An Optimization Path for Sb₂(S,Se)₃ Solar Cells to Achieve an Efficiency Exceeding 20%

Abstract

Antimony selenosulfide, denoted as Sb₂(S,Se)₃, has garnered attention as an eco-friendly semiconductor candidate for thin-film photovoltaics due to its light-absorbing properties. The power conversion efficiency (PCE) of Sb₂(S,Se)₃ solar cells has recently increased to 10.75%, but significant challenges persist, particularly in the areas of open-circuit voltage (V_oc) losses and fill factor (FF) losses. This study delves into the theoretical relationship between V_oc and FF, revealing that, under conditions of low V_oc and FF, internal resistance has a more pronounced effect on FF compared to non-radiative recombination. To address V_oc and FF losses effectively, a phased optimization strategy was devised and implemented, paving the way for Sb₂(S,Se)₃ solar cells with PCEs exceeding 20%. By optimizing internal resistance, the FF loss was reduced from 10.79% to 2.80%, increasing the PCE to 12.57%. Subsequently, modifying the band level at the interface resulted in an 18.75% increase in V_oc, pushing the PCE above 15%. Furthermore, minimizing interface recombination reduced V_oc loss to 0.45 V and FF loss to 0.96%, enabling the PCE to surpass 20%. Finally, by augmenting the absorber layer thickness to 600 nm, we fully utilized the light absorption potential of Sb₂(S,Se)₃, achieving an unprecedented PCE of 26.77%. This study pinpoints the key factors affecting V_oc and FF losses in Sb₂(S,Se)₃ solar cells and outlines an optimization pathway that markedly improves device efficiency, providing a valuable reference for further development of high-performance photovoltaic applications.

1. Introduction

With the increasing demand for renewable energy and a heightened focus on environmental sustainability, photovoltaic (PV) technology has emerged as a crucial method for converting solar energy into electricity. Thin-film solar cells, which utilize inorganic materials such as Cu(In,Ga)Se₂ (CIGS) and CdTe, have been commercialized, offering excellent power conversion efficiency (PCE) and especially lighter weights compared to silicon-based solar cells. However, the use of expensive rare earth elements (Ga and Te) and the toxicity of Cd present challenges to the broader application of these thin-film solar cells. Recently, researchers have shown significant interest in antimony selenosulfide semiconductor materials, Sb₂(S_,Se)₃, due to their nontoxic nature, profuse existence in the Earth’s crust, excellent ambient stability, large dielectric constant (ε_r > 15), elevated relative absorption coefficient (α > 10⁵ cm⁻¹), and adjustable bandgap (E_g) ranging from 1.1 to 1.7 eV [1,2]. Despite substantial efforts by researchers to enhance the PCE of Sb₂(S,Se)₃ solar cells, the current champion PCE for Sb₂(S,Se)₃ thin-film solar cells remains at 10.75% [3,4]. Nevertheless, these devices still suffer from a substantial open-circuit voltage (V_oc) loss (defined as E_g/q − V_oc) of approximately 0.8 V, and a fill factor (FF) loss (defined as the difference between the FF of ideal solar cells and the FF observed in practice) of approximately 15%. Moreover, there is still a considerable gap to bridge before reaching the Shockley–Queisser (S–Q) limit, which is based on the detailed balance principle and predicts a maximum efficiency of 33% for single-junction solar cells under standard illumination conditions [5]. Therefore, continued research endeavors aimed at mitigating these V_oc and FF losses in Sb₂(S,Se)₃ solar cells are crucial to advancing towards this theoretical benchmark.

To achieve exceptional performance in Sb₂(S,Se)₃ solar cells, we used a solar cell capacitance simulator (SCAPS) to analyze the limiting factors, including series resistance (R_s), shunt resistance (R_sh), bulk defects, interface recombination, and energy level arrangements between different functional layers. SCAPS is a powerful solar cell simulator that has been validated by numerous studies for accurately adjusting the parameters of each functional layer and interface, simulating photovoltaic device performance, optimizing device structures, and obtaining high-efficiency solar cells. For example, in our previous work [6], we achieved a PCE of over 15% by utilizing SCAPS for guiding interface engineering strategies and optimizing the design of PbS colloidal quantum dot solar cells. Similarly, Chen et al. [7] successfully prepared Sb₂Se₃ solar cells with a certified efficiency of 6.5% using EDT-treated PbS colloidal quantum dots as hole transport layers (HTLs), guided by SCAPS simulation results. Bertens et al. [8] used SCAPS to predict the effect of doping concentration in the active layer on the performance of PbS colloidal quantum dot solar cells and achieved actual devices that matched the predicted performance.

