Cation disorder engineering yields AgBiS2 nanocrystals with enhanced optical absorption for efficient ultrathin solar cells

Strong optical absorption by a semiconductor is a highly desirable property for many optoelectronic and photovoltaic applications. The optimal thickness of a semiconductor absorber is primarily determined by its absorption coefficient. To date, this parameter has been considered as a fundamental material property, and efforts to realize thinner photovoltaics have relied on light-trapping structures that add complexity and cost. Here we demonstrate that engineering cation disorder in a ternary chalcogenide semiconductor leads to considerable absorption increase due to enhancement of the optical transition matrix elements. We show that cation-disorder-engineered AgBiS2 colloidal nanocrystals offer an absorption coefficient that is higher than other photovoltaic materials, enabling highly efficient extremely thin absorber photovoltaic devices. We report solution-processed, environmentally friendly, 30-nm-thick solar cells with short-circuit current density of 27 mA cm−2, a power conversion efficiency of 9.17% (8.85% certified) and high stability under ambient conditions. AgBiS2 nanocrystals with enhanced optical absorption yield efficient ultrathin solar cells.

H igh-performance, lightweight solar cells featuring low cost and environmental friendliness have been a long-sought target in the photovoltaic field. Ultrathin solar cells can reduce material consumption and manufacturing demands, directly lowering the cost. Owing to an absorber thickness that is orders of magnitude lower than conventional solar cells, ultrathin solar cells further allow for flexible and lightweight form factors suited for building-or wearable-integrated photovoltaics. A thinner absorber layer also improves charge carrier collection and reduces bulk recombination, which are particularly prevalent in nanocrystalline solution-processed semiconductors 1,2 , thus improving performance and providing strong light absorption. Furthermore, high absorption in small absorber volumes allows for operating the device at high photogenerated carrier densities, a physical regime that maximizes the open-circuit voltage (V oc ) and permits advanced high-efficiency concepts such as hot carrier solar cells 3 .
Currently, high-performance ultrathin solar cells are mainly realized via different light-trapping strategies, which are employed to compensate for the short-circuit current drop due to incomplete absorption in the ultrathin absorbing layer 4,5 . The use of optical architectures, however, increases non-radiative recombination 4,6 and complicates the manufacturing process, introducing additional obstacles towards low-cost high-efficiency devices.
Typically, the absorption coefficient of a material determines the required thickness for optimal light harvesting under photovoltaic operation. The absorption coefficient of a semiconductor has been considered as a fundamental parameter of the material, with efforts to enhance light absorption in ultrathin absorbers relying on optical means 4,5 . We instead took the view-motivated by the fundamental relationship between atomic geometry, electronic structure and optical absorption-that the absorption coefficient of a semiconductor can be tuned by engineering the atomistic material structure.
Cation disorder is a widely observed phenomenon in multinary materials, referring to the deviation of atomic positions in the cationic sublattice from an ordered crystalline arrangement. This phenomenon substantially impacts the optoelectronic properties of semiconductors [7][8][9] and has traditionally been considered an undesirable (and often unavoidable) effect, due to its entropically driven nature 7,8,10,11 . Here we leverage the modulation of cation disorder homogeneity in multinary semiconductors as a pathway to enhance the optical transition matrix elements such that improved absorption coefficient and photovoltaic device efficiency can be achieved.

Cation disorder homogeneity and absorption behaviour
In this work, we focus on ternary AgBiS 2 nanocrystals (NCs), a solution-processed nanomaterial comprising environmentally friendly elements 12,13 with reported efficiencies exceeding 6% in thin-film solar cells 1,14 . The cation distribution around Ag sites in AgBiS 2 NCs has shown evidence for non-random Ag-Ag correlation 15 , indicating the presence of inhomogeneous cation disorder (that is, cation segregation with local Ag-rich and Bi-rich regions), likely due to growth kinetics during synthesis and surface-ligand interactions [16][17][18] .
