Abstract

Tandem photovoltaics hold great potential to surpass the efficiency limit of single-junction solar cells. Detrimental structural defects and chemical reactions at buried interfaces of subcells considerably impede the performance of integrated tandems. Here, we devise a mercapto-functionalized mesoporous silica layer as a superstructure at the buried interface to modulate the crystallisation, eliminate nanovoids, passivate defects, and suppress the oxidation of Sn(II) in the tin–lead perovskite films, contributing substantially to reduce charge carrier losses and improve stability in positive-intrinsic-negative structured devices. Consequently, the tin–lead perovskite single-junction cells show efficiency values of up to 23.7% with the best open-circuit voltage of 0.89 V. With the enhanced subcells, our double-junction tandems show efficiency values of 29.6% (certified 29.5% and steady-state 28.7%) and 24.7% on solar cells and 11.3 cm² mini-modules, respectively. Encapsulated tandems maintain 90% of initial efficiency after 445 h of maximum power point tracking under simulated 1-sun illumination.

Introduction

All-perovskite tandems constructed with a wide-bandgap (WBG, ~1.80 eV), neat-lead perovskite, front subcell and a narrow-bandgap (NBG, ~1.25 eV), mixed tin–lead (Sn–Pb) perovskite, rear subcell offer superior strategy for new generation sustainable photovoltaics (PVs)^1,2,3,4,5. The highest certified power conversion efficiency (PCE) of the all-perovskite tandem cells has just reached 30.1%⁶, suggesting big room for improvement considering the theoretical maximum at ~45%⁷. To gain performance breakthroughs, fabricating high-quality WBG and NBG perovskite layers is critical. It was unveiled that the structural and electrical defects are primarily located at the top and buried (bottom) surfaces of the perovskite layers in the device, leading to significant non-radiative charge carrier recombination and harmful chemical reactions^8,9,10,11,12. It is therefore crucial to develop robust interface modification strategies, especially for Sn–Pb perovskites^13,14, considering its rapid crystallization and facile oxidation of Sn(II) to Sn(IV)^{15,16,17,18,19}. On the other hand, in comparison to the readily post-treatable top interface, accessing the buried interface of the perovskite layer in devices is relatively challenging and less studied^9,14.

As for tin-containing perovskites, the current successful fabrication of efficient solar cells largely relies on the utilization of poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) as the hole transport layer (HTL) and the substrate component for film deposition^10,12,20. However, the acidity and hygroscopic nature of this material can induce undesirable oxidative reactions that drastically deteriorate the perovskite material and operational stability of its devices under elevated temperature and light illumination^21,22. In addition, the possible spatial heterogeneity of PEDOT:PSS layer and the rapid growth of tin-based perovskites could lead to the generation of a high density of morphological nanovoids and crystallographic defects, unfavourable strain, and poor crystallinity at the buried interface^17,23,24. In particular, eye-detectable white spots are found to be easy to form at the PEDOT:PSS/perovskite interface based on previous studies^17,23, and happened to be even more pronounced for films deposited on flat and smooth substrates, e.g., normally used indium tin oxide (ITO) glass. For single-junction cells, this issue could be mitigated by using a rough fluorine-doped tin oxide (FTO) glass substrate (~100 nm peak roughness)^17,23. Unlike the perovskite-on-silicon tandem with pyramid architecture, the surface where the NBG Sn–Pb perovskite layer deposited, however, is—most of the time—very smooth WBG subcells in all-perovskite multijunction cells, posing additional challenges for mitigating the buried interface nanovoids and imperfections.

