Antimony sulfide photovoltaics with high open-circuit voltage not limited by self-trapped excitons

Abstract

Sb₂S₃ is a promising material for low-toxicity, high-stability next-generation photovoltaics, but its device performance is constrained by large open-circuit voltage (V_OC) deficits. From recent spectroscopic investigations, it was hypothesized that this arises from self-trapping, limiting V_OCs to approximately 800 mV, which is indeed the level nearly all Sb₂S₃ solar cells have asymptotically approached. Herein, it is revealed through temperature-dependent mobility measurements that band-like transport, rather than self-trapping, occurs in Sb₂S₃. By lowering the defect density in Sb₂S₃ thin films, the 800 mV threshold is surpassed to achieve a V_OC of 824 mV. This is accomplished by adding citrate ligands to the precursor solution used for chemical bath deposition, lowering the grain boundary density in Sb₂S₃ films from 1114 ± 52 nm μm⁻² to 586 ± 11 nm μm⁻². The likely performance-limiting defects in Sb₂S₃ are identified to be S vacancies or Sb on S anti-sites by comparing deep level transient spectroscopy measurements with defect calculations. This work addresses the debate in the field around whether Sb₂S₃ is limited by defects or self-trapping, showing that it is possible to improve the performance towards the radiative limit through careful defect engineering.

Antimony sulfide solar cells offer low toxicity and high stability, but efficiencies are limited by open circuit voltage. Zhou et al. find performance to not be limited by self-trapping, and that this voltage threshold can be surpassed by defect reduction through grain size increases.

Introduction

Thin film photovoltaics are important alternatives to silicon-based solar cells because of their high performance, lower materials use, compatibility with fabrication into larger-area modules, and lower levelized cost of electricity^1,2. For example, CdTe and Cu(In,Ga)(S,Se)₂ (CIGS) have achieved remarkable certified power conversion efficiencies (PCEs) of 23.1% and 23.6% at the laboratory scale, respectively³. Nevertheless, the use of toxic (i.e., Cd) and scarce (i.e., In, Ga) elements impedes their widespread deployment at the multi-terawatt level. The ongoing development of highly efficient, cost-effective, earth-abundant solar cells that have low environmental impact and carbon dioxide equivalent (CO₂eq) footprint has led to the continuous emergence of light-harvesting materials for next-generation thin film photovoltaics, including Sb₂S₃, Sb₂Se₃, SnS, GeSe, CuSbS₂, CuSbSe₂, Cu₂ZnSnS₄, Cu₂ZnSn(S,Se)₄^4–12. Antimony chalcogenides are at the forefront of emerging sustainable photovoltaic materials due to their excellent electronic and optical properties^4,7,13–16. These materials exhibit a high absorption coefficient (>10⁵cm⁻¹ in the visible range), tunable bandgap (1.1–1.7 eV), and excellent thermal and environmental stability. Additionally, the quasi-one-dimensional (quasi-1D) crystal structure that comprises numerous [Sb₄S₆]_n or [Sb₄Se₆]_n ribbons enables efficient charge-carrier transport in the out-of-plane direction if the crystal orientation of antimony chalcogenide thin films can be effectively controlled^17,18. Sb₂(S,Se)₃ solar cells have recently exceeded 10% PCE under 1-sun (i.e., AM 1.5 G) illumination, making them competitive in the emerging thin film photovoltaics field^5,7,13,19.

The binary compound semiconductor Sb₂S₃ possesses a bandgap in the range of 1.7–1.8 eV, close to the optimal value for indoor photovoltaics (IPVs) and top-cells for silicon-based tandem photovoltaics^20–22. According to the conventional Shockley–Queisser (S–Q) detailed balance limit for the single p-n junction, under standard 1-sun illumination, the theoretical device parameters achievable with a 1.70 eV bandgap light-harvester are an open-circuit voltage (V_OC) of 1.40 V, a short-circuit current density (J_SC) of 22.46 mA cm⁻², a fill factor (FF) of 91%, and a PCE of 28.64%^23,24. Here, it is worth noting that this standard detailed balance formalism assumes a step-function absorptance at the bandgap and radiative recombination only^24,25. Over the past decade, Sb₂S₃ solar cells have made notable strides in performance. However, the most efficient Sb₂S₃ solar cells reported thus far (8.32% PCE) still fall below the conventional S-Q detailed-balance limit²⁶. Like other chalcogenide light absorbers, the performance of Sb₂S₃ solar cells is primarily limited by the large V_OC deficit². At present, the highest V_OC reported so far for Sb₂S₃ solar cells is 811.5 mV, and was achieved through in-situ passivation of hydrothermal-processed absorber films²⁷; however, most Sb₂S₃ devices still show V_OCs in the range of 550–770 mV, much smaller than other photovoltaic devices based on absorbers with similar or smaller bandgaps, such as CdTe, GaAs, CIGS, InP, CH₃NH₃PbI₃ or crystalline-Si, as summarized in Fig. 1a^1,28. To date, the V_OC of 753 mV obtained in the highest-efficiency (i.e., 8.32% PCE) Sb₂S₃ device is only 53.7% of the conventional S–Q V_OC limit, suffering from a V_OC deficit greater than 600 mV^25,26. The V_OC deficit is defined as $V_{\text{OC}}^{\text{SQ}}-V_{\text{OC}}$, where $V_{\text{OC}}^{\text{SQ}}$ is the S-Q limit V_OC, evaluated using the empirical equation $V_{\text{OC}}^{\text{SQ}}=0.932\times E_{\mathrm{g}}/q-0.167$ (E_g is the bandgap of absorber; Fig. 1a)²⁹. Overcoming the V_OC bottleneck is critical to ensure that progress with Sb₂S₃ photovoltaics does not stagnate.

Fig. 1. Proposed mechanisms for factors limiting the open-circuit voltage (V_OC) of Sb₂S₃ solar cells.

a Reported V_OC values of well-developed thin film photovoltaics, as well as the most efficient antimony chalcogenides^1,28. Theoretical S–Q limit of V_OC (calculated based on step-function absorptance) as a function of bandgap (solid blue line) is highlighted. b Qualitative adiabatic potential energy curve (left) showing the self-trapping effect: photoexcitation from ground state (GS) to excited state (ES) evolves into a self-trapped exciton (STE) state from lattice distortions and loses substantial energy. Schematic (right) showing the defect-trapping effect: the photoexcited electrons and holes suffer from carrier recombination at the defect levels.

The origin of the V_OC bottleneck for Sb₂S₃ solar cells remains under debate, with two perspectives illustrated in Fig. 1b. One hypothesis, proposed by Yang et al., is the self-trapping of photogenerated charge carriers³⁰. The proposed mechanism involves excitation from the ground state (GS) to the excited state (ES), before relaxing to self-trapped exciton (STE) states due to electron-phonon coupling, leading to energy losses and reductions in the quasi-Fermi level splitting (Fig. 1b, left). This mechanism is linked to the experimental observation of linearly polarized photoluminescence (PL) that was 600 meV red-shifted compared to the optical bandgap of Sb₂S₃³⁰. These features were attributed to emission from STE states, and from this data, it was hypothesized that the maximum V_OC would be 600 mV below the radiative limit of 1.4 V for a 1.7 eV bandgap semiconductor; that is, the maximum V_OC would be only 800 mV for Sb₂S₃ if this hypothesis were true³⁰. Similar observations were made for Sb₂Se₃, where it was also proposed that self-trapping fundamentally limits the V_OC³¹. Given that self-trapping is an intrinsic process, materials engineering to lower defect densities would not allow the V_OC and efficiency to exceed the limits set by this process, thus inhibiting future progress with these materials. Indeed, a V_OC of 800 mV is the value most Sb₂S₃ photovoltaics have asymptotically approached over the past decade of efforts made with this material (Supplementary Table 1). In contrast to this hypothesis, first-principles analysis of electron-lattice interactions and charge-carrier mobility suggests that the low effective masses in Sb₂S₃ lead to band-like transport in these materials, and the key limiting factor for V_OC is defect-mediated rather than self-trapping³². A deep level residing in the semiconductor bandgap between the conduction band (CB) and valence band (VB) provides an intermediate state to accelerate the carrier recombination process, where excess energy is dissipated as phonons (Fig. 1b, right). Several experimental studies have linked the high V_OC deficit in Sb₂S₃ solar cells to a complex set of defects with deep levels^29,33,34. For example, we previously showed that lowering the defect density in Sb₂S₃ by reducing the grain boundary (GB) density results in an increase in device performance, including improvements in V_OC¹⁴. Moreover, the justification for self-trapping and V_OC loss hypothesized by Yang et al. was based on the observed large red-shift in PL compared to the optical bandgap; however, through a careful literature analysis based on reliable reports of PL from Sb₂S₃ prepared by a variety of processing methods, the red-shift of PL for Sb₂S₃ was found to be only 0–0.1 eV in nearly all other reports (Supplementary Table 2). This further motivates the re-examination of this self-trapping hypothesis in detail. Therefore, in-depth investigations combining theory and experiments are needed to resolve this debate to understand whether Sb₂S₃ is fundamentally limited in performance, or has hope still of further improvements towards the radiative limit.

