MDA²⁺, the V_OC, J_SC and FF of the PSCs are overall increased with a narrow distribution (Supplementary Table 5).

Fig. 4: Photovoltaic performance and device stability.

Conclusions

We demonstrate a divalent cation replacement strategy, partially substituting the A-site using MDA²⁺ cations, capable of stabilizing wide-bandgap perovskites with intrinsically inhibited ion migration and photoinduced halide segregation. This is attributed primarily to the bivalent state of MDA²⁺, resulting in strong interactions with the inorganic sublattice and, thus, raising the energy barrier of ionic movement. In addition, the photoelectric properties of perovskite films were also improved due to the reduced defect density. Single-junction PSCs wih 1.67–1.68 eV bandgap afforded a champion efficiency of 23.20% (certified 22.71%) with enhanced operational stability. We also achieved 30.13% and 23.41% efficiencies on four-terminal perovskite/CIGS tandem and flexible monolithic perovskite/CIGS tandem photovoltaics, respectively. Overall, these represent state-of-the-art four-terminal and flexible monolithic perovskite/CIGS tandem photovoltaic technologies. Besides, they may inspire broader explorations of the potential of MDA²⁺ in the perovskite community and represent a pioneering work on multivalent cation replacement strategies to suppress ion migration in halide perovskites, thus opening new avenues for stabilizing perovskites for a wide range of optoelectronic applications beyond photovoltaics.

Methods

Materials

Lead iodide (PbI₂), lead bromide (PbBr₂), caesium iodide (CsI), nickel oxide particle (NiO_x), lithium fluoride (LiF), bathocuproine (BCP) and C₆₀ were purchased from Advanced Election Technology. Formamidinium iodide (FAI), methylammonium bromide (MABr), methylamine chloride (MACl), methylenediammonium dichloride (MDACl₂), methylenediammonium diiodide (MDAI₂), formamidinium chloride (FACl) and guanidinium chloride (GACl) were bought from Xi’an Polymer Light Technology; 4- trifluorophenylethylammoniumiodide (CF₃-PEAI) was obtained from Xi’an E-Light New Material; and 4-(3,6-dimethyl-9H-carbazol-9-yl)butyl]phosphonic acid (Me-4PACz) was purchased from TCI. Anhydrous solvents involving dimethylformamide (DMF), dimethyl sulfoxide (DMSO), isopropanol (IPA), ethyl acetate (EA) and ethanol were purchased from Sigma-Aldrich.

Device fabrication

Opaque wide-bandgap PSCs

The prepatterned indium tin oxide (ITO) glass substrates were cleaned with a detergent in an ultrasonic bath and then washed several times by ultrapure water, followed by sonication in ethanol. The cleaned glass/ITO substrates were dried under a N₂ flow and treated by UV–ozone for 20 min. The NiO_x thin layers were prepared by spin-coating the NiO_x/H₂O dispersive liquid (10 mg ml⁻¹) on the glass/ITO substrates at 3,000 rpm for 30 s and annealed at 150 °C for 10 min in ambient air. Then, they were transferred into an N₂ glovebox. For Me-4PACz deposition, 0.6 mg ml⁻¹ Me-4PACz in ethanol was spin-coated onto the NiO_x layer at 3,000 rpm for 30 s, followed by heating at 110 °C for 10 min. To deposit wide-bandgap perovskite films, a pristine precursor solution (1.4 M) was prepared by mixing PbI₂ (1.05 M, containing 5 mol% excess PbI₂), PbBr₂ (0.42 M), CsI (0.07 M), FAI (1.12 M), MABr (0.21 M) and MACl (0.14 M, as additive) in mixed solvents of DMF and DMSO with a volume ratio of 4:1 with incorporation of 1.5% H₂O in volume ratio. The aim of adding H₂O is to enable rapid dissolution of MDACl₂ in the perovskite solution. For MDA²⁺ doping, MDACl₂ powder was weighed separately in a new sample bottle. Then, a certain amount of completely dissolved pristine perovskite solution (vigorously shaken for 2–4 h) was transferred into the bottle that contained MDACl₂ to ensure a specific molar ratio of MDACl₂ relative to Pb. Because MDA²⁺ is relatively unstable at neutral pH, aprotic polar solvents such as DMSO, DMF and the as-prepared perovskite solution are typically shaken for a few minutes for use after introducing MDACl₂ or MDAI₂ into the well-prepared pristine precursor solution. A two-step rotation procedure of 1,000 rpm@10 s followed by 5,000 rpm@40 s was used to spin-coat the precursor solution. During spinning, 200 μl of EA was dropped onto the film 20–18 s before the end of the second step. The as-cast pristine films were annealed at 110 °C for 30 min in the glovebox. After the perovskite films cooled down, 15 μl of CF₃-PEAI solution (1.5 mg ml⁻¹ in IPA) was dynamically spin-coated onto the perovskite film at 6,000 rpm for 30 s, then annealed at 90 °C for 3 min. Subsequently, 1 nm of LiF (0.1 Å s⁻¹), 25–40 nm of C₆₀ (0.2 Å s⁻¹) and 6 nm (0.1 Å s⁻¹) of BCP were thermally deposited in sequence. Then, 120 nm (1.5 Å s⁻¹) of silver electrodes were prepared by thermal evaporation with shadow masks, defining a working area of 0.107 cm² for each device. Finally, 130 nm LiF (1 Å s⁻¹) was evaporated as antireflective coating on the glass sides.