This exhaustive investigation delves into the multifaceted factors that currently impede the enhancement of Sb₂(S,Se)₃ solar cell efficiency, with the ultimate goal of identifying optimization strategies to attain a PCE exceeding 20%. By utilizing numerical methods, we constructed a theoretical model for the most efficient Sb₂(S,Se)₃ solar cell structure reported thus far, featuring a fluorine-doped tin oxide (FTO)/CdS/Sb₂(S,Se)₃/Spiro-OMeTAD/Au configuration. Initially, through meticulous optimization of R_s and R_sh, we significantly reduced the FF loss from 10.79% to 2.80%, increasing the PCE from 10.72% to 12.18%. For the device exhibiting 12.18% efficiency, by refining the alignment of the conduction band between the electron transport layer (ETL) and the absorber layer, we achieved a notable increase in V_oc, increasing it from 0.64 V to 0.76 V. This adjustment minimized the V_oc loss and increased the PCE to 15.31%. Building upon this improved device, we further optimized the interface recombination, achieving a substantial 43% decrease in the V_oc loss relative to that of the initial device, with FF losses decreasing below 1% and a substantial increase in the PCE to 23.75%. In the final phase of optimization, we targeted the absorber defects and thickness, resulting in an increase in the PCE to 26.77%, accompanied by an increase in the short-circuit current density (J_sc) to 30.93 mA·cm⁻². The simulation results revealed that under conditions of low V_oc and FF, the internal resistance exerted a more substantial constraint than nonradiative recombination on the FF. Additionally, the spike-like energy band offset (EBO) increase at the FTO/ETL interface could impede the formation of a flat or slightly spiked EBO at the ETL/absorber interface, thus impeding further enhancements in the PCE. Importantly, mitigating interface recombination at the ETL/absorber interface has emerged as a paramount strategy for enhancing the overall performance of Sb₂(S,Se)₃ solar cells, surpassing the importance of reducing recombination at the absorber/HTL interface. Remarkably, as the absorber layer thickness increased to 600 nm, the Sb₂(S,Se)₃ solar cell achieved a noteworthy J_sc exceeding 30 mA·cm⁻², consequently achieving a PCE of 26.77%. This study elucidates the critical factors influencing the performance of Sb₂(S,Se)₃ solar cells, providing valuable guidance for further experimental work in this field.

2. Methods and Details

2.1. Structure of the Solar Cells

The proposed device structure, depicted in Figure 1a, follows this configuration: FTO/CdS/Sb₂(S,Se)₃/Spiro-OMeTAD/Au. This setup has been widely adopted in various high-efficiency Sb₂(S,Se)₃ solar cells [3,4,9,10,11,12,13,14,15]. FTO (SnO₂:F) serves as a transparent conductive oxide for charge collection, CdS acts as the ETL, Sb₂(S,Se)₃ functions as the absorber layer, Spiro-OMeTAD is utilized as the HTL, and Au is used as the electrode for charge collection.

2.2. Simulation Principles and Details

SCAPS has been meticulously crafted and generously offered by the University of Gent [16,17]. It is specifically designed to simulate a wide array of solar cells, including crystalline silicon, thin films, and emerging photovoltaic technologies. The software incorporates sophisticated numerical algorithms to solve the relevant physical equations governing charge transport, recombination, and optical properties within the device.

The primary function of SCAPS is to solve the Poisson equation related to the electrostatic potential (ψ) and the continuity equation controlling the dynamics of free electrons and holes in one-dimensional heterojunctions [18]. The specific Equations are as follows:

$${\displaystyle \frac{\partial }{\partial x}}\left(\epsilon {\displaystyle \frac{d\psi }{dx}}\right)+q[p-n+N_{\mathrm{D}}-N_{\mathrm{A}}+{\rho }_{\mathrm{p}}-{\rho }_{\mathrm{n}}]=0$$

(1)

$$-{\displaystyle \frac{1}{q}}{\displaystyle \frac{\partial J_{\mathrm{n}}}{\partial x}}-R_n+G={\displaystyle \frac{\partial n}{\partial t}}$$

(2)

$$-{\displaystyle \frac{1}{q}}{\displaystyle \frac{\partial J_{\mathrm{p}}}{\partial x}}-R_p+G={\displaystyle \frac{\partial p}{\partial t}}$$

(3)

$$J_{\mathrm{n}}=-{\mu }_{\mathrm{n}}n{\displaystyle \frac{d{E}_{\mathrm{F}\mathrm{n}}}{dx}}, J_{\mathrm{p}}={\mu }_{\mathrm{p}}p{\displaystyle \frac{d{E}_{\mathrm{F}\mathrm{p}}}{dx}}$$

(4)

where ε represents the dielectric constant; q represents the electron charge; p and n symbolize the free hole and electron densities; N_A and N_D represent the densities of the acceptor and donor types, respectively; ρ_n and ρ_p indicate the densities of trapped electrons and holes, respectively; J_n and J_p denote the current densities of the electrons and holes, respectively; G designates the photogeneration rate; and, R_n and R_p are defined as the recombination rates of the electrons and holes, respectively. Additionally, μ_n and μ_p denote the electron and hole mobilities, respectively, and E_Fn and E_Fp represent the acceptor and donor quasi-Fermi levels, respectively.

To model the device structure via SCAPS, we compiled material parameters obtained from calculations and the relevant literature [3,4,9,18,19,20,21,22,23,24,25], which are summarized in Table S1 (see the Supplementary Material). Additionally, we standardized the thermal velocities of electrons and holes to 10⁷ cm·s⁻¹ across all the layers. The specific bulk defects for the absorber layer are presented in Table S2, while Table S3 provides the detailed interface characteristics essential for the simulation. The absorption spectral data for FTO and CdS were obtained from the default file provided by SCAPS software (version 3.3.10; University of Gent, Belgium) support, and the absorption spectral data for the Sb₂(S,Se)₃ material obtained from reference [4] were utilized in the simulation process. All the simulations were carried out at 300 K, neglecting radiative and Auger recombination, under the AM 1.5 G spectrum.