In this work, we developed Sb₂S₃ solar cells with V_OC exceeding the 800 mV threshold by using a complexing agent-mediated chemical bath deposition (CBD) method, which enables the deposition of high-quality Sb₂S₃ thin films with GB density approximately halved. The reduced impact of defects for Sb₂S₃ films, confirmed by deep-level transient spectroscopy (DLTS) characterization and first-principles calculations, is revealed to contribute to the smaller V_OC deficit. The obtained V_OC of 824 mV is the current record for antimony chalcogenide solar cells. Computations further indicate that the V_OC of Sb₂S₃ solar cells can exceed 800 mV by mitigating the effects of the main killer defects in this material, which we found to be sulfur vacancies and antimony on sulfur anti-sites. This work reveals that defect-mediated recombination is a key limitation to the device V_OC and PCE, and the low performance of Sb₂S₃ photovoltaics is surmountable through defect engineering to reach towards the radiative limit.

Results

Device performance of planar Sb2S3 solar cells

In this work, a modified CBD method was explored to deposit large-grained Sb₂S₃ absorber films. It is known that additive engineering in CBD solutions by incorporating reasonable complexing agents is an effective strategy to regulate the film properties (including surface morphology, GB density, defect density, and carrier concentration) via the facile modulation of in-situ chemical environment for film deposition^23,35. Here, antimony potassium tartrate (C₄H₄KO₇Sb·0.5H₂O, APT) and sodium thiosulfate (Na₂S₂O₃·5H₂O, STS) were employed as the Sb and S sources, respectively, and a small amount of sodium citrate (SC) was used as a complexing additive in the precursor solution to manipulate the nucleation and growth kinetics of Sb₂S₃ films. An interpretation of the deposition mechanism for CBD in the presence of SC is detailed in Supplementary Note 1. For convenience, the Sb₂S₃ samples obtained with the SC concentrations of 1 mM, 2 mM, 4 mM, and 8 mM in the precursor solutions are labeled as 1mM-SC, 2mM-SC, 4mM-SC, and 8mM-SC, respectively. The planar n-i-p device configuration used is FTO/SnO₂/CdS/Sb₂S₃/Spiro-OMeTAD/Au (Fig. 2a). Here, Sb₂S₃ is the absorber, and SnO₂/CdS and Spiro-OMeTAD act as the electron transport layer (ETL) and hole transport layer (HTL), respectively. The fabrication processes of Sb₂S₃ solar cells are illustrated in Supplementary Fig. 1 and detailed in Methods. The photovoltaic parameters of Sb₂S₃ solar cells, each based on 12 cells, including V_OC, J_SC, FF, and PCE, achieved under 1-sun illumination (AM1.5 G, 100 mW cm⁻²), are summarized in the box plots of Fig. 2b, c and Table 1. Here, all devices were obtained with 8 h of CBD of the Sb₂S₃ films. As shown, these devices exhibit excellent performance and repeatability. The device PCE increases at first and then decreases with the increase of the SC concentration in the CBD precursor solution. The control Sb₂S₃ devices obtained without the use of SC deliver an average PCE of 6.23%, whereas the average PCE is increased to 7.46% for the 4mM-SC devices. The current density–voltage (J-V) curves of the best-performing control and 4mM-SC Sb₂S₃ solar cells are given in Fig. 2d. The control device yields a V_OC of 787 mV and a PCE of 6.42%; the 4mM-SC device affords a V_OC of 817 mV and a PCE of 7.67%, with a champion V_OC of 824 mV (Table 1). That is, the incorporation of 4 mM SC leads to the relative PCE increasing by nearly 20% compared to the control device. The external quantum efficiency (EQE) spectra of the control and 4mM-SC solar cells, as given in Fig. 2e, reveal that both devices present broad light responses ranging from 350 to 750 nm wavelength. Compared to the control device, the 4mM-SC device exhibits enhanced EQE, exceeding 90% at around 530 nm wavelength. The integrated J_SC obtained from the EQE spectra are 14.95 and 16.13 mA cm⁻² for the control and 4mM-SC devices, respectively, consistent with the J_SC measured from J–V curves (within 5% deviation). Figure 2f summarizes the V_OC evolution of well-developed planar and sensitized Sb₂S₃ solar cells (detailed in Supplementary Table 1). As shown, the V_OC has progressively improved over the past decade, especially for the planar configuration, but has increased slowly, in contrast to the rapid increase in PCE. To the best of our knowledge, the champion V_OC of 824 mV obtained for the 4mM-SC device is the highest value reported for Sb₂S₃ solar cells. Interestingly, this V_OC value is beyond the threshold predicted for Sb₂S₃ if it had self-trapping³⁰. We also found that CBD-processed Sb₂S₃ photovoltaics exhibited excellent environmental stability. The unencapsulated 4mM-SC Sb₂S₃ solar cell retained 97.4% of its initial efficiency after 30 days of storage in the dark under ambient temperature in a cabinet with 15% relative humidity (Supplementary Fig. 2).

Fig. 2. Photovoltaic performance of planar Sb₂S₃ thin film solar cells.

a Schematic of the planar FTO/SnO₂/CdS/Sb₂S₃/Spiro-OMeTAD/Au device stack used in this work. b, c Distribution of the performance parameters of Sb₂S₃ solar cells obtained without (i.e., control) and with the addition of different concentrations of sodium citrate (SC) additives to the precursor solution. Twelve devices were measured for each type of device, and the performance metrics of each device are shown as individual data points. The statistical distributions for the PCE, V_OC, J_SC, and FF were obtained from 12 devices, and the lower whisker, lower box edge, middle line, upper box edge, and upper whisker refer to the minimum, 25th percentile, median, 75th percentile, and maximum of the dataset, respectively. d Current density–voltage (J–V) curves of best-performing control and 4mM-SC Sb₂S₃ solar cells, measured under 1-sun (AM 1.5 G, 100 mW cm⁻²) illumination. e External quantum efficiency (EQE) spectra of control and 4mM-SC Sb₂S₃ solar cells. f Evolution in the record V_OC values of planar and sensitized Sb₂S₃ solar cells.

Table 1.

Photovoltaic parameters of the control and SC-Sb₂S₃ solar cells

Device	VOC (mV)	JSC (mA cm⁻2)	FF (%)	PCE (%)
Control	782 ± 8 (795)	14.87 ± 0.20 (15.15)	53.60 ± 0.42 (53.90)	6.23 ± 0.11 (6.42)
1mM-SC	791 ± 10 (806)	15.40 ± 0.21 (15.76)	55.02 ± 0.90 (56.58)	6.70 ± 0.15(6.98)
2mM-SC	797 ± 8 (807)	15.69 ± 0.45 (16.23)	55.85 ± 0.86 (56.75)	6.98 ± 0.21 (7.29)
4mM-SC	814 ± 8 (824)	16.18 ± 0.15 (16.44)	56.68 ± 0.67 (57.70)	7.46 ± 0.12 (7.67)
8mM-SC	799 ± 3 (803)	14.65 ± 0.31 (15.26)	56.60 ± 0.67 (56.99)	6.62 ± 0.19 (6.93)

Devices measured under 1-sun (AM 1.5 G, 100 mW cm⁻²) illumination. Format: average ± standard deviation (best value).

Moreover, it is known that the bandgap of Sb₂S₃ is ideal for IPVs³⁵. Thus, we further measured the IPV performance of Sb₂S₃ solar cells under illumination from white light-emitting diodes (WLEDs) with a correlated color temperature (CCT) of 3000 K. Details of the spectral irradiance, temporal stability of the light source, and IPV performance for the 4 mM-SC device are shown in Supplementary Figs. 3 and 4, along with Supplementary Table 3. The J_SC is approximately linearly proportional to the light intensity, while the V_OC and FF increase approximately logarithmically with irradiance. As a result, the highest Sb₂S₃ IPV efficiency is under 1000 lux, with a state-of-the-art indoor PCE of 18.56%. This exceeds our previous report of Sb₂S₃ IPVs (17.55% indoor PCE), and is comparable to the current state-of-the-art for not just Sb₂S₃, but also other Sb- and Bi-based solar absorbers for IPV^35–37. The loss in V_OC from 1000 lux to 200 lux in the 4 mM-SC IPVs is 61 mV, which is a small reduction compared to other established and emerging IPVs³⁸.