Bare this in mind, in this work, we devise a superstructure scaffold, composed of (3-mercaptopropyl)trimethoxysilane (MPTS) functionalized mesoporous silica nanoparticles (denoted as MSN-SH), to improve the buried interface of perovskite layers in tandem devices (Fig. 1a). Specifically, the silica nanoparticles primarily suppress the formation of nanovoids, release the residual strain, and improves the crystallinity of Sn–Pb perovskite films at the buried interface. The nucleophilic thiol end-groups at the scaffold surface of the substrate are designed to passivate the undercoordinated metal cations at the perovskite lattice and suppress the generation of iodide and oxidation of Sn(II). As a result, the NBG Sn–Pb perovskite solar cells (PSCs) show efficiency values of up to 23.7% and enhanced stability, especially under thermal conditions. In addition, this buried interface modification strategy also shows positive effects on neat lead perovskite materials under a series of bandgaps, i.e., 1.52, 1.68, and 1.77 eV. For instance, the resultant WBG, 1.77 eV, devices deliver efficiencies of up to 20.6%. With these improved subcells, the all-perovskite tandem devices show a certified PCE of 29.5% (certified steady-state PCE of 28.7%). Meanwhile, the modified tandems maintain 90% of their initial efficiency after 445 h of maximum power point tracking (MPPT) under simulated 1-sun illumination at room temperature and 82% of the initial efficiencies after 150 h of 85 °C thermal stressing.

Fig. 1: Characterizations of the buried interface.

Results and discussion

Improving substrate contact

We deposit the NBG mixed Sn–Pb perovskite films with a composition of Cs_0.1FA_0.6MA_0.3Sn_0.5Pb_0.5I₃ (FA: formamidinium, MA: methylammonium)¹⁵. Similar to previous reports¹⁷, we observed distinct “white” spots viewed from the glass side of the perovskite films with ~900 nm in thickness on PEDOT:PSS-coated ITO substrate (Supplementary Fig. 1). This phenomenon was also observed for large-area Sn–Pb perovskite films processed via a vacuum-assisted crystallization procedure (Supplementary Fig. 2). We then prepare samples with the previously reported non-destructive peel-off method for scanning electron microscopy (SEM) characterizations to assess the morphology of buried interfaces²⁵ (Supplementary Fig. 3). Intriguingly, we detect dome-shaped nanovoids at the buried interface of Sn–Pb perovskite films which show “white” spots (Fig. 1b and Supplementary Figs. 4 and 5). A similar morphological characteristic is also observed for the Sn–Pb perovskite sub-absorber deposited on WBG subcell/PEDOT:PSS substrate during tandem cell fabrication (Supplementary Fig. 6). The appearance of such voids was previously reported for neat-Pb perovskites deposited from a dimethyl sulfoxide (DMSO)-containing solvent system and it appears to be more pronounced in thick and large-area perovskite films^26,27. This phenomenon was attributed to the formation of an impermeable solid shell at the top of the “wet” films during a “top-down” crystallization of the films, leading to solvent-filled space at the buried interface and hence the formation of voids at the buried interface due to the film volume contraction after further solvent removal via annealing^28,29. In our mixed Sn–Pb perovskite films, we find that only the specific combination of films with PEDOT:PSS substrate induced the formation of voids regardless of the thickness (Supplementary Fig. 1). We suppose that voids present at the buried interface might be associated with the spatial heterogeneity of PEDOT:PSS and/or unoptimized crystallization of perovskite films^17,23. Furthermore, PEDOT:PSS is known to “swell” when coated in aprotic solvents such as N,N-dimethylformamide (DMF) and DMSO, which may also lead to additional solvent entrapping at this buried interface³⁰.

To address issues at this interface, we design a mesoporous silica nanoparticle (MSN)-constructed superstructure on PEDOT:PSS-based substrate before the deposition of perovskite films. The superstructure could serve as a nucleation seed of the perovskites deposited atop and hence contribute to the following crystallization process to improve buried interface^31,32,33. We also find that further functionalization of MSN nanoparticles using MPTS, largely improves the dispersibility and stability of the MSN ink, which enables the deposition of a uniform superstructure with better reproducibility compared to Al₂O₃ and pristine MSN mesoporous scaffolds (Supplementary Note 1, Supplementary Figs. 7 and 8). Additionally, the essential characterization data of MSN nanoparticles before and after MPTS functionalization were summarized (Supplementary Note 2, Supplementary Figs. 9 and 10).