2.3. Device Validation and Optimization Route

Simulation 1 of the Sb₂(S,Se)₃ solar cell was established utilizing the parameters outlined in Tables S1–S3 of the Supplementary Material. When R_s = 3 Ω·cm² and R_sh = 375 Ω·cm², the simulation results strongly agree with the experimental findings reported in [4], particularly the current density–voltage (J–V) characteristic curves and external quantum efficiency (EQE) spectra, as evident in Figure 1b,c, respectively. To further confirm the accuracy of the model, a comparative analysis was conducted on how V_oc correlates with variations in light intensity. According to the data presented in Figure 1d, the ideal factor (n_ID) values of the experimental and simulated devices are 1.35 and 1.39, respectively, revealing strong consistency between the measurements and simulations. Additionally, an n_ID value between 1 and 2 indicates that interface recombination predominates in Sb₂(S,Se)₃ solar cells [26]. As depicted in Figure 1e, the band alignment diagram clearly illustrates that the Sb₂(S,Se)₃ absorber layer is fully depleted, indicating a strong electric field throughout the entire layer. This robust electric field serves as a driving force, greatly enhancing the separation efficiency of photogenerated electron–hole pairs.

In our simulated device, the Sb₂(S,Se)₃ absorber has an E_g of 1.43 eV, which approaches the nearly ideal bandgap (E_g = 1.34 eV) of the S–Q efficiency limit [5,27]. However, the actual device performance only reaches a maximum efficiency of 10.75%, which is significantly below the S–Q efficiency limit. For instance, at an E_g of 1.43 eV, the S–Q limit predicts a PCE of 32.54% with a V_oc of 1.17 V and an FF of 89.53% [5]. A strong correlation exists between FF and V_oc, where the maximum achievable FF (FF_m) theoretically depends solely on V_oc [3,28,29], assuming a negligibly small R_s (R_s ≈ 0) and an ideal R_sh (R_sh → ∞).

$${\mathrm{F}\mathrm{F}}_{\mathrm{m}}={\displaystyle \frac{{\nu }_{\mathrm{o}\mathrm{c}}-\mathrm{l}\mathrm{n}({\nu }_{\mathrm{o}\mathrm{c}}+0.72)}{{\nu }_{\mathrm{o}\mathrm{c}}+1}}, with {\nu }_{\mathrm{o}\mathrm{c}}={\displaystyle \frac{q{V}_{\mathrm{o}\mathrm{c}}}{n_{\mathrm{I}\mathrm{D}}{k}_{\mathrm{B}}T}}$$

(5)

The relationship between FF_m and V_oc is primarily influenced by n_ID, which represents the nonradiative recombination rate. However, in actual devices, R_s and R_sh cannot be neglected. R_s and R_sh are considered in Equation (5), as shown in Equation (6) [30,31].

$$\mathrm{F}\mathrm{F}={\mathrm{F}\mathrm{F}}_{\mathrm{s}}\left(1-{\displaystyle \frac{{\nu }_{\mathrm{o}\mathrm{c}}+0.7}{{\nu }_{\mathrm{o}\mathrm{c}}}} {\displaystyle \frac{{\mathrm{F}\mathrm{F}}_{\mathrm{s}}}{r_{\mathrm{s}\mathrm{h}}}}\right), with {\mathrm{F}\mathrm{F}}_{\mathrm{s}}={\mathrm{F}\mathrm{F}}_{\mathrm{m}}\left(1-1.1r_{\mathrm{s}}\right)+{\displaystyle \frac{r_{\mathrm{s}}^2}{5.4}}, r_{\mathrm{s}\mathrm{h}}={\displaystyle \frac{J_{\mathrm{s}\mathrm{c}}{R}_{\mathrm{s}\mathrm{h}}}{V_{\mathrm{o}\mathrm{c}}}} and r_{\mathrm{s}}={\displaystyle \frac{J_{\mathrm{s}\mathrm{c}}{R}_{\mathrm{s}}}{V_{\mathrm{o}\mathrm{c}}}}$$

(6)

Applying Equations (5) and (6), the FF and FF_m of Sb₂(S,Se)₃ solar cells were determined on the basis of empirical V_oc–FF plots, where the n_ID value was varied from 1 to 2. According to Figure 1f, with R_s = 0 Ω·cm² and R_sh = 10⁷ Ω·cm², at a V_oc of approximately 0.63 V (that is, from point 1 to point 2 on the graph), the calculated FF increased from 68.35% to 78.91%. On the other hand, by decreasing n_ID from 1.39 to 1.0, the FF increased from 68.35% at 0.63 V to 79.94% at the S–Q limit, with a V_oc of 1.17 V (that is, moving from point 1 to point 3). On the basis of these findings, after the respective optimizations, the FF constrained by the internal resistance (78.91%) was lower than that constrained by the nonradiative recombination (79.94%). Consequently, within the regimes of low V_oc and FF, the internal resistance exerted a more significant limiting effect on the FF than nonradiative recombination did. These results highlight the rationale behind implementing a phased strategy employing staged optimization to reduce V_oc loss and FF loss in Sb₂(S,Se)₃ solar cells. This strategy involves initially optimizing internal resistances before addressing nonradiative recombination in Sb₂(S,Se)₃ solar cells (that is, from point 1 to point 2 and then to point 4, as illustrated in Figure 1f). Additionally, point 5 in Figure 1f represents the high-efficiency Sb₂(S,Se)₃ solar cell with the current lowest V_oc loss [3], whereas points 1′–5′ represent the results from five simulated devices obtained following our designed optimization route.