Semitransparent wide-bandgap PSCs

The fabrication processes for the semitransparent perovskite devices are essentially the same as described above, except that the thickness of the C₆₀ layer was fixed at 25 nm and the BCP was replaced by SnO₂ and indium zinc oxide (IZO). Besides, the silver electrode adopted a ring-type electrode with a thickness of 400 nm. Finally, 140 nm of LiF on the top side and 130 nm of LiF on the glass side were thermally evaporated. The preparation of the SnO₂ and IZO layers is described as follows.

The SnO₂ layers were prepared by atomic layer deposition using a Veeco system. The temperature of the substrates was maintained at 80 °C in the vacuum chamber. Tetrakis(dimethylamino)tin(IV) (TDMASn) was used as the Sn precursor by holding at 60 °C in a stainless-steel container during operation. Water was adopted as the oxidant without active heating. The precursor delivery manifold was heated to 150 °C. The TDMASn/wait/H₂O/wait times were 0.015 s/10 s/0.05 s/10 s with a nitrogen flow of 20 sccm. A total of 140 cycles were carried out. The IZO transparency electrodes (40 nm) were deposited by radiofrequency sputtering (Angstrom EvoVac sputtering system) from a 3-inch IZO ceramic target (a radiofrequency power of 50 W) with shadow masks (an aperture area of 0.16 cm²). The chamber pressure was controlled at 0.6 mTorr with an argon flow rate of 15 sccm and oxygen flow rate of 0.06 sccm.

CIGS solar cells

First, the Mo back contact layer (~1 μm) was sputter-deposited on the cleaned stainless-steel substrate. A three-stage co-evaporation process was used to grow the CIGS absorber layer (~2 μm) in a vacuum chamber. An alkali postdeposition treatment was subsequently performed. The CdS buffer layer (∼35 nm) was grown via chemical bath deposition, and the intrinsic ZnO (i-ZnO) layer (~50 nm) and ZnO:Al layer (~200 nm) were prepared by radio frequency (RF) sputtering in sequence, followed by nickel/aluminium/nickel grid deposition for current collection.