When integrated into the buried interface, the enhanced affinity and curvature of dispersed MSN-SH particles (~100 nm in size) lead to a decreased contact angle of the perovskite precursor solution with the substrate (Supplementary Fig. 11). This would affect the nucleation/growth of the perovskite films (Supplementary Note 3) and its quality. As shown in Fig. 1c and Supplementary Fig. 5f, the MSN-SH-based perovskite films show well-crystallized and dense domains without nanovoids. In addition, it is observed that the MSN-SH nanoparticles are nicely embedded into the perovskite bottom surface, and mainly located at the grain boundaries. These results suggest that the introduction of MSN-SH improves the quality of perovskite films, especially in the buried region, although there is no obvious change in the average grain size and surface roughness (Supplementary Figs. 12 and 13).

To further examine the effect of substrate on the crystallinity of perovskite films near the buried interface, we perform depth-resolved grazing incidence wide-angle X-ray scattering (GIWAXS) measurements at the exposed perovskite bottom surfaces, following film lift-off³⁴ (Fig. 1d, e). The MSN-SH-based Sn–Pb perovskite films show stronger diffraction intensity compared to the control under a series of tested incidence angles, suggesting a higher crystallinity and lower degree of amorphous phases (Supplementary Fig. 14). The reduced amorphous region could reflect the reduction in defect density at the bottom of the perovskite film³⁵. We further evaluate the uniformity of the bottom interface using fluorescence lifetime imaging microscopy (FLIM) characterizations. The MSN-SH-based perovskite film exhibits a relatively uniform and enhanced photoluminescence (PL) lifetime over the probed region, 50 by 50 µm, indicating suppression of non-radiative recombination at the buried interface (Fig. 1f). Moreover, the presence of nanovoids and weaker crystalline amorphous phases at the buried interface often diminish the interfacial adhesion between the perovskite layer and the underlying substrate^25,36,37. To validate the mechanical durability enhancement conferred by the MSN-SH superstructure at the buried interface, we conduct tensile strength measurements on the samples with a configuration of glass/ITO/PEDOT:PSS/perovskite/epoxy/glass. The stress-strain curves reveal the gradual evolution of the applied tensile stress versus strain until the occurrence of delamination (Fig. 1g)³⁷. The critical tensile strength of the perovskite/PEDOT:PSS interface is determined to be 0.26 MPa at 0.17% strain for the control sample and 0.67 MPa at 0.29% strain for the MSN-SH sample. The determined specific fracture energy increases from 25 to 83 kJ m⁻³, thanks to the elimination of nanovoids and the promotion of cohesive adhesion by the MSN-SH superstructure. As previously reported, the improvement of the buried interface contact could assist in the release of residual stress for perovskite films²⁵. We thus conduct grazing-incidence X-ray diffraction (GIXRD) measurements at an incidence angle of 0.3° to examine the residual stress state of the exfoliated samples at the macroscopic level (Supplementary Fig. 15). The results show that the control film presents tensile stress at the region near PEDOT:PSS layer, while the insertion of MSN-SH material effectively releases the stress from 72.2 down to 4.6 MPa (Fig. 1h and Supplementary Note 4). We speculate that this released residual stress is mainly associated with the elimination of nanovoids and enhanced interaction at the buried interface^36,38.

It was reported that the widely used [4-(3,6-dime-thyl-9H-carbazol-9-yl)butyl]phosphonic acid (Me-4PACz) material bearing nonpolar methyl terminal groups leads to a surface with insufficient wettability for solution processing, resulting in poor coverage of perovskite films (Supplementary Fig. 16)^39,40. Interestingly, the Me-4PACz/MSN-SH bilayer substantially alleviated this wetting issue, yielding well-covered perovskite films. We also find that the introduction of MSN-SH as a meso-superstructure ensures homogeneous and compact films with no detectable nanovoids at the bottom interface of the neat lead films (Supplementary Fig. 17). This result suggests good compatibility of MSN-SH superstructure in both Sn–Pb and Pb perovskites for improved buried interface contact and film quality.

Enhancing interface stability

Based on the understanding of the buried interface degradation mechanisms, we expect the potential capability of our MSN-SH approach to enhance the stability of the buried interface by reducing the concentration of Sn (V_Sn) and iodide (V_I) vacancies. We propose that the potential chelating between the sulfhydryl group and metal cations, i.e., Sn(II) and Pb(II), from the perovskites, and the reducibility of the sulfhydryl group⁴¹ at the surface of the MSN-SH superstructure, will increase the iodide migration energy and impede the generation of oxidative I₂.