An illustration of inhomogeneous cation disorder within AgBiS 2 NCs is shown in Fig. 1a. The valence band maximum (VBM) of AgBiS 2 primarily derives from Ag d and S p states, whereas the conduction band minimum (CBM) arises from Bi p and S p interactions 19,20 (Fig. 1b and Supplementary Fig. 1). A clear spatial separation of the Ag-derived VBM and Bi-derived CBM for the cation-segregated configuration can be observed in the local electronic density of states (Fig. 1c). In contrast, under homogeneous cation disorder, we predict a VBM and CBM delocalized over the entire material (Fig. 1d), with the correlation between cation distribution and spatial (de)localization of the band extrema (Fig. 1e).
The theoretically simulated absorption spectra of AgBiS 2 for both inhomogeneous and homogeneous cation disorders are provided in Fig. 2a. As expected, we find a substantially increased refractive index n and transition dipole matrix element ( Supplementary  Fig. 2) and therefore enhanced optical absorption on homogenizing disorder.
To experimentally tune the cationic disorder, we first assessed the thermodynamics of atomic reordering, particularly the formation energy difference needed to induce disorder. Density functional theory (DFT) was employed to calculate the inter-site cation exchange energy. Under the highest level of theory employed for phase energetics (hybrid DFT including spin-orbit-coupling effects), the bulk order-disorder enthalpy difference is calculated as 17.4 meV per atom, indicating the accessibility of cation site swapping in AgBiS 2 under mild annealing conditions. The mechanism behind cation inter-site exchange probably is defect-mediated ionic migration. Indeed, cation mobility aided by Ag vacancies and bond anharmonicity has been demonstrated in AgBiS 2 NCs 21-23 . Considering the low inter-site cation exchange energy in AgBiS 2 , we sought to anneal AgBiS 2 NCs under low-temperature conditions to facilitate cation inter-site exchange and thus an entropically driven transition to homogeneous cation distribution. Figure 2b plots the absorption coefficient of our NC films on annealing under different temperatures. Comparing Fig. 2a and b, the simulated absorption spectrum for cation segregation configurations (inhomogeneous disorder) matches well with the as-prepared AgBiS 2 NC film, both exhibiting Urbach band tailing at longer wavelengths, which is pernicious for photovoltaic devices 24,25 . However, in the homogeneous cation-disordered structure, the simulated absorption coefficient is much higher than the cation-segregated case, with reduced band tailing, manifesting favourable properties for optoelectronic applications 26 . As shown in Fig. 2b, the absorption coefficient of AgBiS 2 NC films is enhanced by up to a factor of two after annealing, alongside reduced Urbach energy from 173 to 26 meV ( Supplementary Fig. 3), as predicted by ab initio calculations. Furthermore, this enhanced absorption is stable in the ambient atmosphere, as spontaneous cation segregation is thermodynamically and entropically unfavourable ( Supplementary Fig. 4). With this low-energy, scalable annealing process, we produce a semiconducting material that exhibits an absorption coefficient 5-10 times greater than any other material currently used in photovoltaic technology 4,27-31 , across a wide spectral range from 400 to 1,000 nm (Fig. 2c).
With the high absorption coefficient of our films, an ultrathin layer of AgBiS 2 NCs would be sufficient to absorb most of the light in the visible range. To assess the potential of our strongly absorbing NC films, we calculate the maximum achievable short-circuit current density J sc using the transfer matrix method (TMM) 32,33 , assuming 100% internal quantum efficiency (IQE) ( Supplementary  Fig. 5). Figure 2d plots the maximum J sc as a function of the active layer thickness for different annealing temperatures, corresponding to varying degrees of cation disorder homogeneity. On increasing the annealing temperature, we witness an increase in J sc at low active layer thicknesses (t < 200 nm). We predict a maximum J sc of ~28 mA cm −2 (32 mA cm −2 ) for AgBiS 2 NC films annealed at 115 °C (150 °C), with a thickness of only ~30 nm. Furthermore, the spectroscopic limited maximum efficiency (SLME) was calculated assuming only radiative recombination in the devices 34 . As shown in  , a high photovoltaic efficiency up to 26% was predicted for a 30 nm absorber layer, indicating the performance potential of ultrathin solar cells based on AgBiS 2 NC films. Furthermore, with the thickness reduction of the AgBiS 2 absorber from 500 nm (common photovoltaic thickness) to 30 nm, we estimate ~50% cost reduction over the full photovoltaic device cost (Supplementary Fig. 6 and Supplementary Note).