3. Results and Discussion

3.1. Optimization of the Series and Shunt Resistances

The series and shunt resistances are crucial factors influencing the performance of solar cells. Simulation 1 effectively replicates the experimental J–V curves, EQE spectra, and ideality factor (n_ID), aligning closely with published data [4]. This validation highlights the predictive accuracy of subsequent simulations in predicting experimental outcomes. To explore the detailed effects of R_s and R_sh, R_s was adjusted to fall within the range of 0 to 10 Ω·cm², and the range specified for R_sh extended from 10² to 10⁷ Ω·cm². The simulation calculation was carried out while the other parameters in Simulation 1 remained unchanged. As illustrated in Figure 2a–d, changes in R_s have a more pronounced effect on the PCE and FF than variations in R_sh do. When R_s decreased to 0 Ω·cm² and R_sh was maintained at 10⁵ Ω·cm², the FF notably increased from 68.35% to 79.55%. Conversely, the V_oc and J_sc values are least affected by changes in R_s, which is consistent with previous reports [32,33]. Moreover, Figure 2e demonstrates that n_ID remains stable with variations in R_s when R_sh remains constant but shifts noticeably from 2.14 to 1.10 as R_sh varies from 10² Ω·cm² to 10⁵ Ω·cm². Compared with Simulation 1, the J–V curve of Simulation 2 (R_s decreased to 0 Ω·cm² and R_sh increased to 10⁵ Ω·cm²) significantly improved the FF, whereas the PCE also increased from 10.72% to 12.57% (Figure 2f). This enhancement primarily results from a marked decrease in FF loss, decreasing from 10.79% to 2.80% as detailed in

Table 1. Photovoltaic parameters in five simulated devices.

	Voc (V)	FF (%)	Voc Losst (a) (V)	FF Loss (b) (%)	nID	Jsc (mA·cm−2)	PCE (%)
Simulation 1	0.64	68.35	0.79	10.79	1.39	24.63	10.72
Simulation 2	0.64	79.55	0.79	2.80	1.10	24.79	12.57
Simulation 3	0.76	81.31	0.67	3.02	1.11	24.86	15.31
Simulation 4	0.98	86.34	0.45	0.96	1.08	27.93	23.75
Simulation 5	0.99	87.09	0.44	0.31	1.08	30.93	26.77

^(a) V_oc loss is equal to E_g/q − V_oc, where E_g represents the bandgap of the active absorber and q is the elementary charge. ^(b) FF loss is equal to FF_m − FF, where FF_m denotes the maximum achievable FF across varying V_oc values in a single solar cell.

, emphasizing the critical role of R_s and R_sh optimization in enhancing solar cell performance.

The findings underscore the efficacy of a dual-pronged approach in enhancing solar cell efficiency and mitigating FF losses: reducing R_s and augmenting R_sh. An increase in R_s stems from increased electrode and charge–transfer interface resistances, whereas a decrease in R_sh is tied to reduced functional layer coverage and the proliferation of pinholes. Despite the inherent challenge of fully eradicating internal resistance, these results underscore the imperative for experimental endeavors to craft electrodes with exceptional conductivity and minimal sheet resistance, alongside strategies to diminish interface charge–transfer resistance. The key determinants of this interfacial charge transfer resistance include the electrode–semiconductor contact resistance, the bulk resistance intrinsic to the semiconductor, barriers arising from interface band offsets, and recombination losses at the interface, exacerbated by impurities and defects [34]. To increase the overall performance of Sb₂(S,Se)₃ solar cells to unprecedented levels, concerted optimization endeavors targeting interface band alignment, interface recombination processes, and absorber defects are of paramount importance.

3.2. Optimization of the Energy Band Offset

Despite significant advancements in enhancing the efficiency of Sb₂(S,Se)₃ solar cells through meticulous optimization of the internal resistance, resulting in a notable improvement in the FF, increasing the V_oc remains a formidable challenge. To overcome this obstacle, it is imperative to meticulously optimize the internal energy band arrangements within the solar cell architecture. Optimal energy level alignment can facilitate the seamless transportation of photogenerated electrons toward the front contact and holes toward the back contact, emanating from the absorber layer, thereby reducing the interface-induced recombination losses in Sb₂(S,Se)₃ solar cells. Establishing an ideal energy band offset (EBO) at the interfaces, which increases carrier transport properties and minimizes recombination losses, is of paramount importance [35]. Notably, the formation of EBO, a crucial aspect of Sb₂(S,Se)₃ solar cells, is closely linked to disparities in the electron affinity and energy gap across the material interface. Addressing these challenges through meticulous interface engineering is essential for mitigating recombination losses, enhancing V_oc, and ultimately achieving higher overall efficiencies for these solar cells. The conduction band offset (CBO) existing at the junction of the ETL and absorber is fundamentally dictated by the disparity in electron affinities between these two layers (${\chi }_{\mathrm{a}\mathrm{b}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{e}\mathrm{r}}$ and ${\chi }_{\mathrm{E}\mathrm{T}\mathrm{L}}$, respectively), as follows:

$$\mathrm{C}\mathrm{B}\mathrm{O}={\chi }_{\mathrm{a}\mathrm{b}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{e}\mathrm{r}}-{ \chi }_{\mathrm{E}\mathrm{T}\mathrm{L}}$$

(7)

The interface between materials can exhibit three distinct band alignment configurations, each characterized by the CBO. A negative CBO induces a steep cliff-like EBO, whereas a positive CBO yields a more pronounced spike-like EBO. When the CBO is zero, a flat band alignment is observed [36]. There is a general consensus among researchers that either a flat band alignment or a mild spike-like CBO is conducive to efficient charge transfer and the minimization of interface recombination losses [37].