To verify this, we first perform the density functional theory (DFT) calculations to evaluate the V_I formation energy and the iodide migration barrier when the sulfhydryl group binds to the perovskite framework. To simplify the model, we refer to the previous report using butanethiol⁴² to represent MSN-SH. From the calculation results, we find that the V_I formation energy increases from about 1.70 to about 2.15 eV when the sulfhydryl group binds to Pb-I or Sn-I terminals (Supplementary Fig. 18). The I⁻ migration barrier also increases from 0.45 to 0.66 eV and 0.40 to 0.45 eV in the case of Pb-I and Sn-I terminals, respectively (Fig. 2a and Supplementary Fig. 19). To experimentally verify the increase of ion migration active energy, we further measure the temperature-dependent conductivity of the films (Fig. 2b–d). The activation energy for MSN-SH films is calculated to be 0.58 eV, twice that of the control, 0.29 eV. We in addition verify that MSN-SH should be capable of reducing and suppressing the formation of I₂ and Sn(IV) in Sn–Pb perovskites (Supplementary Note 5, Supplementary Figs. 20 and 21).

Fig. 2: Stability of the buried interface.

Methods

Materials

Lead iodide (PbI₂, 99.99%), lead bromide (PbBr₂, 99.99%), methylammonium iodide (MAI) and formamidinium iodide (FAI) were purchased from Advanced Election Technology Co., Ltd. Caesium iodide (CsI, >99.0%), guanidine thiocyanate (GuaSCN, >99.0%), bathocuproine (BCP, >99.0%), dibutyl sulfoxide (DBSO, >96.0%) and [4-(3,6-dime-thyl-9H-carbazol-9-yl)butyl]phosphonic acid (Me-4PACz, >99.0%) were purchased from TCI chemicals. PEDOT:PSS aqueous solution (Al-4083), ethylenediammonium diiodide (EDAI₂, 99.99%), fullerene (C₆₀, 99%), and 1,3-propanediamine dihydriodide (PDAI₂, 99.99%) were purchased from Xi’an Yuri Solar Co., Ltd. Potassium iodide (KI, >99.0%), glycine hydrochloride (GlyHCl, ≥99%), tin(II) fluoride (SnF₂, 99%), and tin(II) iodide (SnI₂, beads, 99.99%, trace metals basis) were purchased from Sigma-Aldrich. Tetrakis(dimethylamino) tin (IV) (99.9999%) for atomic layer deposited (ALD) SnO_x was bought from Nanjing Ai Mou Yuan Scientific Equipment Co., Ltd. MSN and MSN-SH dispersions (100 nm, 50 mg mL^–1 in isopropanol) were purchased from Haian Zhichuan Battery Material Technology Co., Ltd. The process of functionalization of MSN into MSN-SH was similar to that previously reported⁴⁷. Al₂O₃ dispersion (100 nm, 20 wt% in isopropanol) was purchased from Macklin. Unless stated, otherwise, all solvents were purchased from Sigma-Aldrich. All materials were used as received without further purification.

Perovskite precursor solution

WBG FA_0.8Cs_0.2Pb(I_0.6Br_0.4)₃ perovskite

The precursor solution (1.2 M) was prepared by dissolving 0.96 mmol FAI, 0.24 mmol CsI, 0.48 mmol PbI₂, 0.72 mmol PbBr₂, and 0.024 mmol KI in mixed solvents of DMF and DMSO with a volume ratio of 3:1 and stirred at room temperature overnight.

NBG Cs_0.1FA_0.6MA_0.3Pb_0.5Sn_0.5I₃ perovskite

The precursor solution (2.0 M) was prepared by dissolving 1.2 mmol FAI, 0.6 mmol MAI, 0.2 mmol CsI, 1.0 mmol PbI₂, 1.0 mmol SnI₂, 0.1 mmol SnF₂, 0.04 mmol GuaSCN and 0.04 mmol GlyHCl in mixed solvents of DMF and DMSO with a volume ratio of 3:1. The precursor solution was stirred at 45 °C for 1 h and then filtered using a 0.22-μm PTFE membrane before use.