Characterization of CBD-processed Sb₂S₃ films

Figure 3a, b shows top-view scanning electron microscopy (SEM) images of Sb₂S₃ thin films prepared without the SC additive (i.e., the control sample) and with 4 mM SC in the precursor solution, respectively. It can be seen that the control Sb₂S₃ film sample displays grain sizes smaller than 3 μm based on the long diameters of polygon-shaped grains, consistent with that reported for CBD-processed Sb₂S₃ films in the literature⁴. With the addition of 4 mM SC, the grain size of Sb₂S₃ films involves an obvious increase, with many Sb₂S₃ grains exceeding 5 μm. Top-view SEM images of Sb₂S₃ films prepared with the use of other SC concentrations are provided in Supplementary Fig. 5. The increase in grain size is accompanied by a decrease in GB density, which is defined as the GB length per unit area. Figure 3c gives the dependence of GB density on the SC concentration for different Sb₂S₃ films. As shown, the GB density on the surface of Sb₂S₃ films decreases from 1114 ± 52 nm μm⁻² for the control sample to 666 ± 17, 641 ± 16, 586 ± 11, and 901 ± 31 nm μm⁻² for 1mM-SC, 2mM-SC, 4mM-SC, and 8mM-SC film samples, respectively.

Fig. 3. Morphological properties of highly crystalline Sb₂S₃ thin films.

a, b Top-view scanning electron microscopy (SEM) images of Sb₂S₃ films prepared without (i.e., control) and with the addition of 4 mM SC. The GBs are highlighted to clearly show the changes in GB density. Scale bar, 5 µm. c Change in GB density with SC concentration in the precursor solution. Three samples were used to determine the mean GB density values shown, and the error bars denote the standard deviation. d Cross-sectional transmission electron microscopy (TEM) image of 4mM-SC Sb₂S₃ sample deposited on FTO/SnO₂/CdS substrate. Scale bar, 100 nm. e, f High-resolution TEM images performed at points A1, A2, and A3 (see part D), and corresponding fast Fourier transform (FFT) patterns. Scale bar, 5 nm⁻¹.

To further confirm the single-crystalline nature of individual Sb₂S₃ grains observed from SEM images, we performed characterization based on the Sb₂S₃ lamella sample (4mM-SC film) prepared by focused ion beam (FIB). The cross-sectional transmission electron microscopy (TEM) image (Fig. 3d) indicates that the Sb₂S₃ sample is compact and composed of large grains spanning the thickness of the Sb₂S₃ film. Figure 3e shows the high-resolution TEM (HRTEM) images of three arbitrarily selected points A1, A2, and A3, as labeled in Fig. 3d. As shown, points A1, A2, and A3 share identical crystallographic orientations, revealing that the crystal planes extend from the top to the bottom of the Sb₂S₃ film. Lattice fringes with interplanar spacings of 1.125 nm, corresponding to the (100) plane in orthorhombic Sb₂S₃, were identified¹⁴. The nearly identical fast Fourier transform (FFT) patterns of HRTEM images of points A1, A2, and A3 (Fig. 3f) further confirm that the individual microstructural units bounded by GBs are indeed single crystals. The cross-sectional elemental mapping images (Supplementary Fig. 6) indicate the uniform distribution of Sb and S across the absorber layer and the conformal growth of Sb₂S₃ on top of the CdS buffer layer. The HRTEM image at the CdS/Sb₂S₃ interface (Supplementary Fig. 7) reveals the lattice fringes assigned to Sb₂S₃ and CdS¹⁴. The results confirmed that Sb₂S₃ films with large single-crystalline grains could be easily produced via CBD.

X-ray diffraction (XRD) patterns of Sb₂S₃ films (Supplementary Fig. 8a) show that the diffraction peaks can be well indexed to orthorhombic Sb₂S₃ (JCPDS #42-1393)²³. The diffraction peaks of Sb₂S₃ films reveal negligible shifts with the use of SC, indicating that the SC additive could not be incorporated into the Sb₂S₃ lattice or interstitial sites. We further calculated the texture coefficient (TC) of the dominant (hk0) and (hk1) planes to quantify the degree of preferred orientation of Sb₂S₃ films (Supplementary Fig. 8b). The addition of SC does not cause significant changes to the film orientation. Additionally, compared to the control film, the SC-Sb₂S₃ films involve a gradual reduction in the dominant diffraction peak intensities, such as (120), (130), (211), (221), with the increase in the SC concentration. This should be closely associated with the decrease in the film thickness, as reflected in the cross-sectional SEM images of Sb₂S₃ films (Supplementary Fig. 9). As shown, the film thickness gradually decreases from 506 ± 26 nm for the control sample to 394 ± 10 nm, 347 ± 28 nm, 318 ± 15 nm, and 116 ± 32 nm for 1mM-SC, 2mM-SC, 4mM-SC, and 8mM-SC samples, respectively.

Atomic force microscopy (AFM) maps of the morphology of the Sb₂S₃ films (Supplementary Fig. 10) confirm that the 4mM-SC film shows larger grain sizes with fewer GBs than the control. Furthermore, the addition of SC leads to a reduction in the root-mean-square roughness from 21.9 nm (control sample) to 16.3 nm (4mM-SC sample). Conductive-atomic force microscopy (c-AFM) images, with the corresponding morphology and current maps (Supplementary Fig. 11) reveal that, compared to the control sample, the 4mM-SC films have more uniform electrical conductivity over the 5 × 5 μm² area measured. We further performed Kelvin probe force microscopy (KPFM) to map the surface potential of Sb₂S₃ films (Supplementary Fig. 12), which reveals a higher surface potential for the 4mM-SC film in contrast to the control sample. Given that an increase in the surface potential corresponds to a reduced work function (WF) (i.e., Fermi level closer to vacuum level), the smaller WF for the 4mM-SC sample implies an upshift of its Fermi level^39,40. This is consistent with the band structure of Sb₂S₃ solar cells, obtained from ultraviolet photoelectron spectroscopy (UPS) spectra (Supplementary Fig. 13) and absorption spectra (Supplementary Fig. 14). Compared to the control Sb₂S₃ film, the Fermi level of SC-Sb₂S₃ is shifted up towards the CB, indicating an increase in the electron carrier concentration for n-type Sb₂S₃.

We further investigate the underlying mechanism that could explain the impact of the SC complexing agent on Sb₂S₃ film properties. For the CBD of Sb₂S₃ films, the substrate is exposed to soluble precursors, which react or decompose to form the desired film materials⁴¹. From the perspective of nucleation and growth, an intricate balance of growth parameters is necessary to achieve high-quality films. The formation of Sb₂S₃ grains typically involves nucleation and growth, which are greatly influenced by the chemical environment of precursor solutions^42–44. We measured the contact angles of the substrate treated by precursor solutions with different SC concentrations and further analyzed the ratio of the free energies of homogeneous and heterogeneous nucleation as a function of the contact angle (Supplementary Fig. 15a, b, detailed in Supplementary Note 1). The results demonstrate that the incorporation of SC would promote the heterogeneous nucleation of Sb₂S₃ on the substrate. Our proposed mechanism is schematically illustrated in Supplementary Fig. 15c. We suggest that adding SC changes the growth mode of Sb₂S₃ films from cluster deposition to ion-by-ion deposition. For the pristine CBD solution without the use of SC, the strong complexation effect of APT would cause the formation of many aggregates in the precursor, which serve as homogeneous nucleation centers for Sb₂S₃⁴⁵. These small clusters created within the solution further migrate and adhere onto the substrate surface, resulting in the deposition of Sb₂S₃ films in the cluster mechanism. For the ion-by-ion deposition mechanism, the complexing agent enables the slow release of free metal ions to directly react with anions onto the substrate in a more controlled manner, being capable of forming well-textured crystalline or even monocrystalline films⁴¹. Ion-by-ion deposition therefore promotes heterogeneous nucleation on the substrate and suppresses homogeneous nucleation in the precursor solution, similar to the scenario demonstrated for the CBD of other metal chalcogenide thin films, such as ZnS⁴⁶. High-density small nuclei formed on the substrate would further coalesce into a large-grained Sb₂S₃ film during the CBD process. Hence, the formation of stable citrate-complexed Sb³⁺ succeeds in controlling the nucleation and growth rate of Sb₂S₃, contributing to the deposition of large-grained Sb₂S₃ films. In fact, previous studies also demonstrated that films grown by ion-by-ion deposition are usually associated with larger crystalline size compared to those grown by cluster deposition⁴¹. In addition, the decrease in the release rate of Sb³⁺ further reduces the film thickness, explaining the thickness evolution of Sb₂S₃ films with the addition of SC. Apart from the complexation of citrate, we speculate that pH might be another critical factor influencing the deposition of Sb₂S₃ films. The influence of pH on the deposition of Sb₂S₃ films is further discussed in Supplementary Note 2. It is revealed that, besides the complexation of Sb³⁺ with citrate, an increase in pH should also contribute to a reduction in the deposition rate. However, controlling pH alone does not lead to increases in PCE as high as with the addition of SC (Supplementary Fig. 16). Furthermore, since the incorporation of SC leads to a change in Sb₂S₃ film thickness, we also investigated how the performance of Sb₂S₃ solar cells depends on absorber thickness (Supplementary Fig. 17). We found that the optimal device PCE of the control sample was still lower than that of the SC-Sb₂S₃ samples, confirming that the change in film thickness caused by the use of SC is not the dominant contributor to the efficiency enhancements obtained here. These results imply that the increase in PCE for SC-Sb₂S₃ solar cells is mainly associated with the complexation of Sb³⁺ with citrate, which lowers the GB density and reduces the surface roughness of Sb₂S₃ absorber films.