Here, the band arrangements at the ETL/absorber interface were investigated by varying the χ_ETL from 4.3 eV to 3.7 eV, with the χ_absorber maintained at 3.81 eV. This range of χ_ETL corresponded to a CBO ranging from −0.49 eV to 0.19 eV, as depicted in Figure S1a. As the CBO shifted from negative to positive values, a distinct spike-like EBO emerged in the conduction band at the ETL/absorber interface, as expected. However, a remarkable observation was made at the FTO/ETL interface, where a considerably more prominent spike-like EBO manifested in the conduction band, as clearly shown in Figure S1b. This enhanced EBO brings additional obstacles to the transfer of electrons to the front electrode, ultimately hindering charge transfer with the increase in CBO. Therefore, when CBO decreases below −0.17 eV, the electrons can surmount the potential barrier at the FTO/ETL interface and reach the front electrode, thus avoiding computational convergence issues, as shown in Figure S1c. When ${\chi }_{\mathrm{E}\mathrm{T}\mathrm{L}}$ was tuned from 4.3 eV to 3.98 eV (corresponding to a CBO from −0.49 eV to −0.17 eV), remarkable linear enhancements were observed in the PCE, V_oc, and FF, whereas the J_sc remained relatively stable, as shown in Figure 3. This behavior originated from the reduction in cliff-like interfacial characteristics between the ETL and absorber, coupled with an enhanced built-in electric field at both the ETL/absorber and FTO/ETL interfaces (Figure S1d), resulting in reduced electron capture at the interface [38]. Thus, the Sb₂(S,Se)₃ solar cell reached its optimal performance at a CBO of −0.17 eV.

Certainly, the refinement of the CBO at the ETL/absorber interface significantly enhances the transport of photogenerated electrons. Nevertheless, the employment of an appropriate HTL is of paramount importance in facilitating the migration of photogenerated holes toward the back contact while simultaneously impeding the undesirable reverse flow of electrons. Thus, the valence band offset (VBO) at the interface between the absorber and HTL critically governs the transport dynamics of photogenerated holes toward the back electrode in the Sb₂(S,Se)₃ absorber layer. The VBO value can be calculated as follows:

$$\mathrm{VBO}={\mathrm{E}}_{\mathrm{v}\text{\_}\mathrm{absorber}}-{\mathrm{E}}_{\mathrm{v}\text{\_}\mathrm{HTL}}={\mathrm{E}}_{\mathrm{g}\text{\_}\mathrm{absorber}}+{\chi }_{\mathrm{a}\mathrm{b}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{e}\mathrm{r}}-({\mathrm{E}}_{\mathrm{g}\text{\_}\mathrm{HTL}}+{\chi }_{\mathrm{H}\mathrm{T}\mathrm{L}})$$

(8)

As shown in Figure 4a, the PCE demonstrates a consistent trend of an initial rise followed by a subsequent decline at all values of N_A in the HTL, when the VBO varies from −0.4 eV to 0.2 eV. This VBO variation corresponds to a range of E_{v_HTL} from 4.84 eV to 5.44 eV, with E_{v_absorber} fixed at 5.24 eV. Notably, across N_A values ranging from 10¹⁶ cm⁻³ to 10¹⁹ cm⁻³, the peak PCE occurs at a VBO of −0.1 eV. In Figure 4b, the FF exhibits a similar trend to that of the PCE. However, V_oc remains almost unchanged as the VBO increases to −0.1 eV, whereas J_sc initially remains constant and subsequently rapidly decreases after the VBO exceeds 0 eV (see Figure 4c,d). When the VBO exceeds 0 eV, the PCE, FF, and J_sc of the simulated device undergo rapid deterioration. This significant decline can be explained by the emergence of an energy barrier at the valence band of the absorber/HTL interface. This barrier considerably impedes the seamless flow of photogenerated holes toward the back electrode, leading to their accumulation at the interface. This accumulation, in turn, intensifies the surface recombination processes, further reducing the performance metrics of the device. When VBO is −0.1 eV (E_{v_HTL} = 5.14 eV) and N_A ranges between 10¹⁸ cm⁻³ and 10¹⁹ cm⁻³, the device exhibits optimal performance.

As demonstrated by the simulation results, extreme positive or negative values of either the CBO or VBO adversely affect device performance. By optimizing the energy level alignment, we achieved an optimal CBO of −0.17 eV and VBO of −0.1 eV, which were applied in Simulation 3. Simulation 3 achieved a PCE of 15.31%, a V_oc of 0.76 V, a J_sc of 24.86 mA·cm⁻², and an FF of 81.32%. Compared with Simulation 2, the device performance in Simulation 3 showed significant improvements, with a significant reduction of 15.19% in V_oc loss and a noteworthy 21.80% increase in the PCE, as detailed in Table 1. These results highlight the critical role of precise control over energy level alignment in optimizing photovoltaic device performance. To achieve this optimization while keeping the absorber material’s energy levels constant, the electron affinity of the ETL (CdS) needs to be reduced from 4.1 eV to 3.98 eV, and the electron affinity of the HTL (spiro-OMeTAD) needs to be reduced from 2.1 eV to 2.0 eV. In practice, it is necessary to optimize the conduction band energy levels of each functional layer material by adjusting doping elements or introducing specific functional groups to achieve better energy level matching, thereby constructing more efficient solar cell structures.