1.68 eV-bandgap FA_0.8Cs_0.2Pb(I_0.8Br_0.2)₃ perovskite

The precursor solution (1.5 M) was prepared by dissolving 1.2 mmol FAI, 0.3 mmol CsI, 1.05 mmol PbI₂, 0.45 mmol PbBr₂ and 0.03 mmol KI in mixed solvents of DMF and DMSO with a volume ratio of 3:1 and stirred overnight.

1.52 eV-bandgap FA_0.98Cs_0.02PbI₃ perovskite

The precursor solution (1.5 M) was prepared by dissolving 1.47 mmol FAI, 0.03 mmol CsI, 1.5 mmol PbI₂ and 0.15 mmol DBSO in mixed solvents of DMF and NMP with a volume ratio of 6:1 and stirred overnight.

Device fabrication

NBG PSCs

Glass/ITO substrates were consecutively cleaned by sequential ultrasonication for 15 min with detergent solution, deionized water, and ethanol. The cleaned substrates were dried with high-pressure N₂ gas flow and then were cleaned by UV-ozone treatment for 30 min. The PEDOT:PSS solution was spin-coated onto the ITO substrate at 5000 rpm for 30 s, then annealed at 150 °C for 20 min in ambient air and finally transferred into an N₂-filled glovebox before use. For the MSN-SH modified layer, MSN-SH dispersions (20 mg mL^–1) were dropped on the HTL and spin-coated at 2000 rpm for 30 s, followed by annealing at 100 °C for 10 min. The 60 μL of perovskite solution was spin-coated onto the substrate with the two-step process (1000 rpm for 10 s and 4000 rpm for 40 s). Then 350 μL of chlorobenzene (CB) was quickly dropped onto the centre of the spinning substrate during the second spin-coating step at 20 s before the end of the procedure. The substrates were then thermally annealed at 100 °C for 10 min. For the passivation layer, EDAI₂ (0.5 mg in 1 mL IPA and toluene mixed solvent at the volume ratio of 1:1, filtered before use) was spin-coated on top of perovskite films at 4000 rpm for 20 s and annealed at 100 °C for 5 min. Finally, 20 nm C₆₀, 5 nm BCP, and 100 nm Ag were sequentially thermally evaporated under a high vacuum (<5 × 10⁻⁴ Pa).

WBG PSCs

Me-4PACz (0.8 mg mL⁻¹) dissolved in ethanol was spin-coated on the ITO substrates at 3000 rpm for 25 s and then annealed at 100 °C for 10 min. The MSN-SH dispersion (20 mg mL^–1) was deposited by spin-coating at 2000 rpm for 30 s, followed by annealing at 100 °C for 10 min. Then the perovskite solution was spin-coated on the substrate at 5000 rpm for 60 s with an acceleration of 1000 rpm s^–1, during which 400 μL ethyl acetate was dripped onto the center of film at 30 s before the end of spin-coating. The as-coated precursor films were subsequently annealed on a hotplate at 100 °C for 10 min. After cooling down, 100 μL of PDAI₂ (1.5 mg mL⁻¹ in IPA) solution was spin-coated onto the as-prepared perovskite films at 4000 rpm for 20 s with an acceleration of 3000 rpm s^–1 and annealed at 100 °C for 5 min. The deposition of C₆₀/BCP/Ag was the same as described in the NBG PSCs.

All-perovskite tandem devices

For the WBG subcell, the deposition of Me-4PACz, MSN-SH dispersion, perovskite film, PDAI_2, and C₆₀ layers were the same as WBG PSCs. Then the films were transferred to the ALD chamber to deposit 30 nm SnO_x at 100 °C using precursors of tetrakis(dimethylamino) tin (IV) (99.9999%) and deionized water. After SnO_x deposition, the substrates were transferred to the evaporation chamber to deposit 1 nm Au. Next, the diluted PEDOT:PSS solution with IPA at a volume ratio of 1:2 was spin-coated onto the WBG subcell at 4000 rpm for 30 s, followed by annealing at 100 °C for 15 min in the ambient. After the samples were transferred to an N₂-filled glovebox, the MSN-SH dispersion, perovskite films, EDAI₂, C₆₀, BCP, and Ag electrodes were deposited in full accordance with the above sequence of NBG PSCs preparation process. Finally, the all-perovskite tandem solar cell with an architecture of glass/ITO/Me-4PACz/MSN-SH/WBG perovskite (~350 nm)/PDAI₂/C₆₀/ALD-SnO_x (30 nm)/Au (1 nm)/PEDOT:PSS/MSN-SH/NBG perovskite (~900 nm)/EDAI₂/C₆₀/BCP/Ag was successively prepared.