Experimental and theoretical insights into the defect physics of Sb₂S₃

Understanding the nature of active defects in Sb₂S₃ is necessary to design strategies to minimize their impact. DLTS is a powerful technique offering insights into the trap energy, defect type and defect concentration in thin film solar cells^47–50. DLTS utilizes the transient capacitance of a p-n junction at varying temperatures as a probe to reflect the changes in the charge state of a deep defect center. The traps within the device are filled with carriers by applying a voltage pulse, which in turn alters the capacitance associated with the p-n junction. Figure 4a, b illustrates the mechanism of DLTS measurements. Here, we take the minority traps (i.e., electron traps in p-type semiconductors) as an example to show the change of transient capacitance caused by electron capture and emission. For a p-n junction, when a constant reverse bias (U_R) is applied, a stable space charge region (SCR) is established, corresponding to a stable capacitance (C_R). If an extremely short fill voltage pulse (U_P) is applied as a perturbation, the SCR width and capacitance change due to the injection of majority carriers into the SCR, causing the traps to be filled during this process. Once the voltage pulse is removed, the SCR and capacitance cannot immediately recover to their original state. This delayed recovery occurs because the trapped carriers are emitted to the CB or VB at a specific rate, rather than instantaneously. The capacitance changes (ΔC = C_t2 – C_t1) within a time window (t₂ – t₁) vs. the different temperatures (T) are sampled as the DLTS signals. In particular, the trap type is determined by the ΔC. If ΔC < 0 and the DLTS signal peaks are negative, they correspond to the minority-carrier traps; otherwise, they would be associated with majority-carrier traps^50–52. The basic principles of DLTS are detailed in Supplementary Note 3.

Fig. 4. DLTS characterization of defect physics in Sb₂S₃ solar cells.

a Schematic illustration of the mechanism of DLTS measurements. Here, we take the minority traps (i.e., electron traps in p-type semiconductors) as an example to illustrate the change of transient capacitance caused by electron capture and emission. b Variation of the depletion width and the process of carriers being trapped and emitted during the measurement. c DLTS signals from the control and 4mM-SC Sb₂S₃ solar cells. d Arrhenius plots derived from DLTS signals. Data points are achieved by calculating internal transients included in DLTS signals with the discrete Laplace transform, and the solid lines are corresponding linear fits. e, f Schematic of band edge positions and defect levels of the control and 4mM-SC Sb₂S₃, respectively, including conduction band minimum (E_C) and valence band maximum (E_V), Fermi level (E_F) and defect levels (H1, H2), relative to the vacuum level.

As shown in Fig. 4c, the control device and 4mM-device both present two negative DLTS signal peaks in the high-temperature region, denoted as H1 and H2, due to the effect of multiple minority-carrier traps, i.e., hole defects in n-type Sb₂S₃ films⁶. The defect characteristic parameters, including trap energy (E_T) and capture cross-section (σ), and trap concentration (N_T), can be extracted from the linear fittings of the Arrhenius plots as given in Fig. 4d, with the results summarized in Table 2. Both devices share similar types of deep levels with densities of approximately 10¹⁵cm⁻³. The trapping behavior can be quantified by using the thermal trapping rate (C_trap), expressed by $C_{\text{trap}}=1/{\tau }_{\text{trap}}=v\sigma N_{\mathrm{T}}$⁴⁹, where τ_trap is the carrier lifetime associated with the trap-assisted Shockley–Read–Hall (SRH) recombination, which is inversely proportional to σ ∙ N_T, and v is the thermal velocity of charge related to the intrinsic charge transport feature of semiconductors. The values of σ ∙ N_T for the control and 4mM-SC devices are summarized in Table 2. Compared to H1, H2 dominates the charge trapping in absorber films with a larger σ ∙ N_T value and greater energy depth. Compared to the control device, the σ ∙ N_T value for the H2 defect in 4mM-SC Sb₂S₃ is decreased. The band edge position and defect levels are illustrated in Fig. 4e, f, with the hole traps situated 0.4–0.7 eV above the valence band maximum (VBM). Since the trap energy reflects the difficulty of charge emission from the traps, the H1 and H2 defects located at more than 0.3 eV above the VBM would trap carriers without re-emission and act as recombination centers due to their high ionization energy, contributing to severe non-radiative recombination. In particular, the deep-level defects would cause a fluctuation in the bandgap and bring band tail states within the bandgap, giving rise to a further V_OC loss. Hence, the 4mM-SC Sb₂S₃ film with reduced defect density is suggested to effectively suppress charge-carrier recombination in solar cells.

Table 2.

Defect characteristic parameters

Devices	Trap	ET (eV)	σ (cm2)	NT (cm−3)	σ ∙ NT (cm−1)
Control	H1	EV + 0.487	4.43 × 10−17	2.42 × 1015	0.107
	H2	EV + 0.643	7.35 × 10−16	1.39 × 1015	1.020
4mM-SC	H1	EV + 0.483	2.08 × 10−17	9.14 × 1014	0.019
	H2	EV + 0.635	6.62 × 10−16	1.03 × 1015	0.682

These parameters are the trap energy level (E_T), capture cross-section (σ), and concentration (N_T), obtained using DLTS measurements in the control and 4mM-SC Sb₂S₃ solar cells.

To identify the defect species, we performed first-principles calculations combined with a global searching strategy, implemented in the doped⁵³ and ShakeNBreak packages⁵⁴, to systematically explore all symmetry-inequivalent configurations of intrinsic point defects in Sb₂S₃. It is known that quasi-1D Sb₂S₃ consists of [Sb₄S₆]_n chains which have five nonequivalent atomic sites, i.e., Sb(1), Sb(2), S(1), S(2) and S(3), as illustrated in Fig. 5a. First principles calculations have shown that Sb₂S₃ involves intricate defect types, including five vacancies (V_Sb(1), V_Sb(2), V_S(1), V_S(2) and V_S(3)), five anti-sites (S_Sb(1), S_Sb(2), Sb_S(1), Sb_S(2) and Sb_S(3)), and twelve interstitials. The interstitials were identified using the Voronoi scheme⁵⁵, despite the material being comprised of only two elemental components^56–58. Our calculation details are provided in Ref. ⁵⁶ and Methods. The equilibrium defect concentrations as a function of the Sb/S chemical potential are shown in Fig. 5b. Under Sb-rich conditions (i.e., synthesis conditions for control and 4mM-SC Sb₂S₃ devices), Sb_S, V_S, and V_Sb are the most dominant point defects with concentrations higher than 10¹⁴cm⁻³. The corresponding defect levels are shown in Fig. 5c and summarized in Supplementary Table 4. Except for V_Sb(2), most of these defects have traps that match those observed experimentally via DLTS (as indicated by the dashed gray lines). This highlights the challenges in identifying specific defects based solely on defect concentrations or energy levels in Sb₂S₃. Moreover, our global search reveals that all intrinsic point defects in Sb₂S₃ are amphoteric, exhibiting both donor- and acceptor-like charge states. Therefore, directly comparing experimental defect levels with simulations under the assumption that each defect acts exclusively as a donor or an acceptor may be misleading⁵⁷, since amphoteric defects introduce additional possibilities for matching the measured levels.