Flexible monolithic perovskite/CIGS tandem solar cells

A 20 nm IZO layer was first deposited on the CIGS/CdS/i-ZnO/AZO substrate by using RF sputtering (Angstrom EvoVac sputtering system). Before sputtering, the samples were treated with UV–ozone for 20 min. Then, the NiO_x thin layers were prepared by spin-coating the NiO_x/H₂O dispersive liquid (10 mg ml⁻¹) on the UV–ozone-treated substrates at 3,000 rpm for 30 s and annealing at 110 °C for 10 min in ambient air. The samples were subsequently transferred to an N₂ glovebox. For Me-4PACz deposition, 0.8–1.0 mg ml⁻¹ Me-4PACz in ethanol was spin-coated onto the NiO_x layer at 3,000 rpm for 30 s, followed by heating at 110 °C for 10 min. The perovskite layers were prepared by spin-coating 1.4 M precursor solution at 1,000 rpm@10 s followed by 5,000 rpm@40 s. During spinning, 200 μl of EA was dropped onto the film 20–18 s before the end of the second step. The as-cast pristine films were annealed at 110 °C for 10 min in the glovebox. After the perovskite films cooled down, 15 μl of CF₃-PEAI solution (1.5 mg ml⁻¹ in IPA) was dynamically spin-coated onto the perovskite film at 6,000 rpm for 30 s, then annealed at 90 °C for 3 min. After that, 1 nm of LiF (0.1 Å s⁻¹) and 25 nm of C₆₀ (0.2 Å s⁻¹) were thermally deposited in sequence using an Angstrom EvoVac system. The SnO₂ layers were then prepared by atomic layer deposition using a Veeco system with 140 cycles. The transparency electrodes (40 nm) were deposited by RF sputtering IZO (Angstrom EvoVac sputtering system) with an O₂/Ar ratio of 0.4%. To complete the device preparation, 300 nm ring silver electrodes (defining an active area of 0.12 cm²) were deposited by thermal evaporation with a deposition rate of 3 Å s⁻¹, followed by 140 nm LiF antireflective coating.

Sample characterizations

Steady-state PL

Steady-state PL measurements were conducted using a FLS1000 fluorescence spectrometer (Edinburgh Instruments). A 450 nm monochromatic light was used as the excitation source by filtering the white light from a 450 W xenon arc lamp. The intensity of the excitation light can be adjusted by changing the slit width. PL emission spectra with wavelengths ranging from 650 nm to 900 nm were collected. For time-dependent PL characterization to examine the photostability of perovskite films, steady-state PL tests were repeatedly performed on a perovskite film with a step size of 1 nm and a dwell time of 0.2 ms. The test interval between each spectrum was about 5 s. The slit width for the excitation source was fixed at 4 nm to ensure the same irradiation intensity for different samples. The power density of the 450 nm excitation light source was measured to be 27 mW cm⁻². The total duration of the measurement for each sample was about 30 min, and about 22 steady-state PL spectra were recorded.

Temperature-dependent electric conductivity

The temperature-dependent electric conductivity measurements were performed on a low-temperature probe electrical measurement system. Lateral devices with a configuration of Au/perovskite (150 μm)/Au were fabricated, and the perovskite layers were deposited on glass substrates. The temperature of the lateral device was controlled by a cryogenic probe station (Lakeshore CRX-4K) in a vacuum chamber. Before testing, the temperature was first cooled to 160 K for 30 min. The current response was recorded at different temperatures by a semiconductor parameter analyser (Keithley 4200-SCS) under an applied voltage of 10 V. The temperature was raised step by step from 160 K to 340 K. Each step was stabilized at that temperature for 10 min before the current measurement was conducted.

The activation energy of ion migration could be extracted by fitting the raw data points using the Nernst–Einstein relation: σ(T) = (σ₀/T)exp(−E_a/kT), where k is the Boltzmann constant, σ₀ is a constant and T is the temperature. The ln(σT)–1/kT plot consists of two linear regions. Linear fitting of these two regions results in slopes corresponding to activation energy for ion migration (at higher temperature) and charge carrier transport (at lower temperature), respectively.

PL mapping

PL imaging characterizations were carried out using a confocal Raman imaging microscope (WITec alpha300 R). For in situ observation of the variation of perovskite films under an applied electric field by PL mapping, lateral devices (Au/perovskite/Au) were prepared with a channel width of 150 μm. A continuous-wave laser with a wavelength of 532 nm was used as the excitation source. A 50× objective lens with a numerical aperture of 0.55 (Zeiss LD EC Epiplan-Neofluar) was selected to both focus the laser excitation onto the sample and collect the PL spectra from the sample. Spatial information was obtained by moving the microscope stage, and therefore the sample, in the XY directions and acquiring an array of PL spectra that were then used to generate two-dimensional PL maps. The PL spectrum was detected using an electron-multiplying charge-coupled device, which is similar to a regular charge-coupled device but contains an additional on-chip electron-multiplying amplification stage that enables faster data readouts while preserving the high sensitivity. The scanning range was set to 300 μm × 300 μm, and the centre wavelength for detection was 730 nm. When the device is biased at 9 V, successive PL maps were acquired with each image acquisition time of about 80 s.