1.68 eV-bandgap PSCs

The preparation process was the same as that of the WBG PSCs.

1.52 eV-bandgap PSCs

The deposition of Me-4PACz, MSN-SH dispersions was the same as for WBG PSCs. The perovskite solution was spin-coated on the substrate at 5000 rpm for 60 s. At the 12th second of spinning, 500 μL of ethyl acetate was dripped onto the centre of the substrate. The as-coated precursor films were subsequently annealed on a hotplate at 130 °C for 15 min. Then 100 μL of 3,5-bis(trifluoromethyl)phenethylammonium iodide⁴⁴ (1 mg mL⁻¹ in IPA) were spin-coated onto the as-prepared perovskite films at 5000 rpm for 30 s; the films were subsequently dried at 100 °C for 5 min. The deposition of C₆₀/BCP/Ag was the same as described in the WBG PSCs.

Mini-modules fabrication

As illustrated in Supplementary Fig. 40, the mini-modules were fabricated on the 5.0 cm × 5.0 cm sized glass/ITO substrate using a 532 nm nanosecond laser scribing with a power of 4 W to form P1 lines isolated subcells with a width of 6.8 mm. The preparation process of the mini-module is the same as that of the above small-area devices, the only difference is that the acceleration in all spin-coating processes needs to be changed to 1000 rpm s^–1 to ensure that the solution can be evenly coated on the substrate. To prevent the oxidation of NBG perovskite when exposed to ambient air, we deposited ALD-SnO_x with a thickness of 10 nm on the C₆₀ layer before the P2 scribing (0.5 W) as previously reported⁴⁸. Then the Cu (100 nm) based metal electrode was deposited. Finally, effective monolithically interconnected modules were formed by laser scribing (0.5 W) to form P3 lines. For module encapsulation, the connection was extended by attaching tinned copper ribbon strips to metal electrodes. The edge of the sealing glass was sealed with butyl tape with a width of approximately 0.5 cm, and vacuum lamination was performed using an industrial laminator at 100 °C for 10 min. All encapsulation operations were completed in an N₂-filled glovebox.

Mechanical strength measurements

Stress-displacement curve measurements were performed on an electronic universal testing machine (LGD-500) by using the double-cantilever beam delamination technique³⁷. The samples adopted a device structure of glass/ITO/PEDOT:PSS/perovskite/UV epoxy/glass with a substrate size of 1.3 × 1.5 cm². Perovskite films with and without MSN or MSN-SH layer were prepared on PEDOT:PSS-coated ITO/glass as described above. Then, UV epoxy was coated on a 1 × 1 cm² glass substrate and adhered to the centre of the perovskite films, followed by UV solidification for 1 min. The samples were mounted on a tensile test fixture and stretched at an operating rate of 0.5 mm min^–1 to delaminate the interface. To calculate the specific fracture energy (W), the following equation is used: W = ∫σdε, where σ is the measured stress and ε is the measured strain.