Fig. 5. First-principles calculations to identify defect species.

a Illustration of a [Sb₄S₆]_n unit in the Sb₂S₃ crystal structure. b Calculated equilibrium defect concentration at 300 K in Sb₂S₃ crystals grown at 643 K as a function of growth conditions based on the defect energies reported in ref. ⁵⁶. The numbers in the legend represent different inequivalent sites. c Calculated charge transition levels of intrinsic point defects with high concentrations under Sb-rich conditions in Sb₂S₃. Metastable charge states are marked with asterisks (*). The Fermi level is referenced to the valence band maximum (VBM). Dashed gray lines indicate trap levels in control and 4mM-SC Sb₂S₃ devices, determined by DLTS. d, e 1D configuration coordinate diagram for charge transitions between V_S(3)⁺ and V_S(3)⁰ as well as Sb_S(2)⁰ and Sb_S(2)⁻. Q represents the generalized configuration coordinate, which describes the collective atomic displacement along the reaction pathway during charge transition. The equilibrium structures of V_S(3)⁺ and Sb_S(2)⁰ are set as references with Q = 0 amu^1/2 Å and total energy E = 0 eV. Solid circles are data points obtained by DFT calculations and used for fitting, while hollow circles are discarded for fitting due to charge delocalization. Solid lines represent best fits to the data.

While defect formation energies and defect levels calculated from simulations provide insights into the thermodynamic stability, they do not directly account for kinetic factors, such as carrier capture processes under real device conditions. Experimental techniques are sensitive to defects that actively capture charge-carriers. To identify the most relevant defects, we first selected those with defect levels and equilibrium concentrations close to the experimental values (Supplementary Table 5), then investigated the potential energy surfaces associated with charge transition processes. Capture cross-sections were then calculated for each transition using configuration coordinate (CC) diagrams⁵⁶. The magnitude of the cross-sections was used to determine whether each defect predominantly behaves as an electron or a hole trap. Based on the combined information from defect levels, concentrations, and capture cross-sections, we suggest V_S(3) and Sb_S(2) as the defects that are most consistent with the experimental observations, with calculated trap levels located at 0.59 and 0.61 eV above the VBM and calculated capture cross-sections of 3.77 × 10⁻¹⁶ and 4.00 × 10⁻¹⁷ cm⁻², respectively. These calculated levels are closest to the experimentally observed H2 levels, differing by approximately 0.05 eV for V_S(3) and 0.03 eV for Sb_S(2). Their differences from the H1 levels are larger but remain on the order of 0.1 eV. We note that the calculated transition levels are the thermodynamically stable states at absolute zero temperature, whereas DLTS extracts activation energies from finite temperature carrier emission processes. The small differences between the calculated and experimental trap levels on the order of 0.1 eV or less are consistent with the typical uncertainty in comparing state-of-the-art hybrid functional defect calculations with experimental defect levels^59,60. We do, however, acknowledge that these deviations prevent us from unambiguously assigning the experimental H1 and H2 levels to V_S(3) and Sb_S(2). Regardless, this does not affect the conclusion that V_S(3) and Sb_S(2) are deep hole traps with efficient non-radiative capture.

The CC diagrams for V_S(3) and Sb_S(2) are shown in Fig. 5d, e. A larger displacement along the generalized coordinate Q corresponds to stronger lattice relaxation during the charge transition process. For both defects, the energy barriers for hole capture are very small, and the corresponding phonon wavefunctions of the initial and final states exhibit large overlap. A small capture barrier combined with large phonon overlap greatly enhances the transition probability, leading to large hole capture cross-sections on the order of 10⁻¹⁶ ~ 10⁻¹⁷ cm².

We also evaluated the Franck-Condon relaxation energies and defect transition Stokes shifts for these hole capture processes from the CC diagrams (Supplementary Fig. 18, Supplementary Tables 6 and 7, detailed in Supplementary Note 4). The calculated Stokes shifts are 1.26 eV for V_S(3) and 0.68 eV for Sb_S(2), consistent with large lattice relaxation. Together with the large capture cross-sections, these large Stokes shifts suggest efficient non-radiative multiphonon capture, so any radiative signatures from these deep defect transitions would likely be weak or masked rather than directly observable as PL red-shifts. That is, we would not expect these two point defects to contribute substantially to the PL observed from Sb₂S₃ thin films.

Based on the most-probable limiting defects identified (V_S(3) and Sb_S(2)), and their measured trap densities and capture cross-sections, we predicted the trap-limited V_OC accounting for both radiative (band-to-band) and defect-mediated non-radiative recombination processes (Supplementary Note 5 and Supplementary Fig. 19). It is worth noting that, within the conventional S-Q detailed balance framework, a material-specific radiative reference based on the finite-thickness absorptance of Sb₂S₃ is used for the trap-limited V_OC analysis. The predicted V_OC reaches 1.15 V for the control sample and 1.26 V for the 4mM-SC sample, both exceeding the 0.8 V threshold. The predicted improvement in performance and V_OC by lowering trap density for the 4 mM-SC sample is qualitatively consistent with the improvement observed experimentally. At the same time, these predictions show that other loss processes are present, beyond non-radiative losses from V_S(3) and Sb_S(2).

Charge-carrier transport properties and device physics

To verify the formation of delocalized large polarons instead of small polarons in Sb₂S₃, we determined the temperature dependence of the mobility through time-of-flight (TOF) measurements⁶¹. It is known that large polarons show a reduction in the overall mobility with increasing temperature because of increased phonon scattering. On the other hand, if small polarons dominate charge-carrier transport, the mobility should increase as the temperature increases because small polaron formation changes the transport mechanism to hopping-based. The device structure for TOF measurements was FTO/Sb₂S₃/Au, and the measurement details can be found in Methods. Note that CBD was unable to grow compact films directly on the FTO substrates, and so we used close-spaced sublimation (CSS) to form continuous thin films that avoid shunting; we would not expect any differences in the trends in mobility with temperature for CBD vs. CSS-grown Sb₂S₃. Figure 6a shows the obtained mobilities of Sb₂S₃ at different temperatures ranging from 100 to 400 K based on the bilogarithmic plots of transient current vs. transit time (Supplementary Fig. 20). The observation of an obvious decrease in mobility with an increase in temperature is consistent with the behavior of large polarons. The obtained mobilities are surprisingly as low as 10⁻⁵–10⁻⁶ cm² V⁻¹ s⁻¹. Previous studies also demonstrated very low mobilities with similar magnitudes, such as 4.9 × 10⁻⁵ cm² V⁻¹ s⁻¹ based on defect-resolved mobility measurements⁶², 2.2 × 10⁻⁵ cm² V⁻¹ s⁻¹ based on space-charge-limited current (SCLC)⁶³, 3 × 10⁻³ cm² V⁻¹ s⁻¹ based on time-resolved microwave conductivity (TRMC) measurements⁶⁴. By fitting a power law model to the mobility data, the exponent was found to be −1.01 ± 0.08. However, this exponent does not straightforwardly imply any particular scattering mechanism⁶⁵.

Fig. 6. Charge-carrier transport properties and device physics.

a Temperature-dependent mobility of Sb₂S₃ films determined using time of flight (TOF) measurements, fitted with a power law model that indicates $\mu \propto T^{-1.01\pm 0.08}$. Here, ±0.08 is the uncertainty of the exponent obtained by fitting the data across all temperatures. b, c Photoinduced absorption (PIA) kinetics (scatter) measurements monitored at 560 nm from transient absorption (TA) spectroscopy, along with phenomenological biexponential curve fits (solid line) for the TA spectra of the control and 4mM-SC Sb₂S₃ films. Excitation was with a 400 nm wavelength pulsed laser at a repetition rate of 1000 Hz. ΔA is defined as the change in the absorption of the sample before and after pumping. d Space-charge-limited current density (SCLC) measurements of the control and 4mM-SC devices based on the electron-only device, with the configuration: FTO/SnO₂/CdS/Sb₂S₃/PCBM/Au. Here, both devices share thickness-matched absorber films of 318 ± 15 nm to exclude the influence of film thickness on the electrical properties. e, f Dependences of V_OC and J_SC on the light intensity for the control and 4mM-SC Sb₂S₃ solar cells.