Cation configuration transition
To further verify the proposed cation homogenization as the underlying mechanism responsible for the optical absorption enhancement in AgBiS 2 NC films, film thicknesses were first measured to exclude NC densification as the dominant factor. Negligible thickness changes were observed between the as-prepared and the samples annealed at 115 °C ( Supplementary Fig. 7), with only a slight decrease for the films annealed at 150 °C, contributing to a very small (~8%) absorption enhancement for this sample. These film thickness measurements demonstrate that the densification effect is not the dominant factor in the absorption enhancement of these materials. Furthermore, we used X-ray diffraction (XRD) and transmission electron microscopy (TEM) to probe the changes in the crystal structure due to cation disorder homogenization on annealing. Interestingly, although XRD analysis suggested increased crystallite size (from 4.2 to 6.2 nm) on annealing at 115 °C, high-resolution transmission electron microscopy (HRTEM) showed no measurable size differences in these samples ( Supplementary Fig. 8).
The sharpening of the XRD peaks despite negligible NC growth indicates improved crystallinity due to atomic rearrangements within the NCs. Further increasing the annealing temperature to 150 and 200 °C causes the NCs to fuse into larger crystals (28 and 47 nm, respectively; Supplementary Fig. 8). Point defects are observable in the HRTEM data after high-temperature annealing, which could be harmful for optoelectronic applications 35 (Supplementary Fig. 9). In addition to peak narrowing in the XRD patterns, the peak positions were also found to shift to higher angles on annealing (Fig. 3a). To deconvolute the effect of crystal size and cation arrangement, as well as explain the apparent changes in crystallinity, we calculated the expected XRD patterns for homogeneously disordered cubic AgBiS 2 (space group Fm3m; Supplementary Fig. 10), with crystal size as the only variable parameter ( Supplementary Fig. 11). The full-width at half-maximum of all the peaks sharpens with crystal growth, whereas the peak positions remain essentially the same, as expected. However, when transitioning from cation-segregated configurations to homogeneous cation disorder, as well as fixing the crystallite size, the simulated XRD patterns of AgBiS 2 show distinct peak shifts to higher angles and peak narrowing (Fig. 3b), matching the experimental observations of improved crystallinity on annealing. These XRD peak shifts primarily originate from the shortening of the Ag-S bond lengths, whereas peak narrowing occurs due to narrowing of the bond length distributions and reduction in octahedral distortion on homogenization of the cation distribution ( Supplementary Fig. 12). This phenomenon was further confirmed with HRTEM measurements (Fig. 3c,d), with integrated line profiles of the {200} plane showing a slight shrinkage after annealing, further confirming the transition from cation segregation to homogeneous disorder. Considering the difference in local bonding environments for different cation configurations, changes in the Madelung potential were expected 36 . We calculate the average Madelung potential at the Bi sites as 3.29 and 4.66 V for segregated and homogeneous cation configurations, respectively, using Bader atomic charges. A greater Madelung potential suggests a decrease in the X-ray photoelectron (XPS) binding energy, on transitioning from inhomogeneous to homogeneous cation disorder 36,37 . As shown in Fig. 3e, the Bi 5d peaks in the simulated XPS spectra are noticeably shifted to lower binding energies for homogeneous cation disorder, compared with cation-segregated configurations. Likewise, the annealed AgBiS 2 NCs show a small but notable chemical shift to a lower energy, compared with the as-prepared samples (Fig. 3f,g), in agreement with our proposition of cation homogenization on annealing.

ultrathin AgBiS 2 NC solar cells
Having developed a material with such strong optical absorption, we next sought to produce highly efficient ultrathin solution-processed solar cells with these NCs. The solar cells were fabricated with an architecture of glass/indium tin oxide (ITO)/SnO 2 /AgBiS 2 / hole transport layer (HTL)/MoO 3 /Ag (Fig. 4a). Cross-sectional TEM confirms the ultrathin nature of the device layers (Fig. 4b).