Computational details

The first-principle-based geometry optimization calculations were carried out within density-functional theory (DFT), implemented in the Vienna Ab Initio Simulation Package (VASP) code⁴⁹, using the frozen-core projector augmented-wave (PAW) method to describe the interaction between the atomic cores and the valence electron density⁵⁰. The exchange-correlation potential was approximated within the generalized gradient approximation (GGA) using the Perdew-Burke Ernzerhof (PBE) functional⁵¹. The dispersion-corrected DFT-D3 schemes were employed to describe the Van der Waals (vdW) interactions⁵². Plane-wave cutoff energy was set to 500 eV. The conjugate gradient algorithm was used in ionic optimization, convergence threshold was set to 10⁻⁵ eV atom⁻¹ in electronic relaxation and below 0.3 eV Å⁻¹ in Hellmann–Feynman force on each atom. We have constructed the slab model of the (001) crystal plane with 3*3*2 supercell, where the vacuum layer was set to 20 Å. The three atom layers of the slab model were fixed from bottom to top as a bulk phase structure, including two atom layers with Pb and Sn mixed configuration, and one-layer organic molecules between the atoms layer of Pb and Sn mixed configuration. The rest of the one-atom layer with Pb and Sn mixed configuration and one-layer organic molecules were relaxed as surface structures. The Brillouin zone in reciprocal space was sampled by a Γ-centered Monkhorst–Pack scheme with 1 × 1 × 1 k-point grids for geometry optimization, due to the a = b = 18.95 Å of lattice parameters for the slab model of (001) crystal plane⁵³. The climbing image nudged elastic band (CI-NEB) method was used to estimate the diffusion barrier of the I atom. The models of transition state calculation were constructed with seven I atoms using the linear interpolation method, and then the VASP program based on the CI-NEB method was implemented to converge the transition and intermediate states⁵⁴. The positions of I atoms were continuously optimized to obtain the empirically reasonable transition and intermediate states.

Device characterization

The J?V curves of the devices were measured using a Keithley 2400 source measurement unit and a solar simulator (Oriel, model 9119) with an AM1.5 G spectrum. The light intensity was calibrated using a certified WPVS standard silicon reference cell (Enlitech) at 100 mW cm⁻². The aperture area of devices was determined by the black masks of 0.0498 cm², 0.0930 cm², and 11.3 cm² area. The stabilized power output was achieved by monitoring the stabilized current density output under MPP bias voltage (extracted from the reverse scan J-V curves). EQE spectra were performed in ambient air using a QE system (Enlitech Co., Ltd.). For EQE measurements of tandem solar cells, two highly bright LEDs with emission peaks of 850 and 460 nm were used for the measurements of the WBG and NBG subcells, respectively. The Transient photovoltage (TPV), transient photocurrent (TPC), and Mott-Schottky plots were obtained by a Zennium electrochemistry workstation (Zahner, Germany). External electroluminescence quantum efficiency (EQE_EL) measurement was measured on ELCT-3010 (Enlitech Co., Ltd.). The operational stability tests were carried out under AM1.5G solar simulator illumination source (Beijing Saifan Photoelectric Instrument Co., Ltd.) with an intensity of 100 mW cm⁻² using a maximum power point tracking system (Wuhan Jiuyao Optoelectronic Technology Co., Ltd.) in ambient conditions.

Films characterization

SEM images were taken with a Nova NanoSEM 450 scanning electron microscope at 10 kV operating voltage. XRD spectra were measured on an X-ray diffractometer (PANalytical B.V. Co.) with Cu K_α radiation. The GIWAXS measurements were performed at beamline BL14B1 of the Shanghai Synchrotron Radiation Facility. The wavelength of X-rays was 1.24 Å (10 KeV), and diffraction patterns were collected by using a two-dimensional Mar225 detector with different incidence angles and 30 s exposure times. The GIXRD patterns were acquired by using a Rigaku Smartlab with Cu K_α radiation in the 2θ range of 30.6 to 32.6°. The FLIM images were measured by FLIM300. TRPL measurements were conducted by HORIBA DeltaFlex spectrometer. The in-situ PL measurements were conducted with laser excitation at 532 nm and the area of interest was fixed on the micro-spectral measurement system (ProSp-Micro40-VIS), together with spectrograph (Ocean Insight, USA). Absorption spectra were measured using a Lambda 950 UV-vis spectrophotometer (PerkinElmer Co., USA). XPS was measured with a monochromatic Al K_α X-ray source (1486.6 eV) operating at 100 W (Thermo ESCALAB 250XI). Quasi-Fermi level splitting (QFLS) values were calculated by the data extracted from photoluminescence quantum yield (PLQY) measurements using QuantaMaster 8000 (HORIBA, Canada) with an 808 nm laser to photoexcite the films placed in an integrating sphere. The laser intensity was adjusted to 1 sun equivalent intensity using a PSC to obtain a current density at 0 V equal to its J_SC.