Ultrafast transient absorption (TA) spectroscopy analysis was further performed to understand the charge-carrier kinetics of FTO/SnO₂/CdS/Sb₂S₃ films, where we focused on CBD-grown Sb₂S₃, in order to be consistent with our device measurements, and because Sb₂S₃ grown by CBD forms continuous films on CdS. The TA spectra of both the control sample and the 4mM-SC sample (Supplementary Fig. 21a, b) display distinct negative differential absorbance (ground state bleach (GSB) peaks), as well as regions of positive differential absorbance (photoinduced absorption (PIA) peaks). The GSB peaks observed at the wavelengths of 460–520 nm and 610–680 nm can be ascribed to the state filling of CdS and the GS absorption of Sb₂S₃, respectively. The PIA peaks centered at 520 to 610 nm wavelength can be assigned to the formation of sulfide radicals (${\mathrm{S}}^{-\mathrm{\bullet }}$) as a result of the localization of photogenerated holes on the S atom within the Sb₂S₃ lattice^6,14,66. The transient kinetic decays monitored at 560 nm for both the control and 4mM-SC films can be extracted from the pseudocolor images for the TA spectra of both samples (Supplementary Fig. 21c, d), as presented in Fig. 6b, c. The transient dynamics are fit well with a phenomenological biexponential model in order to quantitatively compare between samples. The gradual decrease of the PIA peak can be attributed to the decay of trapped holes, i.e., the ${\mathrm{S}}^{-\mathrm{\bullet }}$ species, which we here attribute to non-radiative charge-carrier recombination in Sb₂S₃. The 4mM-SC sample delivers higher average time constant (τ_avg) values (14.36 ns) compared to the control sample (12.69 ns). Such lifetime values lie within the range of 4–60 ns that are commonly reported for antimony chalcogenides³³. In general, the charge-carrier lifetime of the absorber material is inversely related to the reverse-bias saturation current density (J₀) of the device. Hence, a long carrier lifetime is the prerequisite for achieving high V_OC of solar cells.

We further investigated the device physics of Sb₂S₃ solar cells to fully understand the underlying mechanism of the performance enhancements we obtained. The SCLC measurements of the dark currents from the electron-only devices (FTO/SnO₂/CdS/Sb₂S₃/PCBM/Au) are given in Fig. 6d. In the low-voltage Ohmic region, the curve is generally linear. When the voltage exceeds the trap-filling limit, the current increases substantially, implying that the injected carriers have completely occupied the trap states²⁶. The trap-filled limiting voltage (V_TFL) values for the control and 4mM-SC device are estimated to be 0.464 V and 0.287 V, respectively. The trap state density (n_τ) of Sb₂S₃ films can be evaluated according to the equation $V_{\text{TFL}}=q{n}_{\mathrm{\tau }}{L}^2/2{\epsilon }_{\mathrm{r}}{\epsilon }_0$, where q is the elementary charge, $n_{\mathrm{\tau }}$ is the trap state density, L is the thickness of the absorber film (here the control and 4mM-SC devices share thickness-matched absorber films of 318 nm), ${\epsilon }_0$ is the vacuum permittivity (8.85 × 10⁻¹² F m⁻¹), and ${\epsilon }_{\mathrm{r}}$ is the relative permittivity of Sb₂S₃ (6.67 for the static dielectric constant)⁶⁷. As a result, the trap state densities for the control and 4mM-SC devices are estimated to be 3.39 × 10¹⁵cm⁻³ and 2.12 × 10¹⁵cm⁻³, respectively. The overall reduction in trap state density for the 4mM-SC Sb₂S₃ sample is consistent with the reduction in GB density, and the order of magnitude of the trap density is consistent with DLTS measurements. Here, it is worth noting that the reduced trap density in absorber films could arise from lower GB density caused by the incorporation of SC additives, or could be due to lower bulk trap density as a result of improved growth conditions.

The dependencies of V_OC and J_SC on the light intensity for both solar cells were determined to further understand trap-assisted charge recombination loss mechanisms, as shown in Fig. 6e, f. The relationship between V_OC (and J_SC) and the light intensity I can be described by $V_{\text{OC}}\propto \left(n{k}_{\mathrm{B}}T/q\right)\ln \left(I\right)$ and $J_{\text{SC}}\propto I^{\alpha }$, where k_B is the Boltzmann constant, T is the absolute temperature, q is the elementary charge, and α and n reflect the level of charge-carrier recombination^68–70. Under open-circuit, all photogenerated charge-carriers recombine. For ideal trap-free solar cells, the slope of V_OC versus ln(I) is k_BT/q. The slopes for the control and 4mM-SC devices were found from fitting to be 2.31k_BT/q and 1.87k_BT/q, respectively. The reduced slope for the 4mM-SC device reflects the suppression of trap-assisted charge-carrier recombination. The parameter α should ideally be unity, but α < 1 suggests the loss of photogenerated charge-carriers caused by the incomplete collection. The α values for the control and 4mM-SC devices are estimated to be 0.924 and 0.951, respectively, implying improved charge-carrier collection for the 4mM-SC device⁷⁰. Impedance spectroscopy analysis (Supplementary Fig. 22 and Supplementary Table 8) shows the 4mM-SC device delivers an increased recombination resistance at the CdS/Sb₂S₃ interface (R_rec = 10.66 kΩ cm²) compared to the control device (R_rec = 4.51 kΩ cm²). The increase in the recombination resistance suggests suppressed charge-carrier recombination and improved charge-carrier collection for the 4mM-SC device. The reduced J₀ and diode ideality factor, obtained from the analysis of J–V curves of both devices measured in the dark (Supplementary Fig. 23 and Supplementary Note 6), is also consistent with suppression of trap states in the absorber films⁶⁹.

Discussion

There have been substantial efforts over the past decade to develop light absorbers that can replicate the exceptional optoelectronic properties of lead-halide perovskites and overcome their toxicity and stability limitations^71,72. A critical limitation of many of these perovskite-inspired materials (especially with Sb- and Bi-based compounds) is carrier localization, which has been so widely found that it was being labeled a hallmark of these materials⁷³. This prevents their performance from approaching that of lead-halide perovskite solar cells, despite exhibiting improved stability⁷¹. Sb₂S₃ was thought to be an example of a material with this limitation³⁰. Despite continuous improvements in the performance of Sb₂S₃ solar cells over the past decade, device optimization of these materials has mostly been based on trial-and-error materials engineering approaches. A more general understanding of the physics behind charge-carrier generation, recombination, and transport is an indispensable prerequisite for revealing fundamental limitations and prospects of Sb₂S₃ for optoelectronic applications, as well as offering essential feedback for further device improvements. Our experimental and computational results here demonstrate that the previously-proposed hypothesis of self-trapping in Sb₂S₃ is not present, showing that Sb₂S₃ avoids the carrier localization limitations prevalent among other Sb- and Bi-based solar absorbers, and that this material has the potential to reach significantly higher efficiencies. This motivates detailed investigations to understand the underlying principles behind the delocalized nature of charge-carriers in Sb₂S₃, which can be generalized to other classes of perovskite-inspired materials.

Although Yang et al. observed PL that was red-shifted to the optical gap, and used this as part of their proposition of self-trapping in Sb₂S₃, other studies reported broad PL emission near the band-edge, with significant temperature-dependence of the PL intensity, which is consistent with defect-dominated emission^64,74. Optical pump terahertz probe (OPTP) measurements are also often used to probe whether self-trapping occurs. But previous room-temperature OPTP measurements of solution-processed Sb₂S₃ films were inconclusive on whether the initial fast decay in photoconductivity arose from self-trapping or defect-mediated recombination⁶⁴. In this regard, the temperature-dependent mobility measurements we obtained here provide a clearer indication of large polarons being present. Furthermore, extensive investigations into Sb₂S₃ films have shown high defect densities >10¹⁵cm⁻³ to be common, with a strong correlation between the concentration of defects and device performance^6,66,75. These experimental findings support our findings made here, where lowering defect densities in the Sb₂S₃ films was critical to achieve the high V_OCs obtained. Moreover, our previous first-principles analyses have also challenged the hypothesis of self-trapping in Sb₂S₃, where delocalized electrons and holes were found to occur in a perfect supercell³². Taken together, our new experimental and computational analyses of defects, coupled with prior polaron calculations, disprove the hypothesis of self-trapping in Sb₂S₃, showing that it is possible to improve the performance of this material towards its radiative limit through defect engineering.