We first used poly[ [4,8- [3,4-b]thiophenediyl]] (PTB7) as an electron-blocking layer, in accordance with previous studies 1, 14 . The devices showed an average power conversion efficiency (PCE) of 6.4 ± 0.6%, with a champion device reaching a PCE of 7.6% (Table 1)-higher than the previously reported record performance of 6.3% (refs. 1,14,[38][39][40]. Atomic force microscopy (AFM) revealed a surface roughness of 0.6 nm for a 4 nm PTB7 film ( Supplementary Fig. 13), which undermines the performance of the cells by introducing interface recombination 41 . We sought to replace PTB7 with an alternative electron-blocking layer with improved morphological characteristics. We found that poly(triaryl amine) (PTAA) yielded improved uniformity (root-mean-square roughness of 0.4 nm), a prerequisite for suppressing current leakage and interface recombination. To further assess the superiority of PTAA, transient photocurrent and transient photovoltage were measured under a bias of one sun light (Supplementary Fig. 14). Devices with PTAA showed a faster photocurrent decay and longer carrier lifetime than that with PTB7 as the HTL, which indicates improved charge extraction and reduced interface recombination. As a result, replacing PTB7 with PTAA leads to substantial improvement in V oc and fill factor (FF) (Supplementary Fig. 13) and results in an ~20% increase in PCE to 8.7 ± 0.3%, with the best device reaching 9.17% (Fig. 4c,d). One of our champion devices was sent to an accredited photovoltaic calibration laboratory (Newport, USA), which certified the PCE of 8.85% under AM1.5G full-sun illumination, with negligible hysteresis ( Fig. 4e and Supplementary Fig. 15). The measured J sc of a 25   27 mA cm −2 was further confirmed by the external quantum efficiency (EQE) spectrum, which gives a value of 26.5 mA cm −2 (Fig. 4f). In addition, the measured EQE spectrum matched well with the TMM-predicted EQE, indicating a near-unity IQE. However, unannealed devices showed not only lower absorption (that is, the predicted EQE) in the near-infrared region but also a  lower IQE (Fig. 4f) and larger V oc deficit, which is ascribed to slower charge extraction, Urbach band tailing and higher trap density ( Supplementary Fig. 16). Higher-temperature annealing leads to remarkably lower performance, which is consistent with the defects forming from uncontrolled NC fusing ( Supplementary Figs. 8  and 17). Analysing the absorption loss of our record-performance ultrathin devices, a large part of the incident light (~10 mA cm −2 ) was reflected (Supplementary Fig. 18) and further improvement in device performance is expected by introducing an antireflection layer or advanced light-trapping techniques.
On the other hand, thicker (200 nm) devices are also fabricated for direct comparison with ultrathin devices: as expected, a low J sc (~15 mA cm −2 ) was obtained (Supplementary Fig. 19). To further understand the devices, time-of-flight data were employed to investigate the charge carrier mobilities in our AgBiS 2 NC films ( Supplementary Fig. 20). The hole and electron mobilities are calculated to be 1.2 × 10 −4 and 5.7 × 10 −5 cm 2 V −1 s −1 , respectively. Combining with the carrier lifetime extracted from transient photovoltage measurements, the diffusion length is estimated to be ~25.4 nm, which rationalizes the near-unity IQE in our 30 nm devices and the low performance in 200-nm-thick devices. Mid-gap trap density was estimated from the transient photocurrent/transient photovoltage measurements ( Supplementary Fig. 16). In our optimal AgBiS 2 NC films, the trap density is ~9 × 10 16 cm −3 . Although this trap density is four times lower than that before annealing (~4 × 10 17 cm −3 ), efforts are needed to further passivate the trap states for higher V oc and thus higher efficiency.