PL lifetime mapping

Fluorescence lifetime imaging was performed using a Leica Stellaris 8 FALCON confocal fluorescence microscope. A Leica 63× oil immersion objective (numerical aperture 1.40) was used for the measurement. Samples were placed on a cover glass with a thickness of 0.17 mm with the front surface downwards during the measurement. The excitation light source was a 448 nm laser line (repetition rate 2.5 MHz) extracted from a pulsed supercontinuum laser using an acousto-optical beam splitter (AOBS). With the excitation intensity fixed at 1.5%, the power was maintained at approximately 0.07 µW. The scanning speed was set to 100 Hz (lines s⁻¹), with each line being accumulated 16 times. The image size was about 10.25 µm × 10.25 µm with a resolution of 512 × 512 pixels. The data were analysed and processed using Leica application suite (LAS) X FLIM software.

Trap density measurement

The distribution of trap density in energy was revealed through TAS analysis. TAS tests were performed on an electrical measurement system using an impedance analyser (Keysight E4990A). The devices were mounted on a temperature-control platform with low vacuum. The applied a.c. voltage signal had an amplitude of 20 mV, with a frequency range of 20 Hz to 1 MHz, and the d.c. bias was 0 V. The tDOS (N_t) is calculated by the following equation: ?t(??)=−?bi??d?d????, where V_bi, w, C, ω, q, k and T are the build-in potential, depletion width, capacitance, angular frequency, elementary charge, Boltzmann constant and temperature, respectively. The frequency axis is transformed into an energy axis by E_ω = kTln(ω₀/ω), where ω₀ is the attempt-to-escape angular frequency that equals 2πν₀T². The reduced attempt-to-escape frequency ν₀ is determined by a preceding Arrhenius evaluation of ln(T²/ω) = E_t/kT − ln(2πν₀) based on temperature-dependent capacitance–frequency (C–f) measurements.

Other characterizations

SEM images were obtained using a scanning electron microscope (Zeiss Gemini 450) with an accelerating voltage of 5 kV and a beam current of 200 pA. XRD measurements were performed on an X-ray diffractometer (Bruker D8 Advance) with Cu Kα radiation (λ = 1.5418 Å) operating at 40 kV and 40 mA. The UV–visible absorption spectra were acquired using a Shimadzu UV 2700 spectrophotometer. XPS spectra were recorded on an X-ray photoelectron spectrometer (Thermo Fisher Escalab Xi+) by using a monochromatized Al Kα source (hv = 1,486.6 eV). The FTIR spectra were acquired using a FTIR spectrometer (Nicolet iS50, Thermo Scientific). The ToF-SIMS measurements were conducted on the ULVAC-PHI instrument with a Bi³⁺ (30 keV) primary ion beam for analysis and a gas (Ar/O₂) gun (2 keV) for sputtering. Data were acquired for both positive ions and negative ions. The dynamic light scattering (DLS) measurements were performed using a light scattering/zeta potential analyser (BI-200SM/NanoBrook ZetaPALS). ¹H NMR spectra were acquired on a Bruker 600 MHz solution NMR spectrometer (room temperature probe).