In conclusion, we have succeeded in overcoming the 800 mV V_OC threshold that has been a bottleneck on progress with Sb₂S₃ photovoltaics. This achievement was realized through the formation of large-grained thin films by adding SC to the CBD precursor solution. The growth of high-quality uniform films produces Sb₂S₃ solar cells with a PCE of 7.67% under 1-sun illumination and a V_OC of 824 mV, which is the current record value. Temperature-dependent mobility measurements confirm large polaron formation in Sb₂S₃, rather than small polarons or STEs. Defect characterization and computations reveal that the reduced defect activity in Sb₂S₃ films strongly correlates with the increase in device V_OC. We therefore conclude that antimony chalcogenides have the potential to approach their fundamental limit in performance for optoelectronic devices through careful defect engineering. By comparing defect calculations with the energy of the two deep traps determined from DLTS measurements, we suggest S vacancies and Sb on S anti-sites to be critical defects to address.

Methods

Materials

Ethanol (99.0%), acetone (99.0%), methanol (99.0%), ammonia solution (25%-28%, in water), thiourea (99.0%), cadmium chloride (CdCl₂·2.5H₂O, 99.0%), antimony potassium tartrate (C₄H₄KO₇Sb·0.5H₂O, 99.0%), and sodium thiosulfate (Na₂S₂O₃·5H₂O, 99.0%) were purchased from Sinopharm. Cadmium nitrate (Cd(NO₃)₂·4H₂O, 99.0%) were purchased from Macklin. SnO₂ colloidal dispersion (15.0% in H₂O) was purchased from Alfa Aesar. Sodium citrate (C₆H₅O₇Na₃·2H₂O, 99.0%), acetonitrile (99.9%), chlorobenzene (99.5%), and tert-butylpyridine (TBP, 96%) were purchased from Aladdin. 2,2’,7,7’-tetrakis(N,N-di-p-methoxyphenylamine)-9,9’-spirobifluorene (Spiro-OMeTAD,99.8%) and lithium bis(trifluoromethylsyfonyl)imide salt (99.95%) were purchased from Xi’an Polymer Light Technology. [6,6] phenyl-C61-butyric acid methyl ester (PC₆₁BM, 99.5%) was purchased from Xi’an Yuri Solar Energy Technology. Gold wires were purchased from Tim Advanced Materials. Sb₂S₃ powders (99.999%, 100 mesh) were purchased from Beijing Hawk Science & Technology. All the chemicals and materials were purchased and used as received.

Device fabrication

The SnO₂/CdS ETL was deposited onto pre-cleaned fluorine-doped tin oxide (FTO, ~15 Ω sq⁻¹, NSG) conductive glass substrates. The detailed fabrication processes can be referred to from our previous work¹⁴. Specifically, the commercial SnO₂ colloidal dispersion diluted seven times with deionized (DI) water was spun onto the FTO substrate at a speed of 3000 rpm for 30 s to form an ultrathin SnO₂ layer, followed by annealing at 150 °C for 30 min. The CdS buffer layer was deposited using the CBD method. Typically, 30 mL of 15 × 10⁻³ M Cd(NO₃)₂·4H₂O and 39 mL of ammonia solution in water were mixed together and stirred for 2 min, followed by adding 19.2 mL of 1.2 M thiourea and 210 mL of DI water and stirring for another 2 min. The FTO/SnO₂ substrates were vertically immersed in such precursor solutions and maintained at 65 °C for 14 min with continuous stirring. Here, the thicknesses of SnO₂ and CdS layers in FTO/SnO₂/CdS substrates were about 10 and 60 nm, respectively. Afterward, as-prepared CdS layers were treated with CdCl₂ by spin-coating 0.088 M CdCl₂·2.5H₂O in methanol solution onto CdS, followed by annealing in air at 400 °C for 10 min. The Sb₂S₃ films were further deposited onto FTO/SnO₂/CdS substrate via a CBD method. Typically, C₄H₄KO₇Sb·0.5H₂O and Na₂S₂O₃·5H₂O were employed as Sb and S sources, respectively. 0.5009 g C₄H₄KO₇Sb·0.5H₂O (37.5 mM) and 1.985 g Na₂S₂O₃·5H₂O (200 mM) were dissolved into 40 mL DI water in a small bottle, stirred for 6 min. For the case with the use of SC additive, a small amount of SC with different concentrations of 1 mM, 2 mM, 4 mM, and 8 mM were added into the above mixture solution. The substrates were immersed in the precursor solution with the conducting side facing down and tilted at a certain angle of ~58° to the wall of the bottle. The bottle was then sealed and kept at 95 °C for a certain duration (8 h unless otherwise stated). The substrates were taken out immediately once the reaction ended, followed by rinsing with DI water and drying with nitrogen flow. The as-deposited films were then annealed at 370 °C for 10 min in a nitrogen-filled glovebox. Furthermore, the Spiro-OMeTAD layer was spin-coated onto the Sb₂S₃ layer as the HTL, and the detailed deposition procedure for Spiro-OMeTAD can be found in the literature¹⁴. Specifically, the HTL precursor was prepared by mixing 36.6 mg spiro-OMeTAD, 14.5 μL tert-butylpyridine, and 9.5 μL 0.52 g mL⁻¹ of lithium bis(trifluoromethylsyfonyl)imide salt dissolved in acetonitrile in 1 mL chlorobenzene. Then the as-obtained precursor was deposited onto absorber films by spin-coating at a speed of 3000 rpm for 30 s, followed by annealing at 100 °C for 10 min on a hot plate. Finally, the superstrate Sb₂S₃ solar cells were completed by evaporating a ~ 80 nm gold layer as the back electrode.

Materials and devices characterization

The XRD characterization of film samples was performed on a diffractometer (X’Pert PRO MPD, λ = 1.54056 Å). SEM images were collected on a JEOL field emission scanning electron microscope (JSM-6700F). The GB densities of films were obtained by depicting the GB grooves in corresponding SEM images using Adobe Photoshop software. AFM images were recorded on a Bruker atomic force microscope (Dimension Icon). Absorption spectra were recorded using a CARY 5000 Agilent spectrophotometer. UPS spectra were collected on a Thermo ESCALAB XI instrument. J–V curves of devices were measured under 1-sun illumination (AM 1.5 G, 100 mW cm⁻², calibrated with a standard cell from Newport) using a Newport Oriel Sol 3 A Solar Simulator, combined with a Keithley 2400 digital source meter. The active device area was defined using a 0.06-cm² mask. EQE measurements were performed on a QTest Station 1000 ADI system (Crowntech. Inc) under the DC mode, and the excitation source was a 300 W xenon lamp (CT-XE-300) which was split into specific wavelengths via a M24-S 1/4 m monochromator. The IPV efficiencies of Sb₂S₃ solar cells were measured on a home-made platform. The lux levels of WLED lamps (Ccobalance T5/5w) were measured using a luxmeter (TES-1330A), and the spectral irradiance of the diffuse indoor light source of 3000 K WLED was obtained with a high-precision fiber-optic spectrometer (Maya2000 Pro, Ocean Optics). The illustration of the home-made platform and calibration of the spectrometer can be referred to our previous work³⁵. Impedance spectra were acquired on a Zahner workstation (Zennium Pro.) under an applied voltage of 0.7 V, a scanning range of 0.5 Hz to 1 MHz, and an AC amplitude of 20 mV under dark; the impedance data were then fitted using a Z-view software. DLTS measurements were performed using a Phystech FT-1230 HERADLTS system. The samples were mounted on a SEMISHARE SCG-O-2 cryostat stage controlled by a Lakeshore 336 temperature controller. DLTS spectra were collected with a reverse bias of –0.3 V and a trap filling forward pulse amplitude of 0.3 V, and the filling pulse length was 10 ms. Ultrafast TA spectra of films were collected using a Helios Ultrafast pump-probe system. For this system, a nondegenerate pump-probe configuration was used to probe the transient dynamics within the femtosecond to nanosecond time range (50 fs to 7 ns) under ambient conditions. The pump pulses at a wavelength of 400 nm were generated by doubling the 800 nm pulse using a beta barium borate crystal on an optical parametric amplifier. The white light continuum probe pulses were formed by 800 nm femtosecond with a 2 mm sapphire plate for the 400–800 nm range. TOF measurements were performed under 100 to 400 K based on a device configuration of FTO/Sb₂S₃/Au, which was contained in an optically and electrically shielded box. Here, the thick Sb₂S₃ film was deposited using CSS, and the processing conditions are detailed in our previous work⁷⁶. The thickness of Sb₂S₃ film was measured to be around 2.2 μm using a KLA-Tencor D100 step profilometer based on three measurements for each sample. TOF measurements were carried out using a Keithley 2400 as the power source, and an Agilent DSOS054A high-definition oscilloscope for acquiring the transient signals. A pulsed laser with 405 nm wavelength, corresponding to ~100 nm absorption depth in Sb₂S₃, was used to excite the thick Sb₂S₃ film from the transparent FTO side. The hole mobility could be extracted by ${\mu }_{\mathrm{h}}=d^2/V{\tau }_{\mathrm{t}}$, where μ_h is hole mobility, d is film thickness, V is the driving voltage varying from 36 to 72 V and τ_t is the transit time defined by the turning point in the bilogarithmic plot of photocurrent versus decay time.