In addition to PCE, stability is another important figure of merit of photovoltaic devices. Therefore, to assess the stability of our AgBiS 2 NC solar cells, we first measured their shelf lifetime by storing the un-encapsulated devices in ambient conditions (temperature, ~25 °C; relative humidity, ~30%). The device showed a gradual improvement in the first 20 days (Supplementary Fig. 21), which is probably a result of the oxidation of the MoO x layer and better band alignment 42 (Supplementary Fig. 22). Furthermore, the device retained its original performance after aging for four months. The operational stability was further investigated by subjecting the un-encapsulated device to AM1.5G one-sun illumination in the ambient atmosphere (relative humidity, ~60%). The device performance was measured by applying a forward bias fixed at the maximum power point (MPP). As shown in Fig. 4g, the PCE of the PTB7 device dropped below 2% after 20 min illumination, whereas the PTAA device demonstrated much better operational stability under continuous operation. After 10 h of MPP testing on the un-encapsulated cell in ambient conditions, the device retained 85% of its original efficiency. Longer stability at the MPP was also recorded with a class AA solar light source, showing ~80% of the original performance after 40 h test in ambient air ( Supplementary  Fig. 23). To the best of our knowledge, the devices reported here set a record among low-temperature and solution-processed, non-toxic inorganic solar cells in terms of stability and performance [43][44][45][46] . These results support the fact that AgBiS 2 NCs are an extremely promising material for low-cost, efficient, stable and environmentally friendly solar cells.
In conclusion, we have demonstrated that the absorption coefficients of ternary AgBiS 2 NCs can be enhanced via cation disorder homogenization under mild annealing conditions. Ultrahigh absorption coefficients were obtained in annealed AgBiS 2 NC films, with a calculated SLME of over 26% for a 30 nm NC film. The transition in cation configuration was further confirmed by the combination of ab initio calculations with XRD, HRTEM and XPS measurements. Ultrathin solar cells are fabricated based on ultra-absorbing AgBiS 2 NCs. A high J sc of 27 mA cm −2 and a record efficiency of up to 9.17% were obtained with an independent certification of 8.85% from Newport, USA. The air stability and photostability were also recorded in high-performance devices. Our work not only establishes the potential of ultrathin AgBiS 2 NC solar cells, which are solution processable and restriction of hazardous substances (RoHS) compliant, but also demonstrates the importance of atomic configuration engineering in multinary systems.

Online content
Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/ s41566-021-00950-4.

Methods
DFT simulations. The AiiDA infrastructure was used to maintain the data provenance for all the calculations performed in this study 47 . The calculations were performed using DFT within periodic boundary conditions through the Vienna ab initio simulation package [48][49][50] . Using the projector augmented-wave method, scalar-relativistic potentials were employed to describe the interaction between the core and valence electrons 51 . The calculations were carried out using Γ-centred k-point meshes with a reciprocal space sampling of 0.11 Å −1 and a plane-wave kinetic energy cutoff of 300 eV (increased to 450 eV for structural relaxations to avoid the possibility of Pulay stress). With these parameter choices, the ground-state energies of all the known structures in the Ag-Bi-S system were converged to within 1 meV per atom.
Cation disorder. To model the effects of varying degrees of cation order/disorder, two approaches were employed. First, to simulate the total random cation disorder, a 64 atom supercell for AgBiS 2 in the Fm3m rock-salt structure was generated using the special quasi-random structure (SQS) method 52 , in which the cation-cation cluster correlations are optimized to obtain the best approximation to an ideal infinite random distribution for a given supercell. Here the alloy theoretic automated toolkit 53 was used to generate the SQS supercell via Monte Carlo-simulated annealing loops [54][55][56] . Eight Monte Carlo simulations were performed, with the structure giving the best match to the true disordered solid solution chosen for further calculations. This corresponded to an 'objective function' of −81.18, considering two-atom clusters with up to 12 Å separation, three-atom clusters up to a maximum of 10 Å pair separation and four-atom clusters up to 8 Å pair separation (using the experimental rock-salt crystal structure) 37 .
The screened hybrid DFT exchange-correlation functional of Heyd, Scuseria and Ernzerhof (HSE06) 38 was used to calculate the structural and electronic properties of Fm3m (using this SQS structure) and R3m AgBiS 2 , unless otherwise stated, having been demonstrated to accurately predict the electronic structures of semiconductor materials 57,58 . To account for relativistic effects, due to the presence of heavy-atom elements Ag and Bi, spin-orbit-coupling (SOC) effects were included in all the electronic and optical calculations.