3.3. Optimization of Interface Recombination

Even if optimal band alignment is achieved in the device structure, the potential effect of nonradiative recombination due to interface defects resulting from lattice mismatches between functional layers must be considered. Sb₂(S,Se)₃ possesses an orthorhombic crystal structure, while CdS typically has a hexagonal structure and spiro-OMeTAD adopts a triclinic structure [39]. The inherent structural incompatibility among the ETL, absorber, and HTL layers leads to the emergence of lattice mismatches at their junctions, fostering the development of interface defects that act as sites for nonradiative recombination. To simulate nonradiative recombination through the Shockley–Read–Hall (SRH) mechanism, the SRH recombination rate (R_SRH) is considered. The R_SRH consists of three main components: bulk recombination (R_bulk) within the absorber layer, interface recombination at the ETL/absorber interface (R_IF1), and interface recombination at the absorber/HTL interface (R_IF2) [39,40,41], as shown in Equation (9):

$$R_{\mathrm{S}\mathrm{R}\mathrm{H}}=R_{\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}}+R_{\mathrm{I}\mathrm{F}1}+R_{\mathrm{I}\mathrm{F}2}={\displaystyle \frac{(np-n_{\mathrm{i}}^2){\sigma }_{\mathrm{n},\mathrm{p}}{\upsilon }_{\mathrm{t}\mathrm{h}}{N}_{\mathrm{t}}}{n+p+2n_{\mathrm{i}}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{h}\frac{E_{\mathrm{t}}-E_{\mathrm{i}}}{k_{B}T}}}$$

(9)

where σ_n and σ_p represent the capture cross-sections for electrons and holes, respectively; υ_th denotes the thermal velocity; and n_i and E_i represent the intrinsic density and energy level of materials, respectively. Additionally, N_t and E_t are the density and energy level of the defect states, respectively, and S represents the surface recombination velocity (defined as S = σ_n,pυ_thN_t).

The influence of the surface recombination velocity, namely S₁ at the ETL/absorber interface and S₂ at the absorber/HTL interface, on the performance parameters of Sb₂(S,Se)₃ solar cells is clearly illustrated in Figure 5a–d. When S₂ is held constant and S₁ varies between 10⁶ and 10¹⁰ cm·s⁻¹, the V_oc remains below 0.80 V, with negligible changes in both the PCE and FF. However, when S₂ is less than 10⁴ cm·s⁻¹ and S₁ decreases from 10⁶ to 10² cm·s⁻¹, the PCE gradually increases, ultimately exceeding 20%, and the V_oc progressively increases to nearly 1.0 V. These findings underscore the more significant impact of S₁ than S₂ on the V_oc and PCE of Sb₂(S,Se)₃ solar cells. This result is likely attributed to the presence of a p–n junction formed between the p-type Sb₂(S,Se)₃ absorber layer and the n-type CdS layer, which governs the behavior of holes as minority carriers within the Sb₂(S,Se)₃ thin film. In contrast, a relatively weaker p⁺–p junction is formed with p-type Spiro-OMeTAD. Thus, the optimization of the ETL/absorber interface through meticulous interface engineering can likely lead to a more effective increase in the performance of Sb₂(S,Se)₃ solar cells [42].

Notably, Simulation 4 with optimized parameters of 10² cm·s⁻¹ for S₁ and 10³ cm·s⁻¹ for S₂ attained an impressive PCE of 23.75%, with excellent characteristics, such as an n_ID of 1.08, a V_oc loss of 0.45 V, and a negligible FF loss of 0.96%, as detailed in Table 1. As evident in Figure 5e, compared with simulation 3, optimizing the interface recombination velocities led to a notable increase in V_oc from 0.76 V to 0.98 V, J_sc from 24.86 mA·cm⁻² to 27.93 mA·cm⁻², and PCE from 15.31% to 23.75%. Figure 5f shows that this enhancement was attributed to the improved optical response of the device at wavelengths below 600 nm after reducing interface recombination. Reducing the trap density at the ETL/absorber interface from 10¹⁴ cm⁻² to 10¹⁰ cm⁻² or the capture cross-section from 10⁻¹⁵ cm² to 10⁻¹⁹ cm² is a significant challenge for practical experiments. Indeed, interface modification engineering can passivate surface defects and improve material smoothness and surface impurities, effectively reducing trap density and/or capturing cross-sections. For example, CdS thin films etched with N₂H₄ exhibit higher transmittance, smoother surfaces, and fewer Cd oxychlorides [12]. Additionally, adding insulating polymer layers can further reduce surface roughness and interface states, enhancing device performance [41].

3.4. Optimization of the Sb₂(S,Se)₃ Absorber’s Thickness and Bulk Defects

The thickness of the Sb₂(S,Se)₃ absorber significantly affects various performance aspects of solar cells, including light absorption, carrier mobility, and recombination rates. Consequently, our subsequent simulations delved into the impact of varying the thickness and N_t of the absorber to pinpoint the optimal configuration for enhancing device performance. When N_t remained at 10¹⁶ cm⁻³ and the thickness remained below 600 nm, as evident from Figure 6a–d, there was a slight increase in V_oc and a slight decrease in FF with increasing thickness, whereas both the PCE and J_sc significantly increased. The increase in absorber thickness led to greater photon absorption, resulting in a greater number of photogenerated carriers and thus improving the J_sc and PCE. However, once the thickness exceeds 600 nm, the photon absorption approaches saturation and the PCE almost plateaus, as shown in Figure 6e. Furthermore, increasing the absorber thickness from 100 nm to 1200 nm led to a significant increase in the response of the EQE (see Figure 6f). Nevertheless, this increase in absorber thickness extended the transit distance for the charge carriers before collection and elevated the internal resistance of the device, consequently reducing the FF [42]. At a thickness of 600 nm, the FF stabilized at nearly 86.01%. Consequently, with an Sb₂(S,Se)₃ thickness of 600 nm and an initial N_t of 6.28 × 10¹² cm⁻³, Simulation 5 achieved a PCE of 26.77%, an FF of 87.09%, a V_oc of 0.99 V, and a J_sc of 30.93 mA·cm⁻², as summarized in Table 1.