Device measurements

J–V characteristics

The J–V characteristics of single-junction PSCs were measured in an N₂-filled glovebox at room temperature using a Keithley 2450 sourcemeter under simulated AM1.5 G irradiation (100 mW cm⁻²) from a xenon lamp solar simulator (Enlitech Class AAA). The light intensity was calibrated by a silicon reference cell before measurement, and no preconditioning was applied. The scanning step was 20 mV with a scanning rate of 100 mV s⁻¹ and a delay time of 10 ms. The active areas of the opaque and semitransparent cells were defined by metal masks with aperture areas of 0.084 cm² and 0.0912 cm², respectively. To test the efficiencies of CIGS and four-terminal tandem solar cells, the J–V characteristics were conducted in ambient conditions. The sourcemeter and solar simulator are the same as the ones in the glovebox. The CIGS photovoltaics are flexible with a structure of metal/Mo/CIGS/CdS/i-ZnO/AZO/Ag (finger electrode). The CIGS solar cells were measured with a 1 cm² metal mask either stand-alone or below the semitransparent perovskite device under precalibrated one-sun illumination. When measuring the efficiency of the CIGS subcell, the semitransparent perovskite device without deposition of silver electrode was placed onto the CIGS to act as a light filter. The gap between them was filled with a refractive index matching fluid or liquid to reduce light reflection loss. For testing the monolithic perovskite/CIGS tandem, a metal mask with each aperture area of 0.092 cm² was used.

Stabilized power output

The stabilized power outputs of PSC MPP were recorded by monitoring the current output over time, where the cells were biased at the MPP voltage extracted from the reverse-scanned J–V curves.

EQE measurement

EQE measurements were carried out in ambient conditions using an EQE system (EnliTech). The devices were irradiated with monochromatic light chopped at a frequency of 210 Hz, and their photocurrent was measured with a lock-in amplifier. For the EQE measurements of the monolithic tandems, the EQE of the perovskite front subcell was measured using a light-emitting diode (LED) with an emission peak of 850 nm as the bias illumination. The CIGS subcell was measured by saturating the perovskite top cell using an LED with an emission peak of 550 nm. Before measurements, the EQE setup was calibrated by standard silicon and germanium photodetectors with a known spectral response.

Stability test

The stability (thermal and light stability) of the wide-bandgap perovskite films was examined by placing the perovskite films on a hotplate at 85 ± 1 °C or under simulated one-sun illumination (LED solar simulator) in an N₂ glovebox for different periods of time, and their XRD patterns and/or PL spectra were repeatedly recorded for comparison. To assess the thermal stability of the wide-bandgap PSCs, unencapsulated devices were aged on an 85 ± 1 °C hotplate in a glovebox. To avoid the rapid degradation of the PSCs at such a relative high temperature, each device was covered by a glass substrate. The photovoltaic performances of these cells were monitored periodically through J–V measurements. The operational stability of the unencapsulated devices was measured in an N₂ glovebox using the MPP tracking mode on a custom-built multichannel ageing test system (Shenzhen Puri Materials). The illumination was provided by a white-light LED with intensity calibrated to match the one-sun condition. MPP was tracked by a perturb and observe algorithm that updates the MPP voltage for bias every 60 s, and an interval of 1 h was set for data collection. No active cooling was implemented during the test.

DFT calculations

Computational methodology

Our approach involved using first-principles calculations utilizing DFT with a plane-wave basis set and the projected augmented wave method. To account for atomic exchange-correlation effects, we applied the revised Perdew–Burke–Ernzerhof generalized gradient approximation, known as PBEsol. In addition, Grimme’s DFT-D3 scheme was integrated to address dispersion forces. Initial geometries were derived on the basis of the experimental lattice parameters of FAPbI₃. For self-consistent field calculations and geometry optimizations, a plane-wave basis set with a cut-off energy of 400 eV and a 2 × 2 × 2 gamma-centred k-mesh were utilized. Ionic positions and cell dimensions underwent relaxation via a conjugate gradient algorithm until residual forces were below 0.02 eV Å⁻¹. Unless otherwise specified, all DFT calculations were performed using theVienna Ab-initio simulation package (VASP) following the described methodology.

Iodine migration calculations

To evaluate migration barriers, we analysed the energy changes associated with iodine movement along the reaction pathway. The process involved optimizing both initial and final structures, followed by using a linear interpolation method to generate intermediate structures along the migration trajectory. Energy profiles were established using the nudged elastic band method and constrained energy minimization, considering 16 grid points during the calculations. The energy barriers for iodine migrations were computed by assessing the energy difference between the lowest energy state and the saddle point along the pathway.