Second, to investigate the effects of both partial order and inhomogeneous disorder (that is, cation segregation with Ag-rich and Bi-rich regions) on the cation sublattice, all the possible configurations for AgBiS 2 in a 32 atom rock-salt structure were enumerated using the Transformer package 59-61 , yielding 440 symmetry-inequivalent arrangements. Here the PBEsol 62 semi-local exchangecorrelation functional was used for geometry optimizations and energetic analysis, motivated by its well-established accuracy for the structural relaxation of bulk solids 63 and moderate computational cost. Moreover, this functional was tested against both experiment and computationally intensive HSE06 hybrid DFT functional for bulk geometry optimization and energetics, respectively, using all the known structures in the Ag-Bi-S system. Here PBEsol was found to accurately reproduce experimentally reported crystal structures, with a mean absolute error of <1.5% in the lattice parameters, as well as reproducing the energetic ordering of phases on the convex hull according to both HSE06 and experiment.
To ensure consistency when comparing the results of these calculations to that of Fm3m (SQS) AgBiS 2 , a new 32 atom SQS supercell was generated (using the same procedure as outlined above) and relaxed with PBEsol. In this case, a perfect 'objective function' match to the true disordered solution was obtained. Although appropriate for structural and energetic analysis of cation configurations in AgBiS 2 , semi-local DFT is known to severely underestimate electronic bandgaps [64][65][66][67] ; therefore, the HSE06 + SOC hybrid DFT functional was used to calculate the optical and electronic properties of these configurations. In this case, downsampling of the Fock exchange matrix by a factor of 2 (NKRED = 2) was employed to reduce the computational cost to a manageable level. This choice was confirmed to affect the electronic bandgap by <0.05 eV for the 32 atom SQS supercell.
To investigate the impact of supercell size on the calculated properties, the 32 atom SQS supercell was also relaxed with the HSE06 functional, to then compare with the 64 atom structure. The total energy was found to match that of the 64 atom SQS supercell to <1 meV per atom, whereas the bandgap was found to slightly increase from 0.69 to 0.83 eV for the 32 atom supercell.
Post-processing. Primitive and unfolded electronic band structure diagrams were generated using sumo and PyVaspwfc 44,45 , respectively. Further, effmass was used to calculate the effective masses of the carrier 68 , and the photoemission spectra were generated using Galore [69][70][71] .Crystal orbital Hamilton population analysis and charge-density partitioning were performed using LOBSTER 48 , and the vasppy package 71 was used to calculate the radial distribution functions. The pymatgen package was used throughout for the manipulation and analysis of the calculated inputs and outputs 72 .

Chemicals and materials.
Reagents were purchased from Sigma-Aldrich, except SnO 2 colloid precursor (tin(iv) oxide, 15% in H 2 O colloidal dispersion), which was obtained from Alfa Aesar. PTAA was purchased from EM Index and PTB7 was purchased from 1-Material.
Synthesis of AgBiS 2 NCs. The Schlenk technique was used to synthesize AgBiS 2 NCs, following a previous report with modifications 1,14 . Further, 4 mmol Bi(OAc) 3 , 3.2 mmol Ag(OAc), 24 ml oleic acid and 15 ml 1-octadecene were pumped at 100 °C for 2 h (~0.2 mbar) to remove oxygen and moisture. Then, 4 mmol hexamethyldisilathiane dissolved in 5 ml 1-octadecene was quickly injected into the flask. The heating mantel was removed and the reaction was cooled down in a water bath for ~5 min. After that, the crude solution was stirred for 1 h at room temperature. The NCs were isolated by adding acetone, followed by centrifugation. The extracted NCs were redispersed in toluene, and acetone was added to precipitate the NCs. The redispersion/precipitation was repeated once more. Finally, the obtained AgBiS 2 NC powder was dispersed in anhydrous toluene (20 mg ml −1 ) and stored in the ambient atmosphere for device fabrication.