3.5. Optimization of the Work Function at the Back Contact Layer

The variation in the work function of the back contact (φ_BC) directly impacts the energy band structure at the rear of solar cells, thereby impacting the collection of photogenerated carriers. We conducted a study to examine the influence of φ_BC on the performance of Sb₂(S,Se)₃ solar cells, with a specific focus on the difference Δφ (referred to as E_{v_HTL} − φ_BC). When Δφ ranges from −0.44 eV to 0.46 eV, φ_BC shifts within a range of 4.74 eV to 5.60 eV. Figure 7a reveals a consistent increasing trend in both the PCE and FF, reaching their maximum values at −0.14 eV. Beyond this Δφ value, the PCE and FF remain stable. The downward curvature in the valence band and the characteristic S-shaped curve in the current–voltage characteristics when Δφ falls below −0.14 eV, as depicted in Figure 7b,c, clarify this phenomenon. The varying energy levels across the HTL/back contact interface, causing the emergence of a Schottky barrier within the Δφ range of −0.44 eV to −0.14 eV, are responsible for impeding the unhampered flow of holes from the HTL toward the back electrode, as shown in Figure 7b. Notably, when Δφ approaches or exceeds −0.14 eV, the barrier gradually diminishes, allowing for improved hole transport and reduced resistance at the HTL/back contact interface, and all device parameters are saturated. In other words, when φ_BC exceeds 5.04 eV, the back electrode and HTL form a good ohmic contact conducive to hole collection. The back contact employed in Simulation 5 is gold (φ_BC = 5.1 eV), which falls within the optimized range, and the back contact of the Sb₂(S,Se)₃ solar cell can be unchanged.

3.6. Final Optimized Sb₂(S,Se)₃ Solar Cell Performance

After the above optimization analysis, the final values are as follow: the thickness of Sb₂(S,Se)₃ is 600 nm, and the electron affinities of the ETL (CdS) and HTL (spiro-OMeTAD) are optimized to 3.98 eV and 2.04 eV, respectively; the interface recombination velocities of ETL/absorber and absorber/HTL are optimized at 10² cm·s⁻¹ and 10³ cm·s⁻¹, respectively. Additionally, the back electrode with a work function greater than 5.04 eV (e.g., Au~5.1 eV) can form a better ohmic contact with HTL, and the series and shunt resistances of the device are optimized to 0 and 10⁵ Ω·cm², respectively. As shown in Table 1, the final optimized device (simulation 5) has achieved excellent performance parameters: V_oc = 0.99 V, J_sc = 30.93 mA·cm⁻², FF = 87.09%, and PCE = 26.77%. Compared with other simulation results presented in Table S4, the performance of our simulated Sb₂(S,Se)₃ solar cell is superior, due to the effective optimization path chosen based on V_oc and FF losses to enhance the device structure.

4. Improvement in the PCE of the Sb₂(S,Se)₃ Solar Cells

Based on the preceding simulation outcomes, a two-phased approach is proposed to increase the efficiency of Sb₂(S,Se)₃ solar cells. Initially, an efficiency benchmark of up to 15% was achieved, and subsequently, the goal was to surpass the 20% efficiency threshold.

Approaching 15% efficiency. Although the lowest V_oc loss reported in Sb₂(S,Se)₃ solar cells has an E_g of 1.46 eV [3], the V_oc value remains at approximately 0.69 V, which is notably far lower than the S–Q limit V_oc of 1.19 V. This discrepancy is commonly observed in Sb₂(S,Se)₃ solar cells with PCEs surpassing 10% [3,4,11,13,14,15,43,44,45], highlighting a persistent challenge in their performance improvement [26]. To overcome this challenge, feasible methods for enhancing carrier transport properties, minimizing recombination losses, and improving the internal resistance of Sb₂(S,Se)₃ solar cells include the following:

(1)

Regulation of the absorption film to reduce the internal resistance. The Sb₂(S,Se)₃ compound possesses a unique quasi-1D ribbon architecture characterized by [Sb₄S(e)₆]_n ribbons [46]. This structural peculiarity engenders favorable grain morphology and anisotropic carrier mobility, most notably along the [hk1] direction. This specific transport pathway underscores the prospect of significantly elevated device performance, particularly in comparison with transport along the [hk0] direction. Different synthesis/fabrication strategies have been used to develop [hk1]-oriented Sb₂(S,Se)₃ films. A highly efficient method lies in rapid hydrothermal deposition, which kinetically promotes the growth of [221]-oriented crystals [15]. Additionally, during synthesis processes such as close space sublimation (CSS) [47], rapid thermal evaporation (RTE) [45], and vapor transport deposition (VTD) [48], carefully balancing the temperature between the evaporation source and the substrate has been shown to be crucial for promoting [hk1] orientation and enhancing the crystallinity of Sb₂(S,Se)₃ films. High-quality crystals, characterized by low defect density, extended carrier lifetimes, elevated electron and hole mobilities, and uniform crystal structures, play a pivotal role in reducing internal resistance and optimizing carrier transport in solar cells.