Computational methods

The formation energy of a defect D in charge state q is obtained by:

$$△H_f^{D,q}=E^{D,q}-E^{\mathrm{pristine}}-{\sum }_i{n}_i{\mu }_i+q{E}_{\mathrm{F}}+E_{\mathrm{corr}}$$ 1

Here, $E^{D,q}$ and $E^{\mathrm{pristine}}$ denote the total energies of the defective and pristine supercells, respectively. The term ${\sum }_i{n}_i{\mu }_i$ accounts for the energy change associated with adding (n_i > 0) or removing (n_i < 0) atoms of type i, with μ_i being the corresponding chemical potential. E_corr corrects for finite-size effects arising from charged defects in periodic boundary conditions, following the approach developed by Kumagai and Oba⁷⁷. The underlying density functional theory (DFT) calculations are performed using the HSE06 functional with a plane wave basis set as detailed in ref. ⁵⁰.

The thermodynamic charge transition level ε(q₁/q₂) is calculated as:

$$\epsilon \left(q_1/q_2\right)=\frac{△H_f^{D,q_1}\left(E_{\mathrm{F}}=0\right)-△H_f^{D,q_2}\left(E_{\mathrm{F}}=0\right)}{{q_2-q}_1}$$ 2

where $△H_f^{D,q}\left(E_F=0\right)$ represents the formation energy of defect D in charge state q when the Fermi level is at the VBM.

The equilibrium concentration of defect D,q is determined by:

$$C_{D,q}=g{N}_D{e}^{\frac{-△H_f^{D,q}}{k_{\mathrm{B}}{T}_{\mathrm{anneal}}}}$$ 3

where g accounts for degeneracies from geometry and spin. N_D is the number of defect sites per unit volume in the supercell. k_B is the Boltzmann constant, and T_anneal is the annealing temperature.

The capture cross-section is calculated by

$$\sigma =\frac{C}{⟨v⟩}$$ 4

where $⟨v⟩=\sqrt{3k_{\mathrm{B}}T/m^{*}}$ is the average thermal velocity of the carrier, with $m^{*}$ the average effective mass. The carrier capture coefficient C is derived from the Fermi’s golden rule^78,79.

$$C=\frac{2\pi }{\hslash }Vg{\sum }_m{\omega }_m⟨{\psi }_i∣\frac{\partial \widehat{h}}{\partial Q}∣{\psi }_f⟩{\sum }_n{∣⟨{\chi }_{im}∣Q-Q_0∣{\chi }_{fn}⟩∣}^2\delta \left(\mathrm{\Delta }E+m\hslash {\mathrm{\Omega }}_i-n\hslash {\mathrm{\Omega }}_f\right)$$ 5

Here, V is the volume of the supercell, and g represents the degeneracy factor, accounting for the number of equivalent transition pathways. The subscripts i and f indicate the initial and final states, respectively. The quantum numbers of the ionic states are denoted as n and m, while ${\omega }_m$ represents the thermal occupation. $\widehat{h}$ and ${\psi }_{\left\{i,f\right\}}$ correspond to the single-particle Hamiltonian and single-particle wavefunctions, respectively. ${\mathrm{\Omega }}_{\left\{i,f\right\}}$ refer to the phonon frequencies associated with the initial and final states.

A one-dimensional generalized coordinate Q is used to represent the atomic relaxation

$$Q^2={\sum }_{\alpha }{M}_{\alpha }\mathrm{\Delta }{R}_{\alpha }^2$$ 6

where $M_{\alpha }$ and $\mathrm{\Delta }{R}_{\alpha }$ are the mass and displacement of atom α between the initial and final states, respectively.

The maximum power conversion efficiency (${\eta }_{\max }$) of a solar cell is expressed as:

$${\eta }_{\max }={\max }_V\left(\frac{JV}{e{\int }_0^{\infty }E{\varphi }_{\mathrm{sun}}\left(E\right)\mathrm{d}E}\right)$$ 7

where e is the elementary charge. ${\varphi }_{\mathrm{sun}}\left(E\right)$ is the incident spectral photon flux density at the photon energy E. A standard AM1.5 solar spectrum is used in this work.

Following the methodology by Kim et al.^80,81, the net current density $J\left(V;W\right)$, accounting for both radiative and non-radiative recombination, is given by:

$$J\left(V;W\right)=J_{\mathrm{SC}}\left(W\right)+J_0^{\mathrm{rad}}\left(W\right)\left(1-e^{\frac{eV}{k_{\mathrm{B}}T}}\right)-eR\left(V\right)W$$ 8

where $R\left(V\right)$ is the defect-mediated non-radiative recombination rate. W is the film thickness. $J_0^{\mathrm{rad}}$ is the saturation current density.

Assuming that each absorbed photon contributes one collected electron hole pair, the short-circuit current density $J_{\mathrm{SC}}$ is given by

$$J_{SC}\left(W\right)=e{\int }_{E_g}^{\infty }a\left(E;W\right){\varphi }_{sun}\left(E\right)dE$$ 9

The radiative limit is obtained by setting the defect mediated non-radiative recombination term R(V) to zero and solving $J\left(V_{\mathrm{OC}}^{\mathrm{rad}};W\right)$ = 0, giving

$$V_{\mathrm{OC}}^{\mathrm{rad}}\left(W\right)=\frac{k_{\mathrm{B}}T}{e}\ln \left(\frac{J_{\mathrm{SC}}\left(W\right)}{J_0^{\mathrm{rad}}\left(W\right)}+1\right)$$ 10

The radiative saturation current density is calculated from detailed balance as

$$J_0^{rad}\left(W\right)=e{\int }_0^{\infty }a\left(E;W\right){\varphi }_{\mathrm{bb}}\left(E\right)\mathrm{d}E$$ 11

where ${\varphi }_{\mathrm{bb}}\left(E\right)$ is the black body photon flux. The photon absorptivity $a\left(E;W\right)$ describes the probability of absorption as a function of photon energy. In the Shockley–Queisser model, it is idealized as a step-like function at the bandgap. In our calculation, the absorptivity is defined as $a\left(E;W\right)=1-e^{-2\alpha \left(E\right)W}$, where $\alpha \left(E\right)$ is the optical absorption coefficient of Sb₂S₃ obtained from first-principles calculations using the HSE06 functional⁵⁰. The factor of 2 accounts for a double-pass optical path through the absorber, assuming perfect reflection from the back contact. A film thickness of W = 350 nm was used to match the experimental absorber thickness.

Reporting summary

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

Author contributions

R.Z. and J.Z. designed the experiments and analyzed the data, and also conceived of the idea for this manuscript. R.L.Z.H. provided input on understanding and interpreting carrier localization in these materials. J.Z. and T.S. carried out the experiments, device optimization, and data analysis. X.W. carried out the computations. L.W., J.Y., Z.L., A.W., R.L.Z.H., and R.Z. assisted in experiments and data analysis. R.Z., J.Z., X.W., A.W., and R.L.Z.H. wrote and revised the paper. All authors discussed and edited the manuscript together.

Peer review

Peer review information

Nature Communications thanks Daria Miliaieva, Honghui Shang, Zhaoning Song and other anonymous reviewer for their contribution to the peer review of this work. A peer review file is available.

Funding

The financial support by the National Natural Science Foundation of China (Nos. 52371219 and W2421064) and the Fundamental Research Funds for the Central Universities (No. JZ2024HGTG0295) is greatly acknowledged. J.Y. and R.L.Z.H. thank UK Research and Innovation for funding through a Frontier Grant (no. EP/X029900/1), awarded via the 2021 ERC Starting Grant scheme. They also thank St. John’s College Oxford for funding through the Large Grant scheme. R.L.Z.H. thanks the Royal Academy of Engineering and Science & Technology Facilities Council for funding through a Senior Research Fellowship (no. RCSRF2324-18-68). R.Z. and R.L.Z.H. thank the Royal Society for funding (no. IEC/NSFC/242353).

Data availability

The experimental and computational data generated in this paper and in the Supplementary Information have been deposited in the Oxford Research Archive (ORA) Data Repository, with the link https://doi.org/10.5287/ora-8j95djknz.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-76845-1.