Characterization of AgBiS 2 NCs and films. Films exchanged with 3-mercaptopropionic acid (MPA) were grown on glass substrates, followed by annealing at different temperatures in a glovebox. The thicknesses were measured using a profilometer. The complex refractive index was measured at various angles using a broadband Sopra Ellipsometer GES5E instrument. The SEMILAB spectroscopic ellipsometry analyser software was utilized to fit a model of stacked layers of appropriate optical constants and the thickness from the profilometer was used as an input. The absorption coefficients are calculated from the extinction coefficients. The XRD data were collected using a Rigaku SmartLab powder diffractometer in the Bragg-Brentano geometry with Cu Kα radiation. The XPS measurements were performed with a SPECS PHOIBOS 150 hemispherical analyser under ultrahigh-vacuum conditions (10 −10 mbar), with a monochromatic Kα X-ray source (1,486.74 eV) at the Institut Català de Nanociència i Nanotecnologia. TEM was performed at the Scientific and Technological Centres of the University of Barcelona. The TEM images were obtained using a JEOL 2100 microscope operating at an accelerating voltage of 200 kV.
Optical modelling and SLME. A home-made MATLAB (R2021a) code was used to implement the transfer matrix formalism. We assumed that each layer was flat and considered no scattering effects. The short-circuit current density was calculated with the assumption of 100% IQE. The SLME was calculated according to SLME = Pmax, where e denotes the elementary charge; k, the Boltzmann constant; T, the temperature; and J 0 , the dark saturation current density calculated with the assumption of only radiative recombination: where EQE TMM is the calculated total absorption in the AgBiS 2 NCs layer and ∅ BB is the black-body radiation spectra at 300 K. The films were transferred into the glovebox for 10 min annealing at 115 °C and then stored in dry air before spin coating PTB7 (5 mg ml −1 in dichlorobenzene) or PTAA solution (2 mg ml −1 in toluene) at 3,000 r.p.m. Finally, a Kurt J. Lesker NANO 36 system was used to deposit 3 nm MoO 3 and 120 nm Ag through a shadow mask to produce solar cells with a diameter of 2 mm (area, 3.14 mm 2 ).

Solar cell characterization.
All the device characterizations were performed in air under ambient conditions. Current-voltage (J-V) measurements were performed with a Keithley 2400 sourcemeter and a Newport Oriel Sol3A solar simulator with an AM1.5G filter. The intensity of solar light was calibrated using a Hamamatsu S1336 silicon photodiode that was calibrated at the Fraunhofer Institute of Solar Energy Systems. The solar cells were measured with and without masks, and a slightly lower V oc was observed when measuring with masks due to the masking effect. For certified cells, appropriate masks were always used. The EQE was measured using a Newport Cornerstone 260 monochromator, a Thorlabs MC2000 chopper, a Stanford Research SR570 transimpedance amplifier and a Stanford Research SR830 lock-in amplifier. A calibrated Newport 818-UV photodetector was used as the reference. The shelf stability was obtained from the devices stored in air without encapsulation. For the MPP measurement, the MPP voltage (t = 0) was measured before MPP testing. The device was then held at the MPP voltage (t = 0) for the operation stability test. The device was un-encapsulated under AM1.5G illumination. All the devices were characterized under ambient conditions (relative humidity, >60%; ambient temperature, ~25 °C). Longer-time photostability was measured with a low-cost solar simulator from Abet Technologies. Transient photocurrent and transient photovoltage of the devices were measured with a home-made setup. This setup comprises a light-emitting diode lamp (to provide steady-state white-light bias), a 637 nm laser and an Agilent 4000X oscilloscope. The V oc values of the devices are controlled by the light intensity of the light-emitting diode lamp, and the transient voltage induced by the laser pulse are controlled within 5% of the V oc value. The time-of-flight method is used for the mobility measurements. Electron-only and hole-only devices are fabricated with the structure of ITO/SnO 2 /AgBiS 2 /Phenyl-C61-butyric acid methyl ester (PC60BM)/Ag and ITO/NiO x /AgBiS 2 /PTAA/MoO x /Ag. The thickness of the AgBiS 2 layer was controlled to ~200 nm. A 520 nm nanosecond laser was used as the excitation light. Photocurrent decay was recorded at various biases with an oscilloscope. The mobility was calculated by fitting the d 2 /t-V bias plots, where d is the thickness, t is time and V bias is the bias voltage.
Reporting Summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability
The experimental and computational data that support the current study are available in a public repository (https://doi.org/10.5281/zenodo.5733213).
Supplementary Information data are available from the corresponding author upon reasonable request.