(2)

Band alignment absorber layer and charge-transport layers. To fully unlock the potential of Sb₂(S,Se)₃ solar cells in terms of the PCE, the optimization of the carrier transport path has emerged as a paramount step forward in advancing their performance. This can be achieved through careful adjustment of CBO at the ETL/absorber interface and VBO at the absorber/HTL interfaces [49]. The proper alignment of the energy bands between the absorber layer and charge–transport layers is essential for minimizing energy-level mismatches and reducing the interface energy barriers. Optimizing the interface energy barrier involves using ETLs and HTLs with minimal defects or employing doping strategies to mitigate band mismatch. For example, nitrogen-containing functional groups in ethylenediamine (EDA) can coordinate with CdS, and shift the Fermi level of EDA–CdS toward the conduction band [50]. Alternatively, in situ oxygen doping of CdS films results in a lower conduction band level compared to that of control CdS films [51]. Various configurations of CdS-based ETLs such as SnO₂/CdS [25,52], TiO₂/CdS [53,54], ZnO/CdS [55], and Zn(O,S)/CdS [56] ensure well-matched band alignment, thereby facilitating efficient charge transport in Sb₂(S,Se)₃ solar cells.

Exceeding 20% efficiency. Reducing SRH recombination is a critical aspect of improving the performance of Sb₂(S,Se)₃ solar cells. By implementing appropriate passivation strategies and surface treatments, such as postselenization [57,58] and advanced interfacial engineering [59,60], it is feasible to significantly diminish the defect density within a material. This reduction not only mitigates the entrapment of charge carriers but also increases their lifetime. Achieving an efficiency of more than 20% in Sb₂(S,Se)₃ solar cells requires suitable methods, including the following:

(1)

Regulation of the interface recombination. Annealing and interface treatments are essential for rectifying instability, smoothing out roughness, and enhancing conductivity within ETLs. This helps minimize the defect density and lower carrier recombination at the ETL/absorber junction. For example, oxygen-doped cadmium sulfide (CdS:O) facilitates the tailoring of (Sb₄S(e)₆)_n ribbons to the (221)-textured orientation [61], CdCl₂-modified CdS films passivate surface defects [62], and KCl-treated CdS films promote absorption layer growth [10]. Furthermore, enhancing the p-type characteristics of HTL materials through doping or developing low-cost and efficient alternatives is crucial for increasing hole mobility and improving material conductivity, such as high-mobility and work-function NiO_x [63,64], excellent near-infrared-absorption PbS colloidal quantum dots [7,65], and high-hole-mobility and high-stability CuSCN [66]. These alternative approaches hold significant potential in increasing the performance of solar cells, primarily through the enhancement of hole mobility and the mitigation of interface recombination.

(2)

Balance of the relationship between the thickness of the absorber and bulk defects. Both theoretical calculations [67,68,69] and experimental measurements [3,70] have demonstrated the complex defect mechanisms in Sb₂(S,Se)₃. The thickness of the absorber layer influences both photon absorption and carrier transport [71]. If the absorber layer is too thin, insufficient photon absorption occurs, and pinhole formation increases, thereby resulting in a low J_sc. However, during the actual preparation process, overly thick layers increase photon absorption while also increasing the series resistance and carrier transport distance, thereby intensifying carrier recombination. The thickness of the absorber layer can be controlled by adjusting the synthesis/fabrication time and growth rate. Furthermore, the absorber bulk defects are reduced through empirical methods such as adjusting the Se/S atomic ratio [15,72], postselenization treatments [73], seeding materials [74,75], or additive engineering [4,76].

5. Conclusions

In summary, a numerical model of Sb₂(S,Se)₃ solar cells was developed utilizing the SCAPS software (version 3.3.10; University of Gent, Belgium) package and validated against experimental data from the literature. This model was used to investigate the factors limiting V_oc and FF at various stages of Sb₂(S,Se)₃ solar cell development, and effective strategies were identified to increase the PCE of these cells. The simulation results indicated an improvement in the PCE from 10.72% to 12.57%, as well as a significant increase in the FF from 68.35% to 79.55% after addressing the limiting mechanisms related to R_s and R_sh. Further adjustments in the CBO at the ETL/absorber and VBO at the absorber/HTL interfaces led to an increase in the PCE from 12.57% to 15.31%, along with a notable 18.75% improvement in V_oc. These results highlight the importance of reducing the internal resistance to enhance the FF and show the importance of optimal energy level arrangements for increasing V_oc.

The subsequent optimization of interface recombination led to a notable increase in the overall performance of Sb₂(S,Se)₃ solar cells, resulting in a remarkable PCE exceeding 20%. This was accompanied by a decrease in the V_oc loss to 0.45 V, an increase in the J_sc to 27.93 mA·cm⁻², and a reduction in the FF loss to 0.96%. These results highlight the crucial role of suppressing interface SRH recombination, particularly at the ETL/absorber interface, in improving the overall performance of devices. By striking a balance between the absorber thickness and the bulk defects, the J_sc increased to over 30 mA·cm⁻² at a thickness of 600 nm, consequently increasing the PCE to an impressive 26.77%.

This numerical analysis proposes an optimization roadmap aimed at reducing V_oc and FF losses, thereby successfully enhancing the efficiency of Sb₂(S,Se)₃ solar cells. While numerical simulations cannot completely replace experimental work, they undoubtedly provide significant guidance for future experimental efforts to improve the efficiency of Sb₂(S,Se)₃ solar cells, helping to avoid blind experimental exploration and thus saving valuable time and resources. Furthermore, this study proposes a two-stage strategy based on simulation results to further boost the efficiency of Sb₂(S,Se)₃ solar cells. We hope these findings can also be extended to other solar materials, such as Sb₂Se₃ and Sb₂S₃, thereby broadening their applicability beyond current boundaries.